Consider a linear regression model Y = XB+U, where X is the n k matrix of...

   

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Consider a linear regression model Y = XB+U, where X is the n k matrix of regressors, and 3 is the k-vector of unknown parameters. Let W be another n=k observable matrix. Assume that W'X has rank k, E(U|X, W) = 0, and E(UU'|X, W) = 0 In. a) [5 points] Let 3 = (W'X)-W'Y. Is an unbiased estimator of 3? Carefully justify your answer. b) [5 points] Find Var(8|X, W). c) [5 points] Find Cov(3, B|X, W) where B is the OLS estimator of 3. Consider a linear regression model Y = XB+U, where X is the n k matrix of regressors, and 3 is the k-vector of unknown parameters. Let W be another n=k observable matrix. Assume that W'X has rank k, E(U|X, W) = 0, and E(UU'|X, W) = 0 In. a) [5 points] Let 3 = (W'X)-W'Y. Is an unbiased estimator of 3? Carefully justify your answer. b) [5 points] Find Var(8|X, W). c) [5 points] Find Cov(3, B|X, W) where B is the OLS estimator of 3.