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Mathematica > Data Manipulation > Statistical Data Analysis > Descriptive Statistics > Correlation >

Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Descriptive Statistics > Correlation >

BUILT-IN MATHEMATICA SYMBOL

Correlation

gives the correlation between the vectors

and

Correlation[m]
gives the correlation matrix for the matrix m.

Correlation

gives the correlation matrix for the matrices

and

Correlation[dist]
gives the correlation matrix for the multivariate symbolic distribution dist.

Correlation

gives the

correlation for the multivariate symbolic distribution dist.

MORE INFORMATION

Correlation gives Pearson's correlation coefficient between and .

The lists and must be the same length.

Correlation is equivalent to Covariance[v₁, v₂]/(StandardDeviation[v₁]StandardDeviation[v₂]).

For a matrix m with columns, Correlation[m] is a × matrix of the correlations between columns of m.

For an × matrix and an × matrix , Correlation is a × matrix of the correlations between columns of and columns of .

Correlation works with SparseArray objects.

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:

Correlation between two vectors:

In[1]:=

Out[1]=

Real values:

In[2]:=

Out[2]=

Correlation matrix for a matrix:

In[1]:=

Out[1]=

Real values:

In[2]:=

Out[2]=

Correlation matrix for two matrices:

In[1]:=

Out[1]//MatrixForm=

Real values:

In[2]:=

Out[2]=

Scope (4)

Correlations for machine-precision reals:

Use arbitrary precision:

Find the covariance between vectors of complexes:

Compute the correlation matrix for a SparseArray:

Applications (1)

Compute the correlation between two financial time series:

Properties & Relations (2)

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

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