Regression Analysis for Compensation Professionals: A Practical Guide

The Core Design Challenge

A regression analysis models the relationship between a dependent variable (the thing you are trying to explain — typically salary) and one or more independent variables (the things you think explain it — grade, tenure, performance rating, gender). The output produces a coefficient for each independent variable: the expected change in the dependent variable for a one-unit change in that independent variable, holding all other variables constant. If the grade coefficient is £8,000, it means moving up one grade is associated with £8,000 higher salary, controlling for tenure, performance, and all other included variables.

P-values are the statistical test that tells you whether a coefficient is likely to be a real pattern or likely to be noise. A p-value below 0.05 conventionally means the finding is unlikely to have occurred by chance — less than 5% probability that you would observe this result in a world where there is genuinely no relationship between the variable and salary. A p-value above 0.05 means the finding could easily be random variation in the data, and you should not build a pay decision on it. In pay equity terms: a gender coefficient of -£2,100 with p=0.03 is a finding worth investigating urgently. The same coefficient with p=0.24 is not.

R-squared tells you how much of the variation in salaries your model explains. A salary regression with an R-squared of 0.70 means 70% of the variation in salaries across the population is explained by the variables you included (grade, tenure, performance, etc.). The remaining 30% is unexplained — it reflects individual negotiation differences, market adjustments applied selectively, and genuine random variation in pay decisions. An R-squared of 0.70-0.80 is reasonable for a compensation regression. Values above 0.90 often indicate over-fitting — too many variables relative to the sample size, producing a model that fits the existing data very well but has poor predictive validity.

How the Approach Works

The most important caution in using regression for compensation decisions is the distinction between statistical significance and practical significance. A gender pay gap of £200 that is statistically significant (p=0.02) in a very large sample may not be practically significant — it represents a real but trivial difference that does not warrant the cost of a remediation programme. A gap of £2,100 with p=0.06 is not statistically significant at the conventional threshold but may be practically important enough to investigate even though the finding falls just outside the threshold. Both dimensions — statistical and practical significance — should inform the decision to act.

Sample size is the constraint that most frequently limits the usefulness of regression in compensation contexts. Organisations with fewer than 100 employees in the full analysis group, or fewer than 30 employees in the protected characteristic group, should not rely on regression outputs — the sample is too small for the statistical tests to reliably distinguish genuine patterns from random variation. For these organisations, cohort analysis (comparison within defined groups) is more appropriate, with explicit disclosure of the sample size limitation in any report. Claiming statistical rigour from a small-sample regression is worse than acknowledging a small-sample limitation in a cohort analysis.