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Recall: Given WI....Wm - N(w,o') and =1,...Ex - N(H,G7 ), we can compute m - 1 n - 1 Sp m +n - 2 Sw m + n -2 and test Ho: Ww = = with test statistic t = W-Z (We use w and = to reserve x and y for the simple linear regression model below.) Alternatively, we can construct the linear model i = Bo + Buri + & where for / = 1 to m, we set y = w, and x; = 1, and for / = m+1 to mon, we set y, = =im and x; = 0. (To clarify: the w's and ='s are pooled into a single collection of y's. Each y, which used to be a w is assigned an x, = 1, and each y, which was a = is assigned x; = 0.) (At every step below, you may take the earlier steps as given, even if you did not complete those proofs. If you prefer, you may use the matrix formulation to reach the same results.) a. Show that the least-squares estimates from this formulation will be Bo = 1, B1= W-Z. Hint: Show that Ex = Ex/ =m, Eyi = Ew + Ez, and Exiyi = >wi. Also note that the total sample size for the regression is not n, but m + n. Plug into the usual SLR estimates and simplify. b. Show that the regression error variance estimate is so, the pooled error variance above