Unbiasedness of OLS. Suppose that we have a simple linear regression model yi = Po+ Bx; + u; and that classical assumptions A1 to A3 are satisfied. In this problem, we will show that the OLS estimator 3 is unbiased. (a) (3 points) What does it mean for an estimator to be unbiased? (b) (3 points) Write down the formula for the OLS estimator .. (c) (6 points) Plug Yi = o + 3; + u; into your answer from (b) to show that xi-x (1) i=1 (d) (5 points) Take the expectation of (1) conditional on x to show E[3i|x] = 1. Hint: E[Di=1 w;ui|x] = Di=1 w;E[ui|x] since wi is non-random after conditioning on x. (e) (3 points) If E[31|x] =1,is 31 unbiased?