Consider the standard simple regression model y5 b01 b1x 1 u under the Gauss-Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators b^0 and b^1 are unbiased for their respective population parameters. Let b

&1 be the estimator of b1 obtained by assuming the intercept is zero (see Section 2.6).

(i) Find E1b

&1 2 in terms of the xi

, b0, and b1. Verify that b

&1 is unbiased for b1 when the population intercept 1b0 2 is zero. Are there other cases where b

&1 is unbiased?

(ii) Find the variance of b

&

1. (Hint: The variance does not depend on b0.)

(iii) Show that Var1b

&1 2 # Var1b^1 2. [Hint: For any sample of data, gn i21x2 i $ gn i51 1xi2 x2 2

, with strict inequality unless x5 0.]

(iv) Comment on the tradeoff between bias and variance when choosing between b^1 and b

&

1.