Among the properties I discussed in the previous post, there were a few that I could not explain. In particular, I could not explain the distinction between MeanPredictionBands and SinglePredictionBands. I knew that they were computing confidence intervals for a predicted value of yhat given an observation xo = {1, X1, X2, X4}, but not much more.

Okay, I knew that the MeanPredictionConfidenceIntervalTable listed confidence intervals using the MeanPredictionBands, for yhat for each of the observations in the given data. Similarly, the SinglePredictionConfidenceIntervalTable listed confidence intervals for yhat, using the SinglePredictionBands and the given observations.

The “bands” can be used on any data, however, not just the original observations.

Well, I now know how the two “bands” are computed… and, therefore, I know the distinction between them.

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