Pearson Correlation Coefficient
r = Σ(xᵢ−x̄)(yᵢ−ȳ) / √(Σ(xᵢ−x̄)² Σ(yᵢ−ȳ)²). Linear correlation [−1, 1].
Result
Pearson r
0.991117
Very strong positive correlation (r² = 0.9823).
- n pairs6
- x̄3.5000
- ȳ7.0000
- Σ(x−x̄)(y−ȳ)38.0000
- Σ(x−x̄)²17.5000
- Σ(y−ȳ)²84.0000
- r (Pearson)0.991117
- r² (variance explained)0.982313
- Regression slope2.1714
- Regression intercept-0.6000
- StrengthVery strong
Step-by-step
- Means: x̄ = 3.500, ȳ = 7.000.
- Numerator = Σ(x−x̄)(y−ȳ) = 38.000.
- Denominator = √(17.500 × 84.000) = 38.341.
- r = 38.000 / 38.341 = 0.991117.
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 is the correlation; r² is "% variance explained". r = 0.7 means r² = 0.49 — only 49% explained even with strong correlation.
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