PRESS statistic

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A statistic that provides an indication of the extent to which a multiple regression model can be generalized. This is achieved by fitting the model to every subset of n−1 of the n observed values, y1, y2,…, yn of the response variable. Let ȳ−j be the fitted value for yj based on the model that uses all the observed values except yj. The corresponding residual ε̂j is given by The PRESS statistic is where ȳ is the mean of the n observed values. The abbreviation PRESS is derived from predicted residual sum of squares. The statistic is an analogue of the R2 statistic (see coefficient of determination) and values close to 1 are preferable to those close to 0.

Subjects: Probability and Statistics.

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