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					                    Part 18 – Multiple Regression:2




Statistics and Data
Analysis

Professor William Greene
Stern School of Business
IOMS Department
Department of Economics
               Part 18 – Multiple Regression:2




Statistics and Data Analysis


    Part 18 – Multiple
              Regression: 2
      1/52
                                                                                                                                                                                                                                                                                                                                                          Part 17 – Multiple Regression:2
                                                                                                                                                                                                                                                                                                                                                               18


                                                                                                 Multiple Regression Models

                                                                           Using Minitab To Compute A Multiple Regression
                                                                           Basic Multiple Regression
                                                                           Using Binary Variables
                                                                           Logs and Elasticities
                                                                           Hedonic Regression and Interpretation
                                                                           Trends in Time Series Data
                                                                           Using Quadratic Terms to Improve the Model


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      2/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Application: WHO
                                                                                              Data Used in Assignment 1: WHO data
                                                                                               on 191 countries in 1995-1999.
                                                                                                Analysis of Disability Adjusted Life
                                                                                                 Expectancy = DALE
                                                                                                EDUC = average years of education
                                                                                                PCHexp = Per capita health expenditure

                                                                                              DALE = α + β1EDUC + β2HealthExp + ε

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      3/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 The (Famous) WHO Data




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      4/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      5/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Specify the Variables in the Model




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      6/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      7/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Graphs? Maybe




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      8/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2

                                                                                                 Regression Results




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      9/52
                                                                                                                                                                                                                                                                                                                                                              Part 18 – Multiple Regression:2


                                                                                                 Practical Model Building

                                                                                                  Understanding the regression: The left
                                                                                                   out variable problem
                                                                                                  Using different kinds of variables
                                                                                                                     Dummy variables
                                                                                                                     Logs
                                                                                                                     Time trend
                                                                                                                     Quadratic

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                                Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                        Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                   900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                 14



                                                                                                                                                                                                                                                                                                                          e  mc  
                                                       Pepperoni                                                                                                                                                   99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                         Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                      800000
                                                                                                                                                                                                                   95
                                                                                                                                                                                                                                                                             StDev
                                                                                                                                                                                                                                                                             N
                                                                                                                                                                                                                                                                                       156865
                                                                                                                                                                                                                                                                                           51
                                                                                                                                                                                                                                                                                                          800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          51
                                                                                                                                                                                                                                                                             AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                           700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                 P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                    10
                                                       Garlic                                                                                                                                                      80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                  600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                 Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Percent
                                                       Meatball                                                                                                                                                    70
                                                                                      600000
                                                                                                                        Listing




                                                                                                                                                                                                                                                                                                Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                             8
                                                                                                                                                                                                         Percent




                                                                                                                                                                                                                   60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                  500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                   50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                       40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Listing
         5.8%                                                                                                                     400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                       20                                                                                                                                                                                                                                                             20
                                                                                                                                  300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                   10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                      200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                            0       00     00     00     00      00     00     00     00     00
                                                                                                                                  100000                                                                                                                                                                  100000
                                                                                                                                                                                                                   1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                        15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                   IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      10/52
                                                                                                                                                                                                                                                                                                                                                             Part 18 – Multiple Regression:2


                                                                                                  A Fundamental Result
                                                                                                                     What happens when you leave a crucial
                                                                                                                     variable out of your model? (Bad things)
                                                                                               Regression Analysis: g versus GasPrice (no income)
                                                                                               The regression equation is
                                                                                               g = 3.50 + 0.0280 GasPrice
                                                                                               Predictor      Coef   SE Coef       T     P
                                                                                               Constant     3.4963    0.1678 20.84 0.000
                                                                                               GasPrice   0.028034 0.002809     9.98 0.000
                                                                                               Regression Analysis: G versus GasPrice, Income
                                                                                               The regression equation is
                                                                                               G = 0.134 - 0.00163 GasPrice + 0.000026 Income
                                                                                               Predictor        Coef      SE Coef      T     P
                                                                                               Constant      0.13449      0.02081   6.46 0.000
                                                                                               GasPrice   -0.0016281   0.0004152 -3.92 0.000
                                                                                               Income     0.00002634 0.00000231 11.43 0.000

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                 Boxplot of Listing                              Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                       Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                  900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                14



                                                                                                                                                                                                                                                                                                                         e  mc  
                                                       Pepperoni                                                                                                                                                  99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                        Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                     800000
                                                                                                                                                                                                                  95
                                                                                                                                                                                                                                                                            StDev
                                                                                                                                                                                                                                                                            N
                                                                                                                                                                                                                                                                                      156865
                                                                                                                                                                                                                                                                                          51
                                                                                                                                                                                                                                                                                                         800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         51
                                                                                                                                                                                                                                                                            AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                          700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                   10
                                                       Garlic                                                                                                                                                     80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                 600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Percent
                                                       Meatball                                                                                                                                                   70
                                                                                      600000
                                                                                                                       Listing




