Referring to Table 7.1 in the text:

a. Calculate the \(R^{2}\) for each of the regressions.

b. Calculate the homoskedasticity-only \(F\)-statistic for testing \(\beta_{3}=\beta_{4}=0\) in the regression shown in column (5). Is the statistic significant at the \(5 \%\) level?

c. Test \(\beta_{3}=\beta_{4}=0\) in the regression shown in column (5) using the Bonferroni test discussed in Appendix 7.1.

d. Construct a \(99 \%\) confidence interval for \(\beta_{1}\) for the regression in column (5).

Table 7.1

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TABLE 7.1 Results of Regressions of Test Scores on the Student-Teacher Ratio and Student Characteristic Control Variables Using California Elementary School Districts Dependent variable: average test score in the district. Regressor Student-teacher ratio (X) Control variables Percentage English learners (X2) (1) -2.28 (0.52) (2) (3) (4) -1.10 (0.43) -1.00 -1.31 (5) -1.01 (0.27) (0.34) (0.27) [-3.30, 1.26] [-1.95, -0.25] [-1.53,-0.47] [-1.97, -0.64] [-1.54,-0.49] Percentage eligible for subsidized lunch (X3) Percentage qualifying for income assistance (X4) Intercept -0.650 -0.122 -0.488 -0.130 (0.031) (0.033) (0.030) (0.036) -0.547 -0.529 (0.024) (0.038) -0.790 0.048 (0.068) (0.059) 698.9 686.0 700.2 698.0 700.4 (10.4) (8.7) (5.6) (6.9) (5.5) Summary Statistics SER 18.58 14.46 9.08 11.65 9.08 R 0.049 0.424 0.773 0.626 0.773 n 420 420 420 420 420 These regressions were estimated using the data on K-8 school districts in California, described in Appendix 4.1. Heteroskedasticity- robust standard errors are given in parentheses under coefficients. For the variable of interest, the student-teacher ratio, the 95% confidence interval is given in brackets below the standard error.