The correlation coefficient r is a single number, between −1 and +1, that measures how tightly a cloud of points hugs a straight line — and which way that line tilts. The fastest way to feel what it means is to move the cloud yourself. Drag any point on the scatterplot below; tap an empty spot to drop a new one. The number line, the fitted line and every figure on the page recompute from the dots the instant they move.
The scatterplot
Where r sits, from −1 to +1
Correlationdrag a point to begin
12
Points n12
Correlation r—
r² explained—
Line slope—
Reading r at a glance. The sign is the tilt: + means the line runs uphill (as x rises, y tends to rise), − means downhill. The size is the grip: near ±1 the points sit almost exactly on the line, near 0 they scatter into a shapeless blob. Try this: build a tidy uphill line, then drag one point far below the others — a single stray point can drag r down noticeably, because r feels every point’s distance from the trend.
Two things r cannot do. First, r only sees straight lines. The Curved preset has a strong, obvious relationship, yet r sits near zero — always look at the scatterplot, never trust r alone. Second, correlation is not causation. A large r means two variables move together in this sample; it says nothing about whether one causes the other, and a lurking third variable can manufacture a correlation between things that have no direct link at all.