# What is the coefficient of correlation?

Author:
Harold Averkamp, CPA, MBA

## Definition of Coefficient of Correlation

In simple linear regression analysis, the coefficient of correlation (or correlation coefficient) is a statistic which indicates an association between the independent variable and the dependent variable. The coefficient of correlation is represented by “r” and it has a range of -1.00 to +1.00.

When the coefficient of correlation is a positive amount, such as +0.80, it means the dependent variable is increasing when the independent variable is increasing. It also means that the dependent variable is decreasing when the independent variable is decreasing. However, a high positive correlation does not guarantee there is a cause and effect relationship. (A negative amount indicates an inverse association…the dependent variable is decreasing when the independent variable is increasing and vice versa.)

A coefficient of correlation of +0.8 or -0.8 indicates a strong correlation between the independent variable and the dependent variable. An r of +0.20 or -0.20 indicates a weak correlation between the variables. When the coefficient of correlation is 0.00 there is no correlation.

## Relationship of Coefficient of Correlation to Coefficient of Determination

When the coefficient of correlation is squared, it becomes the coefficient of determination. This means that a coefficient of correlation of +0.80 will result in a coefficient of determination of 0.64 or 64%. (The coefficient of determination of 0.64 tells you that 64% of the change in the total of the dependent variable is associated with the change in the independent variable.) An r of +0.20 or -0.20 will result in an r-squared of only 4% (0.20 x 0.20), which means that only 4% of the change in the dependent variable is explained by the change in the independent variable.

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