Consider a linear regression model where the dependent variable is in logarithmic form: ln(y) = 33,8 + it. You run OLS and obtain the estimator B and estimated AVAR matrix V = AVARQE'). (a) Provide a (1 01) condence interval for E[ln(y)|m = 32*]. (b) Assuming that u is independent of 3:, how would you estimate E[y|a: = 33*]? You may assume that you have an estimator (32 for the parameter or E E(e\"). (0) Write down an expression for the asymptotic standard error of your estimator in part (b). (Hint: Use the delta method. You may assume that you know the asymptotic variance matrix AVAR ( g ), call it 17.) (d) How could you use the bootstrap to come up with an alternative estimator of the standard error of your estimator in part (b)? (e) If you drop the independence assumption on u, explain why it becomes more difcult to estimate E[y|a: = 3:*]. Without going into too much detail, can you think of a way to do it? (Hint: Think about providing an additional regression model to deal with the problematic component of the E[y|$ = 3:*] expression.)