(i) Let 0 and 1 be the intercept and slope from the regression of yi on xi, using n observ...

(i) Let 0 and 1 be the intercept and slope from the regression of yi on xi, using n observations. Let c1 and c2, with c2 ≠ 0, be constants. Let 0 and 1 be the intercept and slope from the regression of c1yi on c2xi. Show that 1 = (c1/c2) 0 and 0 = c1 0, thereby verifying the claims on units of measurement in Section 2.4. [Hint: To obtain 1, plug the scaled versions of x and y into (2.19). Then, use (2.17) for 0, being sure to plug in the scaled x and y and the correct slope.]

(ii) Now, let 0 and 1 be from the regression of (c1 + yi) on (c2 + xi) (with no restriction on c1 or c2). Show that l = 1 and 0 = 0 + c1 - c2 1.

(iii) Now, let 0 and 1 be the OLS estimates from the regression log(yi) on xi, where we must assume yi. > 0 for all i. For c1 > 0, let 0 and 1 be the intercept and slope from the regression of log(c1yi) on xi. Show that .

(iv) Now, assuming that x. > 0 for all i, let 0 and 1 be the intercept and slope from the regression of y. on log(c2 xi). How do 0 and 1 compare with the intercept and slope from the regression of yi on log(xi)?