The data set Cars contains the make, model, equipment, mileage, and Kelley Blue Book suggested retail price of several used 2005 General Motor cars. Kelley Blue Book (www.kbb.com) has been an accurate resource for pricing cars for over 80 years and was used as a source to collect these data. In this activity, you will create a regression model that will describe the association of several explanatory variables (car characteristics) with the retail value of a car.
a. In the Cars data set, liters and cylinders are highly correlated, as they both are a measure of engine size. Instead of using either the liter or the cylinder variable, create the first principal component obtained from a PCA of just these two variables. Use this first principal component, plus mileage, Buick, Cadillac, Chevrolet, Pontiac, and SAAB, in a regression analysis to predict the natural log of retail price, LnPrice.
b. Run a regression analysis with liter, cylinder, mileage, Buick, Cadillac, Chevrolet, Pontiac, and SAAB to predict the natural log of retail price, LnPrice.
c. In Part A, using the first principal component from the PCA of liter and cylinder eliminated multicollinearity, but how did it impact the R2 value? Did using PC1 instead of both liter and cylinder cause you to miss a key explanatory variable? Which model would you suggest is better?