4.1) Suppose that a researcher, using data on class size (CS) and average test s

Question

4.1) Suppose that a researcher, using data on class size (CS) and average test scores from 100 third-grade classes, estimates the OLS regression: TestScore-520.4-5.82 × CS, R-0.08, SER-115. a. A classroom has 22 students. What is the regression'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 regression'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 avcrage of the test scores across the 100 classrooms? (Hini: Review the formulas for the OLS estimators.) d. What is the sample standard deviation of test scores across the 100 classrooms? (Hint: Review the formulas for the R and SER.)

Explanation / Answer

a)

regression prediction =520.4-5.82*22=392.36

b)

for change in number of students =(23-19)=4

hence change in regression prediction =-5.82*4=-23.28

c)as average of both variables fall on regression equation

sample average of test scores =520.4-5.82*21.4=395.852

d)

here SSE =(n-2)*(SER)2 =(100-2)*(11.5)2 =12960.5

hence SST=SSE/(1-R2)=12960.5/(1-0.08)=14087.5

sample std deviation =sqrt(SST/(n-1))=sqrt(14087.5/99)=11.929

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