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.

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

\(PRESS=\sum_{i=1}^{n}(e_{-i})^2\)

e_-i is a deletion residual computed by fitting a model without the i^th run then predicting the i^th 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.