Definition

The correlation coefficient is usually defined by the formula

It is however easier to understand if written in terms of standardised versions of X and Y,

The correlation coefficient is a kind of average of the products of the z-scores.

How does r relate to the shape of a scatterplot?

The following properties of r explain in general terms how its value is related to the strength of a relationship in any particular scatterplot.

−1  ≤  r  ≤  +1