In probability theory and statistics, correlation, also called correlation coefficient, is a numeric measure of the strength of linear relationship between two random variables. In general statistical usage, correlation or co-relation refers to the departure of two variables from independence. In this broad sense there are several coefficients, measuring the degree of correlation, adapted to the nature of data. A number of different coefficients are used for different situations. The best known is the Pearson prod ...

Including:

• Correlation - Pearson's product-moment coefficient
• Correlation - Mathematical properties
• Correlation - The sample correlation
• Correlation - Non-parametric correlation coefficients
• Correlation - Other measures of dependence among random variables
• Correlation - Copulas and correlation
• Correlation - Correlation matrices
• Correlation - Correlation does not imply causation

Read more here: » Correlation: Encyclopedia - Correlation

Correlation - Mathematical properties. The correlation ρX, Y between two random variables X and Y with expected values μX and μY and standard deviations σX and σY is defined as: Since μX = E(X), σX2 = E(X2) − E2(XSee also:

Correlation, Correlation - Pearson's product-moment coefficient, Correlation - Mathematical properties, Correlation - The sample correlation, Correlation - Non-parametric correlation coefficients, Correlation - Other measures of dependence among random variables, Correlation - Copulas and correlation, Correlation - Correlation matrices, Correlation - Correlation does not imply causation

Read more here: » Correlation: Encyclopedia II - Correlation - Pearson's product-moment coefficient

The correlation matrix of n random variables X1, ..., Xn is the n  ×  n matrix whose i,j entry is corr(Xi, Xj). If the measures of correlation used are product-moment coefficients, the correlation matrix is the same as the covariance matrix of the standardized random variables Xi /SD(Xi) for i = 1, ..., n. Consequent ...

See also:

Correlation, Correlation - Pearson's product-moment coefficient, Correlation - Mathematical properties, Correlation - The sample correlation, Correlation - Non-parametric correlation coefficients, Correlation - Other measures of dependence among random variables, Correlation - Copulas and correlation, Correlation - Correlation matrices, Correlation - Correlation does not imply causation

Read more here: » Correlation: Encyclopedia II - Correlation - Correlation matrices