Admission to medical school in the United States is highly competitive. The acceptance rate to the top medical schools could be as low as 2% or 3%. With such a low acceptance rate, medical school admissions consulting has become a growing business in many cities. In order to better serve his clients, Paul Foster, a medical school admissions consultant, wants to build a data-driven model to predict whether or not a new applicant is likely to get accepted into one of the top 10 medical schools. He collected a database of 1,992 past applicants to the top 10 medical schools with the following information: Sex (F = female, M = male), CollegeParent (1 if parents with college degrees, 0 otherwise), GPA (1 if undergraduate GPA of 3.50 or higher, 0 otherwise), and Med (1 if accepted to a top 10 medical school, 0 otherwise). A portion of the data set is shown in the accompanying table. 

a. Create a bagging ensemble classification tree model to determine whether a new applicant is likely to get accepted into one of the top 10 medical schools. What are the overall accuracy rate, sensitivity, and specificity of the model on the validation data? What is the AUC value of the model? 

b. Create a random forest ensemble classification tree model. Select two predictor variables randomly to construct each weak learner. What are the overall accuracy rate, sensitivity, and specificity of the model on the validation data? Which is the most important predictor variable? 

c. Compare the two ensemble models. Which model shows more robust performance according to the AUC value?

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Sex CollegeParent 1 1 LLM F М ⠀ M ⠀ 0 GPA 1 0 ⠀ 0 Med 1 1 ⠀ 0