= Residuals = '''Residuals''' are the difference between a prediction and an observed value. <> ---- == Description == A residual is the difference between a predicted value (as by a model) and an actually observed value. Note that there's substantial mixing of terms with [[Analysis/Error|error]]. Errors are a distinct concept: the difference between a true value and its measurement. Nonetheless, terminology is varied. * '''Sum of squared errors''' ('''SSE''') actually means the sum of squared residuals. * '''Residual sum of squares''' ('''RSE''') means the same thing. * Do not mix up with SSR (sum of squared regression), which often comes up in the same context. ''R^2^ = 1 - SSR/SST'' where SST is the total variation in the dependent variable. * Regarding '''mean squared error''' ('''MSE''')... * In the context of [[Statistics/OrdinaryLeastSquares|regressions]], MSE usually means SSE divided by the number of [[Statistics/DegreesOfFreedom|degrees of freedom]] (i.e., ''n - k - 1''). * In other contexts, MSE usually means a theoretical second moment. For example, when considering the properties of an estimator and how it differs from the true random variable. * '''Root mean squared error''' ('''RMSE''') is the square root of MSE in any context. ---- CategoryRicottone