Fair Lending Regression Analysis: What It Controls For and How to Explain a Pricing Disparity

A fair lending regression tests whether a gap in a lending outcome, such as denial or the rate paid, between a prohibited basis group and a control group survives once the credit factors your policy actually uses are held constant. What survives is the part you will be asked to explain, and the model shows which applications drive it.

This article covers the working side of that: what goes into the model, how to read what comes out, and how examiners use the result. It is the companion to what regression can and cannot prove in fair lending, which deals with the method's limits in detail, quoting the OCC's handbook. If you have not read that one, the short version is that a model can only account for the factors you give it.

What is a fair lending regression actually testing?

Two questions, depending on the outcome. For underwriting, the outcome is a yes or no (approved or denied), and the usual model is logistic regression. For pricing, the outcome is a number (the rate, the rate spread, fees or points), and the usual model is linear regression. In both, the variable of interest is an indicator for membership in the prohibited basis group being tested, and every other variable in the model is there to hold a legitimate difference between applicants constant.

The examiners' own description is close to that. The OCC's Comptroller's Handbook says statistical modeling "can control for differences in various factors and estimate how important each factor is to the outcome," and that an examiner "can conclude with a specific level of certainty about any correlation between membership in a PB group and the outcome." The handbook recommends modeling for high-volume focal points, and for cases where comparable files are hard to find by hand, "such as when a bank applies a complex pricing matrix."

So the test is narrow on purpose. It does not ask whether two groups had different outcomes; a pivot table answers that. It asks whether they had different outcomes among applicants who looked the same on everything your policy says should matter.

Which credit factors should the model control for?

The ones your institution actually uses to decide or to price, and only those. The interagency procedures tell examiners to tailor a pricing review "to the specific factors that the institution considers when determining its pricing, terms, and conditions," and add that "consideration should be limited to factors which examiners determine to be legitimate." The OCC handbook sets the same bar for any factor added to a model after a file review: it "must be legitimately derived from bank policies and occur sufficiently systematically to warrant changes to the model."

For most residential portfolios that produces a familiar list. Each item belongs in the model because a written policy or rate sheet gives it a role, not because it appears on every vendor's default list.

• Credit score. Usually the main input to both the approval decision and risk-based pricing. Enter it the way your policy uses it, by band if your rate sheet prices in bands.
• Debt-to-income ratio. A capacity measure with policy thresholds attached. If your guidelines allow exceptions above a ceiling, the exception is a factor too, and so is who approved it.
• Loan-to-value ratio. A collateral measure that most pricing matrices adjust for directly.
• Loan amount. Fixed costs, fee schedules and some rate adjustments depend on size, so a pricing model without it can attribute a size effect to something else.
• Product and loan type. Fixed against adjustable, conventional against government, term, lien position. Each prices differently by design, so comparing across them without a control compares unlike things.
• Channel. Retail, broker and correspondent loans can carry different compensation and pricing. That is a legitimate control only if channel pricing is set by policy, and it comes with a question of its own, covered in the example below.

Two disciplines matter more than the list. First, the policy has to have been in force for the whole review window. The interagency procedures group applicants "around a range of dates during which the institution's practices for the term or condition being reviewed were the same," and the OCC's data request asks examiners to find out whether policies changed during the period. A rate sheet that changed in June is two models, or one model with a period control. Second, the field has to be accurate. A control built on a miskeyed credit score does not control for anything.

How do you read the output?

Start with the coefficient on the prohibited basis indicator. In a linear pricing model it is the estimated difference between the two groups in the outcome's own units, once every other variable is held constant. In a logistic underwriting model it is a difference in log-odds, which most reports convert to an odds ratio so you can read it as a multiple of the odds of denial.

Its p-value says how likely a difference that size would be by chance if no real difference existed, given the model. Treat it as a reason to look further. The companion article explains why it is not a finding on its own.

Then check the counts. How many applications are left in each group after records with missing fields were dropped? A coefficient resting on a handful of prohibited basis applications is fragile, so read the drop count as closely as the coefficient.

Last come the application-level diagnostics. Residuals show how far each decision or price sits from what the model predicted, and influence measures such as Cook's distance show which applications move the result most. They turn an aggregate number into a list of files to read.

Then compare the coefficient with the raw gap. If the raw difference between groups is large and the controlled coefficient is close to zero, the legitimate factors explain most of the gap. If the controlled coefficient stays close to the raw gap, the factors you entered do not explain it, and that remainder is what an examiner would ask you to account for.

A worked example, using hypothetical numbers

Every figure in this section is invented to show the mechanics. None of it describes a real institution or real lending data.

Suppose an institution reviews a year of conventional fixed-rate purchase loans. The average rate spread for the prohibited basis group is 0.30 percentage points higher than for the control group. That is the raw gap, and on its own it says nothing about why.

The first model controls for credit score band, loan-to-value, debt-to-income and loan amount. The coefficient on the group indicator drops to 0.12 percentage points and is statistically significant at the threshold the institution set in advance. The legitimate factors explain a little over half of the gap, and the rest is unexplained.

The analyst then adds channel, because the pricing policy sets different compensation for broker and retail loans. The coefficient drops to 0.03 and is no longer significant. It is tempting to record the disparity as explained by channel and close the file. Don't.

