As predicted, there were no unusual observations present. We noted the change in the equation, the rise in the R-square, and also the rise in the F-value 7.54 to 8.78. The P-value decreased as we initially thought. In essence, 30 out of the 35 states show normal parameters regarding spending expenditures on students and their composite scores.
Our next task was to determine whether or not we could use the estimated regression developed from this data to estimate the composite scores for the states that did not participate in the study. Since the R-square is at .116, we conclude that the estimated regression can be applied to obtain the estimated composite scores of the non-participating states although the exact accuracy would be a critical issue because there are multiple alternative factors that affect the variables. With this knowledge, we can estimate the scores so as long as the spending per pupil is given for each state and we can use the original equation to compute them.
The following data shows the relationship between states that spent at least $4,000 and not exceeding $6,000 per student and compares that to the complete data set. In short, we wanted to find out whether or not the variables appear to be any different be removing possible non-significant points. Our results are as follows:
Regression Analysis: Spending per pupil ($) versus Composite Score
(chart)