Question 1 (25 points) Consider the following regression: Y, = 10 + 2X; + 14; where n = 100. Suppose you know thatox = 1 (ie. you know the true variance of X ) and SER = 0.5 (where SER is the standard error of the regression). (a) (8 points) Suppose errors are homosckedastic. Construct the standard errors (under homosckodasticity). Hint: Since you knowox, there is no need to estimate it withs*! (b) (5 points) IS , 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 fx = 0, plim(SER) =0. =05, and Var( Xu) = 2. Show that SENOR ,) where the denominator are the standard errors under homosckodasticity. Findy. (d) (4 points) Discuss how the result in part c will affect your inference in the case errors are heteroeckodastic, but you use SE under homosckedasticity. Question 2 (25 points) Consider the following regression of wages Y on education above elementary school X (i.c. X = 0 means no education above elementary school): (1) for i = 1,2, .. ., n Suppose for now that EfulX ] =0 and 18 2 30. (a) (7 points) What is the interpretation of ? What is the implication of the signs in 8 8 2? It is fine to talk about "infinitesimal changes" for the X, even though it is not formally continuous