20. Solve the following problem: A panel of educators in a large urban community wanted to evaluate the effects of educational resources on student performance. They examined the relationship between 12th-grade mean math SAT scores (Y) and the following independent vari- ables for a random sample of 25 high schools: X, = per pupil expenditure (in dollars); X = percentage of teachers with a master's degree or higher, and Xy pupi-teacher ratio. The sums of squares shown next can be used to summarize the key results from the regression of Yon X. Xp, and X SSY = 28,222.23 SSE = 2,248.23 a. Determine the ANOVA table for the regression of Yon X, X2, and X- b. Determine the R²-value for the model in part (a). Based on this value, comment on whether the three educational resource variables appear to be associated with student performance.

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20. Solve the following problem:
A panel of educators in a large urban community wanted to evaluate the effects of
educational resources on student performance. They examined the relationship
between 12th-grade mean math SAT scores (Y) and the following independent vari-
ables for a random sample of 25 high schools: X, = per pupil expenditure (in dollars);
X = percentage of teachers with a master's degree or higher; and Xg = pupi-teacher
ratio. The sums of squares shown next can be used to summarize the key tesults from
the regression of Y on X, Xp, and Xy
SSY = 28,222.23 SSE = 2,248.23
a. Determine the ANOVA table for the regression of Yon X, Xz, and Xg-
b. Determine the R-value for the model in part (a). Based on this value, comment
on whether the three educational resource variables appear to be associated with
student performance.
Transcribed Image Text:20. Solve the following problem: A panel of educators in a large urban community wanted to evaluate the effects of educational resources on student performance. They examined the relationship between 12th-grade mean math SAT scores (Y) and the following independent vari- ables for a random sample of 25 high schools: X, = per pupil expenditure (in dollars); X = percentage of teachers with a master's degree or higher; and Xg = pupi-teacher ratio. The sums of squares shown next can be used to summarize the key tesults from the regression of Y on X, Xp, and Xy SSY = 28,222.23 SSE = 2,248.23 a. Determine the ANOVA table for the regression of Yon X, Xz, and Xg- b. Determine the R-value for the model in part (a). Based on this value, comment on whether the three educational resource variables appear to be associated with student performance.
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