Correlation

Correlation measures how strongly and in what direction two variables move together, summarised as a number from -1 to +1.

A value near +1 means the two tend to rise and fall together; near -1 means one rises as the other falls; and near 0 means they have no consistent linear relationship. The sign tells you the direction, the size tells you the strength. It is one of the most common ways to ask whether two measurements are linked.

How correlation appears in a chart

Correlation is read off a scatter plot, where each point is one pair of values. A tight upward band of points signals a strong positive correlation; a tight downward band, a strong negative one; a shapeless cloud, little or none. The more the points hug an imaginary straight line, the closer the correlation is to +1 or -1. A loose, scattered cloud sits near 0.

A concrete example

Suppose you plot study hours against test score for a group of students and the points form a clear upward band — more hours, higher scores — with a correlation of about +0.8. That is strong and positive: knowing someone studied more lets you predict a higher score fairly well. But it does not prove studying caused the higher scores; a third factor like motivation could drive both. This is the famous caution that correlation is not causation — a strong number describes a pattern, not a mechanism.

Related terms

A regression line is the best-fit line drawn through correlated points, and a trend is the direction they suggest over time. Correlation is best seen visually — see the scatter plot guide for how the point cloud reveals it.