Residualplots 74 Normaland half-normal plots 77 2. 3. 10.
TRANSFORMATIONS OF VARIABLES 80 2. 3. 11. WEIGHTED LEAST SQUARES 82
2. 4. Bibliography 84 Appendix A. 2. 1. Basic equation ofthe
analysis ofvariance 84 Appendix A. 2. 2. Derivation of the
simplified formulae (2. 1 0) and (2. 11) 85 Appendix A. 2. 3. Basic
properties ofleast squares estimates 86 Appendix A. 2. 4. Sums
ofsquares for tests for lack offit 88 Appendix A. 2. 5. Properties
ofthe residuals 90 3. DESIGN OF REGRESSION EXPERIMENTS 96 3. 1.
Introduction 96 3. 2. Variance-optimality of response surface
designs 98 3. 3. Two Ievel full factorial designs 106 3. 3. 1.
DEFINITIONS AND CONSTRUCTION 106 3. 3. 2. PROPERTIES OF TWO LEVEL
FULL FACTORIAL DESIGNS 109 3. 3. 3. REGRESSION ANALYSIS OF DAT A
OBT AlNED THROUGH TWO LEVEL FULL F ACTORIAL DESIGNS 113 Parameter
estimation 113 Effects of factors and interactions 116 Statistical
analysis of individual effects and test for lack of fit 118 3. 4.
Two Ievel fractional factorial designs 123 3. 4. 1. CONSTRUCTION OF
FRACTIONAL F ACTORIAL DESIGNS 123 3. 4. 2. FITTING EQUATIONS TO
DATA OBTAlNED BY FRACTIONAL F ACTORIAL DESIGNS 130 3. 5. Bloclung
133 3. 6. Steepest ascent 135 3. 7. Second order designs 142 3. 7.
1. INTRODUCTION 142 3. 7. 2. COMPOSITE DESIGNS 144 Rotatable
central composite designs 145 D-optimal composite designs 146
Hartley' s designs 146 3. 7. 3.
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