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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. [citation needed]
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.
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.
correlation. so that. where E is the expected value operator. Notably, correlation is dimensionless while covariance is in units obtained by multiplying the units of the two variables. If Y always takes on the same values as X, we have the covariance of a variable with itself (i.e. ), which is called the variance and is more commonly denoted as ...
Correlation function. Visual comparison of convolution, cross-correlation and autocorrelation. A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [ 1] If one considers the correlation function between random variables ...
In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, correlation functions measure quantitatively the extent to ...
In statistics, Spearman's rank correlation coefficient or Spearman's ρ, named after Charles Spearman [ 1] and often denoted by the Greek letter (rho) or as , is a nonparametric measure of rank correlation ( statistical dependence between the rankings of two variables ). It assesses how well the relationship between two variables can be ...
Coefficient of multiple correlation. In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables.