Consider the standard simple regression model y = (0 + (1x + u under the Gauss Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators unbiased for their respective population parameters. Let be the estimator of obtained by assuming the intercept zero (see Section 2.6).
(i) Find E() in terms of the xi, (0, and (1. Verify that is unbiased for when the population intercept ((0) in zero. Are there other cases where is unbiased?
(ii) Find the variance of . (The variance does not depend on (0.)
(iii) Show that Var() ( Var(). [For any sample of data, /( /with strict inequality unless = 0.]
(iv) Comment on the tradeoff between bias and variance when choosing between and .