Question 1 (25 points) Consider the following regression: Y; = 10 + 2Xi + u; where n = 100. Suppose you know thatox = 1 (i.e. you know the true variance off ) and SER = 0.5 (where SER is the standard error of the regression). (a) (8 points) Suppose errors are homoscedastic. Construct the standard errors (under homosckedasticity). Hint: Since you knowox, there is no need to estimate it withs x! (b) (5 points) IS 1 significantly different from zero at 95% level? (c) (8 points) Suppose errors are heteroscedastic, but we do not know the precise form of it. Suppose now that/x = 0, plim(SER) = Ou = 0.5, and Var(Xu) = 2. Show that B 1 3 1 dN(O, v) SEHOR 1) where the denominator are the standard errors under homosckedasticity. Find. (d) (4 points) Discuss how the result in part c will affect your inference in the case errors are heteroscedastic, but you use SE under homosckedasticity. Question 2 (25 points) Consider the following regression of wages on education above elementary school X (i.e. X = 0 means no education above elementary school): Yi BotSIXit3 2X? +u; (1) for i = 1, 2, . . ., n Suppose for now that E[ulX ] = 0 and 18 2 > 0. (a) (7 points) What is the interpretation of 1? What is the implication of the signs in B 13 2? It is fine to talk about "infinitesimal changes" for the X, even though it is not formally continuous