(a) Show that cov(OLS, e) 0 (Since both random variables are normally distributed, this proves their independence) (b) Show that OLS and s2 are independent Hint A linear (Bu) and quadratic (uAu) forms in normal random variables are independent if BA 0 See Graybill (1961) Theorem 4 17

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Question: (a) Show that cov(OLS, e) = 0. (Since both random variables are normally distributed, this proves their independence). (b) Show that OLS and s2 are

(a) Show that cov(βOLS,

e) = 0. (Since both random variables are normally distributed, this proves their independence).

(b) Show that βOLS and s2 are independent. Hint: A linear (Bu) and quadratic (uAu) forms in normal random variables are independent if BA = 0. See Graybill (1961) Theorem 4.17.

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