The multiple linear regression model can be written as Y = X e where Cov(e) = 2In and In is the (n n) identity matrix so that Cov(Y ) = 2In. The fitted or predicted values are given by Y = X = X(XT X)1XT Y = HY where H = X(XT X)1XT . In addition, in the class, we have shown that E[ ] = , Cov( ) = 2(XT X)1. Based on these results and r = (In H)y, show the following (a) E[y] = X, and Cov(y) = 2H. (b) E[r] = 0, and Cov(r) = 2(In H). (c) (4CR) Based on the result that rT r 2 = RSS 2 2 np, show that E[2] = 2