Analysis results
Partial regression plot
Click observations to select them. Selected rows can be excluded temporarily for sensitivity analysis.
Selected observation
Coefficient and diagnostic results
| Term | Coefficient | Std. error | t | p | 95% CI | Std. beta | VIF |
|---|
| Row | Residual | Leverage | Studentized | Cook's D | DFFITS | DFBETAS | Status |
|---|
Sensitivity comparison
| Model | Rows | Coefficient | Std. error | p-value | Partial R² | Adjusted R² |
|---|
All-predictor comparison
| Rank | Predictor | Coefficient | p-value | Partial R² | Incremental R² |
|---|
Interpretation
Formula used
First, regress the target on all selected control predictors. Save those target residuals for the vertical axis. This removes variation explained by the controls.
Next, regress the focal predictor on the same control predictors. Save those focal residuals for the horizontal axis. Their fitted slope equals the focal coefficient from the complete multiple regression model.
Target residual: eᵧ = y − ŷ(controls) Predictor residual: eₓ = x − x̂(controls) Partial regression: eᵧ = βₓeₓ + ε Partial R² = t² / (t² + df)
How to use
Paste data with headers or upload a supported text file. Parse the dataset and confirm the preview. Select one numeric target and one numeric focal predictor.
Choose controls, transformations, model settings, and diagnostic options. Press calculate to residualize both variables and fit the adjusted relationship. Inspect coefficients, bands, VIF values, and influential observations.
Click plotted points to review their original rows. Exclude selected observations only for sensitivity analysis. Export results, residual data, charts, or a printable report.
Example data
The included sample studies house price after adjusting floor area for property age, bedrooms, and city distance. The plot estimates floor area’s unique linear relationship with price. Influential properties remain visible for diagnostic review.
| Property | Price | Floor area | Age | Bedrooms | Distance |
|---|---|---|---|---|---|
| H01 | 258 | 132 | 18 | 3 | 8.2 |
| H02 | 318 | 168 | 7 | 4 | 5.4 |
| H03 | 221 | 119 | 26 | 3 | 10.1 |
Assumptions and limitations
The method assumes a correctly specified linear conditional relationship. Ordinary inference also assumes independent errors with stable variance. Robust fitting reduces outlier sensitivity but changes classical inference.
High multicollinearity can make adjusted coefficients unstable. Transformations and interactions should follow a defensible modeling reason. A partial relationship never proves a causal effect.
Frequently asked questions
What is a partial regression plot?
It plots residualized target values against residualized focal-predictor values. Both residualizations use identical control predictors. The slope matches the focal multiple-regression coefficient.
Why is it called an added-variable plot?
It shows what the focal predictor adds beyond existing controls. The remaining horizontal variation is unexplained by those controls. The remaining vertical variation is similarly adjusted.
Does a steep slope imply causation?
No, the plot describes an adjusted statistical relationship. Unmeasured confounding and model misspecification can remain. Causal conclusions require stronger study design assumptions.
What does partial R-squared mean?
It measures unique target variation explained by the focal predictor. The measure conditions on all selected controls. Larger values indicate stronger incremental explanatory contribution.
Why inspect Cook's distance?
Cook's distance summarizes each observation’s influence on fitted coefficients. Large values identify useful sensitivity checks. They do not automatically justify deleting observations.
What does a high VIF indicate?
A high VIF signals strong predictor redundancy. Coefficients may become unstable and imprecise. Consider data quality, model purpose, and variable definitions.
Can categorical controls be used?
Yes, text controls are dummy encoded automatically. The first observed level becomes the reference. Encoded terms appear within the coefficient table.
When should robust fitting be used?
Use it when unusual residuals strongly affect ordinary estimates. Compare robust and ordinary results carefully. Robust fitting does not repair every model problem.
Why might the calculator reject my data?
The model needs more complete rows than fitted parameters. Singular predictors can also prevent inversion. Review warnings and simplify redundant model terms.
Generated calculator file timestamp: 2026-08-10 12:55:04