Predicted Residual Sum of Squares
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A Predicted Residual Sum of Squares is a point statistic for a residual sum of squares.
- AKA: PRESS.
- See: Cross-Validation Algorithm, Actual Residual Sum of Squares, Regression Analysis, Overfitting.
References
2014
- (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/PRESS_statistic Retrieved:2014-10-19.
- In statistics, the predicted residual sum of squares (PRESS) statistic is a form of cross-validation used in regression analysis to provide a summary measure of the fit of a model to a sample of observations that 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] A fitted model having been produced, each observation in turn is removed and the model is refitted using the remaining observations. The out-of-sample predicted value is calculated for the omitted observation in each case, and the PRESS statistic is calculated as the sum of the squares of all the resulting prediction errors:
: [math]\displaystyle{ \operatorname{PRESS} =\sum_{i=1}^n (y_i - \hat{y}_{i, -i})^2 }[/math]
Given this procedure, the PRESS statistic can be calculated for a number of candidate model structures for the same dataset, with the lowest values of PRESS indicating the best structures. Models that are over-parameterised (over-fitted) would tend to give small residuals for observations included in the model-fitting but large residuals for observations that are excluded.
- In statistics, the predicted residual sum of squares (PRESS) statistic is a form of cross-validation used in regression analysis to provide a summary measure of the fit of a model to a sample of observations that 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] A fitted model having been produced, each observation in turn is removed and the model is refitted using the remaining observations. The out-of-sample predicted value is calculated for the omitted observation in each case, and the PRESS statistic is calculated as the sum of the squares of all the resulting prediction errors:
- ↑ Allen, D. M. (1974), "The Relationship Between Variable Selection and Data Augmentation and a Method for Prediction," Technometrics, 16, 125–127
- ↑ 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