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The expression for the restricted coefficient vector in (6-14) may be written in the form b* = [I − CR] b + w, where w does not involve b. What is C? Show that the covariance matrix of the restricted least squares estimator is σ2 (X X)−1 − σ2(X X)−1 R [R(X X)−1R ]−1 R(X X)−1 and that this matrix may be written as Var[b |X]{[Var(b |X)]−1 − R [Var(Rb) |X]−1R}Var[b |X]. |
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