Part III. [25 pts] Bivariate Regression Following on the previous example, and using the descriptive statistics on this student level dataset, and regression output below, please answer the following questions: studentid int 88.00 Student ID schoolid int %8.0g School ID birthdate str18 $18s Date of birth pre_math byte 89.0g Absolute math score on pre-test mid_math byte $9.0g Absolute math score on mid-test post_math byte 89.0g Absolute math score on post-test 89.0g Dummy for cal treatment numstud int $9.0g Number of students in school-grade cal byte summarize post_math pre_math cal numstud Variable Obs Mean Std. Dev. Min Max post_math pre_math cal numstud 11,950 12,415 12,415 12,415 24.41054 11.76383 .2484897 62.8882 13.55409 11.20755 .4321546 25.99397 0 0 0 50 50 1 150 Regression 2: reg pre_math numstud Source SS df MS Model Residual 1581.95286 1557731.61 1 12,413 1581.95286 125.491953 Number of obs F(1, 12413) Prob > F R-squared Adj R-squared Root MSE 12,415 12.61 0.0004 0.0010 0.0009 11.202 Total| 1559313.56 12,414 125.609277 pre_math Coef. Std. Err. t P>|t| [95% Conf. Interval) numstud cons -.0137331 12.62748 .0038679 .2632062 -3.55 47.98 0.000 0.000 -.0213148 12.11156 -.0061513 13.14341 1. [2 pt] What is the unit of observation in this dataset? 2. [4 pts] What is the predicted math test score for a student who goes to school with 100 students in their school-grade? 3. [4 pts] Interpret the coefficient on numstud using the appropriate units. 4. [6 pts] What will be the estimate of the coefficient on numstud and that of the constant, if we were to transform the pre_math test variable by adding 50pts to all students? gen math=pre_math+50 In particular, using formulas for Bo and B, and the information from Regression 2, compute A and B. reg math numstud Source SS df MS Model Residual 1581.95286 1557731.61 1 12, 413 1581.95286 125.491953 Number of obs F(1, 12413) Prob > F R-squared Adj R-squared Root MSE 12,415 12.61 0.0004 0.0010 0.0009 11.202 Total 1559313.56 12,414 125.609277 math Coef. Std. Err. t p>It [95% Conf. Interval) numstud cons A 5. [4 pts] Construct a 99% confidence interval around numstud. 6. [5 pts] Interpret the R2 of this regression. What does low R2 indicate? Does it tell us anything about the causal interpretation of our results? Part III. [25 pts] Bivariate Regression Following on the previous example, and using the descriptive statistics on this student level dataset, and regression output below, please answer the following questions: studentid int 88.00 Student ID schoolid int %8.0g School ID birthdate str18 $18s Date of birth pre_math byte 89.0g Absolute math score on pre-test mid_math byte $9.0g Absolute math score on mid-test post_math byte 89.0g Absolute math score on post-test 89.0g Dummy for cal treatment numstud int $9.0g Number of students in school-grade cal byte summarize post_math pre_math cal numstud Variable Obs Mean Std. Dev. Min Max post_math pre_math cal numstud 11,950 12,415 12,415 12,415 24.41054 11.76383 .2484897 62.8882 13.55409 11.20755 .4321546 25.99397 0 0 0 50 50 1 150 Regression 2: reg pre_math numstud Source SS df MS Model Residual 1581.95286 1557731.61 1 12,413 1581.95286 125.491953 Number of obs F(1, 12413) Prob > F R-squared Adj R-squared Root MSE 12,415 12.61 0.0004 0.0010 0.0009 11.202 Total| 1559313.56 12,414 125.609277 pre_math Coef. Std. Err. t P>|t| [95% Conf. Interval) numstud cons -.0137331 12.62748 .0038679 .2632062 -3.55 47.98 0.000 0.000 -.0213148 12.11156 -.0061513 13.14341 1. [2 pt] What is the unit of observation in this dataset? 2. [4 pts] What is the predicted math test score for a student who goes to school with 100 students in their school-grade? 3. [4 pts] Interpret the coefficient on numstud using the appropriate units. 4. [6 pts] What will be the estimate of the coefficient on numstud and that of the constant, if we were to transform the pre_math test variable by adding 50pts to all students? gen math=pre_math+50 In particular, using formulas for Bo and B, and the information from Regression 2, compute A and B. reg math numstud Source SS df MS Model Residual 1581.95286 1557731.61 1 12, 413 1581.95286 125.491953 Number of obs F(1, 12413) Prob > F R-squared Adj R-squared Root MSE 12,415 12.61 0.0004 0.0010 0.0009 11.202 Total 1559313.56 12,414 125.609277 math Coef. Std. Err. t p>It [95% Conf. Interval) numstud cons A 5. [4 pts] Construct a 99% confidence interval around numstud. 6. [5 pts] Interpret the R2 of this regression. What does low R2 indicate? Does it tell us anything about the causal interpretation of our results