# R-Squared

The coefficient of determination for a regression equation is commonly referred to as R-squared, or just *R*^{2}. *R*^{2} is often described as the goodness of fit, and measures how well the regressors or independent variables explain the regressand or dependent variables. *R*^{2} can range from 0 to 1. If *R*^{2} is equal to one then the regression model completely explains all of the variability in the dependent variable. If *R*^{2} is equal to zero then the regression does not explain any of the variability in the dependent variable. For a univariate regression, *R*^{2} is equal to the correlation between the dependent and independent variable, squared.

For a regression equation, *Y* = *α* + *β**X* + *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 *R*^{2} can be calculated as follows: