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.
(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 with μ₁ = 18% and σ₂ = 6%, while their debt ratio, x₂, is normally distributed with μ₂ = 30% and σ₂ = 8%. Assume also that x₁ and x₂ are independent. Simulate 1,000 applications to estimate the percent of those that are qualified for a loan.

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.
(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 with μ₁ = 18% and σ₂ = 6%, while their debt ratio, x₂, is normally distributed with μ₂ = 30% and σ₂ = 8%. Assume also that x₁ and x₂ are independent. Simulate 1,000 applications to estimate the percent of those that are qualified for a loan.

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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. (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 with μ₁ = 18% and σ₂ = 6%, while their debt ratio, x₂, is normally distributed with μ₂ = 30% and σ₂ = 8%. Assume also that x₁ and x₂ are independent. Simulate 1,000 applications to estimate the percent of those that are qualified for a loan.

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