Correlation Coefficient Formula

correlation coefficient is a numerical measure of some type of correlation, meaning a statistical relationship between two variables. The variables may be two columns of a given data set of observations, often called a sample, or two components of a multivariate random variable with a known distribution.

Several types of correlation coefficient exist, each with their own definition and own range of usability and characteristics. They all assume values in the range from −1 to +1, where ±1 indicates the strongest possible agreement and 0 the strongest possible disagreement. As tools of analysis, correlation coefficients present certain problems, including the propensity of some types to be distorted by outliers and the possibility of incorrectly being used to infer a causal relationship between the variables (for more, see Correlation does not imply causation).

A complimentary description for this term is that it is a statistic used for quantifying the strength of a linear association between variable inputs and outputs. It ranges from +1 (perfect positive correlation: higher input goes with higher output) to -1 (perfect negative correlation: higher input goes with lower output).


Wikipedia. Correlation Coefficient.