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 Exhibit 17.9.Assuming the debt ratio 30%,compute the increase in the probability of defaulting when the balance ratio goes up from 5% to 15%.

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 Exhibit 17.9.Assuming the debt ratio 30%,compute the increase in the probability of defaulting when the balance ratio goes up from 5% to 15%.

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 Exhibit 17.9.Assuming the debt ratio 30%,compute the increase in the probability of defaulting when the balance ratio goes up from 5% to 15%.