The Hazards of Extrapolation in Regression Analysis

Extrapolation of a fitted regression equation beyong the range of the given data can lead to seriously biased estimates if the assumed relationship does not hold in the region of extrapolation. This is demonstrated by some examples that lead to nonsensical conclusions. Extrapolation from fitted polynomials and from multiple regressions, extrapolation to other environments, and some related topics are also considered. The Inadequacy for extrapolation of the assumed form of the fitted relationship can not always be established by a statistical analysis. Thus, extrapolation can not be supported on statistical grounds alone; It must be justified by physical considerations. Even if the assumed form of the relationship is correct, the extrapolation, though not biased, may be quite imprecise. This can be especially serious when the region of extrapolation is far from the region of the given data, and/or the model is a high-order polynomial or a multiple regression developed from data involving high correlations among the Independent variables.