Read "Interpreting Regression Results for Colleges and Universities" on pages 303 and 304 in the textbook. Refer to thescreenshotof Figure 8.17 with cells lettered A through O.Choose a letter and discuss the meaning of the associated numerical value in the context of the problem.Please title your discussion post "Letter ____" by filling in the blank with your chosen letter.

In addition to your individual assigned cell, what overall conclusions and/or predictions can you make from the results presented here?

8.12

Interpreting Regression Results for theColleges and UniversitiesData

The multiple regression results for the college and university data are shown inFigure8.17.

FIGURE8.17Multiple Regression Results forColleges and UniversitiesData

Figure 8.17 Full Alternative Text

From theCoefficientssection, we see that the model is

Graduation % = 17.92 + 0.072 SAT24.859ACCEPTANCE0.000136EXPENDITURES0.163TOP10%HS

The signs of some coefficients make sense; higher SAT scores and lower acceptance rates suggest higher graduation rates. However, we might expect that larger student expenditures and a higher percentage of top high school students would also positively influence the graduation rate. Perhaps the problem occurred because some of the best students are more demanding and change schools if their needs are not being met, some entrepreneurial students might pursue other interests before graduation, or there is sampling error. As with simple linear regression, the model should be used only for values of the independent variables within the range of the data.

The value ofR2(0.53)

indicates that 53% of the variation in the dependent variable is explained by these independent variables. This suggests that other factors not included in the model, perhaps campus living conditions, social opportunities, and so on, might also influence the graduation rate.

From theANOVAsection, we may test for significance of regression. At a 5% significance level, we reject the null hypothesis becauseSignificance Fis essentially zero. Therefore, we may conclude that at least one slope is statistically different from zero.

Looking at thep-values for the independent variables in the last section, we see that all are less than 0.05; therefore, we reject the null hypothesis that each partial regression coefficient is zero and conclude that each of them is statistically significant.

Figure8.18shows one of the residual plots from the Excel output. The assumptions appear to be met, and the other residual plots (not shown) also validate these assumptions. The normal probability plot (also not shown) does not suggest any serious departures from normality.