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					    What decides the price of used cars?




Group 1

Jessica Aguirre
Keith Cody
Rui Feng
Jennifer Griffeth
Joonhee Lee
Hans-Jakob Lothe
Teng Wang
How we got data

   Collected from kbb.com (Kelley Blue Book)
   Used random number generator

   First collected 140 sets of data from various
    types of cars
   Then collected 160 sets of data from
    Toyota Camrys
Brand Population
                        Dodge        Chevrolet
            Honda        433           1069
             840


      Volksvagen
          425                                     Toyota
                                                   1350



           Ford
           1323

                                   Nissan
                                    1347




                    6787 Vehicles in Population
Models
            Minivan
             242                       SUV
  Hatchback                            1463
     382

  Convertible
     188

    Coupe
     383


                                                           Sedan
                      Pick-Up                               2807
                       1059




                          6524 Model Types in Population
 Average Selling Price by Brand
$25,000.00


                                                    $21,513.60
             $20,543.20                                                        $20,451.60
                                                                  $19,968.70
$20,000.00


                                                                                            $16,441.10
                                       $15,465.60
                          $14,677.65
$15,000.00




$10,000.00




 $5,000.00




     $0.00
             Chevrolet    Toyota       Nissan         Ford       Volkswagon    Honda        Dodge
Assumptions

   Random sample is representative of
    population
   All prices are the selling price
   Residuals are homoskedastic
   Residuals are normally distributed
   The variables we choose affect the price of
    used cars: age, color, etc
Preparations

   Created dummy variables
   e.g. Transmission, automatic = 0, manual = 1
   Color
   Type
   Engine
    (V4 = 4, V8 = 8, etc)
All Cars: Regression of price against independent
variables (age, color, engine, miles and transmission)
Dependent Variable: PRICE
Method: Least Squares
Date: 11/29/10 Time: 16:43
Sample: 1 140
Included observations: 140
                     Variable   Coefficient                 Std. Error   t-Statistic      Prob.
                      AGE       -671.2805                   191.5316     -3.504803       0.0006
                     COLOR       151.6366                   156.6386     0.968067        0.3348
                 ENGINE          1793.689                   292.1268     6.140105        0.0000
                     MILES      -3798.259                   590.6794     -6.430323       0.0000
             TRANSMISSION        1462.702                   1248.129     1.171916        0.2433
                        C        48055.05                   6425.417     7.478900        0.0000
R-squared                        0.555991     Mean dependent var                       16859.54
Adjusted R-squared               0.539424     S.D. dependent var                       6831.670
S.E. of regression               4636.365     Akaike info criterion                    19.76316
Sum squared resid               2.88E+09      Schwarz criterion                        19.88923
Log likelihood                  -1377.421     F-statistic                              33.55917
Durbin-Watson stat               1.676795     Prob(F-statistic)                        0.000000
All Cars: Regression of price against
significant independent variables (p<0.05)
Dependent Variable: PRICE
Method: Least Squares
Date: 11/29/10 Time: 16:40
Sample: 1 140
Included observations: 140
                 Variable    Coefficient                 Std. Error   t-Statistic      Prob.
                     AGE     -630.8791                   190.0333     -3.319834       0.0012
                 ENGINE       1751.229                   289.7728     6.043457        0.0000
                 LNMILE      -4013.936                   576.0638     -6.967866       0.0000
                     C        51372.11                   6106.150     8.413175        0.0000

R-squared                     0.547257     Mean dependent var                       16859.54

Adjusted R-squared            0.537271     S.D. dependent var                       6831.670

S.E. of regression            4647.190     Akaike info criterion                    19.75407

Sum squared resid            2.94E+09      Schwarz criterion                        19.83812

Log likelihood               -1378.785     F-statistic                              54.79716

Durbin-Watson stat            1.655862     Prob (F-statistic)                       0.000000



Price = -631.9880*AGE + 949.8378* ENGINE -0.051251* MILEAGE
        + 1977.688*TRIM + 18866.11
    Some reasons why this model fails

   Color is randomly assigned a number (red = 9, blue = 7, etc)
   Engines: e.g. 4 cylinder = 4, V8 = 8  assumes the V8 is
    twice the price of 4 cylinder
   We suspect that many models leads to low R-Square
 Our solution: New model

     New model where we look at one model and brand (Toyota
      Camry), only two engines (4 cylinder and 6 cylinder), and
      disregard color
     Dummy variable for engine: 6 cylinder = 1, 4 cylinder = 0
     We also introduce a new variable called trim
     Dummy variable for trim: luxury = 1, standard = 0



     Toyota Camry
      o Most Popular Car in America*




* Motor Trend
http://www.motortrend.com/features/auto_news/2010/112_1004_america_top_10_best_selling_vehicle_comparison_2009_2000/index.htm l
Camry Price Histogram
            40
                                                                      37
            35


            30


            25
                                                                           22
Frequency
            20

                                                                                15
            15
                                                                 11                  11
            10                                         9
                                         8
                                                 7           7                            7
                                             6
                                 5
            5                        3                                                        3
                         2   2
                 1   1                                                                            1   1
                                                                                                          0
            0



