4.1 Suppose that a researcher, using data on class size (CS) and average test scores from 50 third-grade classes, estimates the OLS regression:

TestScore = 640.3 - 4.93 * CS, R2 = 0.11, SER = 8.7.

a. A classroom has 25 students. What is the regression’s prediction for that classroom’s average test score?

b. Last year a classroom had 21 students, and this year it has 24 students.

What is the regression’s prediction for the change in the classroom average test score?

c. The sample average class size across the 50 classrooms is 22.8. What is the sample average of the test scores across the 50 classrooms? (Hint:

Review the formulas for the OLS estimators.)

d. What is the sample standard deviation of test scores across the 50 classrooms? (Hint: Review the formulas for the R2 and SER.)