If a linear regression model is severely overfitted, the calculated prediction interval can be pretty tight, but the model won't generalize well to unseen data, so the prediction interval can be totally wrong in this case, is this correct?
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2 Answers
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Yes. The prediction interval includes the error remaining after the regression. If you overfit, this error will be too low, and therefore the prediction interval too tight.
Put another way: Suppose your R-square should really be 70%, but because of overfitting it is 90%. Your prediction interval will be too small.
answered Feb 21, 2017 at 21:13
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I wouldn't say so. Prediction intervals should be accurate depending on the amount of data you put in and if your model well describes what you are trying to model, or in other words has low bias. Over-fitting doesn't have anything to do with it really.
