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%.
Understanding the Coefficient of Determination (R²) in Regression Analysis
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. R² is referred to as the multiple correlation coefficient of determination in multiple linear regression analysis. 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 (SSerror) divided by the Total Sum of Squares (SStotal): R2= 1 – (SSerror / SStotal).
In multiple linear regression, when predictor variables are highly correlated with each other, they can inflate the explained variance. If multicollinearity exists in the regression model for any reason, you should interpret the Adjusted R Squared (Adjusted Coefficient of Determination) instead. 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 increases only when you add more predictor variables to the regression model. Inversely, the Coefficient of Non-Determination explains the amount of unexplained or unaccounted for variance between two variables. It also describes the variance between a set of predictor variables in an outcome variable. Where the Coefficient of Non-Determination is simply 1 – R2.