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. To estimate this probability, she decided to use the logit model,
P = , 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. Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients.
Bob has a balance ratio of 10%, an annual income of $80,000, and $15,000 in total debt. Only applicants with excellent and good ratings qualify for a loan. Find the maximum amount of loan Bob can get if he is required to maintain his excellent or good rating after getting this amount.

Question

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.

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

, 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.

Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients.
Bob has a balance ratio of 10%, an annual income of $80,000, and $15,000 in total debt. Only applicants with excellent and good ratings qualify for a loan. Find the maximum amount of loan Bob can get if he is required to maintain his excellent or good rating after getting this amount.

Quizplus · Accepted Answer

The Answer of 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. To estimate this probability, she decided to use the logit model, P = , 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. Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients. Bob has a balance ratio of 10%, an annual income of $80,000, and $15,000 in total debt. Only applicants with excellent and good ratings qualify for a loan. Find the maximum amount of loan Bob can get if he is required to maintain his excellent or good rating after getting this amount.

A Bank Manager Is Interested in Assigning a Rating to the Holders