311_exam3_2014s

Final Exam, Econ 311, Spring 2014 Total points are 100. But it counts 20% toward your final grade. So the effective total points are 20 Note: (i) please write legibly ; (ii) show me your work in order to get partial credits; (ii) round your answer to 2 decimal spaces Last Name First Name You may use the following facts to answer some questions. Let Z ∼ N (0 , 1) then P ( Z < 1 . 96) = 0 . 975 P ( Z < 1 . 645) = 0 . 950 P ( Z < 1 . 28) = 0 . 900 Q1 (5 points). What is the advantage of using adjusted R-squared over the conventional R-squared ? Q2 (5 points). Briefly explain how to obtain the beta coefficient. 1

Q3 (5 points). We use the House data and obtain the following regression results: log( rpice ) = 10 . 25 + . 27 baths + . 0001738 area . Please interpret 0.27, the coefficient of baths . Q4 and Q5 are based on the following table, which summarizes a multiple regression (sam- ple size = 4137). The dependent variable sat is a student’s SAT score. The independent variable size is the size of graduating class in hundreds , and sizesq is the squared term of size . . reg sat size sizesq ------------------------------------------------------------------------------ sat | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- size | 19.81446 3.990666 4.97 0.000 11.99061 27.63831 sizesq | -2.130606 .549004 -3.88 0.000 -3.206949 -1.054263 _cons | 997.9805 6.203448 160.88 0.000 985.8184 1010.143 ------------------------------------------------------------------------------ Q4 (5 points) Is the marginal effect of size on sat constant? Why? Q5 (5 points) Please find the optimal class size that maximizes sat . Q6, 7, 8, and 9 are based on the following table. The dependent variable is still sat , a student’s SAT score. The independent variable athlete is a dummy variable that equals 2

Q9 (10 points) Please describe in detail how to test the null hypothesis that the effect of athlete on sat does not dependent on the gender of a student. You need to specify the unrestricted and restricted models, and the F test. Q10 (5 points) Suppose we have a variable x =      1 , the student gradutes from a public high school 2 , the student gradutes from a private high school 3 , the student is home-schooled Please explain how to use this information to run a regression that explains a student’s SAT score. 4

Q11 (5 points) What is heteroskedasticity? How to define heteroskedasticity mathemati- cally? Q12 (10 points) What is the null hypothesis of the Breusch-Pagan (BP) test? Please discuss fully how to proceed if we reject the null hypothesis of the BP test? Q13 (5 points) Suppose the true model is y = β 0 + β 1 x + β 2 x 2 + u, E ( u | x ) = 0 , var ( u | x ) = σ 2 so the error term u is homoskedastic in the true model. Please show that if we forget the squared term x 2 and run a short model y = c 0 + c 1 x + e then the short model will suffer heteroskedasticity. 5

Q16 and 17 are based on the following table. The dependent variable is room , the room occupancy in a hotel. The independent variables tr is the trend, and d1, d2, d3 are the dummy variables for the first quarter , second quarter and third quarter, respectively. In total we have 168 monthly observations. . reg room tr d1 d2 d3 Source | SS df MS Number of obs = 168 -------------+------------------------------ F( 4, 163) = 183.07 Model | 2779840.1 4 694960.026 Prob > F = 0.0000 Residual | 618777.015 163 3796.17801 R-squared = 0.8179 -------------+------------------------------ Adj R-squared = 0.8135 Total | 3398617.12 167 20351.0007 Root MSE = 61.613 ------------------------------------------------------------------------------ room | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- tr | 1.947161 .0982537 19.82 0.000 1.753147 2.141175 d1 | -36.14222 13.47414 -2.68 0.008 -62.74858 -9.535858 d2 | 63.65916 13.45801 4.73 0.000 37.08465 90.23367 d3 | 188.2462 13.44832 14.00 0.000 161.6909 214.8016 _cons | 503.8217 12.91715 39.00 0.000 478.3152 529.3282 ------------------------------------------------------------------------------ Q16 (5 points) Is room trending? Why? Q17 (5 points) Suppose the sample ends in December 2013. Please forecast the room occu- pancy in January 2014. You need to find the predicted value explicitly. 7