Interaction models as alternatives to low-order polynomials

John A. Cornell, Douglas Montgomery

Research output: Contribution to journalArticlepeer-review

20 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 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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