Consider the linear regression model y = X B+E, E(€) = 0, Cov(e) = o’In, = : where y: nx1, X: n xp, (p

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Consider The Linear Regression Model Y X B E E 0 Cov E O In Where Y Nx1 X N Xp P N Rank X P 1 (43.64 KiB) Viewed 21 times

Consider the linear regression model y = X B+E, E(€) = 0, Cov(e) = o’In, = : where y: nx1, X: n xp, (p <n, rank(X) = p), B :p x 1 and € : nx1. Answer the following questions: a) Find E(y) and Cov(y). b) Prove that E(Ô) = B and Cov(f) = 02(X'X)-1, where is the least squares estimator of ß. =
= c) Let ġ= XÊ be an unbiased estimate of y. Find Elû), Cov(ŷ) and Cov(y – ġ). Denote ġ = (ŷ1, ... , ûn)'. =