4. buppose we are interested in the linear model 3/; = Do +p1x1; +D2X2i-l e;. Also suppose the commns x1 and x2 of the design matrix for this model have mean 0 and length 1. (That is. x'lxl = 1, and the same is true of X2. This is a very particular situation that won't actually happen; it just makes Our arithmetic easier for a moment.) Then if r is the correlation between x1 and x2, we have the following: 0 Mn 0 o r and (x'xfl = o no r2) r/(1 r2) 1 o r/(1 r2) 1/(1 r2) X'X= 00:: \"tilo (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 02[X'X)_1 (above). (b) Determine what values of r will make the variance of 51 and 32 large. Explain why. using what you know about the variance of the vector ,6