Question

Suppose researchers want to know the effect of elementary school class size on students’ math scores(total score is 100), intuitively they think there exists a negative linear relationship between class size and students’ math scores. The researchers want to know the marginal effect of class size on student’s math scores. 1) Based on the background information, design an linear regression model for this research question, and briefly explain your dependent variable, independent variable and the meaning of the parameters.

Answer 1

Linear regression Model

Student's Math Scores = b0 + b1 * class size (in numbers)

Dependent Variable: Student's Math scores. Since researchers want to see the effect of class size of math scores, the regression equation will tell that how much score changes when class size increases or decreases by 1 unit

Independent Variable: Class size is the independent variable. Since this variable explains the difference in student's math scores, it is also called an explanatory variable

b0: It is the intercept. It basically tells that if the class size is zero, what would be the student's math scores. However, in this context, it does not make much sense

b1: It is the slope. It is basically the change in student's math scores when the class size is changed by 1 unit