Exercise 1. (20 Points) We estimate the following model where price is the price of house j in yeart and is a function of the distance to the nearest recreation park using a dataset with 578 observations. In particular, the variable in the model is measured as the difference between the distance of each house to the park and 150 yards. The OLS regression line is price : = 850000 + 164 (distance;z 150) (150000) (41) Where standard errors of the estimated coefficients are in parentheses. 5 points We run the regression of prices on (distance-150) and add the house size (measured in square feet) to the regression. We note that the coefficient on house size is 5.3 with a standard error of (1.2). Moreover, in that regression, the estimated coefficient of (distance-150) is now 60 with a standard error of (20). What does this tell you in terms of the correlation between the variable (distance-150) and the variable size of the house? 5 points We wish to test the null hypothesis that the coefficient on "distance-150" is equal to 56 and the coefficient on "house size" is equal to 2 at the 5% level. Please perform the 5 steps in hypothesis testing and conclude, given that the Residual standard error from the unrestricted regression is 1.3784 and the Sum of Squared Residuals (SSR) for the restricted regression is 1350. Exercise 1. (20 Points) We estimate the following model where price is the price of house j in yeart and is a function of the distance to the nearest recreation park using a dataset with 578 observations. In particular, the variable in the model is measured as the difference between the distance of each house to the park and 150 yards. The OLS regression line is price : = 850000 + 164 (distance;z 150) (150000) (41) Where standard errors of the estimated coefficients are in parentheses. 5 points We run the regression of prices on (distance-150) and add the house size (measured in square feet) to the regression. We note that the coefficient on house size is 5.3 with a standard error of (1.2). Moreover, in that regression, the estimated coefficient of (distance-150) is now 60 with a standard error of (20). What does this tell you in terms of the correlation between the variable (distance-150) and the variable size of the house? 5 points We wish to test the null hypothesis that the coefficient on "distance-150" is equal to 56 and the coefficient on "house size" is equal to 2 at the 5% level. Please perform the 5 steps in hypothesis testing and conclude, given that the Residual standard error from the unrestricted regression is 1.3784 and the Sum of Squared Residuals (SSR) for the restricted regression is 1350