Consider the one-variable regression model Yi = b0 + b1Xi +
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Consider the one-variable regression model Yi = b0 + b1Xi + ui and suppose that it satisfies the least squares assumptio
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Consider the one-variable regression model Yi = b0 + b1Xi + ui and suppose that it satisfies the least squares assumptions in Key Concept 4.3. The regressor Xi is missing, but data on a related variable, Zi , are available, and the value of Xi is estimated usingX ? i = E(Xi 0 Zi ). Let wi = X ? i - Xi. a. Show that X ? i is the minimum mean square error estimator of Xi using Zi . That is, let Xn i = g(Zi ) be some other guess of Xi based on Zi, and show that E3(Xn i - Xi ) 2 4
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