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In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related.
[1] [2] Both describe the degree to which two random variables or sets of random variables tend to deviate from their expected values in similar ways. If X and Y are two random variables, with means (expected values) μ X and μ Y and standard deviations σ X and σ Y, respectively, then their covariance and correlation are as follows: covariance
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a statistical relationship between two variables. [a] The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.
The sign of the covariance of two random variables X and Y. In probability theory and statistics, covariance is a measure of the joint variability of two random variables. [1] The sign of the covariance, therefore, shows the tendency in the linear relationship between the variables.
Two random variables with nonzero correlation are said to be correlated. Similar to covariance, the correlation is a measure of the linear relationship between random variables. The correlation coefficient between the random variables X {\displaystyle X} and Y {\displaystyle Y} is
In time series analysis and statistics, the cross-correlation of a pair of random process is the correlation between values of the processes at different times, as a function of the two times. Let ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} be a pair of random processes, and t {\displaystyle t} be any point in time ( t {\displaystyle t} may be ...
Correlation functions between the same random variable are autocorrelation functions. However, in statistical mechanics, not all correlation functions are autocorrelation functions. For example, in multicomponent condensed phases, the pair correlation function between different elements is often of interest.