Correlation

Correlation coefficient measures the strength and direction of the linear association between two variables, scaled from −1 (perfect negative relationship) to +1 (perfect positive relationship).

Also known ascorrelation coefficient · r

ByHoang TruongUpdated June 30, 2026

What it is

See it move

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A scatter plot with a fitted line plots advertising spend in €'000s on the x-axis against sales in €'000s on the y-axis, with a Pearson correlation coefficient of approximately 0.997. This near-perfect positive linear association means that as ad spend rises, sales rise almost in direct proportion. The visual notes the bounded scale of r, from −1 to +1, with values near zero indicating the absence of any linear relationship.

The formula

LaTeX

r = \frac{\text{Cov}(X, Y)}{s_X \cdot s_Y}

Variables

$C o v (X, Y)$: sample covariance of X and Y
$s_{X}$: sample standard deviation of X
$s_{Y}$: sample standard deviation of Y

Bounded between −1 and +1. Values near ±1 indicate strong linear association; values near 0 indicate weak or no linear relationship.

Check yourself

PracticeCORE

A data analyst reports a Pearson correlation coefficient of r = −0.92 between monthly hours of preventive machine maintenance and the number of production defects recorded. A colleague concludes that scheduling as much maintenance as possible will eliminate defects almost entirely. What is the main flaw in this reasoning?

Select an answer to check your understanding.