Practice — Logistic Regression & Linear Classifiers (6 questions)

A credit risk model fits:

logit(p_default) = -3.0 + 0.05·utilization + 0.9·late_payment_history

where utilization is credit utilization in percent (0-100) and late_payment_history is 1 if the applicant has any late payment on record, 0 otherwise.

1. Compute the odds ratio for late_payment_history and state it in plain English.
2. For an applicant with utilization = 20 and no late-payment history, compute p_default. Now compute it again with utilization = 60. By how many probability points did it move?
3. A risk analyst says "the coefficient 0.05 means each percentage point of utilization adds 5% to default risk." Correct the statement.

You're fitting a logistic regression to predict loan default from 3 features, including an internal risk_flag. In your training sample, every applicant with risk_flag = 1 defaulted, and every applicant with risk_flag = 0 did not — a perfect split. You fit with ordinary maximum likelihood, no regularization.

What happens to the coefficient on risk_flag?