Covariance and correlation

thumb|400px|right|Several sets of (x, y) points, with the Pearson correlation coefficient of x and y for each set. The correlation reflects the noisiness and direction of a linear relationship (top row), but not the slope of that relationship (middle), nor many aspects of nonlinear relationships (bottom). N.B.: the figure in the center has a slope of 0 but in that case, the correlation coefficient is undefined because the variance of Y is zero.

thumb|upright|The sign of the covariance of two random variables X and Y

nonparametric measure of rank correlation

latin phrase

measure of covariance of components of a random vector

thumb|400px|Visual comparison of convolution, cross-correlation and [[autocorrelation. For the operations involving function , and assuming the height of is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point. Also, the vertical symmetry of is the reason f*g and f \star g are identical in this example.]]

way of inferring information from cross-covariance matrices

concept in probability theory and statistics

type of statistic

general linear model which blends ANOVA and regression

in statistics, a generalization to multiple dimensions of the chi-squared distribution or the gamma distribution

correlation as a function of spatial or temporal distance

atmospheric measurement technique

any of several statistics that measure an ordinal association

scale attenuation effect in statistics

matrix element computed by inserting a product of operators between two states in quantum field theory

measure of spatial autocorrelation

intraclass

factors associated with unlawful behavior

Measure of a system's order

statistical measure of association

measure of the relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample

Function in probability theory

partial correlation of a time series with its lagged values

function that describes the distribution of galaxies in the universe

statistics computed from a sample of data

In probability and statistics, given two stochastic processes \left\{X_t\right\} and \left\{Y_t\right\}, the cross-covariance is a function that gives the covariance of one process with the other at pairs of time points. With the usual notation \operatorname E for the expectation operator, if the processes have the mean functions \mu_X(t) = \operatorname \operatorname E[X_t] and \mu_Y(t) = \operatorname E[Y_t], then the cross-covariance is given by