Consider the following regression: Y = 10+ 2X + where n = 100. Suppose you know that ox = 1 (i.e. 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 homosekedastic. Construct the standard errors (under homosckedasticity). Hint: Since you know ox, there is no need to estimate it with sx! (b) (5 points) Is , significantly different from zero at 95% level? (c) (8 points) Suppose errors are heterosekedastic, but we do not know the precise form of it. Suppose now that pix = 0, plim(SER) = 0, = 0.5, and Var(Xu) = 22. Show that Bi-Bi N(0,0) N, SEHO (31) where the denominator are the standard errors under homosekedasticity. Find v. (d) (4 points) Discuss how the result in part c will affect your inference in the case errors are heterosckedastic, but you use SE under homosckedasticity. Consider the following regression: Y = 10+ 2X + where n = 100. Suppose you know that ox = 1 (i.e. 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 homosekedastic. Construct the standard errors (under homosckedasticity). Hint: Since you know ox, there is no need to estimate it with sx! (b) (5 points) Is , significantly different from zero at 95% level? (c) (8 points) Suppose errors are heterosekedastic, but we do not know the precise form of it. Suppose now that pix = 0, plim(SER) = 0, = 0.5, and Var(Xu) = 22. Show that Bi-Bi N(0,0) N, SEHO (31) where the denominator are the standard errors under homosekedasticity. Find v. (d) (4 points) Discuss how the result in part c will affect your inference in the case errors are heterosckedastic, but you use SE under homosckedasticity