Pearson Correlation Coefficient

Correlation Coefficient

Definition

The coefficient coefficient, , is generally used only for linear correlations. It indicated the strength and direction of a linear relationship.

The value of ranges from to , with being a perfect negative correlation, being no correlation, and being a perfect positive correlation.

Formula

where:

is the sample size
are the individual sample points indexed with
(the sample mean); same with

(see summation notation)

Alternative forms of this formula:

Coefficient of Determination

Definition

The correlation of determination, , is used for any function of best fit (linear and non-linear). It measures how well the curve of best fit matches the points on a scatter plot.

The value of ranges from to . An of means the curves matches the points perfectly, and means the curve does not match the points at all.

Important

The value tells us the percentage of variation in the dependent variable, as predicted by the independent variable (e.g if , then of the variation in is predicted by variation in from the equation of the function of best fit)