Question

5.1.) Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimate the simple linear regression: Test Score = 520.4-5.82 x CS, n= 100, R2 = 0.08. (20.4) (2.21) (a) A classroom has 22 students. What is the model's prediction for that classroom's average test score? (b) Last year a classroom had 19 students, and this year it has 23 students. What is the model's prediction for the change in the classroom average test score? (c) The sample average class size across the 100 classrooms is 21.4. What is the sample average of the test scores across the 100 classrooms? (Hint: review the formulas for the OLS coefficients.) (d) Name one factor in the error term and discuss its correlation with class size and average test score. (e) Construct 95% and 90% confidence intervals for Bi. (f) Calculate the p-value for the two-sided test of the null hypotheis H. : B1 = 0. Do you reject the null hypothesis at the 95% level? At the 1% level? (g) Calculate the p-value for the hypotheses H : B1 = -5.6 v.s. H : B1 + -5.6. Without doing any additional calculations, determine whether -5.6 is contained in the 95% confidence interval for B1.

Answer 1

a).

The estimated regression model is “Test Score = 520.4 – 5.82*CS”. If there are “22 students”, => “CS = 22”.

=> Test Score = 520.4 – 5.82*22 = 520.4 – 5.82*22 = 392.36 > 0. So, the predicted average test score is “392.36”.

b).

Last year the class room had “19 students”, => “CS = 19”.

=> Test Score = 520.4 – 5.82*CS = 520.4 – 5.82*19 = 409.82 > 0. So, the predicted average test score is “409.82”.

This year the class room had “23 students”, => “CS = 23”.

=> Test Score = 520.4 – 5.82*CS = 520.4 – 5.82*23 = 386.54 > 0. So, the predicted average test score is “386.54”.

So, the change in the test score is “386.54 - 409.82 = (-23.28) < 0”. So, as the “CS” increases the test score decreases.

c).

The sample average class size across the 100 classroom is “21.4”. Now, as we know the regression line must pass through the mean value of both variables. The average of the test score is given by.

=> Test Score = 520.4 – 5.82*CS = 520.4 – 5.82*21.4 = 395.85 > 0.

So, the sample average of the test score is “395.85”.

d).

The “average test score” and also depends on “teaching ability of teacher”, as the “teaching ability of teacher” increases the “average test score” of a class also increases given other factor remain same. Now, the “teaching ability of teacher” also depends on “CS”, as the “CS” increases the “teaching ability of teacher” of a class also decreases.