Pearson correlation coefficient

Not to be confused with Coefficient of determination.

"PMCC" redirects here. For other uses, see PMCC (disambiguation).

Several sets of (x, y) points, with the correlation coefficient of x and y for each set. The correlation reflects the strength and direction of a linear relationship (top row), but not the slope of that relationship (middle row), nor many aspects of nonlinear relationships (bottom row). N.B.: the figure in the center has a slope of 0 but in that case the correlation coefficient is undefined because the variance of Y is zero.

In statistics, the Pearson correlation coefficient (PCC), also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), or simply the unqualified correlation coefficient, is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. A key difference is that unlike covariance, this correlation coefficient does not have units, allowing comparison of the strength of the joint association between different pairs of random variables that do not necessarily have the same units. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations. As a simple example, one would expect the age and height of a sample of children from a school to have a Pearson correlation coefficient significantly greater than 0, but less than 1 (as 1 would represent an unrealistically perfect correlation).