1. The data set mantel in the alr4 package has a response ) and three predictors X1, X2 and X3, apply the forward selection and backward elimination algorithms, using AIC as a criterion function. Also, find AIC and BIC for all possible models and compare results. Which appear to be the active regressors? 2. In an unweighted regression problem with n = 54, p = 4, the results included o = 4.0 and the following statistics for four of the cases: ei hii 1.000 0.900 1.732 0.750 9.000 0.250 10.295 0.185 For each of these four cases, computer;, D;, and t;. Test each of the four cases to be an outlier. Make a qualitative statement about the influence of each case on the analysis. 3. The lathe1 data set from the alr4 package contains the results of an experiment on characterizing the life of a drill bit in cutting steel on a lathe. Two factors were varied in the experiment, Speed and Feed rate. The response is Life, the total time until the drill bit fails, in minutes. The values of Speed and Feed in the data have been coded by computing Speed = Actual speed in feet per minute- 900 300 Feed = Actual feed rate in thousandths of an inch per revolution- 13 6 (a) Starting with the full second-order model E(Lifel Speed, Feed) = of Speed- 2Feed- 1Speed # 22Feed2 8 12 Speed Feed, use the Box-Cox method to show that an appropriate scale for the response is the logarithmic scale. (b) Find the two cases that are most influential in the fit of the quadratic mean function for log(Life), and explain why they are influential. Delete these points from the data, refit the quadratic mean function, and compare with the fit with all the data