What decides the price of used cars?

Group 1

Jessica AguirreKeith CodyRui FengJennifer GriffethJoonhee LeeHans-Jakob LotheTeng 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

Models

Average Selling Price by Brand

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 Camryo Most Popular Car in America*

* Motor Trendhttp://www.motortrend.com/features/auto_news/2010/112_1004_america_top_10_best_selling_vehicle_comparison_2009_2000/index.html

Camry Price Histogram

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

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R-Square ≈ 22%

Toyota Camrys: mileage against price

R Square ≈ 66%

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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

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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!