Multiple Regression and Coefficient of Determination (R-Squared)

  • For a multiple regression model, this value represents the percentage of total variation in Y that is explained by the regression equation.
  • The value is between 0 and 1.
  • R-squared has a mathematical relationship with TSS, SSE, and RSS.
  • R2 = RSS/TSS = (TSS-SSE)/TSS = 1- (SSE/TSS)
  • The coefficient of determination alone does not indicate that a model is well specified, for example you could have more independent variables than necessary and the R2 will still be high – in this case your model would be not be considered parsimonious.
  • Adjusted R2 = an alternate measure and will always be smaller than R2