Correlation coefficient
R=corrcoef(X) R=corrcoef(x,y)
a n-by-nbvar matrix of doubles, where nbvar is the number of variables
a n-by-1 or 1-by-n matrix of doubles
a n-by-1 or 1-by-n matrix of doubles
a 1-by-1 or nbvar-by-nbvar matrix of doubles, the linear correlation coefficient.
corrcoef(x,y)
returns the linear correlation
coefficient of x and y.
This is sometimes called Pearson's product-moment coefficient.
The correlation coefficient between x and y is defined by
corrcoef(X)
returns the linear correlation
coefficient between coumns of X.
In this case, the correlation coefficient R and the
covariance matrix C are related by
for i,j=1,2,...,nbvar.
The corrcoef function is compatible with Matlab.
// Source : [1], Example 2.6a x = [24.2;22.7;30.5;28.6;25.5;32;28.6;26.5;25.3;26;24.4;24.8;20.6;.. 25.1;21.4;23.7;23.9;25.2;27.4;28.3;28.8;26.6]; y = [25;31;36;33;19;24;27;25;16;14;22;23;20;25;25;23;27;30;33;32;35;24]; expected = 0.4189 R = corrcoef ( x , y ) // Draw the scatter plot scf(); plot(x,y,"bo") // Source : [1], Example 2.6b x = [12 16 13 18 19 12 18 19 12 14]; y = [73 67 74 63 73 84 60 62 76 71]; R = corrcoef ( x , y ) expected = -0.7638 // For properly chosen data, the linear correlation // coefficient can be close to zero. n = 1000; x = linspace(-%pi/2,3*%pi/2,n); y = sin(x)+distfun_normrnd(0,0.5,1,n); R = corrcoef ( x , y ) // This does not imply that there is no dependency // between the variables scf(); plot(x,y,"bo") // See with one argument [X,txt] = getdata(1); R=corrcoef(X) expected=[ 1. 0.4615668 0.6934031 0.4615668 1. 0.3544662 0.6934031 0.3544662 1. ]; // Compute a correlation matrix // X is uncorrelated X = distfun_normrnd(0,1,30,4); // Put some correlation X(:,4) = sum(X,"c"); R=corrcoef(X) // See that X4 is correlated with other Xi, // since the 4th column and 4th row have higher // values. | ![]() | ![]() |
[1] "Introduction to probability and statistics for engineers and scientists.", Chapter 2 Descriptive statistics, Sheldon Ross
[2] http://en.wikipedia.org/wiki/Correlation_and_dependence
[3] Pearson product-moment correlation coefficient, http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient