Consider a linear regression problem where y = X + E and X is a 100 x 10 matrix with independent columns, and E N100(O, +1). (a) (b) (c) (d) (e) (f) The fitted vector is the projection of y onto what subspace of RIOO? Let P be the projection matrix such that = Py. What is the trace of P? The residuals of the fit are r = Qy where Q is an orthogonal projection onto what subspace of R ICN)? What is the trace of Q? Determine E llr112 = E (yTQy). (Hint: Note that yTQy = (y X") and use a formula given in class.) Find an unbiased estimator of 02.