Wednesday, August 21, 2019

Factors Impacting the Pricing of Late Model Cars

Paul is interviewing for a Price Analyst position with a national independent car dealer.

Question # 1
Interviewer: The correlation matrix (1) is unrestricted, representing the entire inventory without any constraints whatsoever. The correlation matrix (2) is however constrained to those with the balance of the factory warranty, re-certified warranty or special dealer warranty. What is your most important observation here?

Paul:  The dealer Price has the highest negative correlation with Miles, signifying that the higher miles tend to dampen the dealer’s asking prices in the market.

Question # 2
Interviewer: What is the next best predictive variable?

Paul: Given the entire population, Warranty is the next best predictive variable, with extremely low collinearity with the other potential independent variables. When only the warranted cars are evaluated, the homogeneity of the inventory, i.e., lack of distribution, lowers the predictive correlation. Either way, the positive coefficient points to buyer’s preference of the warranted vehicles over their counterparts with expired warranties.

Question # 3
Interviewer: How does the Accident variable impact both populations?

Paul: Unsurprisingly, the Accident variable has a negative impact on the overall dealer pricing. As far as the warranted cars are concerned, the limited period on the road and the resulting capped mileage have made the Accident variable more or less irrelevant (uncorrelated).

Question # 4
Interviewer: How would you interpret the Owner and Service variables?

Paul: Well-maintained cars (Service) are rewarded. Surprisingly, the highest-rated original ownership is unrewarded. The plausible conclusion is that the 3-yr leases are so popular that the first owner is truly the first purchaser after the expiration of the lease. For the warranted cars, the Owner variable has turned into a big positive, suggesting that the original ownership would be rewarded. Service has become the most positive correlation coefficient, emphasizing that the maintenance of the vehicle by the manual would be economically wholesome.

Question # 5
Interviewer: The scatter graph reflects the entire inventory. What is it telling us?

Paul: The scatter graph is depicting the usual negative relationship between the Dealer Prices and Miles. Prices generally decrease commensurately with the increasing mileage. In fact, the graph is essentially confirming the most classic pricing relationship in the pre-owned auto industry.

Question # 6
Interviewer: In that case, the fit would be tighter and the resulting R-squared would be higher. How come we don’t see that?

Paul: Since the scatter reflects the entire inventory of pre-owned cars, it needs removal of some outliers. In fact, this fit would be much tighter with the trimming of outliers, thus paving the way for a much higher R-squared, perhaps to a more customary level. 

Question # 7
Interviewer: If you are asked to develop a regression-based pricing model for the entire inventory, which independent variables are you going to choose?

Paul: Since a limited number of variables are available and multi-collinearity is not an issue here, I would use all of them, letting the model decide their significance and effectiveness.

Question # 8
Interviewer: Do you expect the Miles variable to be the most significant in the regression model?

Paul: No. In multiple regressions, the variables with the most predictive relationships with the dependent variable do not necessarily become the most significant independent variables as they are evaluated alongside other variables in the same equation. Also, the distribution of the variable is important too.

Question # 9
Interviewer: Given your logic, the Service variable which has the least predictive relationship with Price can be significant in the model. Is that what you are saying?

Paul: Precisely. Considering its low multi-collinearity with the other variables, it could be one of the most significant variables.

Thank you,

Sid Som, MBA, MIM
Homequant, Inc.

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