                                                                                                                                                                                                                                                                                               Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                            8
                                                                                                                                                                                                        Percent




                                                                                                                                                                                                                  60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                 500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                  50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                      40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Listing
         5.8%                                                                                                                    400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                      20                                                                                                                                                                                                                                                             20
                                                                                                                                 300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                  10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                     200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                           0       00     00     00     00      00     00     00     00     00
                                                                                                                                 100000                                                                                                                                                                  100000
                                                                                                                                                                                                                  1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                       15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                  IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      11/52
                                                                                                                                                                                                                                                                                                                                                            Part 18 – Multiple Regression:2


                                                                                                 Using Dummy Variables
                                                                             Dummy variable = binary variable
                                                                              = a variable that takes values 0 and 1.
                                                                             E.g. OECD Life Expectancies
                                                                              compared to the rest of the world:
                                                                                                                   DALE = α + β1 EDUC + β2 PCHexp
                                                                                                                             + β3 OECD + ε
                                        Australia, Austria, Belgium, Canada, Czech Republic, Denmark, Finland, France,
                                        Germany, Greece, Hungary, Iceland, Ireland, Italy, Japan, Korea, Luxembourg,
                                        Mexico, The Netherlands, New Zealand, Norway, Poland, Portugal, Slovak
                                        Republic, Spain, Sweden, Switzerland, Turkey, United Kingdom, United States.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                              Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                      Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                 900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                               14



                                                                                                                                                                                                                                                                                                                        e  mc  
                                                       Pepperoni                                                                                                                                                 99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                       Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                    800000
                                                                                                                                                                                                                 95
                                                                                                                                                                                                                                                                           StDev
                                                                                                                                                                                                                                                                           N
                                                                                                                                                                                                                                                                                     156865
                                                                                                                                                                                                                                                                                         51
                                                                                                                                                                                                                                                                                                        800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        51
                                                                                                                                                                                                                                                                           AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                         700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                               P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                  10
                                                       Garlic                                                                                                                                                    80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                               Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Percent
                                                       Meatball                                                                                                                                                  70
                                                                                      600000
                                                                                                                      Listing




                                                                                                                                                                                                                                                                                              Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                           8
                                                                                                                                                                                                       Percent




                                                                                                                                                                                                                 60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                 50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                     40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             Listing
         5.8%                                                                                                                   400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                     20                                                                                                                                                                                                                                                             20
                                                                                                                                300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                 10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                    200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                          0       00     00     00     00      00     00     00     00     00
                                                                                                                                100000                                                                                                                                                                  100000
                                                                                                                                                                                                                 1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                      15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                 IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      12/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 OECD Life Expectancy

                                                                                                                                                                                                                                                                                                                                                                                                                                            According to these
                                                                                                                                                                                                                                                                                                                                                                                                                                            results, after
                                                                                                                                                                                                                                                                                                                                                                                                                                            accounting for
                                                                                                                                                                                                                                                                                                                                                                                                                                            education and health
                                                                                                                                                                                                                                                                                                                                                                                                                                            expenditure
                                                                                                                                                                                                                                                                                                                                                                                                                                            differences, people in
                                                                                                                                                                                                                                                                                                                                                                                                                                            the OECD countries
                                                                                                                                                                                                                                                                                                                                                                                                                                            have a life expectancy
                                                                                                                                                                                                                                                                                                                                                                                                                                            that is 1.19 years
                                                                                                                                                                                                                                                                                                                                                                                                                                            shorter than people in
                                                                                                                                                                                                                                                                                                                                                                                                                                            other countries.


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      13/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Binary Variable in Regression

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     The regression
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     shifts down by
                                                                                                                                                        NonOECD: DALE =36.770 + 2.9962 EDUC
                                                                                                                                                                              + .005079 PCHExp                                                                                                                                                                                                                                                                                                                                       1.191 years for
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     the OECD
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     countries




                                                                                                                                                                                                                                   OECD: DALE =36.770 + 2.9962 EDUC
                                                                                                                                                                                                                                              + .005079 PCHExp – 1.191




                                                                                                           We set PCHExp to 1000, approximately the sample mean.

