Correlation measures the relation between two or more variables. It is given by the correlation coefficient

The correlation ranges from r = -1 to r = +1. The following plots give examples of different correlations:


A correlation coefficient of r = +1 means that there is a totally positive linear relation, thus high values on the X-axis are associated with high values on the Y-axis.

If the correlation is r = -1 high values on the X-axis are associated with low values on the Y-axis thus the relationship is negative linear.

If the x and y values are totally independent the correlation coefficient is r = 0.

Correlation is based on linear regression. For the given values of x and y two linear regressions are calculated: one for x as the independent variable and y as the dependent and another one vice versa. This yields two regression lines with the slopes of and . The geometric mean of theses lines is the correlation coefficient r.


Ulrike Burkard, Dec. 17., 2001