Pearson’s correlation coefficient r measures how closely two variables follow a straight-line relationship. It ranges from −1 (a perfect downward line) through 0 (no linear relationship) to +1 (a perfect upward line). Roughly, |r| above 0.7 is considered strong and below 0.3 weak, though what counts as meaningful varies by field.
Squaring r gives the coefficient of determination r², the share of the variation in Y that the straight line accounts for. An r of 0.8 means r² = 0.64, so 64% of the variation is explained and 36% is left over.
The regression (least-squares) line is the straight line that makes the sum of squared vertical distances from the points as small as possible. Use it to predict Y from X within the range of your data; extrapolating far beyond it is risky.
Frequently asked questions
Does a strong correlation prove causation?
No. Two variables can move together because a third factor drives both, or by coincidence. Ice-cream sales and drowning deaths are correlated because both rise in hot weather.
Can r be near 0 even if the variables are related?
Yes. Pearson’s r only detects straight-line patterns. A U-shaped relationship can have r ≈ 0. Always look at a scatter plot.
What does the p-value tell me?
It tests whether the true population correlation could be zero. A small p-value (say below 0.05) suggests the correlation in your sample is unlikely to be due to chance alone.