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Plotting  For DALE_NonOECD, remove -1.191




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
                                                                                                                                                                                                                                                                                                                                                                        Part 18 – Multiple Regression:2


                                                                                                 Two Plots
                                                                                                                                                                             Life Expectancy in OECD and NonOECD Countries
                                                                                                                             80                                                                                                                                                                                                                                                                                                                                                                         Variable
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        DALE_OECD
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        DALE_NonOECD


                                                                                                                             70
                                                                                                                    Y-Data




                                                                                                                             60




                                                                                                                             50




                                                                                                                             40
                                                                                                                                              0                                            2                                          4                                        6                                                              8                                       10                                                     12
                                                                                                                                                                                                                                                                             EDUC



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                                          Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                                  Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                             900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                           14



                                                                                                                                                                                                                                                                                                                                    e  mc  
                                                       Pepperoni                                                                                                                                                             99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                                   Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                                800000
                                                                                                                                                                                                                             95
                                                                                                                                                                                                                                                                                       StDev
                                                                                                                                                                                                                                                                                       N
                                                                                                                                                                                                                                                                                                 156865
                                                                                                                                                                                                                                                                                                     51
                                                                                                                                                                                                                                                                                                                    800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    51
                                                                                                                                                                                                                                                                                       AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                                     700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                           P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                              10
                                                       Garlic                                                                                                                                                                80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                            600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                           Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Percent
                                                       Meatball                                                                                                                                                              70
                                                                                      600000
                                                                                                                                  Listing




                                                                                                                                                                                                                                                                                                          Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                                       8
                                                                                                                                                                                                                   Percent




                                                                                                                                                                                                                             60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                            500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                             50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                                 40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         Listing
         5.8%                                                                                                                               400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                                 20                                                                                                                                                                                                                                                             20
                                                                                                                                            300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                             10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                                200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                                      0       00     00     00     00      00     00     00     00     00
                                                                                                                                            100000                                                                                                                                                                  100000
                                                                                                                                                                                                                             1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                                  15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                             IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      14/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2



                                                                                                 Dummy Variable in Log Regression

                                                                                      E.g., Monet’s signature equation


                                                                                       Log$Price = α + β1 logArea + β2 Signed

                                                                                       Unsigned: PriceU                                                                                                         = exp(α) Areaβ1
                                                                                       Signed: PriceS                                                                                                           = exp(α) Areaβ1 exp(β2)
                                                                                       Signed/Unsigned                                                                                                          = exp(β2)
                                                                                       %Difference                                                                                                              = 100%(Signed-Unsigned)/Unsigned
                                                                                                                                                                                                                = 100%[exp(β2) – 1]



                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      15/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 The Signature Effect: 253%




                                                                                                                100%[exp(1.2618) – 1] = 100%[3.532 – 1] = 253.2 %

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      16/52
                                                                                                                                                                                                                                                                                                                                                            Part 18 – Multiple Regression:2


                                                                                                 Monet Paintings in Millions
                                                                                                                                                                                                      Scatterplot of Price vs Square Inches
                                                                                                                                        30                                                                                                                                                                                                                                                                                                                     Signed
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                    1
                                                                                                                                        25


                                                                                                                                        20


                                                                                                                                                                                                                                                                                                                                                                       Difference is about 253%
                                                                                                                    Price




                                                                                                                                        15


                                                                                                                                        10


                                                                                                                                             5


                                                                                                                                             0

                                                                                                                                                             0                        1000                               2000                     3000    4000                                                                        5000                             6000                                 7000
                                                                                                                                                                                                                                                 Square Inches




                                                          Predicted Price is exp(4.122+1.3458*logArea+1.2618*Signed) / 1000000


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                             Scatterplot of Listing vs IncomePC                                               Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                      Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                900000                                                                                                                                                                   900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                               14



                                                                                                                                                                                                                                                                                                                        e  mc  
                                                       Pepperoni                                                                                                                                                99                                                                                                                                                                                                                                                                                                                                          Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                       Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                   800000
                                                                                                                                                                                                                95
                                                                                                                                                                                                                                                                           StDev
                                                                                                                                                                                                                                                                           N
                                                                                                                                                                                                                                                                                     156865
                                                                                                                                                                                                                                                                                         51
                                                                                                                                                                                                                                                                                                        800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        51
                                                                                                                                                                                                                                                                           AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                        700000                                                                           90                                                                                      700000
                                                                                      700000                                                                                                                                                                               P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                  10
                                                       Garlic                                                                                                                                                   80                                                                                                                                                                                                                                                                                                                                                                     1000000
                                                                                                                               600000                                                                                                                                                                   600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                               Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Percent
                                                       Meatball                                                                                                                                                 70
                                                                                      600000
                                                                                                                     Listing




                                                                                                                                                                                                                                                                                              Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                           8
                                                                                                                                                                                                      Percent




                                                                                                                                                                                                                60                                                                                                                                                                                                                                                                                                                                                                      800000
                                                                                                                               500000                                                                                                                                                                   500000
                                                                            Listing




