Question 1 Consider the following OLS regression of a student's performance of a math test in grade 3 (MathTest_Gr3) on performance of a math test in grade 1 (MathTest_Gr1), his/her teacher's experience in years (TeacherExper), average hours per week spent on math in class (ClassTime), and average hours of homework assigned per week (Homework). The two tests (one for grade 1, another for grade 3) were administered across all students and the full score for each test is 100 points. The following is the output from Stata: Source SS df Number of obs = 2098 F14, 2093) = "A" Model 1166.45507 4 291.613767 Prob > F = 0.0000 Residual | 707.176147 2093.337876802 R-squared = "B" Adj R-squared = "C" Total 1873.63122 2097.893481744 Root MSE =.58127 MS MathTest_Gr3 Coef. Std. Err. t P>It| [95% Conf. Interval) MathTest_Gr1 .8141928 .0139762 TeacherExper1 .0020718 .0012588 ClassTime .0300209 .0096584 Homework .021293.0213262 _cons -1869632 .0502751 58.26 1.65 3.11 1.00 -3.72 0.000 0.100 0.002 0.318 0.000 .786784 -.0003969 .0110798 -.0205298 - 2855575 .8416016 .0045405 .0489621 .0631158 -.0883688 1. Interpret the coefficients on MathTest_Gr1 and TeacherExper, separately. 2. How would you test whether the model has any explanatory power? List the detailed steps to perform the test and conclude (use 5% significance level). 3. Calculate R2 and adjusted R2 using the output given in the table. 4. What would be your prediction for the third grade math test result of a student who got 50 in grade 1 test, was taught by a teacher with 12 years of experience, spend 4.25 hours on math a week, and was assigned 2.5 hours of homework a week? Question 1 Consider the following OLS regression of a student's performance of a math test in grade 3 (MathTest_Gr3) on performance of a math test in grade 1 (MathTest_Gr1), his/her teacher's experience in years (TeacherExper), average hours per week spent on math in class (ClassTime), and average hours of homework assigned per week (Homework). The two tests (one for grade 1, another for grade 3) were administered across all students and the full score for each test is 100 points. The following is the output from Stata: Source SS df Number of obs = 2098 F14, 2093) = "A" Model 1166.45507 4 291.613767 Prob > F = 0.0000 Residual | 707.176147 2093.337876802 R-squared = "B" Adj R-squared = "C" Total 1873.63122 2097.893481744 Root MSE =.58127 MS MathTest_Gr3 Coef. Std. Err. t P>It| [95% Conf. Interval) MathTest_Gr1 .8141928 .0139762 TeacherExper1 .0020718 .0012588 ClassTime .0300209 .0096584 Homework .021293.0213262 _cons -1869632 .0502751 58.26 1.65 3.11 1.00 -3.72 0.000 0.100 0.002 0.318 0.000 .786784 -.0003969 .0110798 -.0205298 - 2855575 .8416016 .0045405 .0489621 .0631158 -.0883688 1. Interpret the coefficients on MathTest_Gr1 and TeacherExper, separately. 2. How would you test whether the model has any explanatory power? List the detailed steps to perform the test and conclude (use 5% significance level). 3. Calculate R2 and adjusted R2 using the output given in the table. 4. What would be your prediction for the third grade math test result of a student who got 50 in grade 1 test, was taught by a teacher with 12 years of experience, spend 4.25 hours on math a week, and was assigned 2.5 hours of homework a week
