You are conducting an econometric investigation into the effect on house prices of proximity to a power plant, which presumably generates negative externalities for homeowners and others located close to it. The sample data consist of observations for 321 houses that were sold in a single metropolitan area in the year 2012 on the following variables: price : selling price of house i, in dollars. hsize; : house size of house i, in square meters. agei : age of house i, in years. disti : distance of house i from power plant, in meters. Using the given sample data on 321 houses, your trusty research assistant has estimated the following regression equation (1) and obtained the estimation results (with estimated standard errors given in parentheses below the coefficient estimates): price; = Bo + Bihsize; + B2age; + Bzage? + B4disti + B5dist} + u (1) = B. = 17,222 (12,689) B3 = 3.743 (1.059) SST = 597,850,000,000 = B1 = 361.1 B2 = -915.7 (28.54) (163.5) BA = 8.220 B5 = -0.000695 (3.456) (0.000254) SSR = 271,740,000,000 N = 321 (8 marks) (a) Use the estimation results for regression equation (1) to test the joint significance of the slope coefficient estimates B; (j = 1, ...,5) in regression equation (1). State the null and alternative hypotheses, and show how you calculate the required test statistic. State the inference you would draw from the test at the 5 percent significance level. (10 marks) (b) Compute a test of the proposition that the distance from the power plant had an increasing marginal effect on mean prices as the distance increased. State the coefficient restrictions on regression equation (1) implied by this proposition; that is, state the null hypothesis H, and the alternative hypothesis H. Find the p-value of the test (you may write down the expression of the probability without computing the number). Can you reject the null hypothesis at the 10% level? (12 marks) (c) Compute a test of the proposition that the house size was the only factor that affects the house prices and, furthermore, if the house size increases by one square meter, then the predicted house prices increase by 350 dollars. State the coefficient restrictions on regression equation (1) implied by this proposition; that is, state the null hypothesis H, and the alternative hypothesis H. Write the restricted regression equation implied by the null hypothesis H. OLS estimation of this restricted regression equation yields a Residual Sum-of-Squares value of SSR = 357,850,000,000. Use this information, together with the results from OLS estimation of equation (1), to calculate the required test statistic. State the inference you would draw from the test at the 5 percent significance level. = (10 marks) (d) Use the estimation results for regression equation (1) to perform a two-tail test of the null hypothesis B2 -3B, at the 5 percent significance level. The estimated covariance of , and 2 is Cov(B1,B2) = 1418.9597. State the null and alternative hypotheses, show how you calculate the required test statistic, and state its null distribution. State the decision rule you use, and the inference you would draw from the test at the 5 percent significance level