This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.


Correlation coefficients


r = corrcoef(X)
r = corrcoef(X,Y)



Matrix where each row is an observation and each column is a variable.


Matrix where each row is an observation and each column is a variable.


corrcoef for financial time series objects is based on the MATLAB® corrcoef function. See corrcoef.

r=corrcoef(X) calculates a matrix r of correlation coefficients for an array X, in which each row is an observation, and each column is a variable.

r=corrcoef(X,Y), where X and Y are column vectors, is the same as r=corrcoef([X Y]). corrcoef converts X and Y to column vectors if they are not; that is, r = corrcoef(X,Y) is equivalent to r=corrcoef([X(:) Y(:)]) in that case.

If c is the covariance matrix, c= cov(X), then corrcoef(X) is the matrix whose (i,j) 'th element is ci,j/sqrt(ci,i*c(j,j)).

[r,p]=corrcoef(...) also returns p, a matrix of p-values for testing the hypothesis of no correlation. Each p-value is the probability of getting a correlation as large as the observed value by random chance, when the true correlation is zero. If p(i,j) is less than 0.05, then the correlation r(i,j) is significant.

[r,p,rlo,rup]=corrcoef(...) also returns matrices rlo and rup, of the same size as r, containing lower and upper bounds for a 95% confidence interval for each coefficient.

[...]=corrcoef(...,'PARAM1',VAL1,'PARAM2',VAL2,...) specifies additional parameters and their values. Valid parameters are:

  • 'alpha' — A number from 0 through 1 to specify a confidence level of 100*(1-ALPHA)%. Default is 0.05 for 95% confidence intervals.

  • 'rows' — Either 'all' (default) to use all rows, 'complete' to use rows with no NaN values, or 'pairwise' to compute r(i,j) using rows with no NaN values in column i or j.

The p-value is computed by transforming the correlation to create a t-statistic having N – 2 degrees of freedom, where N is the number of rows of X. The confidence bounds are based on an asymptotic normal distribution of 0.5*log((1 + r)/(1 – r)), with an approximate variance equal to 1/(N – 3). These bounds are accurate for large samples when X has a multivariate normal distribution. The 'pairwise' option can produce an r matrix that is not positive definite.


collapse all

This example shows how to generate random data having correlation between column 4 and the other columns.

x = randn(30,4);       % uncorrelated data
x(:,4) = sum(x,2);     % introduce correlation
f = fints((today:today+29)', x);  % create a fints object using x
[r,p] = corrcoef(x);    % compute sample correlation and p-values
[i,j] = find(p<0.05);  % find significant correlations
[i,j]                  % display their (row,col) indices
ans = 

     4     1
     3     2
     2     3
     1     4

Class support for inputs X,Y: float: double and single.

Introduced before R2006a

Was this topic helpful?