R-Squared

The coefficient of determination for a regression equation is commonly referred to as R-squared, or just R2. R2 is often described as the goodness of fit, and measures how well the regressors or independent variables explain the regressand or dependent variables. R2 can range from 0 to 1. If R2 is equal to one then the regression model completely explains all of the variability in the dependent variable. If R2 is equal to zero then the regression does not explain any of the variability in the dependent variable. For a univariate regression, R2 is equal to the correlation between the dependent and independent variable, squared.

For a regression equation, Y = α + βX + ε, if we define the total sum of squares, TSS, the explained sum of squares, ESS, and the residual sum of squares, RSS, as follows:

Then R2 can be calculated as follows: