Suppose we are interested in the linear model yi = 0 + 1x1i + 2x2i + ei. Also suppose the columns x1 and x2 of the design matrix for this model have mean 0 and length 1. (That is, x1x1 = 1 and x2x2 = 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: XX = n 0 0 0 1 r 0 r 1 and (XX)1 = 1/n 0 0 0 1/(1 r2) r/(1 r2) 0 r/(1 r2) 1/(1 r2) (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 (XX)1 (above). (b) Determine what values of r will make the variance of 1 and 2 large. Explain why, using what you know about the variance of the vector .