Question 3 (25 points) Financial institutions use information provided by several applicants for loans to build application scorecards to be able to identify characteristics that are indicative of people who are likely to default on loans, and then use those characteristics to discriminate between good and bad credit risks. The results of the loan are coded as l=loan repaid and 0=loan defaulted. The logistic regression method is used to model the data where the information contained in a loan application is converted into probability that the applicant will repay. The predictor variables include AGE = age in years, INCOME = income (in $1,000) and EMPLOYER = number of years with current employer. The data set contains 410 applicants who did not default on previous loan, and 103 who did default. Partial results for a logistic model t using SAS are given in the appendix. [10]a. Assess the overall utility of the model. [5]b. Construct the 95% condence interval for the odds ratio of income. Interpret in the context of the problem [10]c. A bank that uses the above information has decided to grant loans only if an applicant has the probability to fully repay the loan is at least 95%. This bank has now received applications from individuals with their personal information shown below. Identify the applicant that will be granted the loan. AGE INCOME EMPLOYER Applicant 1 45 130 10 Applicant 2 50 110 15