Pearson's r measures the strength and direction of a LINEAR relationship between two numeric variables, ranging from -1 (perfect negative) to +1 (perfect positive). It does not measure non-linear relationships — two variables can be perfectly related by a curve and still show r close to 0.
Does a strong correlation mean one variable causes the other?+−
No. Correlation shows association, not causation. A strong r can arise from reverse causation, a confounding third variable, or coincidence — establishing causation requires a controlled experiment, not correlation on observational data alone.
What does r² tell me that r doesn’t?+−
r² (the coefficient of determination) is the proportion of variance in one variable explained by its linear relationship with the other, expressed as a percentage. An r of 0.7 gives r² = 0.49 — meaning about 49% of the variation is associated with the other variable, leaving 51% explained by other factors.
Why should I look at the scatter plot, not just the r value?+−
Anscombe's quartet — four data sets with nearly identical r values but wildly different actual shapes — is the classic demonstration that summary statistics alone can mislead. Always look at the scatter plot alongside the number.