corrcoef

Correlation coefficients

📝 Syntax

• R = corrcoef(M)

📥 Input argument

• M - a vector or matrix

📤 Output argument

• R - Correlation coefficients of M.

📄 Description

R = corrcoef(M) returns the matrix of correlation coefficients for M, where the columns of M represent random variables and the rows represent observations.

The Pearson correlation coefficient between variables $X$

and $Y$

is: $r_{XY} = \frac{\text{cov}(X,Y)}{\sigma_X \sigma_Y} = \frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^n (x_i - \bar{x})^2 \sum_{i=1}^n (y_i - \bar{y})^2}}$

where $\bar{x}$

and $\bar{y}$

are the sample means, and $\sigma_X$

, $\sigma_Y$

are the standard deviations.

The correlation coefficient ranges from -1 to +1, where -1 indicates perfect negative correlation, +1 indicates perfect positive correlation, and 0 indicates no linear correlation.

💡 Example

M = [4 -7 3; 1 4 -2; 10 7 9];
R = corrcoef(M)

🔗 See also

cov, mean.

🕔 History

Version	📄 Description
1.0.0	initial version