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(b) Write down the mathematical formula for the Naive Bayes model with the pre- dictors and response in Table 2.3. Use the Naive Bayes model trained on the training data from Table 2.3 to predict the "claim" of the insurance data in Table 2.1 as well as evaluating the performance of the model by calculating the confusion matrix, accuracy, sensitivity, specificity, PPV, NPV of the logistic model. Table 2.3: The training dataset of an insurance claim data for Naive Bayes model. Obs. gender bmi age_bracket previous claim claim 1 female obese 50+ 1 no claim 2 female under_weight 31-50 0 no claim 3 male under_weight 31-50 1 no claim 4 female over_weight 18-30 no_claim 5 female normal_weight 31-50 no_claim 6 female under_weight 31-50 no.claim 7 female obese 18-30 no claim 8 male under_weight 50+ no claim 9 female normal weight 31-50 0 no.claim 10 male over_weight 31-50 no claim 11 female normal weight 50+ claim 12 male over-weight 31-50 1 claim 13 male under weight 31-50 1 claim 14 male over_weight 31-50 1 claim 15 male obese 50+ claim 16 male under_weight 50+ 0 claim 17 female obese 31-50 claim 18 female under-weight 50+ 1 claim 19 female normal weight 50+ 1 claim 20 female under_weight 18-30 claim Note: The default cut-off is 0.5. (4 marks) (b) Write down the mathematical formula for the Naive Bayes model with the pre- dictors and response in Table 2.3. Use the Naive Bayes model trained on the training data from Table 2.3 to predict the "claim" of the insurance data in Table 2.1 as well as evaluating the performance of the model by calculating the confusion matrix, accuracy, sensitivity, specificity, PPV, NPV of the logistic model. Table 2.3: The training dataset of an insurance claim data for Naive Bayes model. Obs. gender bmi age_bracket previous claim claim 1 female obese 50+ 1 no claim 2 female under_weight 31-50 0 no claim 3 male under_weight 31-50 1 no claim 4 female over_weight 18-30 no_claim 5 female normal_weight 31-50 no_claim 6 female under_weight 31-50 no.claim 7 female obese 18-30 no claim 8 male under_weight 50+ no claim 9 female normal weight 31-50 0 no.claim 10 male over_weight 31-50 no claim 11 female normal weight 50+ claim 12 male over-weight 31-50 1 claim 13 male under weight 31-50 1 claim 14 male over_weight 31-50 1 claim 15 male obese 50+ claim 16 male under_weight 50+ 0 claim 17 female obese 31-50 claim 18 female under-weight 50+ 1 claim 19 female normal weight 50+ 1 claim 20 female under_weight 18-30 claim Note: The default cut-off is 0.5. (4 marks)