Question 1 (25 points total)

Kiplinger's "Best Values in Public Colleges" provides a ranking of U.S. public colleges based on a combination of various measures of academics and affordability. The dataset "EX11-18BESTVAL.csv" includes a sample of 25 colleges from Kiplinger's 2015 report. Let's focus on the relationship between the average debt in dollars at graduation (AveDebt, the response variable) and the explanatory variables Admit (admission rate), GradRate (graduation rate), InCostAid (in-state cost per year after need-based aid), and OutCostAid (out-state cost per year after need-based aid).

1. a)(2 points) Write out the statistical model for this analysis, making sure to specify all assumptions.
2. b)(3 points) Run the multiple regression model in R and report the fitted regression equation.
3. c)(5 points) State the null and alternative hypothesis for the overall F test, report the overall F statistic, its degrees of freedom, and the p-value. What do you conclude based on this test result?
4. d)(2 points) Obtain the residuals from part (b), construct a residual plot of residuals against the predicted outcome y, and check assumptions. Is Baruch College an unusual case? Provide a brief summary.
5. e)(3 points) Run the same multiple regression model but this time without Baruch College, and specify the fitted regression equation. Again comment on the residuals (i.e., construct a residual plot of residuals against the predicted outcome y and check assumptions).
6. f)(5 points) For the model in part (e) (i.e., the multiple regression model without Baruch College), report the overall F statistic, its degrees of freedom, and the p-value. What do you conclude based on this test result?
7. g)(5 points) For the model in part (e) that included all p = 4 explanatory variables, only InCostAid is found significant using the individual parameter t tests. This raises the question whether these other three variables further contribute to the prediction of average debt given in-state cost is in the model. Conduct a partial F test to answer this question.