Graduation Rates. Where we considered the regression analysis of graduation rate on the 25th percentile of SAT scores for entering students, the 75th percentile of SAT scores for entering students, the percentage of freshmen in the top 10% of their high school class, the student-to-faculty ratio, the percentage of applicants accepted, and the percentage of alumni giving to the college. Use the technology of your choice to do the following. a. Use the maximum-R2 criterion to obtain a regression equation for these data. b. Use the adjusted-R2 criterion to obtain a regression equation for these data. c. Use the Mallows’ Cp criterion to obtain a regression equation for these data. d. Are the regression equations obtained in parts (a), (b), and (c) the same? e. Use the analysis in parts (a), (b), and (c) to select a regression equation for these data. For the regression equation that you selected, obtain plots of residuals versus fitted values, residuals versus the included predictor variables, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
Graduation Rates. Where we considered the
a. Use the maximum-R2 criterion to obtain a regression equation for these data.
b. Use the adjusted-R2 criterion to obtain a regression equation for these data.
c. Use the Mallows’ Cp criterion to obtain a regression equation for these data.
d. Are the regression equations obtained in parts (a), (b), and (c) the same?
e. Use the analysis in parts (a), (b), and (c) to select a regression equation for these data. For the regression equation that you selected, obtain plots of residuals versus fitted values, residuals versus the included predictor variables, and a normal probability plot of the residuals. Perform a residual analysis to assess the appropriateness of the regression equation, constancy of the conditional standard deviations, and normality of the conditional distributions. Check for outliers and influential observations.
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