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Consider the standard simple regression model y = ß0 + ß|x + u under the Gauss-Markov Assump- tions SLR.l through SLR.5. The usual OLS estimators A, and ß| are unbiased for their respective population parameters. Let ß i be the estimator of ß1 obtained by assuming the intercept is zero (see Section 2.6). (i) Find E(8.) in terms of the xi, ß0, and ß1. Verify that ß| is unbiased for ß| when the population intercept (Ba) is zero. Are there other cases where B, is unbiased? Find the variance of ß1-(Hint: The variance does not depend on A-) Show that Var(ß.) Var(ß.). [Hint,' For any sample of data, S, strict inequality unless x Comment on the tradeoff between bias and variance when choosing between ß1 and ß- (ii) (iii) -S-(x-x), with OJ (iv)
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