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Polynomial regression is a common technique for estimating conditional mean functions of unknown form. Increasing the order of the polynomial increases the flexibility of the estimated function. This note shows with an example how these estimated polynomials, even (perhaps especially) higher-order ones, display undesirable nonlocal effects. That is, values of the response corresponding to a particular value or range of the predictor may have a large and undesirable influence on the predicted response at a very different value of the predictor.
The American Statistician © 1998 American Statistical Association