A detailed study using seven data sets, two standing tree volume estimating models, and a heightdiameter model showed that fit statistics and lack of fit statistics calculated directly from a regression model can be well estimated using simulations of cross validation or double cross validation. These results suggest that cross validation by data splitting and double cross validation provide little, if any, additional information in the process of evaluating regression models.
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Kozak et al. (2003) studied this question.
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