2) For a sample of Californian School Districts, you estimate the simple regression output below. The dependent variable is testscr, which is average district test scores in points and the independent variable is avginc, which is average district income measured in in $1,000 units. Source SS df MS Model Residual 77204.394 74905.1997 1 77204.394 418 179.199042 Number of obs F(1, 418) Prob > F R-squared Adj R-squared Root MSE 420 430.83 0.0000 0.5076 0.5064 13.387 Total 152109.594 419 363.030056 testsce Coef. Std. Br. t P>It! (95% Conf. Intervall avginc 1.87855 625.3836 0905044 1.532405 20.76 408.11 0.000 0.000 1.700649 622.3714 2.05645 628.3958 _cons ge 3 of 15 Then, for the same sample of Californian School Districts, you estimate the multiple regression output below. This model also includes the variables enrl_tot, which is the average student enrolment in each district and teachers, which is the average number of teachers in each district. Source ss df MS Model Residual 81919.3216 70190.2721 3 27306.4405 416 168.726616 Number of obs F(3, 416) Prob > E R-squared Adj R-squared Root MSE 420 161.84 0.0000 0.5386 0.5352 12.989 Total 152109.594 419 363.030056 test SCE Coef. Std. Err. t P>It! (95% Conf. Intervall avginc enrl_tot teachers cons 1.904589 .0007761 -. 0339521 627.3267 0895519 0021769 .0453566 1.541372 21.27 0.36 -0.75 406.99 0.000 0.722 0.455 0.000 1.728558 -.0035031 -. 1231087 624.2968 2.08062 .0050553 .0552045 630.3565 a) In the multiple regression model, are the coefficients on enrl_tot and teachers individually statistically significant? Explain. (3 marks) b) Using the relevant information from both model outputs above, calculate the F Statistic and use it to test whether or not the coefficients on enrl_tot and teachers are jointly statistically significant? (6 marks) c) Do you think enrl_tot and teachers are highly correlated? Explain. What implications would the correlation between enrl_tot and teachers have for the estimated results? Does this help explain the output above? (6 marks) 2) For a sample of Californian School Districts, you estimate the simple regression output below. The dependent variable is testscr, which is average district test scores in points and the independent variable is avginc, which is average district income measured in in $1,000 units. Source SS df MS Model Residual 77204.394 74905.1997 1 77204.394 418 179.199042 Number of obs F(1, 418) Prob > F R-squared Adj R-squared Root MSE 420 430.83 0.0000 0.5076 0.5064 13.387 Total 152109.594 419 363.030056 testsce Coef. Std. Br. t P>It! (95% Conf. Intervall avginc 1.87855 625.3836 0905044 1.532405 20.76 408.11 0.000 0.000 1.700649 622.3714 2.05645 628.3958 _cons ge 3 of 15 Then, for the same sample of Californian School Districts, you estimate the multiple regression output below. This model also includes the variables enrl_tot, which is the average student enrolment in each district and teachers, which is the average number of teachers in each district. Source ss df MS Model Residual 81919.3216 70190.2721 3 27306.4405 416 168.726616 Number of obs F(3, 416) Prob > E R-squared Adj R-squared Root MSE 420 161.84 0.0000 0.5386 0.5352 12.989 Total 152109.594 419 363.030056 test SCE Coef. Std. Err. t P>It! (95% Conf. Intervall avginc enrl_tot teachers cons 1.904589 .0007761 -. 0339521 627.3267 0895519 0021769 .0453566 1.541372 21.27 0.36 -0.75 406.99 0.000 0.722 0.455 0.000 1.728558 -.0035031 -. 1231087 624.2968 2.08062 .0050553 .0552045 630.3565 a) In the multiple regression model, are the coefficients on enrl_tot and teachers individually statistically significant? Explain. (3 marks) b) Using the relevant information from both model outputs above, calculate the F Statistic and use it to test whether or not the coefficients on enrl_tot and teachers are jointly statistically significant? (6 marks) c) Do you think enrl_tot and teachers are highly correlated? Explain. What implications would the correlation between enrl_tot and teachers have for the estimated results? Does this help explain the output above? (6 marks)