In this question, we are interested in understanding the consequences of measurement error in the data. Suppose the true model is given by yi = 0 + 1xi + ui and we are interested in estimating 1. Suppose our sample is i.i.d and E[ui|xi] = 0. Sometimes we are interested in "de-meaning" our data. This is also called "centering" the data. It simply means to remove the mean of your observables from your data as follows: 1 n x : = x x = x x & y : = y y = y y 1 n iinii iinii i=1 i=1 Suppose you are running the following regression: y = + x + i01ii a. (5 Points) Show that OLS is an unbiased estimator for . 11 b. (5 Points) Show that OLS is a biased estimator of . What is the direction of the bias? 00