Car Retail Price The analyst continues to explore the effects of the physical characteristics of..

Car Retail Price The analyst continues to explore the effects of the physical characteristics of a car on its suggested retail price. The variables he would like to use in the same data file cars.csv are Y = Suggested Retail Price; x1 = Engine size; x2 = Cylinders; x3 = Horse power; x4 = Highway mpg; x5 = Weight; x6 = Wheel Base; x7 = Hybrid, a dummy variable which is 1 for so-called hybrid cars. (a) Fit a linear model for Y and x1, x2,…, x7, and explain the potential problems. (b) The multivariate version of the Box-Cox method was used to transform the predictors, while a log transformation was used for the response variable to improve interpretability. This resulted in the following model log Y = ß0 + ß1x 1^0.25 + ß2 log x2 + ß3 log x3 + ß4×4 ^-1 + ß5×5 + ß6 log x6 + ß7×7 + e (1) Fit this model, and explain the potential problems, especially problematic observations. (c) Remove the problematic observations, refit the model (1), and answer the following questions. i. Check all assumptions. ii. Give the ANOVA table, ie., SST, SSReg and SSE with appropriate df. iii. An engineer suggests that model (1) is not sufficient because x1, x2 and x3 may have interaction effects on the retail price. Test if this is the case. iv. If he is only concerned if x4 and x6 in model (1) should be there together or not, implement an appropriate test for him.v. Run an exhaustive variable selection algorithm for model (1) using BIC, Cp and PRESS, and make some suggestions to simplify the current model. vi. Run stepwise regression using AIC for model (1). Does this give you the same results as in the previous part? Which would make more sense? Explain why.

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