EC 421 Classwork 4: Hypothesis Testing (analytical) Var(u) In chapter 2, we determined that (given some assumptions): is distributed N(1, (r(2)2). Var(u) is unknown since u is unobservable, so we have to approximate it using the regression residuals e. Because of this, we also use the t-distribution, which is similar to the Normal distribution, but with slightly fatter tails. We define "standard error" as our estimate of the standard deviation of the regression coefficient. The formula for a simple regression standard error of B is (n-2) (e) (x-2)* 1) We'd like our standard errors to be as small as possible so we can our estimates. If we increased the number of observations (assuming all else is held errors increase or decrease? 2) All else held equal, if the sample variance of x; decreased, should we errors would increase or decrease? For the sake of building some intuition, an example of this: increase the precision of equal), will our standard expect that the standard Take 2 studies designed to find the effect of a blood pressure medication on health. Study A: 9 people take the placebo; 1 person takes the medication, so X = (0, 0, 0, 0, 0, 0, 0, 0, 0, 1). Study B: 5 people take the placebo; 5 people take the medication so X = (0, 0, 0, 0, 0, 1, 1, 1, 1, 1). . (v. 7)2 Calculate the sample variance of X in both of these studies (sample variance = yield a more confident estimate of the effect, and which study has a lower Var(X)? n-1 Which study will 3) Finally, if we decreased the variance of u by including more explanatory variables (if we used the second model instead of the first model below), should we expect that the standard error on will increase or decrease? wage Bo+Beducation; +ui wager = o + Beducation; + Bsexi + Bracei + B4 family wealth; +ui