Consider the regression model Yi = BXi + Ui, where E(ui) = 0 and Var(ui) > 0 for the regressors Xi which are positive and fixed (non-random), and the error terms Ui are independent. Let b denote an estimator of B that is constructed as b = (X'X)^(-1)X'Y, where X = [X1, X2, ..., Xn]' and Y = [Y1, Y2, ..., Yn]'.
(a) Carefully explain the concept of a linear unbiased estimator: Is b a linear unbiased estimator of B? Prove your answer.
(b) Is b the most efficient estimator of B? Explain why or why not.
(c) Prove that b is a consistent estimator of B. Use the assumption that T, converges to a positive constant 4 when n approaches infinity.