This is fine if you are seeking a summary measure for a large population. The confidence interval tells you where the population mean is, with known probability. Siegel, in Practical Business Statistics, 2012 9.5 Prediction Intervals
Since α and β are not known, it seems reasonable to use their estimators A and B and thus use A + B x 0 as the predictor of a new response at input level x 0.Īndrew F. Now, it is clear that the best predictor of Y ( x 0 ) is its mean value α + β x 0. Suppose first that we are interested in a single value (as opposed to an interval) to use as a predictor of Y ( x 0 ), the response at level x 0. (On the other hand, if a series of experiments were to be performed at input level x 0, then we would probably want to estimate α + β x 0, the mean yield.) For instance, if an experiment is to be performed at temperature level x 0, then we would probably be more interested in predicting Y ( x 0 ), the yield from this experiment, than we would be in estimating the expected yield - E = α + β x 0. It is often the case that it is more important to estimate the actual value of a future response rather than its mean value. Ross, in Introduction to Probability and Statistics for Engineers and Scientists (Sixth Edition), 2021 9.4.4 Prediction interval of a future response
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