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# 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[v1, v2] gives Pearson's correlation coefficient between v1 and v2.
• The lists v1 and v2 must be the same length.
• For a matrix m with p columns Correlation[m] is a p×p matrix of the covariances between columns of m.
• For an n×p matrix m1 and an n×q matrix m2 Correlation[m1, m2] is a p×q matrix of the correlations between columns of m1 and columns of m2.
Correlation between two vectors:
Real values:
Correlation matrix for a matrix:
Real values:
Correlation matrix for two matrices:
Real values:
Correlation between two vectors:
 Out[1]=
Real values:
 Out[2]=

Correlation matrix for a matrix:
 Out[1]=
Real values:
 Out[2]=

Correlation matrix for two matrices:
 Out[1]//MatrixForm=
Real values:
 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:
A correlation matrix is a covariance matrix scaled by standard deviations:
The diagonal elements of a correlation matrix are equal to 1:
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