1. Introduction
Regression analysis is central to pay equity work because it allows organizations to assess how legitimate, measurable factors—such as job grade, performance, age, and tenure—explain differences in pay between groups. The results help determine how much of the observed pay gap is due to structural or individual differences, and how much remains unexplained, potentially indicating inequity.
This article provides a comprehensive explanation of how to interpret regression outputs in pay equity analysis, including:
Positive vs. negative factor contributions
Explained vs. unadjusted pay gaps
R² and Adjusted R²
Standard errors
p-values
Interpretation of coefficients in the Direct Method Model Evaluation
All explanations reflect the data presented in the provided materials.
2. Interpreting Positive and Negative Percentage Contributions
In regression-based pay equity models, each factor shows a percentage contribution to the pay gap.
Positive contribution
A positive percentage indicates that the factor is increasing the overall unadjusted pay gap and thereby reducing the adjusted gap.
This occurs when:
The advantaged group has higher values for a factor that increases pay (e.g., more men in higher grades).
Or the disadvantaged group has higher values for a factor that lowers pay.
Negative contribution
A negative percentage indicates that the factor is reducing the overall pay gap and therefore increasing the adjusted gap.
This occurs when:
The disadvantaged group has higher values for a factor that increases pay (e.g., longer tenure).
Or the advantaged group has higher values for a factor that lowers pay.
These effects are essential for understanding whether structural differences widen or narrow observed pay gaps.
3. Explained vs. Unadjusted Pay Gap
Regression models decompose the pay gap into:
Explained portion
The proportion of the gap attributable to legitimate, measurable factors.
Examples from the data:
Age: Men being slightly older explains 14.1% of the gap.
Performance: Women slightly outperform men, reducing the gap by –2.4%.
Grade seniority: Men being in more senior roles explains 88.3% of the gap.
Unadjusted gap contribution
Shows how much each factor contributes to the raw gap before modelling:
Age → 15.4%
Performance → –2.6%
Seniority → 96.8%, the strongest driver
This breakdown helps distinguish structural drivers (representation at levels) from individual drivers (performance).
4. Model Strength: R² and Adjusted R²
The R-squared and Adjusted R-squared values measure how much of the salary variation the model explains.
Interpretation:
>0.70 → Strong model
0.50–0.70 → Moderate strength (still actionable)
<0.30 → Weak model
In the provided Direct Method Model:
R² = 60.3% → Moderate strength
Adjusted R² = 59.8% → Moderate strength
This means the model explains a substantial proportion of salary variation, but structural improvements (better factors, refined job architecture) may increase predictability.
5. Standard Errors: Precision of Estimates
Standard errors measure how precisely each coefficient is estimated.
Small standard error → reliable estimate
Large standard error → effect uncertain
Examples from the Direct Method Model:
Factor | Standard Error | Interpretation |
Grade | 0.0034 | Very precise; high reliability |
Performance | 0.0069 | Standard error almost equals estimate → uncertain effect |
Age | 0.0008 | Extremely precise estimate |
Female | 0.0181 | Much larger than estimate → very low reliability |
These metrics help determine whether the factor’s contribution can be trusted.
6. p-Values and Statistical Significance
The p-value indicates whether a factor’s effect on salary is statistically significant.
p < 0.05 → statistically significant
p > 0.05 → not statistically significant
Interpretation examples from the model:
Factor | p-value | Meaning |
Female | 0.9289 | Gender does not significantly predict salary |
Grade | 7.5E–60 | Very strong predictor; highly significant |
Performance | 0.3149 | Not significant; effect uncertain |
Age | 1.33E–09 | Significant predictor |
Special case: Gender coefficient (female indicator)
A high p-value for the gender coefficient is often a positive indication, meaning:
After adjusting for legitimate factors, gender does not have a meaningful effect on pay.
The model finds no statistically significant gender-based disparities.
A low p-value would indicate that gender remains a significant predictor of salary, suggesting potential inequities that require investigation.
7. Interpretation of the Direct Method Coefficient Table
The Direct Method Model provides insight into how each factor affects salary:
Intercept (Estimate 7.7616)
Baseline salary level when all predictors are set to zero.
Female (Estimate 0.0016)
Effect is extremely small
Standard error (0.0181) is far larger → highly unreliable
p-value = 0.9289 → gender does not significantly influence pay
Conclusion: No detectable pay difference attributable to gender after controls
Grade (Estimate 0.0687)
Large effect
Very small standard error (0.0034) → highly precise
p-value extremely low → strongest predictor
Conclusion: Grade level is the primary driver of salary differences
Performance (Estimate 0.0069)
Modest effect
Standard error nearly equal → uncertain estimate
p-value = 0.3149 → not significant
Conclusion: Performance may not reliably explain salary differences in this dataset
Age (Estimate 0.0051)
Small but very precise effect
Very small standard error (0.0008)
Highly significant p-value
Conclusion: Age contributes meaningfully and reliably
8. Combined Interpretation: What the Model Tells Us
Based on all indicators:
Grade is the most significant factor driving pay variation
Age contributes meaningfully and predictably
Performance shows uncertain effect and may need further review (e.g., inconsistent scoring practices)
Gender is not a significant predictor of salary
The model overall has moderate strength, meaning it explains most—but not all—salary variation
Remaining unexplained variance may relate to:
variables not included
data quality
organizational pay practices needing refinement
9. Summary
The regression outputs demonstrate how different factors contribute to pay differences and help distinguish legitimate explanations from unexplained disparities. Positive and negative contributions show how structural factors widen or narrow gaps. R² values indicate model reliability, while standard errors and p-values determine the precision and significance of each variable.
The Direct Method Model indicates that job grade and age significantly explain salary variation, performance has uncertain impact, and gender does not statistically influence pay after adjustments.