Consider a linear regression model with p parameters,fit by least squares to a set of training data (x1; y1); : ; (xN; yN) drawn at random from a...

Consider a linear regression model with p parameters,fit by leastsquares to a set of training data (x1; y1); : : : ; (xN; yN) drawn at randomfrom a population. Let B be the least squares estimate. Suppose wehave some test data (~x1; ~y1); : : : ; (~xM; ~yM) drawn at random from thesame population as the training data. If Rtr(B) = 1NPN1 (yi - BT xi)2and Rte(B) = 1MPM1 (~yi ô€€€ T ~xi)2, prove thatE[Rtr( ^ )] E[Rte( ^ )];where the expectations are over all that is random in each expression.

4. Consider a linear regression model with p parameters, t by least squares to a set of trainingdata (x1; y1); : : : ; (xN; yN) drawn at random from a population. Let β ^ be the least squares...