                                                     Price
Toyota Camry: Regression of price against independent
variables (age, engine, mileage, trim and transmission)

Dependent Variable: PRICE
Method: Least Squares
Date: 11/29/10 Time: 20:09
Sample: 1 160
Included observations: 160
                     Variable   Coefficient                 Std. Error   t-Statistic      Prob.
                      AGE       -625.4328                   64.45118     -9.703978       0.0000
                 ENGINE          917.0942                   324.9508     2.822256        0.0054
                 MILEAGE        -0.051027                   0.005406     -9.438689       0.0000
                      TRIM       1972.208                   309.7351     6.367400        0.0000
             TRANSMISSION        967.9415                   1104.742     0.876170        0.3823
                        C        17888.66                   1141.740     15.66789        0.0000
R-squared                        0.828216     Mean dependent var                       14937.87
Adjusted R-squared               0.822638     S.D. dependent var                       3587.486
S.E. of regression               1510.845     Akaike info criterion                    17.51551
Sum squared resid               3.52E+08      Schwarz criterion                        17.63082
Log likelihood                  -1395.240     F-statistic                              148.4947

Durbin-Watson stat               1.275033     Prob(F-statistic)                        0.000000
Toyota Camry: Regression of price against
independent variables (age, engine, mileage and trim)
Dependent Variable: PRICE
Method: Least Squares
Date: 11/29/10 Time: 20:10
Sample: 1 160
Included observations: 160
                     Variable           Coefficient                 Std. Error   t-Statistic      Prob.
                      AGE               -631.9880                   63.96748     -9.879833       0.0000
                 ENGINE                  949.8378                   322.5527     2.944753        0.0037
                 MILEAGE                -0.051251                   0.005396     -9.497941       0.0000
                      TRIM               1977.688                   309.4398     6.391189        0.0000

                        C                18866.11                   242.7181     77.72850        0.0000

R-squared                                0.827359     Mean dependent var                       14937.87

Adjusted R-squared                       0.822904     S.D. dependent var                       3587.486

S.E. of regression                       1509.713     Akaike info criterion                    17.50798

Sum squared resid                       3.53E+08      Schwarz criterion                        17.60408

Log likelihood                          -1395.638     F-statistic                              185.7048


Durbin-Watson stat                       1.286429     Prob(F-statistic)                        0.000000


     Price = -631.9880 * AGE + 949.8378 * ENGINE -0.051251 * MILEAGE + 1977.688 * TRIM + 18866.11
All Cars: mileage against price
               120000

               100000
                                            R-Square ≈ 22%

                80000
     MILEGAE




                60000

                40000

                20000

                    0
                        0   10000   20000     30000    40000

                                    PRICE
Toyota Camrys: mileage against price
             200000

                                       R Square ≈ 66%

             150000
   MILEAGE




             100000



              50000



                  0
                      0   5000   10000 15000 20000 25000

                                   PRICE
Alternative Model
PRICE^(1/2) = -0.0002263673136*MILEAGE + 4.59824795*ENGINE - 2.952776402*AGE +
7.704044111*TRIM + 139.1536581
Dependent Variable: NewPRICE

Method: Least Squares

Date: 11/30/10 Time: 12:16

Sample: 1 160

Included observations: 160

                     Variable        Coefficient                   Std. Error   t-Statistic      Prob.

                     MILEAGE          -0.000226                    2.23E-05     -10.16426       0.0000

                     ENGINE           4.598248                     1.331262     3.454051        0.0007

                      AGE             -2.952776                    0.264011     -11.18429       0.0000

                      TRIM            7.704044                     1.277142     6.032253        0.0000

                        C             139.1537                     1.001764     138.9087        0.0000

R-squared                             0.871118     Mean dependent var                         121.1827

Adjusted R-squared                    0.847276     S.D. dependent var                         15.94425

S.E. of regression                    6.230994     Akaike info criterion                      6.527700

Sum squared resid                     6017.920     Schwarz criterion                          6.623799

Log likelihood                        -517.2160    F-statistic                                221.5239

Durbin-Watson stat                    1.222753     Prob(F-statistic)                          0.000000
      New Price                                        vs             Original Price
                                                                                                              25000
                                                   160
                                                                                                              20000
                                                   140
                                                                                                              15000
                                                   120
                                                         6000
                                                   100                                                        10000
20                                                       4000
                                                   80                                                         5000
10                                                       2000
                                                   60
                                                                                                              0
 0                                                          0

-10                                                      -2000

-20                                                      -4000
       20   40   60    80      100   120   140   160             20   40    60    80      100   120   140   160

            Residual        Actual     Fitted                          Residual        Actual     Fitted
Conclusions

   As expected, older, higher mileage cars are
    worth less than newer cars.
   Bigger engines and nicer levels of trim cost
    more
   Our model explains 82% of price variations
What we learned from this project

   Communication can be difficult
   EViews is amazingly fun and can be useful in
    analyzing social and economic phenomena



   Thanks!

				
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posted:11/5/2011
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