Consider the following house sale price regression model: log(price;- )= Bu+ B1 age; + [32 bedrooms,- + B3 bathsrl- B4 poof.+ [35 fireplace: + 36 waterfront: + Ui where price: sale price of the house in thousands of dollars, age: age of the house in years, bedrooms: number of bedrooms in the house, baths: number of bathrooms in the house, pool: a dummy (binary) variable which takes the value of 1 if the house hals a swimming pool and the value of 0 otherwise, fireplace: a dummy (binary) variable which takes the value of 1 if the house has a replace and the value of 0 otherwise. waterfront: a dummy (binary) variable which takes the value of 1 if the house has a waterfront view the value of 0 otherwise, Estimation results using 1030 observations and modied versions of the regression model obtained by dropping some of the variables are displayed in the table below. House Sale Price Estimates Dependent Variable: log(price) Coefficients Estimates and (Standard Independent Variables Errors) Equation 1 Equation 2 Equation 3 Intercept 5.683 6.676 5.682 (0.052) (0.021) (0.054) Age -0.004 -0.005 (0.001) (0.001) Bedrooms 0.136 0.132 (0.017) (0.018) Baths 0.407 0.489 (0.022) (0.022) Pool 0. 109 0.278 (0.038) (0.051) Fireplace 0. 192 0.422 (0.022) (0.028) Waterfront 0.211 0.433 (0.040) (0.054) N (number of observations) 1080 1080 1080 SSR (Sum of Squared Residuals) 114.799 218.207 127.887 R-squared 0.613 0.265 0.569 (a) Using Equation 1 estimates calculate the predicted dollar value of a brand-new 4 bedroom, 3 bathroom house which has a pool and a fireplace but does not have a waterfront view. (2 Marks) (b) Using the estimates from Equation 1, keeping all else constant, predict the new approximate sale value of a $820,000 house if it is renovated to have a fireplace. (2 Marks) (c) Interpret the coefficient estimate of dummy variable waterfront in Equation 1 and determine if having a waterfront is a significant factor in determining house sale price at 5% level of significance.(d) Test whether all of the dummy independent variables (pool, fireplace, waterfront) included in Equation 1 are jointly significant at 5 % level of significance. State your null and alternative hypotheses clearly. (4 Marks)