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
See it move
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
Variables
- sample covariance of X and Y
- sample standard deviation of X
- 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
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?