# Anova: PRESS¶

The Predicted Residual Sum of Squares for the model. A measure of how well a particular model fits each point in the design. The coefficients for a new model are calculated with one point “deleted”. The new model’s prediction is subtracted from the “deleted” observation to find the predicted residual. This is done for each data point. The predicted residuals are squared and added together to form the PRESS.

$$e_{-i} = y_i - \hat{y}_{-i} = \frac{e_i}{1 - h_{ii}}$$

$$PRESS = \begin{matrix} n\\ \sum\\ i=1 \end{matrix}(e_{-i})^2$$

$$e_{-i}$$ is a deletion residual computed by fitting a model without the ith run then predicting the ith observation with the resulting model.

$$e_i$$ is the residual for each observation left-over from the model fit to all the data.

$$h_{ii}$$ is the leverage of the run in the design.