Empirical Correlation Coefficient

The Correlation of a data sequence.

r(x,t)=c(x,t)V(x)V(t)r(\boldsymbol{x}, \boldsymbol{t})=\frac{c(\boldsymbol{x}, \boldsymbol{t})}{\sqrt{V(\boldsymbol{x}) V(\boldsymbol{t})}}

with Sample Covariance and Sample Variance.

Important

It measures the deviation from linear dependence.

In the case of a Linear Regression the sign of the empirical correlation coefficient is the slope of the regression line.