Question: In the regressionmodel y = X???? + u (T 1), X (T k) is fixed with rank k, E(u) = ????, and E(uu)

In the regressionmodel y = X???? + u (T × 1), X (T × k) is fixed with rank k, E(u) = ????, and E(uu′) = ????2????.

(a) Consider the function S

(b) = (y − Xb)′????−1(y − Xb).

Given a vector ̃ ????, define ̃u = y − X ̃ ????. Show that if X′????−1 ̃u = ????, (8.21)

then S is minimized by setting b = ̃ ????.

(b) Obtain the formula for ̃ ???? by solving equation (1) in part (a). Obtain the mean and the variance matrix of ̃ ????.

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