Correlation coefficient (Pearson r)

strength of a straight-line relationship

r = Σ(x − x̄)(y − ȳ) / √(Σ(x − x̄)² · Σ(y − ȳ)²)

A number from −1 to +1 that describes how closely two variables follow a straight line. +1 is a perfect rising line, −1 a perfect falling line and 0 no linear relationship. In simple regression r² equals R².

Correlation does not mean causation: both variables may follow a third factor.

Calculate it

Regression and Correlation: Simple and multiple regression, correlation, R², p-values and residual plot.

Related terms

• R² (coefficient of determination): share of the variation the model explains
• p-value: probability of the observed result under the null hypothesis