Question 1: Suppose you are interested in the effect of pollution on House Prices. You obtain data for 506 regions on nox (nitric oxide concentration in the air, parts per 100m), crime (crimes committed per capita), price (median house prices in the region in 1000 S), rooms (average number of rooms), dist (weighted distance to 5 employment centers), and proptax (property tax per $1000) and stratio (the average student to teacher ratio in the school district). a. In column (2), calculate the expected effect on the median house price of adding 2 rooms to the house with 2 rooms and then the effect of adding 2 rooms to a house with 4 rooms. Why do the effects differ? Is there a positive relationship between the house price and the number of rooms? Why or why not? House Prices and Pollution =================================================== Statistic N Mean St. Dev. Min Pctl(25) Median Pct (75) Max | b. in column (3). calculate the expected effect on the median house price of adding 2 rooms to the house with 2 rooms. How does the effect differ from the one calculated in part (a)? price 506 22.51 9.20 506 5.55 1.16 rooms 506 6.28 0.70 dist 506 3.80 2.11 proptax 506 40.82 16.85 strato 506 18.46 2.17 5 16.85 3.85 4.49 3.56 5.88 1.13 2.10 18.70 27.90 12.60 17.40 21.2 24.99 50 5.38 6.24 8.71 6.21 6.62 8.78 3.21 5.19 12.13 33.00 66.60 71.10 19.10 20.20 22.00 c. How do you test whether model 4 is better than a linear model in rooms? Set-up the hypothesis carefully and explain how you would decide. d. Suppose you run a F-test on models. The R output of the test is a follows: Linear hypothesis test You decide to introduce some nonlinearities in your model and you estimate the following regressions available in the table below. Column (1) presents Model 1, Column (2) presents Model 2, and column (3) presents Model 3, and so on. Hypothesias Ifron 2) - Irons) - 0 Iron 1) - 0 " It') - 0 Note: Irooms2) stands for rooms2, I(rooms 3) stands for rooms^3, and so on. Model 1: restricted model Model 2: price/1000 - Box + atratio + rocas + Ifoons 2) + Idroom'3) + Ilroom 4) + Iroon 5) + dist Housing and Pollution - Polynomial Dependent variable: Note: Coefficient covariance matrix supplied. House Price thousands (3) (6) (5) 12) 1 2 Res.Df of PE() 501 497 108.02