Suppose that you have estimated the following relationship between the price of a house in thousands of dollars (price), the number of rooms in the house (bdrms), the square footage of the house (sqrft), and the size of the lot that the house sits on in square feet (lotsize). price = -21.77 + 13.85* bdrms + 0.002 * lotsize+ 0.123 * sarft (29.48) (9.01) DD(0.001) O D(0.013) D n = 348, R2 = 0.6724, Adjusted R2 = 0.6607 a. If you wanted to test the joint hypothesis that neither lot size nor square footage affects house price, what would your null hypothesis be? What would your restricted and unrestricted regressions be? How many degrees of freedom would your F-statistic have? Remember, there are two sets of degrees of freedom for the F-distribution. b. Do you think the OLS estimate of the effect of lot size on house price is consistent? Why or why not? c. Let's say that you want to account for the possible nonlinear effect of lot size on price. You estimate the following regression with logs. In (price) -1.30 + 0.037 * bdrms+ 0.168 * In (lotsize) + 0.700 * In(sqrft) (0.651)D(0.028) 0 (0.038) (0.093) n = 348, R2 = 0.6430, Adjusted R2 = 0.6302 Interpret the coefficient on In (lotsize). d. Now you estimate the following regression with a quadratic term in lot size. price -45.59+20.78* bdrms + 0.012 * lotsize - 1.13 x 10-7 * lotsize2 + 0.088 * sarft (26.08) (7.96) D(0.002) D D12.15 x 10-8) D(0.013) 2 n=348, R2 = 0.7541, Adjusted R2 = 0.7422 What is the effect of an increase in lot size on predicted house price for a house on a 9000 square foot lot? What about for a house on a 15,000 square foot lot? Show your work. Remember that for y = Be + B1x + Bax, = Bi + 2 Bax Ax e. Is the coefficient on lotsize statistically significant at the 5% level? Show your work. f. Is there evidence for increasing, decreasing or constant returns to lot size? In your answer, you must include references to coefficients and/or tests for statistical significance. Suppose that you have estimated the following relationship between the price of a house in thousands of dollars (price), the number of rooms in the house (bdrms), the square footage of the house (sqrft), and the size of the lot that the house sits on in square feet (lotsize). price = -21.77 + 13.85* bdrms + 0.002 * lotsize+ 0.123 * sarft (29.48) (9.01) DD(0.001) O D(0.013) D n = 348, R2 = 0.6724, Adjusted R2 = 0.6607 a. If you wanted to test the joint hypothesis that neither lot size nor square footage affects house price, what would your null hypothesis be? What would your restricted and unrestricted regressions be? How many degrees of freedom would your F-statistic have? Remember, there are two sets of degrees of freedom for the F-distribution. b. Do you think the OLS estimate of the effect of lot size on house price is consistent? Why or why not? c. Let's say that you want to account for the possible nonlinear effect of lot size on price. You estimate the following regression with logs. In (price) -1.30 + 0.037 * bdrms+ 0.168 * In (lotsize) + 0.700 * In(sqrft) (0.651)D(0.028) 0 (0.038) (0.093) n = 348, R2 = 0.6430, Adjusted R2 = 0.6302 Interpret the coefficient on In (lotsize). d. Now you estimate the following regression with a quadratic term in lot size. price -45.59+20.78* bdrms + 0.012 * lotsize - 1.13 x 10-7 * lotsize2 + 0.088 * sarft (26.08) (7.96) D(0.002) D D12.15 x 10-8) D(0.013) 2 n=348, R2 = 0.7541, Adjusted R2 = 0.7422 What is the effect of an increase in lot size on predicted house price for a house on a 9000 square foot lot? What about for a house on a 15,000 square foot lot? Show your work. Remember that for y = Be + B1x + Bax, = Bi + 2 Bax Ax e. Is the coefficient on lotsize statistically significant at the 5% level? Show your work. f. Is there evidence for increasing, decreasing or constant returns to lot size? In your answer, you must include references to coefficients and/or tests for statistical significance
