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What is the coefficient of determination?

The coefficient of determination is a statistic which indicates the percentage change in the amount of the dependent variable that is "explained by" the changes in the independent variables.

For example, a manufacturer may have found through simple linear regression analysis involving 15 monthly observations that 64% of the change in the total cost of electricity (the dependent variable) was associated with the change in the monthly production machine hours (the independent variable). In this example the coefficient of determination is 0.64 or 64%.

The coefficient of determination is symbolized by r-squared, where r is the coefficient of correlation. Hence, a coefficient of determination of 0.64 or 64% means that the coefficient of correlation was 0.8 or 80%. (The range for the coefficient of correlation is -1 to +1, and therefore the range for the coefficient of determination is 0 to +1.)

It is important to note that a high coefficient of determination does not guarantee that a cause-and-effect relationship exists. However, a cause-and-effect relationship between the independent variable and the dependent variable will result in a high coefficient of determination.