4. We are interested in the effect on test scores of the student-teacher ratio (STR). The following regression results have been obtained using the California data set. All the regressions used average test scores in the district as the dependent variable. Many factors potentially affect the average test scores in a district. Three variables are considered: (i) the fraction of students who are still learning English/HiEL (a dummy taking 1 if the fraction is larger than 10%, 0 otherwise), (ii) the percentage of students who are eligible for receiving subsidized free lunch at school, and (iii) average district income (in logarithm). Different regressions use different combinations of regressors, and quadratic and cubic terms of STR, and the interaction terms. The entries in the table include estimated coefficients, standard errors (in parenthesis), F-statistics and their p-values (in parenthesis below the values of F-statistic), and other summary statistics (SER, adjusted R). The significance of each variable is indicated by ** (1%) and * (5%). Dependent variable: average test score in district; 420 observations. Regressor (1) Student-teacher ratio (STR) -1.00** (0.27) (2) -0.73** -0.97 (0.26) (0.59) (3) (4) (5) (6) (7) -0.53 64.33** 83.70** 65.29** (0.34) (24.86) (28.50) (25.26) STR -3.42** -4.38** -3.47** (1.25) (1.44) (1.27) STR 0.059** 0.075** 0.060** (0.021) (0.024) (0,021) % English learners % English learners 10%? (Binary, HIEL) HIEL STR -0.122** -0.176** (0,033) (0.034) 5.64 -0.166** (0.034) 5.50 -5.47** 816.1* (19.51) (9.80) (1.03) (327.7) -1.28 (0.97) -0.58 (0.50) HIEL STR HIEL STR % Eligible for subsidized lunch -0.547** -0.398** (0.024) (0,033) -0.411** (0.029) -123.3 (50.2) 6.12* (2.54) -0.101* (0.043) -0.420 (0.029) (0.029) (0,033) -0.418** -0.402** Average district income (logarithm) 11.57** (1.81) Intercept 700.2** (5.6) 12.12** (1.80) 658.6** 682.2** 653.6** 122.3 (8.6) (11.9) (9.9) (163.6) (185.5) 11.75** 11.80** 11.51** (1.78) (1.78) (1.81) 252.0 244.8 (165.7) F-Statistics and p-values on Joint Hypotheses (a) All STR variables and interactions -0 (b) STR, STR = 0 (c) HIEL X STR, HIEL STR, HIEL X STR=0 SER R 5.64 6.31 (0.004) 5.92 4.96 (0.003) (