Quadratic Regression by HC11121318410

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									SUMMARY OUTPUT                             Quadratic Regression
                                           (This model uses both X and X Squared)
          Regression Statistics
Multiple R                       0.99576
R Square                         0.99154
Adjusted R Square                0.98967
Standard Error                  12.25369
Observations                          12

ANOVA
                              df                SS            MS                     F       Significance F
Regression                            2      158477.5403    79238.7701              527.7204          0.0000
Residual                              9        1351.3764      150.1529
Total                                11      159828.9167

                         Coefficients   Standard Error        t Stat               P-value          Lower 95%
Intercept                       51.3409       12.6645             4.0539               0.0029            22.6917
Period                         -18.5592         4.4792           -4.1435               0.0025           -28.6918
Squared                          3.8254         0.3354           11.4051               0.0000             3.0667


                                                                                                      Period Residual Plot
RESIDUAL OUTPUT
                                                                            30.00000
                                                               Residuals


     Observation        Predicted Sales      Residuals                      20.00000
                    1          36.60714        -11.60714                    10.00000
                                                                             0.00000
                    2          29.52423         -1.52423                   -10.00000 0          2            4
                    3          30.09216          4.90784                   -20.00000
                    4          38.31094         10.68906
                    5          54.18057         11.81943
                    6          77.70105         10.29895
                    7         108.87238         -8.87238
                    8         147.69456         -7.69456                                             Squared Residual Plot
                    9         194.16758         -9.16758
                   10         248.29146         -9.29146                    30.00000
                                                               Residuals




                   11         310.06618        -10.06618                    20.00000
                                                                            10.00000
                   12         379.49176         20.50824                     0.00000
                                                                           -10.00000 0                  50
                                                                           -20.00000
          Upper 95%   Lower 95.0% Upper 95.0%
              79.9901      22.6917     79.9901
              -8.4266     -28.6918     -8.4266
               4.5842       3.0667      4.5842


 Period Residual Plot




            6            8   10     12       14

                Period



Squared Residual Plot




                 100          150           200

             Squared
SUMMARY OUTPUT                           Linear Regression
                                         This output uses only X in the model
     Regression Statistics
Multiple R           0.932386        This output has been included to show that for data that
R Square             0.869343        shows a curved trend, Linear regression has a much greater
Adjusted R Square 0.856278           standard error (45.69 in this case) when compared to the
Standard Error       45.69761        appropriate non-linear regression. For this data, the next output,
Observations               12        using quadratic regression, shows a standard error of 12.25.
                                     In reality, it is not necessary for you to do the simple linear regression when you can
ANOVA                                that the data has a curved trend.
                      df      SS         MS              F    Significance F
Regression                1 138946.2 138946.2 66.53645 9.93E-06
Residual                 10 20882.72 2088.272
Total                    11 159828.9

                            Standard Error t Stat
                  Coefficients                    P-value Lower 95%Upper 95%          Upper 95.0%
                                                                            Lower 95.0%
Intercept            -64.697 28.12494 -2.30034 0.044229 -127.363 -2.03069 -127.363 -2.03069
Period             31.17133 3.821426 8.156988 9.93E-06 22.65666       39.686 22.65666     39.686




RESIDUAL OUTPUT

                             Residuals
   Observation Predicted Sales
                                                                   Period Residual Plot
                1 -33.5256 58.52564
                2 -2.35431 30.35431
                3 28.81702 6.182984                        100
                                              Residuals




                4 59.98834 -10.9883                         50
                5 91.15967 -25.1597                          0
                                                           -50 0         5             10              15
                6 122.331      -34.331
                                                          -100
                7 153.5023 -53.5023
                8 184.6737 -44.6737                                          Period
                9 215.845      -30.845
               10 247.0163 -8.01632
               11 278.1876 21.81235
               12 309.359 90.64103
ar regression when you can see




Upper 95.0%
Quadratic Regression Model: Squared X term added to model

                      Period
            Period   Squared     Sales
                 1         1        25                          Sales
                 2         4        28
                 3         9        35      500
                 4        16        49      400
                 5        25        66      300
                 6        36        88      200
                 7        49      100
                                            100
                 8        64      140
                                              0
                 9        81      185
                                                  0         5           10   15
                10       100      239
                11       121      300
                12       144      400
     Sales




15

								
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