It is a Stat Question

Question 1. [15 marks] In this question we consider derivation of Mallows' Op statistic for model selection discussed in lectures. Suppose the experimenter proposes a model y = X171 13101 + 51 (P1 Paralneters), where X111 is n x p1 matrix and vector 3111 contains p1 parameters. The \"true" model however contains additional p2 parameters described by vector 31,2. So the "true" model is given by y = Xtt + 6 (p1 +p2 parameters), where Xtt = X171 pl + Xp2 [31,2 . In this model Xp2 is n X p2 matrix and 3102 contains p2 parameters. Assume that errors 8 are uncorrelated with mean zero and common variance 0'2. Consider fitting the proposed general linear model to data and write 391' for the fitted value at 931' and MSE(i) for its mean squared error. Recall that if the error variance 0'2 is known, then an estimator of L=1 MSECIL') _ 23:1 Var(17) L1 Biaszh) + 0'2 0'2 0'2 is A2 2 (n P1X\" 0 ) p. + 2,