Question

The California Standardized Testing and Reporting (STAR) dataset contains data on test performance, school characteristics and student demographic backgrounds. The data used here are from all 420 K-6 and K-8 districts in California with data available for 1998 and 1999. Test scores are the average of the reading and math scores on the Stanford 9 standardized test administered to 5th grade students. TESTSCR: AVG TEST SCORE (= (READ_SCR+MATH_SCR)/2 ); STR: STUDENT TEACHER RATIO (ENRL_TOT/TEACHERS); Using the provided table, write down the population equation, and report the estimated regression equation in standard form? What is the estimated intercept? What is the estimated slope? Use the estimated regression to answer this question: How does the average value of test score change when we reduce 2 students per teacher? Are estimated coefficients (both intercept and slope) significant at 10% 5% and 1% significance level? What does it mean: a coefficient is significant at 5%? Bob’s class size is 20. Predict Bob’s average test score using the regression equation. If Bob was in a class of 15 how would the prediction of his average test change?

Number of obs = 420 , F(1, 418) = 22.58, Prob > F =0.0000 , R-squared = ? , Adj R-squared = 0.0490 , Root MSE =?

Source SS df MS

Model 7794.11004 1 7794.11004

Residual 144315.484 418 345.252353

Total 152109.594 419 363.03005

testscr coef. std. Err. t P>|t| [95% conf interval]

str -2.279808 .4798256

_cons 698.933 9.467491

Answer 1

a. The estimated regression in standard form can be written as:

Test Scores = 698.933 - 2.28 * Student Teacher Ratio

b. The equation above shows that the estimated intercept is 698.933

c. The estimated slope of the regression equation is 2.28. It is negative because as student teacher ratio declines, test scores of students increase.

d. Reducing 1 student per teacher , increases the average value of the test score by 2.28. Thus, reducing 2 students per teacher, will increase the average value of the test score by 2.28 * 2= 4.56.