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SinglePredictionBands versus MeanPredictionBands from NonlinearModelFit

GROUPS:
Hello, from my statistic lectures I know the term confidence and prediction interval, whereas the confidence interval is smaller than the prediction interval. If I plot the mean and single prediction bands with the same confidence level in Mathematica, than the mean prediction band is smaller than the single prediction band interval.

Anyone who can explain me what are the differences between the “SinglePredictionBands” and “MeanPredictionBands” which are standard properties from NonlinearModelFit? Or is it just a different terminology for confidence and prediction interval used by Mathematica? If no it would be useful if someone can tell me which properties I have to apply for the confidence and the prediction interval.

Thanks for your support.

Markus
POSTED BY: Markus Linder
Answer
1 year ago
Yes, "MeanPredictionConfidenceIntervals" / "MeanPredictionBands" and "SinglePredictionConfidenceIntervals" / "SinglePredictionBands" is exactly different terminology for confidence and prediction intervals / bands respectively.

The following section of the documentation may be of interest

Statistical Model Analysis

as well as some demonstrations, for example

Mean and Single Prediction Bands for a Nonlinear Model

Confidence and Prediction Bands
POSTED BY: Ilian Gachevski
Answer
1 year ago
Thanks Ilian, that was exactly the confirmation I need.

Regards, Markus
POSTED BY: Markus Linder
Answer
1 year ago