The generated data set in this question is taken from Mantel XXXXXXXXXXThe data are igiven in Table 7.3 and can be found on the book web site in the file Mantel.txt. Interest centers on using variable...

The generated data set in this question is taken from Mantel (1970). The data are igiven in Table 7.3 and can be found on the book web site in the file Mantel.txt. Interest centers on using variable selection to choose a subset of the predictors to model Y. The data were generated such that the full model
Y = /30 +13,X, + (32X2+133X3+e (7.8) Rs a valid model for the data. Output from R associated with different variable selection procedures based on knodel (7.8) appears below.
Exercises 253
Table 7.3 Mantel's generated data Case Y X1 X2 X3 1 5 1 1004 6 2 6 200 806 7.3 3 8 —50 1058 II 4 9 909 100 13 5 II 506 505 13.1
(a) Identify the optimal model or models based on R2adj, AIC and BIC from the approach based on all possible subsets. (b) Identify the optimal model or models based on AIC and BIC from the approach based on forward selection. (c) Carefully explain why different models are chosen in (a) and (b). (d) Decide which model you would recommend. Give detailed reasons to sup-port your choice.