The expression for the restricted coefficient vector in (5-23) 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']⁻¹R(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].