Coefficient of Determination

• To determine how much variance two variables share, or how much variance is explained, or accounted for, by a set of variables (predictors) in an outcome variable.

• Values can range from 0.00 to 1.00, or 0 to 100%.

• In terms of regression analysis, the coefficient of determination is an overall measure of the accuracy of the regression model.

• In simple linear regression analysis, the calculation of this coefficient is to square the r value between the two values, where r is the correlation coefficient.

• In a multiple linear regression analysis, R² is known as the multiple correlation coefficient of determination.

• It helps to describe how well a regression line fits (a.k.a., goodness of fit). An R² value of 0 indicates that the regression line does not fit the set of data points and a value of 1 indicates that the regression line perfectly fits the set of data points.

• By definition, R² is calculated by one minus the Sum of Squares of Residuals (SS_error) divided by the Total Sum of Squares (SS_total):  R² = 1 – (SS_error / SS_total).

• In the case of a multiple linear regression, if the predictor variables are too correlated with one another (referred to as multicollinearity), this can cause the coefficient of determination to be higher in value. 

• If, for whatever reason, there is multicollinearity in the regression model, the Adjusted R Squared (Adjusted Coefficient of Determination) should be interpreted.  The Adjusted R² can take on negative values, but should always be less than or equal to the Coefficient of Determination.  Note: The Adjusted R² will only increase if more predictors variables are added to the regression model.

• Inversely, the Coefficient of Non-Determination explains the amount of unexplained, or unaccounted for, variance between two variables, or between a set of variables (predictors) in an outcome variable. Where the Coefficient of Non-Determination is simply 1 – R².