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Pearson Correlation

Linear correlation coefficient r

📊Pearson Correlation Coefficient

Pearson's r measures the strength and direction of the linear relationship between two continuous variables. r ranges from −1 (perfect negative) to +1 (perfect positive); r=0 means no linear relationship.

  1. 1r = Σ(xi−x̄)(yi−ȳ) / √[Σ(xi−x̄)² × Σ(yi−ȳ)²]
  2. 2Positive r: both variables increase together
  3. 3Negative r: one increases as the other decreases
  4. 4r² = proportion of variance in Y explained by X
r = 0.85 between height and weight=Strong positive correlation · r²=0.72Height explains 72% of weight variation

Fun Fact

Correlation does not imply causation. Ice cream sales and drowning rates are strongly correlated — both peak in summer — but ice cream does not cause drowning.

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