Question 1 (25 points) 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 homosckedastic. Construct the standard errors (under homosckedasticity). Hint: Since you know ox, there is no need to estimate it with sx! (b) (5 points) Is B, 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 yx = 0, plim(SER) = 0u = 0.5, and Var(Xu) = 22. Show that Bi-B1 & N(0,0) SEHO(1) where the denominator are the standard errors under homosckedasticity. Find v. (a) (4 points) Discuss how the result in part e will affect your inference in the case errors are heterosckedastic, but you use SE under homosekedasticity. Question 1 (25 points) 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 homosckedastic. Construct the standard errors (under homosckedasticity). Hint: Since you know ox, there is no need to estimate it with sx! (b) (5 points) Is B, 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 yx = 0, plim(SER) = 0u = 0.5, and Var(Xu) = 22. Show that Bi-B1 & N(0,0) SEHO(1) where the denominator are the standard errors under homosckedasticity. Find v. (a) (4 points) Discuss how the result in part e will affect your inference in the case errors are heterosckedastic, but you use SE under homosekedasticity