Fitting models to data: interaction versus polynomial? Your choice!

John A. Cornell, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Polynomials are widely used for fitting models empirically to data. Low-degree polynomials (specifically, degrees 1, 2, and at most 3) have stood the test of time by proving their versatility when it comes to fitting a wide variety of different surface shapes over limited regions of interest. However, when faced with modeling a surface over an experimental region whose boundaries extend beyond some localized neighborhood or limited-sized region of interest, a polynomial of degree 2, or even of degree 3, may not be adequate. For this situation we propose fitting an interaction model which is a reduced form of higher-degree polynomial. Some examples of actual experiments are presented to illustrate the improvement in fit by an interaction model over that of a standard polynomial, even for response surfaces with uncomplicated shapes.

Original languageEnglish (US)
Pages (from-to)2531-2555
Number of pages25
JournalCommunications in Statistics - Theory and Methods
Issue number11
StatePublished - 1996


  • Adequacy of fit
  • Experimental region
  • Interaction model
  • Local approximation
  • Model misspecification
  • Polynomial
  • Response surface

ASJC Scopus subject areas

  • Statistics and Probability


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