Question: Please solve the question 1. (20 pts) Suppose we have an independent and identically distributed sample (i.i.d.) {wage;, edu }-1 where wage; denotes hourly wages

Please solve the question

1. (20 pts) Suppose we have an independent and identically distributed sample (i.i.d.) {wage;, edu }-1 where wage; denotes hourly wages and edu; years of education. Further suppose that wage; = B1 + Bzedui + ci with E[eledu] = 0. We estimate this model by linear regression and obtain the following output 61 5.4 = Var(bi) Cov(b1, b2) 02 = 4. 1.3 Cov(b1, b2) Var(b2) (a) What is your estimate for E[wageledu = 16] - i.e. what is your estimate for expected wages conditional on having 16 years of education? (b) What is the variance of your estimator for part (a)? (c) Build a 99% confidence interval for E[wageledu = 16] employing a normal approximation. (d) A friend who has sixteen years of education asks you to guess her wages. Is the probability that her wages lie in the confidence interval from part (c) approximately 99%? Why or why not? (e) Suppose you use your answer to part (a) as your guess for your friend's wages. Let f be your guess and Y be the actual wage. Provide an estimate for the variance of f - Y

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