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If in this situation you had assumed incorrectly that the

Consider the following regression-through-the origin model:
Yi = βXi + ui, for i = 1, 2

You are told that u1 ∼ N(0, σ 2 ) and u2 ∼ N(0, 2σ 2 ) and that they are sta- tistically independent. If X1 = +1 and X2 = -1, obtain the weighted least- squares (WLS) estimate of β and its variance. If in this situation you had assumed incorrectly that the two error variances are the same (say, equal to σ2), what would be the OLS estimator of β? And its variance? Compare these estimates with the estimates obtained by the method of WLS? What general conclusion do you draw?

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