The California Standardized Testing and Reporting (STAR) dataset contains data o

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);

Find the R-Squared from ANOVA table. Does student to teacher ratio explains a large fraction of the variance in test score across students? Explain

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 7794.1100 residual 144315.484 418 345.252353 total 152109.594 419 363.03005

Explanation / Answer

R-Squared = ESS/TSS = 7794.11/152109.594 = 0.05. The R-square tell tells the variation in explained variable explained by the explanatory variable. Since the R-squared calculated is very small therefore, the student to teacher ratio do not explains the variance in test score.

ESS = Sum of squares(Model)

TSS = Total sum of square.

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