Suppose that the true observation model is given by Y=X+ where XRn2, and satisfies E[]=0 and E[]=2I. Further assume that the X1,X2 Rn are the two columns of X,X12=X22=1, and the inner product X1,X2=r. Denote by ^:=(XX)1XY and OLS estimator using the full model, and ^r:=(X1X1)1X1Y the OLS estimator using the reduced model. - [1pts] Suppose that we are only interested in estimating the first coordinate, 1. Compute E[^1] and var(^1) (express the answers using , and r ). - [2pts] Compute E[^1r] and var(^1r). - [2pts] Use the bias-variance tradeoffs to compute the mean square errors of ^1 and ^1r (defined as E[^112] and E[^1r12] ). Show that the reduced model has a smaller mean square error when 2