Reconsider Problem 3.17. The historical data for annual income and credit score have each now been binned into five categories (Low, Medium Low, Medium, Medium High, and High) on the Binned Data worksheet tab. Apply naïve Bayes to the binned dataset to classify each of the three applicants from Problem 3.17 (a, b, and c) as to whether they are likely to default (defined as greater than a 10 percent chance of default). 

Data from Problem 3.17. Part a, b and c.

As first described in Problem 2.16, Friendly Bank is very active with making loans to deserving people in the local community. However, the bank does need to carefully evaluate each loan to make sure that the recipient of the loan will likely repay the loan as scheduled. Therefore, the bank needs to obtain a prediction of whether this is likely and what the probability is. The bank primarily uses the annual income and the credit rating of the person applying for the loan as the predictor variables for obtaining this prediction. The bank has compiled all of the historical records of substantial loans and their outcomes over recent years. This information is provided in the spreadsheet titled Friendly Bank Data available in www.mhhe.com/Hillier7e. Only loans that have concluded (either paid off in full or ending in default) are included, resulting in 4,985 total records. The bank currently is evaluating the three loan applications described below. Using all the data (unpartitioned) on the Clean Data worksheet tab with the data rescaled using standardization, apply the KNN algorithm with k = 10 to this problem to classify each of the following applicants as either likely to default (defined as more than a 10 percent chance of default) or not likely to default (defined as a 10 percent chance of default or less). Also indicate the estimated probability of default for each. 

a. The loan applicant has an annual income of $110,000 and a credit rating of 640. 

b. The loan applicant has an annual income of $58,000 and a credit rating of 740. 

c. The loan applicant has an annual income of $82,000 and a credit rating of 700.