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.
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.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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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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