A bank manager is interested in assigning a rating to the holders of credit cards issued by her bank. The rating is based on the probability of defaulting on credit cards and is as follows.

Rating Probability of Defaulting

Excellent p 0.05

Good 0.05 <p 0.10

Fair 0.10 <p 0.25

Poor p> 0.25

To estimate this probability, she decided to use the logit model,

P=exp(0+1x1+2x2)1+exp(0+1x1+2x2),

where

y= a binary response variable which is 1 if the credit card is in default and 0 otherwise

x₁= the ratio of the credit card balance to the credit card limit (in %)

x₂= the ratio of the total debt to the annual income (in %)

The following output is obtained.

VariableLogistic Model

Intercept8.98 (p-value = 0.0089)

x₁- Balance Ratio0.13 (p-value = 0.0054)

x₂- Debt Ratio0.17 (p-value = 0.0067)

Note: Thep-values of the corresponding tests are shown in parentheses below the estimated coefficients.

(Using Excel or R)Suppose that only applicants with excellent and good ratings are qualified for a loan. Assume that the balance ratio,x₁,of those who apply is normally distributed with₁= 18%and₂= 6%,while their debt ratio,x₂,is normally distributed with₂= 30%and₂= 8%.Assume also thatx₁andx₂are independent. Simulate 1,000 applications to estimate the percent of those that are qualified for a loan.