                                                                                                                                                                                                                50                                                                                                                                                                                                                                                              40
       Sausage                                                                        500000                                                                                                                    40                                                                                                                                                                         6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             Listing
         5.8%                                                                                                                  400000                                                                           30                                                                                      400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                    20                                                                                                                                                                                                                                                              20
                                                                                                                               300000                                                                                                                                                                   300000                                                                             4
                                                                                                                                                                                                                10                                                                                                                                                                                                                                                                                                                                                                      400000
                                                                                      300000                                   200000                                                                           5                                                                                       200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                          0       00     00     00     00      00     00     00     00     00
                                                                                                                               100000                                                                                                                                                                   100000
                                                                                                                                                                                                                1                                                                                                                                                                          0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                     15000   17500   20000   22500    25000   27500   30000   32500                  0    200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                IncomePC                                                             Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      17/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      18/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                      Dummy Variable for One
                                                                                                      Observation
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  Proofs:
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  See p. 40.
                                                 Single out one observation for special attention.

                                                 The equation will predict that observation
                                                  perfectly.

                                                 For the other coefficients, it is the same as
                                                  removing that observation from the sample.




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      19/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2

                                                                                                 A “London Effect” on UK
                                                                                                 Electronic Store Sales?




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     20/52




                                                                                                                                                                                                                                                                                                                                       Observation 2 is London
                                                                                                                                                                                                                                                                                                                                       Fit = Actual, Residual=0.




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      21/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Logs in Regression




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      22/52
                                                                                                                                                                                                                                                                                                                                                              Part 18 – Multiple Regression:2


                                                                                                     Elasticity
                                                                                                The coefficient on log(Area) is 1.346
                                                                                                For each 1% increase in area, price
                                                                                                 goes up by 1.34% - even accounting
                                                                                                 for the signature effect.
                                                                                                The elasticity is +1.34

                                                                                                Remarkable. Not only does price
                                                                                                 increase with area, it increases faster
                                                                                                 than area.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                    Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                        Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                   900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                 14



                                                                                                                                                                                                                                                                                                                          e  mc  
                                                       Pepperoni                                                                                                                                                   99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                         Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                      800000
                                                                                                                                                                                                                   95
                                                                                                                                                                                                                                                                             StDev
                                                                                                                                                                                                                                                                             N
                                                                                                                                                                                                                                                                                       156865
                                                                                                                                                                                                                                                                                           51
                                                                                                                                                                                                                                                                                                          800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          51
                                                                                                                                                                                                                                                                             AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                           700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                 P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                    10
                                                       Garlic                                                                                                                                                      80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                  600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                 Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Percent
                                                       Meatball                                                                                                                                                    70
                                                                                      600000
                                                                                                                        Listing




                                                                                                                                                                                                                                                                                                Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                             8
                                                                                                                                                                                                         Percent




                                                                                                                                                                                                                   60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                  500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                   50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                       40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Listing
         5.8%                                                                                                                     400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                       20                                                                                                                                                                                                                                                             20
                                                                                                                                  300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                   10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                      200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                            0       00     00     00     00      00     00     00     00     00
                                                                                                                                  100000                                                                                                                                                                  100000
                                                                                                                                                                                                                   1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                        15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                   IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      23/52
                                                                                                                                                                                                                                                                                                                                                                  Part 18 – Multiple Regression:2


                                                                                                 Monet: By the Square Inch
                                                                                                                                                                                                                                Scatterplot of Price vs Area


                                                                                                                                       20000000



                                                                                                                                       15000000
                                                                                                                    price




                                                                                                                                       10000000



                                                                                                                                               5000000



                                                                                                                                                                      0

                                                                                                                                                                                             0                              1000                                2000                                                3000    4000                                                                      5000                                       6000                                       7000
                                                                                                                                                                                                                                                                                                                       Area




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                                    Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                            Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                       900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                     14



                                                                                                                                                                                                                                                                                                                              e  mc  
                                                       Pepperoni                                                                                                                                                       99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                             Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                          800000
                                                                                                                                                                                                                       95
                                                                                                                                                                                                                                                                                 StDev
                                                                                                                                                                                                                                                                                 N
                                                                                                                                                                                                                                                                                           156865
                                                                                                                                                                                                                                                                                               51
                                                                                                                                                                                                                                                                                                              800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              51
                                                                                                                                                                                                                                                                                 AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                               700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                     P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                        10
                                                       Garlic                                                                                                                                                          80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                      600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                     Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Percent
                                                       Meatball                                                                                                                                                        70
                                                                                      600000
                                                                                                                            Listing




                                                                                                                                                                                                                                                                                                    Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                                 8
                                                                                                                                                                                                             Percent




