Partial Correlation Calculator
Enter aligned X, Y and control Z percentage-point returns to calculate the remaining linear X–Y association after removing each series’ fitted linear contribution from Z. Pairwise coefficients, residual rows and the NIST F-reference probability stay visible without a significance, causal or trading verdict.
Enter X, Y and one control series
Every X, Y and Z row must describe the same observation period under the same preprocessing and cost convention.
Enter 5 to 500 values without percent signs; one complete aligned observation per row.
The Y row count and order must match X exactly.
Z must contain the same complete aligned rows; the calculator cannot decide whether it is a valid control.
Partial-correlation arithmetic
Entered Return Relationship Diagnostics 1.0.0.
On smaller screens, scroll horizontally to inspect the complete audit table.
| Row | X | Y | Control Z | X residual | Y residual | Residual product |
|---|
How one-control partial correlation is calculated
F = (n − 3)rXY.Z² ÷ (1 − rXY.Z²)
The model first calculates Pearson correlations for X with Y, X with Z and Y with Z from the same complete aligned rows. Those three coefficients enter the published one-control partial-correlation identity.
As an independent arithmetic reconciliation, X is fitted on Z and Y is fitted on Z with separate ordinary least-squares lines. The residuals are the portions not explained by each fitted linear relation with Z; their Pearson correlation must equal the direct partial coefficient.
The NIST reference statistic uses one numerator degree of freedom and n minus three denominator degrees of freedom. Its upper-tail F probability is displayed as a conditional null reference only, with no significant/not-significant or relationship decision.
Worked example from the audited fixture
The audited 10-row fixture has pairwise r(X,Y) = 0.95915656, r(X,Z) = 0.97032701 and r(Y,Z) = 0.97152497.
- After applying the one-control formula, partial correlation is 0.28730108. Correlating the separately residualized X and Y rows independently reproduces 0.28730108.
- The F reference is 0.62977632 with degrees of freedom 1 and 7, giving upper-tail p = 0.45349327. The page reports that number without declaring the remaining association significant, causal, useful or tradeable.
Reproduce it: select “Load audited example” above. The governed engine retains full precision and rounds only the visible interface.
How to interpret the result
- Compare the raw X–Y coefficient with the partial coefficient to see how the entered linear control changes the measured association.
- The residual correlation is an audit check on the direct formula, not a second independent piece of evidence.
- A smaller partial coefficient can indicate that Z accounts for part of the entered linear co-movement; it does not prove Z caused the original association.
- The p-value is calculated under the stated reference assumptions and is not the probability that the relationship is real, false or profitable.
- Changing the control series, sample window, return convention or alignment changes the question and can change the result.
Assumptions and limits
- Enter 5 to 500 complete aligned rows for X, Y and exactly one control Z series.
- The model controls only a fitted linear contribution and does not remove nonlinear effects, omitted variables, measurement error or reverse causality.
- A nearly perfect X–Z or Y–Z relation creates singular control geometry and is withheld.
- Serial dependence, heteroskedasticity, heavy tails, structural breaks, outliers and selected samples can invalidate the F reference.
- The calculator cannot judge whether Z is economically meaningful, temporally prior or suitable as a control.
- No significance, causality, validated relationship, predictive edge, forecast, grade, signal or recommendation verdict is generated.
Which relationship diagnostic answers which question?
Pearson correlation, partial correlation, directional regression and a historical multi-pair matrix describe different evidence. The comparison keeps direction, control variables, uncertainty and source boundaries visible instead of presenting one coefficient as a universal dependence or strategy-validation score.
| Tool | Evidence entered | Primary output | Main boundary |
|---|---|---|---|
| Correlation Confidence Interval | Two aligned series | Symmetric Pearson coefficient plus Fisher limits | No causal, stable-dependence or forecast verdict. |
| Partial Correlation | X, Y and one control Z | Residual X–Y linear association after controlling Z | One linear control does not remove all confounding. |
| Linear Regression | Predictor X and response Y | Directional slope, intercept, residual scale and coefficient intervals | No alpha/beta label, extrapolation or hedge advice. |
| Historical Correlation Matrix | Governed multi-pair market history | Many pairwise historical coefficients | Source window and currency coverage differ from manual inference. |
Frequently asked questions
- It measures the remaining linear association between entered X and Y after removing each series’ fitted linear contribution from one entered control Z.
- Version 1.0.0 supports exactly one complete aligned control series so the published NIST one-control formula and residual audit remain transparent.
- The model calculates the direct three-correlation identity and independently correlates residuals from fitting X on Z and Y on Z; the two results must reconcile.
- It is an upper-tail reference probability under the stated null and assumptions, not the probability that a relationship is true, useful or profitable.
- A constant series or nearly perfect X-Z or Y-Z linear relation makes the control denominator singular, so the calculator fails closed.
- No. It removes only the fitted linear contribution of the entered Z series and cannot address omitted variables, nonlinear effects or causal timing.
- No. It cannot determine whether Z is economically meaningful, measured correctly, temporally appropriate or selected after viewing the data.
- No. The page generates no significance, causality, predictive-edge, strategy-validation, forecast, grade, signal or recommendation verdict.
Sources and methodology
- NIST — Partial Correlation — Published one-control formula and F-reference probability.
- NIST — Correlation — Published pairwise Pearson coefficient used by the partial identity.
Version 1.0.0 was locked only after the formulas and assumptions were checked against the cited NIST material. Canonical fixtures were independently recomputed with SciPy 1.13.1 before comparison with the browser engine. The calculator performs arithmetic locally and does not upload the entered observations.
Continue the controlled-association review
Verify the paired return evidence before interpreting relationships
Reconcile the exact statement window, sampling frequency, timestamps, missing rows, realized P&L, spread, commission, financing, currency conversion and preprocessing across every series. Correct relationship arithmetic cannot repair mismatched, selected or cost-inconsistent evidence.
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