Questions tagged [correlation]

Correlation is a measure of relationship between two or more mathematical variables or measured data values. It refers to any of a broad class of statistical relationships involving dependence. This refers to any situation in which random variables do not satisfy probabilistic independence. Tough correlation can refer to any departure of two or more random variables from independence, technically it refers to any of several more specialized types of relationship between mean values. There are several correlation coefficients, often denoted ρ or r, measuring the degree of correlation.

The most common of these is the Pearson correlation coefficient, which is commonly called simply "the correlation coefficient". It is obtained by dividing the covariance of the two variables by the product of their standard deviations.

This parameter is sensitive only to a linear relationship between two variables (which may exist even if one is a nonlinear function of the other). The numerator of cor(X,Y) is known as the covariance between X and Y.

The Pearson correlation is +1 in the case of a perfect positive (increasing) linear relationship (correlation), −1 in the case of a perfect decreasing (negative) linear relationship (anticorrelation). The closer the coefficient is to either −1 or 1, the stronger the correlation between the variables. As it approaches zero there is less of a relationship and we say that the data is uncorrelated.

Other correlation coefficients have been developed to be more robust than the Pearson correlation – that is, more sensitive to nonlinear relationships. Mutual information can also be applied to measure dependence between two variables.

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