Mantel (1970) preferred backward elimination to forward selection. The following data illustrate a situation in which FS might fail to detect an optimal subset.

a. Determine the correlation matrix, and note that zy is highly correlated with the response while x; and any appear to be unrelated to the response. h. Show that the FS algorithm would select ry first and, depending on the criterion for inclusion, might terminate with one predictor.

e. Evaluate all possible subsets and note the role of x, and zy as predictors. Data for Exercise 4.15 0 1999 60 1 150 851 80 2 92 910 110 3 903 100 130 4 450 554 150 5 75 930 175