11.18 Predicting college debt: Multiple regression. Refer to Exercises 10.12 (page 579) and 10.17 (page 580) for a description of the problem. Let’s now consider fitting a model using Admit, GradRate, InCostAid, and OutCostAid as the explanatory variables.

  1. (a) Write out the statistical model for this analysis, making sure to specify all assumptions.

  2. (b) Run the multiple regression model and specify the fitted regression equation.

  3. (c) Obtain the residuals from part (b) and check assumptions. Is Baruch College still an unusual case? Provide a brief summary.

  4. (d) Run the same multiple regression model but this time without Baruch College. Again comment on the residuals.

  5. (e) Should we proceed with inference using the entire data set? Or the data set without Baruch College? Explain your reasoning.