Pearson Correlation Coefficient
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² Σ(yᵢ−ȳ)²). Linear correlation [−1, 1].
Result
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How to use this calculator
- Enter paired x and y values, comma-separated.
- Calculator pairs them in order.
- Read r, r², and regression line.
About this calculator
Pearson r measures linear correlation between two variables: r = +1 (perfect positive), 0 (none), −1 (perfect negative). r² = "coefficient of determination" — fraction of variance in y explained by linear relationship with x. Pearson assumes linear, normally-distributed data. For non-linear or rank-based associations, use Spearman ρ. Correlation does not imply causation — always.
Frequently asked
r vs. r²?+
r is the correlation; r² is "% variance explained". r = 0.7 means r² = 0.49 — only 49% explained even with strong correlation.
Pearson vs. Spearman?+
Pearson: linear relationships, continuous data. Spearman: ranks, monotonic but non-linear. Use Spearman for ordinal data.
Correlation = causation?+
No. Strong correlation might be coincidence, common cause, or reverse causation. Need experiment or causal inference to claim causation.
Outlier impact?+
Pearson is sensitive to outliers — one extreme point can flip r. Always plot data. Spearman is more robust.
Sample size minimum?+
r is unreliable with n < 10. For inference, n ≥ 30 + plot residuals.
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