The interagency procedures list among the indicators of steering "significant differences in the percentage of prohibited basis applicants in one of the lending channels compared to the percentage of prohibited basis applicants of the other lending channel," along with a lack of "clear, objective and consistently implemented standards" for referring applicants to lending channels. A control can absorb a disparity by carrying it. If prohibited basis applicants were disproportionately placed in the more expensive channel, the channel variable has not explained the pricing gap; it has moved the question from pricing to placement. The next step is to look at how applicants reach each channel, and the residuals from the first model show which files to start with.

When is regression not enough?

When the numbers are too small to model, when the race or ethnicity data behind the group indicator is estimated, not reported, and when a factor you know matters is not in the data at all. Each has its own treatment. Small volumes go to file review, and the difference between the two review methods examiners use is set out in comparative file review versus matched-pair testing. Proxied demographics carry their own error, covered in where the BISG proxy method is known to fail. And a missing factor is the omitted variable problem, for which the OCC publishes a three-part reliability test, quoted in full in what regression can and cannot prove.

How do examiners use regression results?

At three points in an examination, according to the agencies' own procedures.

To choose what to examine. The CFPB's ECOA examination procedures tell examiners, working with Headquarters, to "use statistical analyses whenever appropriate to scope fair lending examinations." A focal point, in the CFPB's definition, is "a combination of loan product(s), market(s), decision center(s), time frame and prohibited basis to be analyzed." The interagency procedures add that circumstances such as "the use of credit scoring or a large volume of residential lending" may call for "regression analysis or other statistical methods" under an agency's own specialized procedures.

To test the result against your files and your policies. When the OCC's statistical team (the handbook calls it CRAD) models a focal point, it asks examiners to obtain the electronic data, identify the staff who know the data, and collect the policies and procedures behind the decision, including any changes during the period. A file review run alongside the model is meant to find data errors and missing policy factors, and the handbook is explicit that its goal "is not to replicate or replace the statistical model's results."

To ask you for an explanation. Part IV of the interagency procedures tells examiners to present to management, among other findings, "any statistically significant average difference in either the frequency or amount of pricing disparities between control group and prohibited basis group applicants," and to explain that unless there are "legitimate, nondiscriminatory explanations" the agency could conclude there is a violation. The CFPB's procedures describe the same step as "sharing our statistical analyses with the creditor and asking for comments and explanations," after which examiners may "refine our statistical models and re-analyze."

This is the step that rewards running the model yourself first. If you have already modeled the same focal point on the same factors, you know roughly what the examiner's model will show, and you have had time to find out why before anyone asks.

How should you document an explanation for a disparity?

Examiners judge an explanation against your records, not your argument. The interagency procedures tell them to evaluate whether a response is consistent "with previous statements, information obtained from file review, documents, reasonable banking practices, and other sources." They also warn examiners not to accept a legitimate reason they notice in a file "unless it is clear that, at the time of the denial, the institution actually based the denial on that reason." An explanation assembled after the fact, however reasonable, is weaker than one the file already shows. A defensible record usually contains the following.

• The rate sheet, pricing matrix or underwriting guideline that gives each control its role, with the dates it was in force.
• The model specification: every variable entered and how it was coded, the selection method with its entry and removal thresholds, and the population with every exclusion and its count.
• How the fields in the model were verified. The CFPB's procedures call for data integrity checks on any HMDA data an examiner's model relies on, so expect the same fields to be checked from the other side.
• Every version of the model, including the ones that showed a disparity, and why a variable was added or removed between them. A disparity that vanishes after an undocumented change of specification invites an obvious question.
• For the applications the residuals flagged, what each file shows and whether it confirms the factor the model credits.
• What you did about anything left unexplained. A residual disparity that was investigated, explained or remediated is a different finding from one nobody looked at.

One caution on sharing. The interagency procedures distinguish self-tests from self-evaluations, and say institutions "must share all information regarding 'self-evaluations' and certain limited information related to 'self-tests.'" Treat the regression record as something an examiner may read, and keep it in a state where you are content for them to read it. Our step-by-step guide to a fair lending self-assessment covers where the regression sits in the wider review.

How Comply Fair Lending runs these tests

Comply Fair Lending runs logistic regression for underwriting and linear regression for pricing, with field values transformed and dummy-coded automatically and consistency-verification tools to flag relationships between variables before they distort a model. Variable selection is a stated method: forward selection, stepwise or backward elimination, each with explicit p-value thresholds to enter and to stay, and variables can be locked into the model whatever the selection would do with them.

Standardized and studentized residuals and Cook's distances are calculated as standard, and every application-level result can be filtered, sorted and used in a scorecard, so a rule can group every application with a standardized residual past ±3 for review. The files you then pull can be sampled by the CFPB/FRB review methods or by OCC numerical sampling at a reliability and precision level you set. A model saves as a reusable definition, so the next run repeats the same specification on new data. The detail is in the regression features, and the wider fair lending overview covers the rest of the review.

If you want to see a model built on your own kind of data, with the specification and residuals on screen, schedule a fair lending demonstration.

Sources

• Comptroller's Handbook, Consumer Compliance: Fair Lending, Version 1.0
  Office of the Comptroller of the Currency, January 2023, as amended July 14, 2025; quotations from pages 18 and 19. Retrieved October 13, 2026.
• Interagency Fair Lending Examination Procedures
  Federal Financial Institutions Examination Council member agencies, August 2009 (copy hosted by the NCUA); Part III.D and Part IV. Retrieved October 13, 2026.
• Equal Credit Opportunity Act (ECOA) Examination Procedures
  Consumer Financial Protection Bureau, October 2015; sections C and D. Retrieved October 13, 2026.

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