A longitudinal experiment was conducted in Tennessee beginning in 1985 and ending in 1989. A single cohort of students was followed from kindergarten through third grade. In the experiment children were randomly assigned within schools into three types of classes: small classes with 13-17 students, regular-sized classes with 22-25 students, and regular-sized classes with a full-time teacher aide to assist the teacher. Student scores on achievement tests were recorded as well as some information about the students, teachers, and schools. Data for the kindergarten classes are contained in the data file star5_small. [Note: The data file star5 contains more observations and variables.]

a. Using children who are in either a regular-sized class or a small class, estimate the regression model explaining students' combined aptitude scores as a function of class size, TOTALSCORE \(E_{i}=\) \(\beta_{1}+\beta_{2} S M A L L_{i}+e_{i}\). Interpret the estimates. Based on this regression result, what do you conclude about the effect of class size on learning?

b. Repeat part (a) using dependent variables READSCORE and MATHSCORE. Do you observe any differences?

c. Using children who are in either a regular-sized class or a regular-sized class with a teacher aide, estimate the regression model explaining students' combined aptitude scores as a function of the presence of a teacher aide, TOTALSCORE \(=\gamma_{1}+\gamma_{2} A I D E+e\). Interpret the estimates. Based on this regression result, what do you conclude about the effect on learning of adding a teacher aide to the classroom?

d. Repeat part (c) using dependent variables READSCORE and MATHSCORE. Do you observe any differences?

Data From Part C:-

Using children who are in either a regular-sized class or a regular-sized class with a teacher aide, estimate the regression model explaining students' combined aptitude scores as a function of the presence of a teacher aide, TOTALSCORE \(=\gamma_{1}+\gamma_{2} A I D E+e\). Interpret the estimates. Based on this regression result, what do you conclude about the effect on learning of adding a teacher aide to the classroom?

Data From Part A:-

Using children who are in either a regular-sized class or a small class, estimate the regression model explaining students' combined aptitude scores as a function of class size, TOTALSCORE \(E_{i}=\) \(\beta_{1}+\beta_{2} S M A L L_{i}+e_{i}\). Interpret the estimates. Based on this regression result, what do you conclude about the effect of class size on learning?