4. (20 pts) Let {salehsqftlzl be a random sample with sale; denoting the sale price of a house [in thousands) and sqft its square footage. Suppose that we estimate the regression model 5318a? = I31 + 52qu? + 6 and nd bl = 340, I32 2 0.001, sh) 2 36.4, and ag) 2 1/(1000)? (a) What is your estimate for the expected sale price of one thousand square feet house? (b) Call the derivative of E[sale|sqft} with respect to sqft as the marginal eect of sqft. What is your estimate of the marginal effect of sqft when at one thousand square feet? (c) What is the variance of the estimate you found in part (b). (Hint: Recall Var[c.V) = a2Var(V) for any random variable V and constant a). 2 (d) We are interested in testing the null hypothesis that the marginal return at 1000 sqft equals 1.7 against the alternative that it is larger. Use a normal approximation to compute a pvalue. Would you reject the null hypothesis at the 5% level