Question

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4. (10 marks) Let βο and βι be the intercept and slope from the regression of y on xi, using n observations Let c1 and c2, with c#0, be constants. Let ß0 and ßl be the intercept and slope from the regression ofciyi on c2xi. Show that ßi-(c1/c2) B\ and Bo -cißo, thereby verifying the claims on units of measurement in Section 2-4. [Hint: Plug the scaled versions of x and y into A-s. (xi-x)(y 29) . Then, use Po -y - P1x for P0, being sure to plug in the scaled x and y and the correct slope.] Now, let A and βι be from the regression of cı + yi 0n c2 + xi (with no restriction on c1 or c2). Show that ß,-β, and β,-A, + c1-c2βι Now, let β0 and β, be the OLS estimates from the regression log(y) on Xi, where we must assume y>0 for all i. For cư0, let βο and βι be the intercept and slope from the regression of log(cy) on Xi. Show that β,-A, and βο-log(c10+ A- Now, assuming that Xi>0 for all i, let β0 and β1 be the intercept and slope from the regression 2P1 111 1V of yi On log(cXi). How do ß0 and ß, compare with the intercept and slope from the regression of yi on log(x)?

Answer 1

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