Pearson Correlation
Linear correlation from paired data.
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Formula
r = Σ(x−x̄)(y−ȳ) ÷ √[Σ(x−x̄)² Σ(y−ȳ)²]
Pearson r measures linear association between −1 and 1. R² is fraction of variance explained.
Worked example
Four points with mostly linear trend yield r around 0.8 — check calculator for exact value.
Where this can give the wrong answer
- Needs variation in both variables.
- Outliers strongly pull r.
- Correlation ≠ causation.
FAQ
- At least two pairs; inference needs more — four here is illustrative only.