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- 1. How do US Drivers Choose the Cars They Buy SHIH-WEN HUANG, SHEN YAN, LIYAN WANG Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 2. Survey Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 3. Source of data This is a consumer study undertaken across the US by Kelley Blue Book(known as KBB), a vehicle valuation and automotive research company that is recognized by both consumers and the automotive industry. The purpose of this analysis is to find out how US drivers choose the cars they buy. Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 4. Data Cleansing Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 5. Missing values removed Sorted in alphabet order Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 6. Dataset Variables Dependent Variable: OCRAT1(Consumer Reports numerical score) Number of observations: n=170 1. Mcode(Manufacturer Code) 5. OGAS1(Gas mileage mpg) 9. OSAF1(Consumer Reports rating of safety ) 2. CRREC(Recommended by Consumer Reports = 1) 6. ORLGRM1(Rear leg room inches) 10. OHAND1(Consumer Reports rating of handling) 3. OREL1(Consumer Reports reliability rating - 5 pt. scale) 7. OACCEL1(Acceleration 0- 60 mph) 11. ORIDE1(Consumer Reports rating of ride) 4. OLCAP1(Luggage capacity cu. ft.) 8. OFSEAT1(Consumer Reports rating of front seat comfort) Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 7. Descriptive Statistics Variable Name Mean Standard Deviation CRREC 3.112 1.0793283 OREL1 31.048 16.5318098 OLCAP1 18.647 3.4287537 OGAS1 28.644 1.8149920 ORLGRM1 9.077 1.8248783 OACCEL1 3.900 0.5509540 OFSEAT1 4.323 0.7672302 OSAF1 3.288 0.7333012 OHAND1 3.224 0.6772110 Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 8. Variable Correlation All correlations between independent variables are <0.5 except for the following: OLCAP1 with OGAS1 = -0.559 OHAND1 with OGAS1 = 0.504 Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 9. Variable Correlation Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 10. Transformation
- 11. Variable Selection Maximum R-squared Stepwise Selection GLMSelection AIC Selection Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 16. Selected Model OCRAT1= -107.53353+ 0.88959*Mcode+ 1.52307* OLCAP1+ 3.59932* OGAS1- -8.34379* OACCEL1+ 17.88028* OFSEAT1+ 15.66684* OSAF1+ 39.36924* OHAND1+ 27.44342* ORIDE1;
- 17. Regression Conclusion R Squared: 0.5754 Adjusted R-squared: 0.5543 Number of influence point is 17 Overall F-statistic: 27.27 P-value for Overall F-test: <0.0001 VIF=PRESS/SSR=1.1433
- 18. PROC REG Source Code PROC REG data=car_new; MODEL OCRAT1= Mcode OLCAP1 OGAS1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1 / r p influence vif; PLOT r.* p. r.* nqq.; RUN; Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 19. Selected Model Parameter Estimates Variable DF Parameter Standard t Value Pr > |t| Estimate Error --------------------------------------------------------------------------- Intercept 1 -210.36703 36.06039 -5.83 <.0001 Mcode 1 0.65258 0.28073 2.32 0.0215 OLCAP1 1 1.59184 0.21803 7.30 <.0001 OGAS1 1 5.58281 1.11826 4.99 <.0001 OACCEL1 1 -6.79223 1.60769 -4.22 <.0001 OFSEAT1 1 18.78770 5.61708 3.34 0.0011 OSAF1 1 21.18837 3.99055 5.31 <.0001 OHAND1 1 35.98280 4.59454 7.83 <.0001 ORIDE1 1 38.90925 4.57810 8.50 <.0001 Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 20. Selected Model Cross-validation Estimates --------------Cross Validation Estimates--------------- Parameter 1 2 3 4 5 Intercept -215.22 -221.657 -240.976 -190.66 -174.67 Mcode 0.78 0.471 0.884 0.51 0.64 OLCAP1 1.54 1.563 1.470 1.79 1.61 OGAS1 5.35 5.461 5.613 6.15 5.39 OACCEL1 -6.38 -6.281 -5.785 -7.92 -8.46 OFSEAT1 20.39 19.546 22.426 15.83 15.27 OSAF1 22.50 22.200 22.450 17.85 21.28 OHAND1 34.11 36.681 33.626 39.38 35.78 ORIDE1 38.68 40.296 42.117 35.96 37.25 Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 21. Analysis of Variance for Model R-squared: 0.7782 Adjusted R-squared: 0.7659 Overall F-statistic: 63.17 P-value for Overall F-test: <0.0001 VIF=PRESS/SSR:1.1715 Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 22. PROC REG -- Influence Points and Multicollinarity Inspection of 𝑧𝑖 ∗ and ℎ𝑖𝑖 for all observations shows that there are 10 influence points. Here are the VIF values: Variable VIF ------------------------------- Intercept 0 Mcode 1.27290 OLCAP1 1.77977 OGAS1 1.95318 OACCEL1 1.24724 OFSEAT1 1.19959 OSAF1 1.16904 OHAND1 1.62568 ORIDE1 1.17256 Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 23. Residual Plot Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 24. Normal Plot of Residuals Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 25. Conclusions The final model holds up under cross-validation. The R-squared value is relatively high: 𝑅2 =.7782. There are 10 influence points which can be accepted given the sample number. There is no multicollinarity. The residual plot satisfies the assumption: the residuals are unbiased and homoscedastic. The residuals are normally distributed. Kelley Blue Book. © Kelley Blue Book Co, Inc. All Rights Reserved.
