Credit scoring: fit a model, read the ROC curve, set the cutoff

A credit scorecard answers one question for every applicant: how likely is this loan to default? Logistic regression remains the industry workhorse for that question because its coefficients read as odds ratios and its output is a probability that can feed pricing, provisioning and capital models. This module fits one live, in the browser, on 2,000 synthetic personal-loan applicants described by debt-to-income, credit utilisation, length of credit history and recent delinquencies, and shows the fitted coefficients next to the true ones that generated the data.

Validation is where most of the practical judgement lives. The model is trained on 70% of applicants and measured on the 600 it has not seen. The ROC curve and its summary, AUC (or Gini = 2·AUC − 1 in credit-industry convention), measure how well it ranks bad borrowers above good ones; at the defaults AUC is about 0.83. The KS statistic marks the score where the two groups are furthest apart. A threshold slider turns scores into approve/decline decisions and fills in the confusion matrix, approval rate and bad rate among approved loans, and a "why was this applicant declined?" box lists the principal reasons for the declined applicant closest to the cutoff: the kind of specific reasons US lenders must give under ECOA and Regulation B.

The cutoff itself is an economic decision, not a statistical one. With a profit per good loan and a loss per default, a loan is worth booking only if its default probability is below gain / (gain + loss): 0.17 at the defaults ($1,200 profit, $6,000 loss), far from the naive 0.5, which would approve almost everyone. A reliability plot then checks calibration: a model can rank well and still mis-state default rates, which matters for IFRS 9 and CECL provisioning and for risk-based pricing. The data are synthetic and the model is illustrative, not a validated scorecard.