Empirical Model-Building and Response SurfacesAn innovative discussion of building empirical models and the fitting of surfaces to data. Introduces the general philosophy of response surface methodology, and details least squares for response surface work, factorial designs at two levels, fitting second-order models, adequacy of estimation and the use of transformation, occurrence and elucidation of ridge systems, and more. Some results are presented for the first time. Includes real-life exercises, nearly all with solutions. |
Contents
THE USE OF GRADUATING FUNCTIONS | 20 |
Appendix 2A A Theoretical Response Function | 32 |
Appendix 3A Iteratively Reweighted Least Squares | 89 |
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Common terms and phrases
analysis of variance approximation B₁ B₂ Biometrics Biometrika canonical analysis canonical form center points central composite design coded coefficients column composite design consider contours cube degree polynomial design of experiments df MS F distribution Draper example experimental design experiments factorial design fitted equation fractional factorial fractional factorial designs lack of fit least squares levels linear main effects Math matrix maximum mean square method nonlinear normal observations obtained order rotatable designs orthogonal orthogonally blocked parameters plot predictor variables Pure error quadratic reaction region of interest regression replicated residuals response function response surface methodology ridge runs second degree second order second-order model Source SS df standard errors Statist steepest ascent sum of squares Suppose Technometrics temperature third-order transformation two-factor interactions values variance table vector x₁ Y₁ yield z₁ Z₂ zero