Every year, hundreds of thousands of international students apply to graduate programs in the United States. Two of the most important admissions criteria are undergraduate GPAs and TOEFL scores. An English language preparation school in Santiago, Chile, wants to examine the acceptance records of its former students who had applied to graduate school in the United States during the past two years. The results will be used to help advise new students about their chance of acceptance to their first choice of graduate programs. A portion of the data set is shown in the accompanying table with the following variables: Accept (1 if accepted, 0 otherwise); GPA (1 for below 3.00, 2 for 3.00–3.49, 3 for 3.50 and above); and TOEFL (H for 80 or above, L for below 80).

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

c. Can the naïve Bayes model be used to effectively classify the data? Explain your answer.

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Accept 1 0 I 0 GPA 1 1 B 1 TOEFL H II H ⠀ L