Question: Problem #4 Consider the standard simple regression model y = Bo + B121 + u under the Gauss-Markov Assumptions. The usual OLS estimators Bo and

Problem #4 Consider the standard simple regression model y = Bo + B121 + u under the Gauss-Markov Assumptions. The usual OLS estimators Bo and Bi are un- biased for their respective population parameters. Let Bi be the estimator of Bi obtained by assuming the intercept is zero (i) Find E() in terms of the ri, Bo, and B1. Verify that B1 is unbiased for 1 when the population intercept (Bo) is zero. Are there other cases where B1 is unbiased? (ii) Find the variance of . (Hint: The variance does not depend on Bo.) (iii) Show that Var(@) (x; -7)2, with strict inequality unless 7 = 0.] (iv) Comment on the tradeoff between bias and variance when choosing between bi and bi

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