Exhibit 17.9.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 logistic model: ,
where,
y = a binary response variable with value 1 corresponding to a default,and 0 to a no default,
x₁ = the ratio of the credit card balance to the credit card limit (in percent),
x₂ = the ratio of the total debt to the annual income (in percent).
Using Minitab on the sample data,she arrived at the following estimates: Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients.
Refer to Exhibits 17.9.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 are qualified 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

Exhibit 17.9.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 logistic model:

,
where,
y = a binary response variable with value 1 corresponding to a default,and 0 to a no default,
x₁ = the ratio of the credit card balance to the credit card limit (in percent),
x₂ = the ratio of the total debt to the annual income (in percent).
Using Minitab on the sample data,she arrived at the following estimates:

Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients.
Refer to Exhibits 17.9.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 are qualified 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 Exhibit 17.9.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 logistic model: , where, y = a binary response variable with value 1 corresponding to a default,and 0 to a no default, x₁ = the ratio of the credit card balance to the credit card limit (in percent), x₂ = the ratio of the total debt to the annual income (in percent). Using Minitab on the sample data,she arrived at the following estimates: Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients. Refer to Exhibits 17.9.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 are qualified 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.