PRESS statistic

In statistics, the predicted residual sums of squares (PRESS) statistic is used in regression analysis to provide a summary measure of the fit of a model to a sample of observations. These observation were not themselves used to estimate the model. It is calculated as the sums of squares of the prediction residuals for those observations.^[1][2][3]

Having produced a fitted model, each of predictors is removed and the model is refitted to the remaining points. The predicted value is calculated at the excluded point and the PRESS statistic is calculated as the sum of all the resulting errrors.

$\sum_{i=1}^n (y_i - \hat{y}_{i, -i})^2$^[4]

References

1. ^ http://www.statsoft.com/textbook/statistics-glossary/p/button/p/ Statsoft:StatSoft.com Electronic Statistics Textbook - Statistics Glossary (Accessed September 2011)
2. ^ Allen, D. M. (1974), "The Relationship Between Variable Selection and Data Augmentation and a Method for Prediction," Technometrics, 16, 125–127
3. ^ Tarpey, Thaddeus (2000) A Note on the Prediction Sum of Squares Statistic for Restricted Least Squares, The American Statistician, Vol. 54, No. 2, May, pp. 116–118
4. ^ http://www.oga-lab.net/RGM2/func.php?rd_id=qpcR:PRESS R Graphical Manual:Allen's PRESS (Prediction Sum-Of-Squares) statistic, aka P-square (Accessed Sep 2011)

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