Logistic Regression Basics: Predicting Loan Repayment from Borrower Income

The Scenario

Crestline Bank is a regional lender processing approximately 900 personal loan applications per quarter. In a recent internal audit, the credit risk team noticed that a disproportionate number of charge-offs were concentrated among borrowers in lower income brackets — but the current loan approval process relies heavily on a loan officer's subjective judgment rather than any quantitative model. The Head of Retail Lending has tasked the analytics team with a focused question: does a borrower's annual income meaningfully predict whether they will repay their loan? If it does, the bank wants a model that can translate any income figure into a concrete repayment probability to support faster, more consistent credit decisions.

The Statistical Challenge

The credit team has pulled records for 900 closed loans, each containing the borrower's annual income (in thousands of USD) and the final outcome — repaid (1) or defaulted (0). While it seems intuitive that higher-income borrowers are less likely to default, the question is whether this relationship holds up statistically and how strong it actually is. You have been brought in to build a Logistic Regression model — the standard approach for predicting a binary outcome (repaid vs. defaulted) from a continuous predictor (income). Unlike linear regression, logistic regression outputs a probability between 0 and 1, making it directly interpretable as a repayment likelihood. You will also compute the odds ratio for income, which tells you how the odds of repayment change for every additional $1,000 in annual income.

What's at Stake

A validated income-based repayment model would give Crestline Bank a simple, auditable, and data-driven starting point for credit decisions. If income is a statistically significant predictor, the bank can set income-based probability thresholds to flag high-risk applications for additional review — reducing charge-offs without turning away creditworthy borrowers. If the model shows no meaningful relationship, the bank knows to look elsewhere (credit scores, debt-to-income ratios) for predictive power. Your analysis is the foundation on which the bank's first quantitative credit model will be built.