Question: (OLS) Let E[y | X] = X 0 and Var[y | X] = 0 where 0 R k and X is full-row

(OLS) Let E[y | X] = Xβ0 and Var[y | X] = Ω0 where β0 ∈ Rk and X is full-row rank.

(a) Find the conditional variance matrix of $ \hat{\beta}_{OLS} $ = Pxy given X.

(b) Also find Var[y - $ \hat{\beta}_{OLS} $| X].

(c) Show that y - $ \hat{\beta}_{OLS} $ and $ \hat{\beta}_{OLS} $ are generally correlated.

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