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| Preface to the Third Edition | |
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| Preface to the Second Edition | |
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| Introduction | |
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| The Original Mixture Problem | |
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| General Remarks About Response Surface Methods | |
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| A Factorial Experiment or a Mixture Experiment? | |
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| An Historical Perspective | |
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| References and Recommended Reading | |
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| Questions | |
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| The Original Mixture Problem: Designs and Models for Exploring the Entire Simplex Factor Space | |
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| The Simplex-Lattice Designs | |
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| The Canonical Polynomials | |
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| The Polynomial Coefficients as Functions of the Responses at the Points of the Lattices | |
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| Estimating the Parameters in the {q, m} Polynomials | |
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| Properties of the Estimate of the Response, y(x) | |
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| A Three-Component Yarn Example Using a {3, 2} Simplex-Lattice Design | |
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| The Analysis of Variance Table | |
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| Analysis of Variance Calculations of the Yarn Elongation Data | |
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| The Plotting of Individual Residuals | |
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| Testing the Degree of the Fitted Model: A Quadratic Model or Planar Model? | |
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| Some Comments on the Use of Check Points for Testing Model Lack of Fit | |
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| A Numerical Example Illustrating the Use of Check Points for Testing Lack of Fit | |
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| The Simplex-Centroid Design and the Associated Polynomial Model | |
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| An Application of a Four-Component Simplex-Centroid Design. Blending Chemical Pesticides for Control of Mites | |
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| Axial Designs | |
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| Comments on a Comparison Made Between an Augmented Simplex-Centroid Design and a Full Cubic Lattice for Three Components Where Each Design Contains Ten Points | |
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| Reparameterizing Scheffe's Mixture Models to Contain a Constant ([beta subscript 0]) Term: A Numerical Example | |
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| Questions to Consider at the Planning Stages of a Mixture Experiment | |
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| Summary | |
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| References and Recommended Reading | |
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| Questions | |
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| Least-Squares Estimation Formulas for the Polynomial Coefficients and Their Variances: Matrix Notation | |
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| Cubic and Quartic Polynomials and Formulas for the Estimates of the Coefficients | |
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| The Partitioning of the Sources in the Analysis of Variance Table When Fitting the Scheffe Mixture Models | |
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| The Use of Independent Variables | |
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| Transforming from the q Mixture Components to q-1 Mathematically Independent Variables | |
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| A Numerical Example: Sensory Flavor Rating of Fish Patties | |
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| Defining a Region of Interest Inside the Simplex: An Ellipsoidal Region | |
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| A Numerical Illustration of the Inverse Transformation from the Design Variables to the Mixture Components | |
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| Enlarging the Unit Spherical Region of Interest | |
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| Some Discussion on Design Strategy When Fitting Response Surfaces | |
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| Rotatable Designs | |
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| A Second-Order Rotatable Design for a Four-Component System | |
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| Defining a Cuboidal Region of Interest in the Mixture System | |
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| Summary | |
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| References and Recommended Reading | |
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| Questions | |
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| An Alternative Transformation from the Mixture Component System to the Independent Variable System | |
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| A Form of the Orthogonal Matrix T | |
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| Multiple Constraints on the Component Proportions | |
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| Lower-Bound Restrictions on Some or All of the Component Proportions | |
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| Introducing L-Pseudocomponents | |
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| A Numerical Example of Fitting an L-Pseudocomponent Model | |
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| Upper-Bound Restrictions on Some or All of the Component Proportions | |
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| An Example of the Placing of an Upper Bound on a Single Component: The Formulation of a Tropical Beverage | |
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| Introducing U-Pseudocomponents | |
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| The Placing of Both Upper and Lower Bounds on the Component Proportions | |
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| Formulas for Enumerating the Number of Extreme Vertices, Edges, and Two-Dimensional Faces of the Constrained Region | |
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| Some Procedures for Calculating the Coordinates of the Extreme Vertices of a Constrained Region | |
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| Multicomponent Constraints | |
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| Some Examples of Designs for Constrained Mixture Regions: CONVRT and CONAEV Programs | |
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| The Use of Symmetric-Simplex Designs for Fitting Second-Order Models in Constrained Regions | |
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| Multiple Lattices for Major and Minor Component Classifications | |
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| Categorizing the Mixture Components: An Ellipsoidal Region of Interest | |
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| A Numerical Example of a Categorized Component Experiment | |
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| Summary | |
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| References and Recommended Reading | |
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| Questions | |
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| An Orthogonal Matrix for the Categorized-Components Problem | |
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| The Relationship Between the Coefficients of the Terms in the Double-Scheffe Model (4.82) and the Interaction Model (4.83) | |
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| The Analysis of Mixture Data | |
