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Statistical classification is the problem of identifying the sub-population to which new observations belong, where the identity of the sub-population is unknown, on the basis of a training set of data containing observations whose sub-population is known. Therefore these classifications will show a variable behavior which can be studied by statistics.

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Is there a way to find the specific number of predictors necessary for my caret random fores...

You can add features until the increase is not more than some error bars. More importantly, make sure you make this decision before you evaluate on your final test set (e.g. with either nested cross-v …
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