Interaction models as alternatives to low-order polynomials

John A. Cornell, Douglas Montgomery

Research output: Contribution to journalArticle

15 Scopus citations


One of the most popular classes of models that people fit empirically to data is the class of polynomials. One reason for this is, over limited-sized regions of interest, lower-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. 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 a higher-degree polynomial. Several 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)163-176
Number of pages14
JournalJournal of Quality Technology
Issue number2
StatePublished - Apr 1 1996


  • Factorial Design
  • Interactions
  • Lack of Fit
  • Misspecified Model
  • Polynomial Model
  • Response Surface Methodology

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

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