From AMS Glossary
- When used without further qualification, the statistical term correlation usually refers to simple, linear correlation between two variables x, y and is measured by the product-moment coefficient of correlation ρ or its sample estimate r defined as follows, where the respective population mean values of x and y are denoted by ξ and ζ, the respective standard deviations by σ(x) and σ( y), and where E is the expected value:The product moment E[(x - ξ) (y - ζ)] is usually called the covariance of x and y. In connection with correlation, the word "simple" is used in contradistinction to other qualifiers such as "multiple" or "partial." The word "linear" refers to a linear relationship between the two variables, or more precisely, to a linear approximation of the regression function of either variate with respect to the other.
See autocorrelation, multiple correlation, partial correlation.