##
**Empirical model-building and response surfaces.**
*(English)*
Zbl 0614.62104

Wiley Series in Probability and Mathematical Statistics. New York etc.: John Wiley & Sons. XIV, 669 p. £43.25 (1987).

As the title indicates this book concerns itself with empirical model building in which response surface methodology plays a central role. There are fifteen chapters in all. Chapters 1 and 2 deal with various fundamental concepts such as the iterative nature of experimental learning processes, empirical versus mechanistic models and approximating response functions by polynomials in one or more variables. Chapter 3 reviews the algebra and the geometry of least squares theory. Chapters 4 and 5 discuss factorial designs, Yates algorithm for \(2^ k\) factorials, blocking and fractionating \(2^ k\) factorials and Plackett-Burman designs. Chapter 6 treats the method of steepest ascent for maximizing the response with or without constraints.

Fitting second order models, examining the adequacy of fit and the need for higher order terms are discussed in Chapter 7. The use of transformations and the choice of the response metric to validate distributional assumptions are contained in Chapter 8. Chapters 9, 10 and 11 deal with the exploration of maxima and the analysis of ridge systems using second order response surfaces. Connections between mechanistic models and empirical models is the main topic of Chapter 12. Chapter 13 deals with the role of variance, bias and lack of fit in the choice of a design.

Orthogonal designs and rotatable designs are discussed in Chapter 14 along with an explanation and the role of A-, D- and E-optimality criteria. The final chapter (Chapter 15) treats in detail the considerations that must go into the choice of a response surface design in practice.

There are numerous examples in the text and several exercises at the end of most chapters. Answers to the exercises are given at the end along with various statistical tables and a long list of references. Experimenters and statisticians alike will find this book to be a valuable addition to their library.

Fitting second order models, examining the adequacy of fit and the need for higher order terms are discussed in Chapter 7. The use of transformations and the choice of the response metric to validate distributional assumptions are contained in Chapter 8. Chapters 9, 10 and 11 deal with the exploration of maxima and the analysis of ridge systems using second order response surfaces. Connections between mechanistic models and empirical models is the main topic of Chapter 12. Chapter 13 deals with the role of variance, bias and lack of fit in the choice of a design.

Orthogonal designs and rotatable designs are discussed in Chapter 14 along with an explanation and the role of A-, D- and E-optimality criteria. The final chapter (Chapter 15) treats in detail the considerations that must go into the choice of a response surface design in practice.

There are numerous examples in the text and several exercises at the end of most chapters. Answers to the exercises are given at the end along with various statistical tables and a long list of references. Experimenters and statisticians alike will find this book to be a valuable addition to their library.

Reviewer: H.Iyer

### MSC:

62K99 | Design of statistical experiments |

62K15 | Factorial statistical designs |

62J99 | Linear inference, regression |

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

62K05 | Optimal statistical designs |

62J05 | Linear regression; mixed models |