Please write in R language

5. An analyst for the auto industry has asked for your help in modeling data on the prices of new cars. Interest centers on modeling suggested retail price as a func- tion of the cost to the dealer for 234 new cars. The data set, which is available on the book website in the file cars04.csv, is a subset of the data from http://www.amstat.org/publications/jse/datasets/04cars.txt (Accessed March 12, 2007) The first model fit to the data was Suggested Retail Price = B.+B, Dealer Cost+e (3.10) On the following pages is some output from fitting model (3.10) as well as some plots (Figure 3.46). (a) Based on the output for model (3.10) the analyst concluded the following: Since the model explains just more than 99.8% of the variability in Suggested Retail Price and the coefficient of Dealer Cost has a t-value greater than 412, model (1) is a highly effective model for producing prediction intervals for Suggested Retail Price. Provide a detailed critique of this conclusion. 80000- Suggested Retail Price Standardized Residuals 0 2 20000 20000 20000 60000 100000 DealerCost e 60000 100000 DealerCost Normal Q-Q Plot 1.5 Square Root(Standardized Residuals) Standardized Residuals 0 - 0.5 20000 60000 100000 DealerCost -3 -2 -1 0 1 2 3 Theoretical Quantiles Figure 3.46 Output from model (3.10) (b) Carefully describe all the shortcomings evident in model (3.10). For each short- coming, describe the steps needed to overcome the shortcoming. The second model fitted to the data was log(Suggested Retail Price)= Be + Blog (Dealer Cost)+e (3.11) Output from model (3.11) and plots (Figure 3.47) appear on the following pages. (c) Is model (3.11) an improvement over model (3.10) in terms of predicting Suggested Retail Price? If so, please describe all the ways in which it is an improvement (d) Interpret the estimated coefficient of log(Dealer Cost) in model (3.11). (e) List any weaknesses apparent in model (3.11). Regression output from R for model (3.10) Call: lm( formula = SuggestedRetailPrice - DealerCost) 3.4 Exercises 111 Coefficients: Estimate (Intercept) -61.904248 DealerCost 1.088841 Std. Error 81.801381 0.002638 t value -0.757 412.768 Pr(t) 0.45 101) 0.00924 **