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 (1) (2) (3) (4) (5) Student-teacher ratio (X1) -2.28** -1.10* -1.00** -1.31* -1.01 (0.52) (0.43) (0.27) (0.34) (0.27) -0.650* (0.031) -0.122** (0.033) Percent English learners (X2) -0.488** -0.130** (0.030) (0.036) Percent eligible for subsidized lunch (X3) -0.547* -0.529* (0.024) (0.038) Percent on public income assistance (X4) -0.790** (0.068) 0.048 (0.059) 686.0** (8.7) Intercept 698.9** 700.2** 698.0** 700,4** (10.4) (5.6) (6.9) (5.5) Summary Statistics SER 18.58 14.46 9.08 11.65 9.08 0.049 0.424 0.773 0.626 0.773 п 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. The individual coefficient is statistically significant at the *5% level or **1% significance level using a two-sided test.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
What is a control variable, and how does it differ from a variable of interest?Looking at Table, which variables are control variables? Whatis the variable of interest? Do coefficients on control variables measurecausal effects? Explain.
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