Coefficient of Determination

The coefficient of determination is a statistical measurement that examines how differences in one variable can be explained by the difference in a second variable, when predicting the outcome of a given event.

• 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 R²value 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 R²will 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.