5. Suppose we are interested in the linear model 3;; = g + 513311 + zwzi + 62-. Also suppose the columns x1 and xz of the design matrix for this model have mean 0 and length 1. (That is, x'lxl = 1 and x'2x2 = 1. This is a very particular situation that is unlikely to happen in practice; it just makes our arithmetic easier for a moment). Then if r is the correlation between x1 and X2, we have the following: n O 0 UR 0 0 x'x = 0 1 7' and (x'x)'1 = 0 1/(1 _ r2) _7~/(1 _ 7.2) O r 1 0 7'/(1 7'2) 1/(1r2) (a) In our setup where the predictors have mean 0 and length 1, explain why SXX = 1. Use that to show that the VIF formula on page 203 matches (:2 (X'X)_1 (above). (b) Determine what values of 7" will make the variance of A31 and 32 large. Explain why, using what you know about the variance of the vector {3. \f