Standard errors for the eigenvalues in second-order response surface models

Søren Bisgaard, Bruce Ankenman

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


In the interpretation of the geometry of second-order response surface models, standard errors and confidence intervals for the eigenvalues of the second-order coefficient matrix play an important role. In this article, we propose a new method for estimating the standard errors, and hence approximate confidence intervals, of these eigenvalues. The method is simple in both concept and execution. It involves the refitting of a full quadratic model after rotating the coordinate system to coincide with the canonical axes. The estimated standard errors of the pure quadratic terms from this refitting are then used as approximate standard errors of the eigenvalues. Because this approach is based on the canonical form, it is geometrically intuitive and easily taught. Our method is intended as a way for practitioners to get quick estimates of the standard errors of the eigenvalues. In our justification of the approach, we show that it is equivalent to using the delta method proposed by Carter, Chinchilli, and Campbell.

Original languageEnglish (US)
Pages (from-to)238-246
Number of pages9
Issue number3
StatePublished - Aug 1996


  • Canonical analysis
  • Confidence intervals
  • Delta method
  • Response surface methodology

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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