Consider the usual multiple regression models. Let = (XTX)/2 and 1/2 its (symmetric) square root.

Consider the usual multiple regression models. Let I' = (X TX ) / 02 and W\" its (symmetric) square root. (a) Show that F1/2(3 ,6) 6 R19\" is normal and Specify its mean and covariance. (b) Find the distribution of U2 = (a e)Tr(B 3). ( c) Is 71.2 in the previous part independent of .92? Here .92 = ||e||2/(n p 1) is our usual unbiased estimate of 02. d Show that L; is F distributed Where you specify the degrees of freedom. (p+1)8