error sum of squares

In statistics, the error sum of squares (SSE), also known as the residual sum of squares, quantifies the unexplained variation in a statistical model. It is calculated by summing the squared differences between the observed values and the values predicted by the model. This squaring of differences is crucial because it prevents positive and negative errors from canceling each other out, ensuring that the overall error is accurately represented.

The formula for SSE is:
[ SSE = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 ]
where (y_i) is the observed value, (\hat{y}_i) is the predicted value, and (n) is the number of observations. A lower SSE indicates a better fit of the model to the data, meaning the model's predictions are closer to the actual observations. The SSE is a component of the analysis of variance and is used in calculating measures like the coefficient of determination ((r^2)) to assess the goodness of fit for regression models.123