Estimate Default Rates Using Logistic Regression Model
On-site Statistical Role Play: Estimate Credit-Card Default Probability for a New Customer Segment
Context
You have historical account-level data with a 12‑month default label (default = 1, non‑default = 0) and features: account age (months), utilization (balance/limit), and credit score. A new customer segment is being launched (e.g., defined by marketing criteria), and you must:
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Choose and justify a statistical model to estimate default probabilities (PD) using these predictors.
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Produce a 95% confidence interval (CI) for the segment's default rate.
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Explain the CI in business terms to a non‑technical executive.
Assume you can train on historical data and that for the new segment you either have: (a) a list of prospective accounts with features, or (b) a pilot with n opened accounts and k observed defaults after 12 months.
Tasks
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Select and justify a model to estimate PD using account age, utilization, and credit score. Interpret coefficients (odds ratios).
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Compute a 95% CI for the default rate of the new segment using an appropriate method (e.g., Wald/delta method vs. bootstrap, or binomial proportion if a pilot exists).
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Explain the meaning of the 95% CI to a non‑technical executive.
Constraints & Assumptions
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Preserve the scope, facts, inputs, and requested outputs from the prompt above.
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If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
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Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.
Clarifying Questions to Ask
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Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
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Show enough derivation for the interviewer to follow the reasoning.
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Explain how you would validate the result with simulation or sensitivity checks.
What a Strong Answer Covers
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A correct setup with definitions, formulas, and boundary conditions.
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A step-by-step derivation or estimation plan.
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Interpretation of the result, including uncertainty and practical limitations.
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Checks for assumptions, edge cases, and numerical stability.
Follow-up Questions
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How would the result change if the assumptions were relaxed?
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Can you verify the answer with a simulation?
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What is the most likely source of estimation error?