- 26. Follow-up Analysis Is it possible to have more observations in a sample? Is there any other factors, which influence the consumer choice making, that are not included in the original survey? Is this analysis too general? Should we break down into several groups, ex. used cars vs new cars, SUV vs sedan?
- 27. Appendix /* Import data and creat new dataset called car */ PROC IMPORT datafile="C:/datasets/cars.csv" OUT=car DBMS=csv REPLACE; getnames=yes; RUN; PROC PRINT; RUN;
- 28. Appendix /* Descriptive statistics about each variable */ PROC MEANS data=car mean min max stddev p25 p75; VAR OCRAT1 OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1; RUN; PROC SGSCATTER data=car; MATRIX OCRAT1 Mcode OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1; RUN; /* Test the correlation between each independent variable */ PROC CORR data=car; VAR Mcode OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1; RUN;
- 29. Appendix /* Build Linear Regression Model for car dataset */ PROC REG data=car; MODEL OCRAT1= Mcode CRREC OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1 / r p vif; PLOT r.* p. r.* nqq.; RUN; * Model 1 Using MaximumR-squared Selection ; PROC REG data=car ; MODEL OCRAT1= Mcode CRREC OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1 / selection= maxr r p influence vif; PLOT r.* p. r.* nqq.; RUN;
- 30. Appendix * Model 2 Using Stepwise Selection ; PROC REG data=car ; MODEL OCRAT1= Mcode CRREC OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1 / selection= stepwise r p influence vif; PLOT r.* p. r.* nqq.; RUN; *Model 3 Using AIC Selection; PROC RSQUARE AIC; MODEL OCRAT1= Mcode CRREC OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1 / select=2; RUN; * Model 4 Using GLMSelection ; PROC GLMSELECT data=car ; MODEL OCRAT1= Mcode CRREC OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1; RUN;
- 31. Appendix *Initial final model ; PROC REG data=car; MODEL OCRAT1=MCODE OLCAP1 OGAS1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1/r p influence VIF; PLOT r.* p. r.* nqq.; RUN; /* Remove the influence points and rebuild the model */ *Import new data and creat new dataset called car_new ; PROC IMPORT datafile='C:/datasets/cars_new.csv' OUT=car_new DBMS=csv REPLACE; getnames=yes; RUN; PROC PRINT; RUN;
- 32. Appendix /* Build the best regression model */ PROC REG data=car_new; MODEL OCRAT1= Mcode OLCAP1 OGAS1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1 / r p influence vif; PLOT r.* p. r.* nqq.; RUN; /* Cross validation */ PROC GLMSELECT seed=4530; MODEL OCRAT1= Mcode OREL1 OLCAP1 OGAS1 ORLGRM1 OACCEL1 OFSEAT1 OSAF1 OHAND1 ORIDE1 / stats= all cvdetails=all details=summary selection=stepwise(select=cv drop=competitive) cvmethod=random(5); RUN; QUIT;
Editor's Notes
- Data Transform The exploratory data analysis suggests a model that is adequate for fitting the data. Check from the correlation graph (See in Appendix A), the data show the linear relationship; thus, data transform is not necessary in this case.
- Maximum r squared selection, obviously, we ought to look for the biggest R squared model. However, we still take the parameter P-Value into account. We thus get the regression model. In step 9, with the R squared increases, all the P-Value of parameters are significant but if we include 9 independent variables, predictors start to be not significant. In the 9 dependent variable model, the OREL1’ P- Value is 0.2 which is not significant.
- Stepwise selection is pretty easy for model builders because this selection method give us a summary as the PowerPoint shows.
- Smallest AIC, and 1331.2492 is the smallest AIC. So we find out the variables in model.