Two researchers working independently were estimating the same regression model: yi = 0 + 1xi + ui

Using two different random samples each with n observations. Let b1 denote the least squares estimator from the first sample and let e1 denote the least squares estimator from the second sample. If information from both samples was combined, then we might expect to get amore precise estimator of 1. One way to combine the information from both samples is to construct the estimatorb = c1b1 + c22.

Where c1 and c2 are non-negative constants.

1).What condition must c1 and c2 satisfy in order for b to be an unbiased estimator? 2). Compute the conditional (on X) variance of b. It is enough to get a formula that dependson c1, c2, and var(b1|X), var(e1|X) . 3). Find the values of c1 and c2 that make b and unbiased estimator and minimize var(b|X). It is enough to obtain a formula that is a function of var(b1|X) and var(e1|X).