Pearson's Correlation Coefficient

The correlation coefficient r (also called Pearson's product moment correlation after Karl Pearson) is calculated by

The correlation coefficient may take any value between -1.0 and +1.0.

Assumptions:
 

• linear relationship between x and y
• continuous random variables
• both variables must be normally distributed
• x and y must be independent of each other

Please note, that the equation above can be replaced by an equivalent formula which avoids to use the means and is therefore much faster to calculate:

The correlation coefficient stands in close relationship to linear regression. The square of r is called the goodness of fit and denotes the portion of total variance explained by the regression model. The following  interactive example  lets you adjust the correlation coefficient to any arbitrary value.