Exercise 1. (20 Points) We estimate the following model where price jt is the price of house j in year t 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 pricej = 850000 + 164 (distancejt - 150) (150000) (41) Where standard errors of the estimated coefficients are in parentheses. a) 2.5 points Please construct a 95% confidence interval of the predicted average price of a house that is located 150 yards from the nearest park. b) 2.5 points Do you find evidence that distance increases predicted prices at the 10 percent significance level for a one-sided alternative? Do all 5 steps in hypothesis testing. c) 5 points When we predict prices and perform the correlation of actual and predicted prices we obtain a value of 0.48. What is the regression's goodness of fit measure adjusted R-squared's value? Round all calculations and final answer to 4 decimal places. d) 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? e) 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