                                                                                                                                                                                                                       60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                      500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                       50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                           40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Listing
         5.8%                                                                                                                         400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                           20                                                                                                                                                                                                                                                             20
                                                                                                                                      300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                       10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                          200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                                0       00     00     00     00      00     00     00     00     00
                                                                                                                                      100000                                                                                                                                                                  100000
                                                                                                                                                                                                                       1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                            15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                       IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      24/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Elasticities of Demand for Gasoline




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      25/52
                                                                                                                                                                                                                                                                                                                                                             Part 18 – Multiple Regression:2


                                                                                                 Logs and Elasticities
                                                                                                                    Theory: In the equation
                                                                                                                       y = α + β1x1 + β2x2 + … βKxK + ε
                                                                                                                       β = (change in y) / (unit change in x)
                                                                                                                                 Elasticity = β * mean of x / mean of y
                                                                                                                    When the variables are in logs: change in logx = %change in x
                                                                                                                                 log y = α + β1 log x1 + β2 log x2 + … βK log xK + ε
                                                                                                                                 Elasticity = β
                                                                                                                    These will often give approximately the same answer.

                                                                                                                    When in doubt, use logs.


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                               Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                       Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                  900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                14



                                                                                                                                                                                                                                                                                                                         e  mc  
                                                       Pepperoni                                                                                                                                                  99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                        Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                     800000
                                                                                                                                                                                                                  95
                                                                                                                                                                                                                                                                            StDev
                                                                                                                                                                                                                                                                            N
                                                                                                                                                                                                                                                                                      156865
                                                                                                                                                                                                                                                                                          51
                                                                                                                                                                                                                                                                                                         800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                             N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         51
                                                                                                                                                                                                                                                                            AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                          700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                   10
                                                       Garlic                                                                                                                                                     80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                 600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Percent
                                                       Meatball                                                                                                                                                   70
                                                                                      600000
                                                                                                                       Listing




                                                                                                                                                                                                                                                                                               Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                            8
                                                                                                                                                                                                        Percent




                                                                                                                                                                                                                  60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                 500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                  50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                      40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              Listing
         5.8%                                                                                                                    400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                      20                                                                                                                                                                                                                                                             20
                                                                                                                                 300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                  10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                     200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                           0       00     00     00     00      00     00     00     00     00
                                                                                                                                 100000                                                                                                                                                                  100000
                                                                                                                                                                                                                  1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                       15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                  IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      26/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Elasticities




                                                                                                 Price elasticity                                                                            = -0.02070                                                                                                              Income elasticity = +1.10318

                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      27/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 A Set of Dummy Variables

                                                                             Complete set of dummy variables
                                                                              divides the sample into groups.
                                                                             Fit the regression with “group” effects.

                                                                             Need to drop one (any one) of the
                                                                              variables to compute the regression.
                                                                              (Avoid the “dummy variable trap.”)


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      28/52
                                                                                               Nancy Burnett: Journal of Economic                                                                                                                                                                                                                         Part 18 – Multiple Regression:2
                                                                                               Education, 1998

                                                                                               Rankings of 132 U.S.Liberal Arts Colleges
                                                                                                 Reputation=α+β1Religious + β2GenderEcon + β3EconFac +
                                                                                                              β4North + β5South + β6Midwest + β7West + ε




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      29/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Minitab to the Rescue




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      30/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Unordered Categorical Variables

                                                                                                                                                                                                                                                                                                                      House price data (fictitious)
                                                                                                                                                                                                                                                                                                                      Type 1 = Split level
                                                                                                                                                                                                                                                                                                                      Type 2 = Ranch
                                                                                                                                                                                                                                                                                                                      Type 3 = Colonial
                                                                                                                                                                                                                                                                                                                      Type 4 = Tudor
                                                                                                                                                                                                                                                                                                                      Use 3 dummy variables for this kind
                                                                                                                                                                                                                                                                                                                      of data. (Not all 4)
                                                                                                                                                                                                                                                                                                                      Using variable STYLE in the model
                                                                                                                                                                                                                                                                                                                      makes no sense. You could change
                                                                                                                                                                                                                                                                                                                      the numbering scale any way you
                                                                                                                                                                                                                                                                                                                      like. 1,2,3,4 are just labels.


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      31/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Transform Style to Types




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      32/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      33/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 House Price Regression




                                                                                                                                                                                                                                                                                                                    Each of these is relative to a Split
                                                                                                                                                                                                                                                                                                                    Level, since that is the omitted
                                                                                                                                                                                                                                                                                                                    category. E.g., the price of a Ranch
                                                                                                                                                                                                                                                                                                                    house is $74,369 less than a Split
                                                                                                                                                                                                                                                                                                                    Level of the same size with the
                                                                                                                                                                                                                                                                                                                    same number of bedrooms.


