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Pearson Correlation for Paired Data

Calculate linear association from complete paired numeric lists, reject constant inputs and preserve the distinction between correlation and causation.

Use this result well

Inputs that matter
X values, Y values
Output to expect
Pearson r
  • Check the units and required inputs before comparing results.
  • Keep the assumptions with a copied result so you can reproduce the calculation later.
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Reference & details

How it works

Pearson correlation of complete pairs

r = Σ[(x−mean(x))(y−mean(y))] / √[Σ(x−mean(x))² Σ(y−mean(y))²] Unweighted sample Pearson correlation. Constant X or Y has undefined correlation and produces an input error. Outliers, nonlinearity, restricted range, time dependence and group mixtures affect interpretation. The square of r is not a universal model R-squared; its regression identity needs a fitted simple linear model with an intercept on the same sample.

Updated: September 2026

Example Scenarios

Calculate linear correlation from paired numeric observations, with explicit rejection of invalid entries and constant variables.

Common Mistakes to Avoid

Applying pearson correlation of complete pairs outside its stated assumptions

Constant X or Y has undefined correlation and produces an input error. Outliers, nonlinearity, restricted range, time dependence and group mixtures affect interpretation. The square of r is not a universal model R-squared; its regression identity needs a fitted simple linear model with an intercept on the same sample.

FAQ

No. It means no linear correlation in the supplied sample; nonlinear relationships may remain.

No. Study design and an appropriate inferential model are separate.

About Pearson Correlation for Paired Data

Calculate linear association from complete paired numeric lists, reject constant inputs and preserve the distinction between correlation and causation. Choose the mode that matches your measurements or study design, enter the stated units and keep the method and limits with the result.