Suppose the population model is yi = Bo + Bixi + Eiwhere E!- has mean 0 and variance 0'2. Note that this simple regression can actually be seen as a multiple regression with x0: = 1 and x1; = xi. In other words, the first variable (whose coefficient is B0) is = 1. We are interested in estimating [3'1 in a different mannerfrom what we did in class. Let us try the following steps: - 2 a) Regress y; on 1 (don't include xi) In other words, minimize izyi b0 - 1) with respect to 50' What l5 50? z 2 z b) Next, regress xi on 1. In other words, minimize 11-12}; (xi b0 - 1) with respect to be. What is 3'0? c) Define 51: = yi 50 and 62:- : xi 50. And consider the regression: E1: = 17152:" (i.e., regress 551: on ztl- What is b1? What is the relationship between b1 and the least squares estimator of 31 that we derived in class