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 variables for a random sample of 25 high schools: X1 = per pupil expenditure (in dollars); X2 = percentage of teachers with a master's degree or higher; and X3 = pupil-teacher ratio. The sums of squares shown next can be used to summarize the key results from the regression of Y on X1, X2, and X3:
SSY = 28,222.23 SSE = 2,248.23
a. Determine the ANOVA table for the regression of Y on X1, X2, and X3.
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.