\rho_P(x,y) = \frac{{\rm cov}(x,y)}{\sigma(x) \sigma(y)}

where

and	finite arrays of -variable and -variable values
	covariance between -variable and -variable
,	standard deviation of -variable and -variable

Pearson correlation coefficient ranges between -1 and 1 and indicates how accurately the two variables can be approximated by a linear correlation:

y_i = a \, x_i + b, \quad \forall \, i=1..n

with a certain pick on and .

Maximum value relates to perfect linear correlation with (see also Fig. 1)
Zero value relates to absence of correlation between and (see also Fig. 2)
Minimum value relates to perfect linear correlation with (also called anti-correlation) (see also Fig. 3)


Fig. 1. Highly correlated variables	Fig. 2. Poorly correlated variables	Fig. 3. Highly anti-correlated variables

See also