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      34/52
                                                                                                                                                                                                                                                                                                                                                              Part 18 – Multiple Regression:2


                                                                                                     Ordered Categories
                                                                                                            Health Satisfaction:
                                                                                                             1=Poor, 2=So_so, 3=OK, 4=Good, 5=Great
                                                                                                            How to handle such a variable?
                                                                                                               Just use as is? No, So_so – Poor =1, but this is not
                                                                                                                 equal to Great – Good = 1 (necessarily)
                                                                                                               Use 4 of the indicator variables.
                                                                                                            Coding. It is not useful to consider modifications of the
                                                                                                             variable, such as -2,-1,0,1,2 or 2,4,6,8,10. None make
                                                                                                             sense as this is just a label. Could also use 1,4,8,17,26
                                                                                                             which would also make no sense.
                                                                                                            This needs a special kind of model if it is the dependent
                                                                                                             variable – not a regression equation.


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                    Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                        Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                   900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                 14



                                                                                                                                                                                                                                                                                                                          e  mc  
                                                       Pepperoni                                                                                                                                                   99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                         Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                      800000
                                                                                                                                                                                                                   95
                                                                                                                                                                                                                                                                             StDev
                                                                                                                                                                                                                                                                             N
                                                                                                                                                                                                                                                                                       156865
                                                                                                                                                                                                                                                                                           51
                                                                                                                                                                                                                                                                                                          800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          51
                                                                                                                                                                                                                                                                             AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                           700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                 P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                    10
                                                       Garlic                                                                                                                                                      80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                  600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                 Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Percent
                                                       Meatball                                                                                                                                                    70
                                                                                      600000
                                                                                                                        Listing




                                                                                                                                                                                                                                                                                                Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                             8
                                                                                                                                                                                                         Percent




                                                                                                                                                                                                                   60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                  500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                   50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                       40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Listing
         5.8%                                                                                                                     400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                       20                                                                                                                                                                                                                                                             20
                                                                                                                                  300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                   10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                      200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                            0       00     00     00     00      00     00     00     00     00
                                                                                                                                  100000                                                                                                                                                                  100000
                                                                                                                                                                                                                   1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                        15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                   IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      35/52
                                                                                                                                                                                                                                                                                                                                                              Part 18 – Multiple Regression:2


                                                                                                 Hedonic Regression
                                                                                                                                    A theory of prices
                                                                                                                                       Price = sum of prices for components
                                                                                                                                    House price
                                                                                                                                       Land size
                                                                                                                                       Rooms: Fixed amount per room
                                                                                                                                       Swimming pool
                                                                                                                                       View
                                                                                                                                       N car garage
                                                                                                                                       Etc.
                                                                                                                                    Computers
                                                                                                                                       Speed
                                                                                                                                       Screen size
                                                                                                                                       Other features…




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                                Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                        Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                   900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                 14



                                                                                                                                                                                                                                                                                                                          e  mc  
                                                       Pepperoni                                                                                                                                                   99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                         Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                      800000
                                                                                                                                                                                                                   95
                                                                                                                                                                                                                                                                             StDev
                                                                                                                                                                                                                                                                             N
                                                                                                                                                                                                                                                                                       156865
                                                                                                                                                                                                                                                                                           51
                                                                                                                                                                                                                                                                                                          800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          51
                                                                                                                                                                                                                                                                             AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                           700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                 P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                    10
                                                       Garlic                                                                                                                                                      80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                  600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                 Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Percent
                                                       Meatball                                                                                                                                                    70
                                                                                      600000
                                                                                                                        Listing




                                                                                                                                                                                                                                                                                                Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                             8
                                                                                                                                                                                                         Percent




                                                                                                                                                                                                                   60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                  500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                   50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                       40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Listing
         5.8%                                                                                                                     400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                       20                                                                                                                                                                                                                                                             20
                                                                                                                                  300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                   10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                      200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                            0       00     00     00     00      00     00     00     00     00
                                                                                                                                  100000                                                                                                                                                                  100000
                                                                                                                                                                                                                   1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                        15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                   IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      36/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Fumiro Computer Data




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      37/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2

                                                                                                 Transform Manufacturer
                                                                                                 Names to Indicator Variables
                                                                                                           Calc  Make Indicator Variables…




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      38/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Hedonic Regression




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      39/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Time Trends in Regression

                                                                                                  y = α + β 1x + β 2t + ε
                                                                                                       β2 is the year to year increase not
                                                                                                       explained by anything else.
                                                                                                  log y = α + β1log x + β2t + ε
                                                                                                       (not log t, just t)
                                                                                                       100β2 is the year to year
                                                                                                       % increase
                                                                                                       not explained by anything else.
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      40/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Time Trend Regression

                    After accounting for Income, the
                    price and the price of new cars,
                    per capita gasoline consumption
                    falls by 1.25% per year. I.e., if
                    Income and the prices were
                    unchanged, consumption would
                    fall by 1.25%. But, of course,
                    these other things do not remain
                    unchanged.




