Suppose the population model is

3': =30 +31%" +5i where sl- has mean 0 and variance 02. Note that this simple regression can actually be seen as a multiple regression with xm- = 1 and X1: = xi. In other words, the first variable (whose coefficient is [90) is = 1. We are interested in estimating Bl in a different manner from what we did in class. Let us try the following steps: - 2 a) Regress yi on 1 (don't include xi) In other words, minimize 1112:;1071- b0 - 1) with respect to 50. What is 50? z 2 z b) Next, regress xi on 1. In other words, minimize $2}; (x1- b0 - 1) with respect to bo. What is 50? c) Define \"- : yi 50 and zi = xi 50. And consider the regression: A 91: = bleZi- (i.e., regress li on 9321-). What is [71? What is the relationship between b1 and the least squares estimator of 1 that we derived in class