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.

Suppose you can construct a sample that includes 4 second grade students in different elementary schools. Data have been collected on each students’ name, gender, class size( total number of students in the class) and final math scores. ID Name Gender Class size Math scores 1 Andy Female 23 80 2 Alice Female 16 89 3 Bella Female 20 84 4 Mike Male 25 71

If a kid will become a second grade student in an elementary school in NJ, and the class size will be 22, can you predict the student’s final math score?

Answer 1

Suppose, random variables X and Y denote class size and final math score respectively of second grade student.

We know, Regression equation of y on x is given by

Number of pairs of observation

For a kid of second grade in an elementary school in NJ with class size 22 we have,

Predicted final math score of that kid is given by

Hence, predicted final math score is 79 for a kid who will become a second grade student in an elementary school in NJ with class size 22.