(i) Let Bo and B, be the intercept and slope from the regression of y, on x, using n Typo: on the observations. Let c, and c2, with c2 # 0. be constants. Let Bo and B, be the in- third line, tercept and slope from the regression of cy, on cax. Show that B, = (c /c2)Bo and beta_0 hat Bo = Ci Bo, thereby verifying the claims on units of measurement in Section 2.4. [Hint: should be To obtain B, plug the scaled versions of x and y into (2.19). Then, use (2.17) for Po. replaced with being sure to plug in the scaled x and y and the correct slope.] beta 1 hat. (ii) Now, let B, and B, be from the regression of (c, + y,) on (C, + x,) (with no restriction on c, or c2). Show that B, = B, and Bo = A + c - czBI- (iii) Now, let Bo and B, be the OLS estimates from the regression log(y) on x, where we must assume y, > 0 for all i. For c, > 0. let Bo and B, be the intercept and slope from the regression of log(c y,) on x. Show that B, = B, and Bo = log(c,) + Bo- (iv) Now, assuming that x, > 0 for all i, let Bo and B, be the intercept and slope from the regression of y, on log(c, x;). How do B, and B, compare with the intercept and slope from the regression of y, on log(x,)