Consider the standard simple regression model y = β0 + β1x + u under the Gauss-Markov Assu...

Consider the standard simple regression model y = β0 + β1x + u under the Gauss-Markov Assumptions SLR.l through SLR.5. The usual OLS estimators 30 and J3X are unbiased for their respective population parameters. Let 1 be the estimator of β1 obtained by assuming the intercept is zero (see Section 2.6).

(i) Find E(1) in terms of the x, β0, and β1. Verify that 1 is unbiased for β1 when the population intercept (β0) is zero. Are there other cases where β1 is unbiased?

(ii) Find the variance of 1. (Hint: The variance does not depend on β1.)

(iv)Comment on the trade off between bias and variance when choosing between and .