The real data set in this question first appeared in Hald $(1952).$ The data are given in Table $7\mathrm{.}5$ and can be found on the book web site in the file Haldcement. txt$.$ Interest centers on using variable selection to choose a subset of the predictors to model $Y.$ Throughout this question we shall assume that the full model below is a valid model for the data

$Y={}_0+{}_1{x}_1+{}_2{x}_2+{}_3{x}_3+{}_4{x}_4+e$

Output from $R$ associated with different variable selection procedures based on model $(7\mathrm{.}9)$ appears on the following pages: