Here is the question:

Corrected Mallows' Cp Define Cp (M) n-p-q-1 n - P trace (ER] (Y - YM)'(Y - YM) ) + 2d'M Idea: Tradeoff between penalty for lack of fit (first term ) and penalty for too many parameters (second term) Usage: Select model with smallest C'*3. [4 pts] Consider the full multivariate regression model Y = x3 +R R ~ Nnxq(0, In 8 ER) where r is n x p and B is p x q. Show that, when the model M is this full model, the corrected Mallows' Cp, as defined in lecture, reduces to an expression that depends only on n, p, and q (and not on Y or a). Also, find that expression, and simplify it as much as possible. [Hints: What is Y - xBy for the full model? What is the expression for ER in terms of the least squares residual matrix? What is the trace of an identity matrix? ]