Correlation

Correlation[v1,v2]

gives the correlation between the vectors v1 and v2.

Correlation[m]

gives the correlation matrix for the matrix m.

Correlation[m1,m2]

gives the correlation matrix for the matrices m1 and m2.

Correlation[dist]

gives the correlation matrix for the multivariate symbolic distribution dist.

Correlation[dist,i,j]

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

Details

Examples

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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
 (6.0)
 |
Updated in 2010
 (8.0)