Predicting whether or not an entering freshman student will drop out of college has been a challenge for many higher education institutions. Nelson Touré, a senior student success adviser at an ivy-league university, has been asked to investigate possible indicators that might allow the university to be more proactive to provide support for at-risk students. Nelson reviews a data set of 200 former students and selects the following variables to include in his study: Graduate (Graduate = 1 if graduated, 0 otherwise); whether or not the student received a passing grade in his or her first calculus, statistics, or math course (Math = 1 if yes, 0 otherwise); whether or not the student received a passing grade in his or her first English or communications course (Language = 1 if yes, 0 otherwise); whether or not the student had any contact with the advising center during his or her first semester (Advise = 1 if yes, 0 otherwise); and whether or not the student lived on campus during his or her first year at college (Dorm = 1 if yes, 0 otherwise). A portion of the data is shown in the accompanying table.

a. Partition the data to develop a naïve Bayes classification model. Report the accuracy, sensitivity, specificity, and precision rates for the validation data set. 

b. Generate the cumulative lift chart. Does the entire lift curve lie above the baseline? 

c. Generate the ROC curve. What is the area under the ROC curve (or the AUC value)? 

d. Interpret the results and evaluate the effectiveness of the naïve Bayes model.

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Graduate Math 1 1 0 0 ⠀ I 1 1 Language 0 1 ⠀ 1 Advise 0 0 ⠀ 1 Dorm 1 1 ⠀ 1