gives the correlation between the vectors v1 and v2.


gives the correlation matrix for the matrix m.


gives the correlation matrix for the matrices m1 and m2.


gives the correlation matrix for the multivariate symbolic distribution dist.


gives the (i,j)^(th) correlation for the multivariate symbolic distribution dist.



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Basic Examples  (3)

Correlation between two vectors:

Real values:

Correlation matrix for a matrix:

Real values:

Correlation matrix for two matrices:

Real values:

Scope  (12)

Data  (7)

Exact input yields exact output:

Approximate input yields approximate output:

Correlation between vectors of complexes:

Works with large arrays:

SparseArray data can be used:

Find the correlation of WeightedData:

Find the correlation for data involving quantities:

Distributions and Processes  (5)

Correlation for a continuous multivariate distribution:

Correlation for a discrete multivariate distribution:

Correlation for derived distributions:

Data distribution:

Correlation matrix for a random process at times s and t:

Correlation matrix for TemporalData at times and :

Applications  (3)

Compute the correlation of two financial time series:

Correlation can be used to measure linear association:

Correlation can only detect monotonic relationships:

HoeffdingD can be used to detect a variety of dependence structures:

Properties & Relations  (7)

The correlation matrix is symmetric and positive semidefinite:

A correlation matrix is a covariance matrix scaled by standard deviations:

Correlation and AbsoluteCorrelation agree for zero mean and unit marginal variances:

SpearmanRho is Correlation applied to ranks:

CorrelationFunction for a process is the off-diagonal entry in the correlation matrix:

Correlation and Covariance are the same for standardized vectors:

The diagonal elements of a correlation matrix are equal to 1:

Introduced in 2007
Updated in 2010