Regression Analysis
What is regression analysis?
Regression analysis is a statistical method used to examine the relationship between one dependent variable and one or more independent variables. In compensation contexts, the dependent variable is typically pay, while independent variables might include job level, tenure, performance rating, location, education, or business unit. The goal is to understand how much each factor contributes to pay outcomes, and whether any unexplained gaps remain once legitimate factors are accounted for.
Rather than comparing pay across two groups in isolation, regression analysis holds multiple variables constant at once. This makes it possible to isolate the effect of a single factor, such as gender or ethnicity, while controlling for everything else that legitimately influences pay. The output is typically expressed as a coefficient for each variable, showing its estimated effect on pay, along with a measure of statistical significance.
Why is regression analysis important?
Pay decisions are rarely shaped by a single factor. Someone's salary reflects a combination of role, experience, market conditions, location, and performance, layered on top of each other. Simple comparisons, such as looking at average pay by gender without adjusting for role or tenure, can produce misleading conclusions in either direction: they can flag a gap that does not actually exist once legitimate factors are considered, or mask one that does.
Regression analysis addresses this by modeling all relevant factors simultaneously. This gives organizations a defensible, evidence-based way to answer a specific question: after accounting for the factors that should explain pay differences, is there still a gap linked to gender, ethnicity, age, or another protected characteristic? That distinction, between explained and unexplained pay variation, sits at the center of most pay equity analysis, compliance reporting, and compensation planning.
Key forms of regression analysis
Several types of regression models are used in compensation analysis, each suited to different data and questions.
- Simple linear regression examines the relationship between one independent variable and pay. It is rarely sufficient on its own for pay equity work, since pay is influenced by many factors at once, but it can be useful for quick, single-factor checks.
- Multiple linear regression is the most common approach in compensation analysis. It models pay against several independent variables simultaneously, producing a coefficient for each one and allowing analysts to isolate the effect of any single factor.
- Logistic regression is used when the outcome being studied is categorical rather than continuous, such as whether someone was promoted or received a bonus, rather than the size of their salary.
- Weighted least squares regression adjusts for cases where the reliability of data varies across groups, which can matter when sample sizes differ significantly between comparator groups.
The choice of model depends on the structure of the data, the size of the workforce being analyzed, and the specific question being asked.
Why regression analysis matters for defensible pay decisions
A pay gap on its own does not indicate the cause of that gap. Two employees in the same role might be paid differently for entirely legitimate reasons, such as one having significantly more experience or a stronger performance history. Without a method to separate legitimate drivers of pay from unexplained variation, organizations are left guessing at whether a gap reflects bias, inconsistent application of pay policy, or simply differences in the underlying factors.
Regression analysis provides that separation. It gives compensation and HR teams a repeatable, evidence-based method for identifying where pay differences are explained by legitimate factors and where they are not. This matters not only for identifying and correcting inequities, but for demonstrating, to regulators, employees, or auditors, that pay decisions follow a consistent and defensible logic.
Who benefits from regression analysis?
Regression analysis supports several groups within an organization, each with a different stake in the outcome.
- Compensation and benefits practitioners use regression models to design pay structures, evaluate proposed salary adjustments, and identify where policy is not being applied consistently across the workforce.
- HR generalists rely on the results to answer employee questions about pay fairness with evidence rather than assertion.
- Finance leaders use regression-based pay equity analysis to quantify the cost of remediation and forecast the budget impact of closing identified gaps.
- Legal and compliance teams depend on regression analysis to prepare for pay transparency reporting requirements and to establish a documented, defensible rationale for pay decisions ahead of audits or litigation.
- Executive leadership, including the CHRO and CEO, use the aggregated findings to set organizational priorities and report on progress to the board.
Common approaches: pros and cons
Organizations typically choose between a few broad approaches to pay equity analysis, and regression analysis is generally considered the most rigorous of these.
- Simple pay ratio comparisons (comparing average pay by group) are fast and easy to communicate, but they ignore legitimate drivers of pay variation and can produce misleading headline numbers.
- Cohort or matched-pair analysis compares individuals in near-identical roles, which is intuitive but becomes impractical at scale, since it is difficult to find enough true matches across a large or varied workforce.
- Regression analysis accounts for multiple factors simultaneously and scales to large, diverse workforces, but it requires clean, well-structured data and some statistical expertise to build, interpret, and communicate correctly.
The tradeoff is largely one of rigor against complexity: regression analysis demands more upfront investment in data quality and analytical skill, but it produces results that hold up to scrutiny in ways that simpler comparisons typically cannot.
What is the difference between regression analysis and correlation analysis?
Correlation analysis measures the strength and direction of the relationship between two variables, but it does not establish cause and effect, and it cannot control for other factors at the same time. Regression analysis goes a step further: it models the relationship between a dependent variable and multiple independent variables at once, estimating the specific effect of each one while holding the others constant. In practice, correlation might reveal that pay and tenure move together, while regression analysis can quantify how much of a pay gap remains between two groups after tenure, role, and performance are all accounted for.
How do you evaluate regression analysis for pay equity?
Assessing whether a regression-based pay equity analysis is sound involves checking a handful of key indicators.
- Model fit, often measured by R-squared, indicates how much of the variation in pay the model explains. A low R-squared suggests important factors may be missing from the model.
- Statistical significance of each coefficient shows whether an observed effect, including any gap linked to a protected characteristic, is likely to be real rather than due to chance.
- Sample size within comparator groups affects the reliability of results; very small groups can produce unstable or misleading coefficients.
- Variable selection matters as much as the math: including only legitimate, job-related factors (and excluding any that might themselves reflect historical bias) is essential to a credible analysis.
Organizations conducting this work at scale often look for compensation platforms that can automate data preparation, run regression models consistently across pay cycles, and surface results in a format HR and legal teams can act on.
Best practices
- Getting reliable results from regression analysis depends as much on preparation and governance as on the statistical method itself.
- Start with clean, complete data. Missing or inconsistent fields for job level, location, or performance will undermine the model regardless of the technique used.
- Define comparator groups carefully, grouping employees in genuinely similar roles rather than relying on broad job titles that may span very different responsibilities and pay ranges.
- Include only legitimate, job-related variables, and document the rationale for each one included in the model.
- Run the analysis regularly, not just once. Pay equity shifts as people are hired, promoted, and paid, so a single snapshot loses relevance quickly.
- Pair statistical findings with a clear action plan. Identifying a gap is only useful if it leads to remediation, policy changes, or further investigation.
Other frequently asked questions (FAQs)
Is regression analysis the same as a pay audit?
No. A pay audit is a broader review of compensation practices that may include regression analysis as one method, alongside policy review, process checks, and other assessments.
How much data do you need to run a reliable regression analysis?
There is no fixed threshold, but very small comparator groups produce less reliable results. Larger, more diverse workforces generally support more robust models.
Can regression analysis prove there is no pay discrimination?
It can show whether an unexplained gap exists after accounting for legitimate factors, but it cannot fully rule out bias, since some relevant factors may not be captured in the data or may themselves reflect past inequities.
How often should regression-based pay equity analysis be run?
Many organizations run it annually at minimum, with more frequent checks during major compensation cycles such as annual reviews or new hire offers.
What data is typically included in a compensation regression model?
Common variables include job level, tenure, location, performance rating, education, and business unit, alongside the pay outcome and the demographic characteristic under review.
Do smaller organizations need regression analysis, or is it only for large enterprises?
Smaller organizations can use simplified versions of the same approach, though very small comparator groups may limit how much confidence can be placed in the results.
Summary
Regression analysis is a statistical method that models the relationship between pay and the multiple factors that legitimately influence it, making it possible to isolate any pay differences that remain unexplained. It is widely used in pay equity analysis because it accounts for several variables simultaneously, scales to large workforces, and produces defensible, evidence-based findings. Getting reliable results depends on clean data, careful variable selection, and regular analysis, paired with a clear plan to act on what the findings show.





