What is a control variable, and how does it differ from a variable of interest? Looking at Table 7.1, for what factors are the control variables controlling? Do coefficients on control variables measure causal effects? Explain.

Table 7.1

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.