Empirical model-building and response surfaces
An 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.
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THE USE OF GRADUATING FUNCTIONS
Appendix 2A A Theoretical Response Function
Appendix 3A Iteratively Reweighted Least Squares
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analysis of variance appropriate approximation assumptions bias calculated canonical analysis canonical form center points central composite design Chapter coded coefficients column composite design consider contours corresponding cube df MS F direction of steepest distribution example factorial design first-order design fitted equation fitted surface fractional factorial fractional factorial design given input variables investigation lack of fit least squares least-squares estimates levels linear main effects matrix maximum mean square mean squared error normal normal distribution observations obtained orthogonally blocked parameters plot possible predictor variables Pure error quadratic reaction region of interest regression relationship replicated residuals response function response surface response surface methodology rotatable runs second-order model shown in Figure shown in Table shows Source SS df standard errors stationary point Statistical steepest ascent sum of squares Suppose temperature textile data third-order tion transformation two-factor interactions values variance table vector yield zero