Question 3 The management of First Realty is also interested in the price difference between houses with and without swimming pool. The following table is the regression results from a log-log model: In(price) = B1 + Bzin(sqft) + Baln(Age) + B4Pool + e for a sample of 1080 houses. price: sale price of house in US$ sqft: total square feet of house Age: age of house in years Pool: 1 for house with swimming pool 0 for house without swimming pool Model 2: OLS, using observations 1-1080 Dependent variable: In(price) Coefficient Std. Error t-ratio p-value const 4.86302 0.188793 25.7585 In(sqft) 0.928738 0.0241 132 38.5157 --- In(Age) -0.0865897 0.00707252 -12.2431 --- Pool 0.155122 0.0356237 4.3545 --- Mean dependent var 11.79518 S.D. dependent var 0.524535 Sum squared resid 101.7473 S.E. of regression 0.307507 R-squared 0.657269 Adjusted R-squared 0.656314 F(3, 1076) 687.8304 P-value(F) 1.4e-249 (a) State the estimated linear regression equation, In( price ) = b1 + bzln(sqft) + baln(Age) + b4Pool, with the above regression results and interpret the estimates of b2, b3 and b4. (b) The management believes that if the size of houses increases by 100% the sale price will rise by more than 95% (i.e. P2 > 0.95). Use an appropriate hypothesis testing (one-tail or two-tail test) with a = 0.05 level of significance to justify this belief. (Note: You are required to set up the null and alternative hypothesis, compute the test statistic, state the critical values, and draw a conclusion.)