Question 5, 6 and 7

TABLE 9.2 Multiple Regression Estimates of the Student-Teacher Ratio and Test Scores: Data from Massachusetts Dependent variable: average combined English, math, and science test score in the school district, fourth grade; 220 observations. Regressor (1) (2) (3) (4) (5) (6) Student-teacher ratio -1.72** -0.69* -0.64* (STR) 12.4 -1.02** -0.67* (0.50) (0.27) (0.27) (14.0) (0.37) (0.27) STR2 -0.680 (0.737) STR 0.011 (0.013) % English learners -0.411 -0.437 -0.434 (0.306) (0.303) (0.300) % English learners > median? (Binary, HiEL) -12.6 (9.8) HiEL X STR 0.80 (0.56) % Eligible for free lunch -0.521** -0.582** -0.587** -0.709** -0.653** (0.077) (0.097) (0.104) (0.091) (0.72) District income (logarithm) 16.53** (3.15) District income -3.07 -3.38 -3.87* -3.22 (2.35) (2.49) (2.49) (2.31) District income 0.164 0.174 0.184* 0.165 (0.085) (0.089) (0.090) (0.085) District income -0.0022* -0.0023* -0.0023* -0.0022* (0.0010) (0.0010) (0.0010) (0.0010) Intercept 739.6** 682.4** 744.0** 665.5** 759.9** 747.4** (8.6) (11.5) (21.3) (81.3) (23.2) (20.3)Test score 780 Linear regression 760 Linear-log regression 740 720 Cubic regression 700 680 660 640 620 0 10 20 30 40 50 District income (thousands of dollars)QUESTION 5 Model (2) in Table 9.2 of Stock and Watson (on page 20 of Lecture Slides 7) regresses TestScore on STR, Percentage of English Learners (English), Percentage of Student lunch support (Lunch), and logarithm of District Income. Re-estimate the regression model by adding the interaction term, English x STR, in Model (2). What is the estimated coeffcient on STR (two decimal places)? QUESTION 6 Using the estimated model in Question 5, you test Ho: Test Score does not depend on PctEL. What is the p-value for this test (two decimal places)? QUESTION 7 Using the estimated model in Question 5, predict the change in TestScore associated with reducing STR by 2 students at the sample means of the variables on the right-har side. To be specific, you should subtract the fitted value of TestScore evaluated at the sample means of the STR, English, Lunch, and District Income from the fitted value of TestScore (evaluated at the sample means) but after reducing STR by 2 from its sample mean (two decimal places)