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      41/52
                                                                                                                                                                                                                                                                                                                                                              Part 18 – Multiple Regression:2


                                                                                                 Nonlinear Equation

                                                                                                  Using a quadratic (like using logs)
                                                                                                  y = α + β1x + β2x2 + ε

                                                                                                  Usually β1 > 0.

                                                                                                  If β2 > 0              If β2 < 0
                                                                                                                    y                                                                                                                                                                                                                                         y




                                                                                                                                                                                                                                       x                                                                                                                                                                                                                                                                     x
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                                Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                        Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                   900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                                 14



                                                                                                                                                                                                                                                                                                                          e  mc  
                                                       Pepperoni                                                                                                                                                   99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                         Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                      800000
                                                                                                                                                                                                                   95
                                                                                                                                                                                                                                                                             StDev
                                                                                                                                                                                                                                                                             N
                                                                                                                                                                                                                                                                                       156865
                                                                                                                                                                                                                                                                                           51
                                                                                                                                                                                                                                                                                                          800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          51
                                                                                                                                                                                                                                                                             AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                           700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                                 P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                    10
                                                       Garlic                                                                                                                                                      80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                                  600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                                 Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                        Percent
                                                       Meatball                                                                                                                                                    70
                                                                                      600000
                                                                                                                        Listing




                                                                                                                                                                                                                                                                                                Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                             8
                                                                                                                                                                                                         Percent




                                                                                                                                                                                                                   60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                                  500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                   50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                       40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               Listing
         5.8%                                                                                                                     400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                       20                                                                                                                                                                                                                                                             20
                                                                                                                                  300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                   10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                      200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                            0       00     00     00     00      00     00     00     00     00
                                                                                                                                  100000                                                                                                                                                                  100000
                                                                                                                                                                                                                   1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                        15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                   IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      42/52
                                                                                                                                                                                                                                                                                                                                                           Part 18 – Multiple Regression:2

                                                                                                  A Quadratic Income vs. Age
                                                                                                  Regression
                                                                                               +----------------------------------------------------+
                                                                                               | LHS=HHNINC    Mean                  =  .3520836       |
                                                                                               |               Standard deviation    =  .1769083       |
                                                                                               | Model size    Parameters            =          3      |
                                                                                               |               Degrees of freedom    =     27323       |
                                                                                               | Residuals     Sum of squares        =  794.9667       |
                                                                                               |               Standard error of e =    .1705730       |
                                                                                               | Fit           R-squared             =  .7040754E-01 |
                                                                                               +----------------------------------------------------+
                                                                                               +--------+--------------+--+--------+
                                                                                               |Variable| Coefficient | Mean of X|
                                                                                               +--------+--------------+-----------+ Note the coefficient on
                                                                                                 Constant| -.39266196                  Age squared is
                                                                                                 AGE     | .02458140      43.5256898   negative. Age ranges
                                                                                                 AGESQ   | -.00027237     2022.85549
                                                                                                                                       from 25 to 65.
                                                                                                 EDUC    | .01994416      11.3206310
                                                                                               +--------+--------------+-----------+
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                 Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                     Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                                900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                              14



                                                                                                                                                                                                                                                                                                                       e  mc  
                                                       Pepperoni                                                                                                                                                99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                      Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                   800000
                                                                                                                                                                                                                95
                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                    156865
                                                                                                                                                                                                                                                                                        51
                                                                                                                                                                                                                                                                                                       800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                          AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                        700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                              P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                 10
                                                       Garlic                                                                                                                                                   80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                               600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                              Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                     Percent
                                                       Meatball                                                                                                                                                 70
                                                                                      600000
                                                                                                                     Listing




                                                                                                                                                                                                                                                                                             Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                          8
                                                                                                                                                                                                      Percent




                                                                                                                                                                                                                60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                               500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                                50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                    40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Listing
         5.8%                                                                                                                  400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                    20                                                                                                                                                                                                                                                             20
                                                                                                                               300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                                10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                   200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                         0       00     00     00     00      00     00     00     00     00
                                                                                                                               100000                                                                                                                                                                  100000
                                                                                                                                                                                                                1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                     15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                                IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      43/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Implied By The Model




