4. [ll] points) Consider a simple linear regression model Y=u+1X+a (1} under the identifying assumption E[u|Xj = I]. Suppose we have a random sample {,Xg) for i = 1, _.,'.rt and consider the following formulas for the OILS estimators 1'?- Z[ i?}[Xf} a. Show that 311 can be written as b1=1+'= {2) (Hint: average equation [1} to get ? = u + 331? +, then suhstraot this equation from equation {1} evaluated at i to get Ye ? = 1 (X:- f} + it; E which is then replaced in #1}. b. Show E{u|X) = D implies that ha and b1 are unbiased estimators of ,SD and :51 when conditioning on X EI:X11..:XnJi.E. E{bD|X}= n and E[b1| X] = .31. 5. {10 points} Consider the following linear regression model Y=3o+lx+u (3)