## 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. |

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### Contents

THE USE OF GRADUATING FUNCTIONS | 20 |

Appendix 2A A Theoretical Response Function | 32 |

Appendix 3A Iteratively Reweighted Least Squares | 89 |

Copyright | |

25 other sections not shown

### Common terms and phrases

additional analysis application appropriate approximation associated B₁ B₂ blocks calculated canonical center points Chapter choice coded coefficients column consider contours corresponding defined direction discussion distribution effects equation error estimates example experimental experiments factorial factorial design Figure first-order follows four fractional function give given illustration important indicated input interactions interest lack of fit least squares levels linear matrix maximum mean measure method normal Note observations obtained optimal original orthogonal parameters particular plot polynomial possible predictor variables produce quadratic reaction region regression relationship represent residuals response surface ridge rotatable runs scale second degree second-order shown shows signs Source standard Statist steepest ascent sum of squares Suppose Table Technometrics temperature transformation true values variables vector weight x₁ yield zero