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 = XPl 5171 + 51 (p1 parameters), where X111 is 'n, X p1 matrix and vector r3171 contains p1 parameters. The "true" model however contains additional p2 parameters described by vector pz . So the "true" model is given by y = Xtt + 6 (111 +122 parameters), where Xtt = Xp1 pl + Xp2 31,2 . In this model X112 is n X p2 matrix and 31,2 contains p2 parameters. Assume that errors 5 are uncorrelated with mean zero and common variance 02. Consider fitting the proposed general linear model to data and write 371' for the fitted value at mi and MSE(3}Z-) for its mean squared error. Recall that if the error variance 0'2 is known, then an estimator of L1 MSEQJi) = 2L1 Vadi) 2L1 Biaszii) + (72 0'2 0'2 is .2 2 (n P1)(0' 0 ) p1 + 2.