Correlation
Correlation[v1,v2]
gives the correlation between the vectors v1 and v2.
Correlation[m]
gives the sample correlation matrix for observations in 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) correlation for the multivariate symbolic distribution dist.
Details

- Correlation[v1,v2] gives Pearson's correlation coefficient between v1 and v2.
- The lists v1 and v2 must be the same length.
- Correlation[v1,v2] 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 m1 and an
×
matrix m2, Correlation[m1,m2] is a
×
matrix of the correlations between columns of m1 and columns of m2.
- Correlation works with SparseArray objects.
- Correlation[dist,i,j] gives Covariance[dist,i,j]/(σi σj), where σi is the i
component of the standard deviation of dist.
- Correlation[dist] gives a correlation matrix with the (i,j)
entry given by Correlation[dist,i,j].
Examples
open allclose allBasic Examples (3)
Scope (12)
Data (7)
Exact input yields exact output:
Approximate input yields approximate output:
Correlation between vectors of complexes:
SparseArray data can be used:
Find the correlation of WeightedData:
Distributions and Processes (5)
Correlation for a continuous multivariate distribution:
Correlation for a discrete multivariate distribution:
Correlation for derived distributions:
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:
Text
Wolfram Research (2007), Correlation, Wolfram Language function, https://reference.wolfram.com/language/ref/Correlation.html (updated 2010).
CMS
Wolfram Language. 2007. "Correlation." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2010. https://reference.wolfram.com/language/ref/Correlation.html.
APA
Wolfram Language. (2007). Correlation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Correlation.html