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing                                                             Scatterplot of Listing vs IncomePC                                                          Histogram of Listing                                                                    Empirical CDF of Listing
                                                                                                                                                                                                                                    Normal - 95% CI                                                                                                                                                                                                                                                                  Normal
                                                       Category                                                               900000                                                                                                                                                                  900000
                             Meatball                                                 900000                                                                                                                                                                                                                                                                                             14



                                                                                                                                                                                                                                                                                                                      e  mc  
                                                       Pepperoni                                                                                                                                               99                                                                                                                                                                                                                                                                                                                                         Mean    369687
                         Garlic 5.0%                                                                                                                                                                                                                                     Mean      369687                                                                                                                                                                                     100
    Mushroom and Onion
                  9.2%
                         2.3%
                                           Pepperoni
                                           21.8%
                                                       Plain
                                                       Mushroom
                                                       Sausage
                                                                                      800000                                  800000
                                                                                                                                                                                                               95
                                                                                                                                                                                                                                                                         StDev
                                                                                                                                                                                                                                                                         N
                                                                                                                                                                                                                                                                                   156865
                                                                                                                                                                                                                                                                                       51
                                                                                                                                                                                                                                                                                                      800000                                 2                                           12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          StDev
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          N
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  156865
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      51
                                                                                                                                                                                                                                                                         AD         0.994                                                                                                                                                                                     80
                                                       Pepper and Onion                                                       700000                                                                           90                                                                                     700000
                                                                                      700000                                                                                                                                                                             P-Value    0.012
                                                       Mushroom and Onion                                                                                                                                                                                                                                                                                                                10
                                                       Garlic                                                                                                                                                  80                                                                                                                                                                                                                                                                                                                                                                    1000000
                                                                                                                              600000                                                                                                                                                                  600000                                                                                                                                                                  60
                                                                                                                                                                                                                                                                                                                                                                             Frequency




Pepper and Onion




                                                                                                                                                                                                                                                                                                                                                                                                                                                                    Percent
                                                       Meatball                                                                                                                                                70
                                                                                      600000
                                                                                                                    Listing




                                                                                                                                                                                                                                                                                            Listing




            7.3%                                                                                                                                                                                                                                                                                                                                                                         8
                                                                                                                                                                                                     Percent




                                                                                                                                                                                                               60                                                                                                                                                                                                                                                                                                                                                                     800000
                                                                                                                              500000                                                                                                                                                                  500000
                                                                            Listing




                                                                                                                                                                                                               50                                                                                                                                                                                                                                                             40
       Sausage                                                                        500000                                                                                                                   40                                                                                                                                                                        6




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           Listing
         5.8%                                                                                                                 400000                                                                           30                                                                                     400000                                                                                                                                                                                                                                                                          600000
                                                                                      400000                                                                                                                   20                                                                                                                                                                                                                                                             20
                                                                                                                              300000                                                                                                                                                                  300000                                                                             4
                                                                                                                                                                                                               10                                                                                                                                                                                                                                                                                                                                                                     400000
                                                                                      300000                                  200000                                                                           5                                                                                      200000                                                                             2                                                                                     0
             Mushroom                       Plain
                16.2%
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      200000
                                            32.5%
                                                                                      200000                                                                                                                                                                                                                                                                                                                                                                                        0       00     00     00     00      00     00     00     00     00
                                                                                                                              100000                                                                                                                                                                  100000
                                                                                                                                                                                                               1                                                                                                                                                                         0                                                                                                00     00     00     00      00     00     00     00     00
                                                                                                                                    15000   17500   20000   22500    25000   27500   30000   32500                  0   200000   400000    600000     800000   1000000                                      15000   17500   20000   22500    25000   27500   30000   32500                    200000   300000   400000   500000 600000   700000   800000   900000                       10     20     30     40      50     60     70     80     90                                        15000       20000       25000    30000
                                                                                                                                                               IncomePC                                                            Listing                                                                                             IncomePC                                                                              Listing                                                                              Listing                                                                                      IncomePC
                                                                                      100000
      44/52
                                                                                                                                                                                                                                                                                                                                                          Part 18 – Multiple Regression:2


                                                                                                 Case Study: A Huge Sports
                                                                                                 Contract
                                                                                              Alex Rodriguez hired by the Texas Rangers for
                                                                                               something like $25 million per year.
                                                                                              Costs – the salary plus and minus some fine
                                                                                               tuning of the numbers
                                                                                              Benefits – more fans in the stands.
                                                                                              How to determine if the benefits exceed the
                                                                                               costs? Use a regression model.


                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Marginal Plot of Listing vs IncomePC
                   Pie Chart of Percent vs Type                                                Boxplot of Listing                            Scatterplot of Listing vs IncomePC                                              Probability Plot of Listing