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| Techniques Used in the Analysis of Mixture Data | |
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| Test Statistics for Testing the Usefulness of the Terms in the Scheffe Polynomials | |
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| Model Reduction | |
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| An Example of Reducing the System from Three to Two Components | |
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| A Criterion for Selecting Subsets of the Terms in the Scheffe Models | |
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| A Numerical Example Illustrating the Integrated Mean-Square Error Criterion | |
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| Screening Components | |
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| A Seven-Component Octane-Blending Experiment: An Exercise in Model Reduction | |
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| Other Techniques Used to Measure Component Effects | |
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| The Slope of the Response Surface Along the Component Axes | |
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| A Numerical Example Illustrating the Slope Calculations for a Three-Component System: Studying the Flavor Surface Where Peanut Meal Is Considered a Substitute for Beef in Sandwich Patties | |
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| Leverage and the Hat Matrix | |
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| A Three-Component Propellant Example | |
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| Summary | |
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| References and Recommended Reading | |
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| Questions | |
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| The Derivation of the Moments of the Simplex Region | |
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| Other Mixture Model Forms | |
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| The Inclusion of Inverse Terms in the Scheffe Polynomials | |
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| Fitting Gasoline Octane Numbers Using Inverse Terms in the Model | |
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| An Alternative Model Form for Modeling the Additive Blending Effect of One Component in a Multicomponent System | |
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| A Biological Example on the Linear Effect of a Powder Pesticide in Combination with Two Liquid Pesticides Used for Suppressing Mite Population Numbers | |
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| Other Models That Are Homogeneous of Degree One | |
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| The Use of Ratios of Components | |
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| Cox's Mixture Polynomials: Measuring Component Effects | |
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| An Example Illustrating the Fits of Cox's Model and Scheffe's Polynomial | |
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| Log Contrast Models | |
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| A Numerical Example Illustrating the Testing of Inactivity and Additivity Effects of the Components in a Three-Component System Using Log Contrast Models | |
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| Octane Blending Models | |
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| A Numerical Example Illustrating the Calculations Required for Obtaining the Research and Motor Octane Prediction Equations for a Group of Blends | |
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| Fitting a Slack-Variable Model | |
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| A Numerical Example Illustrating the Fits of Different Reduced Slack-Variable Models: Tint Strength of a House Paint | |
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| Summary | |
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| References and Recommended Reading | |
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| Questions | |
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| The Form of the Multiplier Matrix B[subscript 2] for Expressing the Parameters in Cox's Quadratic Model as Functions of the Parameters in Scheffe's Model | |
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| Estimation Equations for Coefficients That Are Subject to Linear Restrictions | |
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| The Inclusion of Process Variables in Mixture Experiments | |
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| Designs Consisting of Simplex-Lattices and Factorial Arrangements | |
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| A Numerical Example of a Fish Patty Experiment: Studying Blends of Three Fish Species Prepared with Three Processing Factors | |
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| Testing the Component Blending Properties and the Effects of the Process Variables When the Set of Mixture Blends Is Embedded in the Processing Conditions | |
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| A Numerical Example of a Three-Component by Two-Process Variable Split-Plot Experiment: Fitting a Quadratic Mixture Model in the Presence of Interacting Process Variables | |
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| A Reparameterization of the Combined Model Form for Measuring the Effects of the Process Variables: An Example of Model Reduction | |
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| The Use of Fractional Designs in the Process Variables | |
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| A Numerical Example of the Fit of a Combined Model to Data Collected on Fractions of the Fish Patty Experimental Design | |
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| Computer-Aided Fractionation of Lattice Designs | |
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| Mixture-Amount Experiments | |
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| Process Variables and q-1 Mixture-Related Variables | |
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| A Numerical Example Involving Three Mixture Components and One Process Variable | |
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| Questions Raised and Recommendations Made When Fitting a Combined Model Containing Mixture Components and Other Variables | |
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| Summary | |
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| References and Recommended Reading | |
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| Questions | |
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| A Generalized Least-Squares Solution for Fitting the Mixed Model in the Mixture Components and Process Variables to Data from a Split-Plot Experiment | |
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| Additional Topics | |
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| Block Designs for Mixture Experiments | |
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| Symmetric-Simplex Block Designs for Fitting the Scheffe Second-Order Model | |
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| An Example of Orthogonal Blocking Using a Symmetric-Simplex Design | |
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| Constructing Orthogonal Blocks Using Latin Squares | |
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| Weighted Versus Unweighted Least-Squares Estimates of the Parameters in the Scheffe Models | |
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| Some Comments on Design Criteria and Some Results Using the ACED Program | |
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| Constant Prediction Variance on Concentric Triangles for Three-Component Systems | |
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| Altering the Terms in the Scheffe-Type Models to Improve the Accuracy and/or Stability of the Coefficient Estimates | |
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| Collinearity Problems Resulting from Performing Experiments in Highly Constrained Regions | |
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| A Numerical Example Illustrating the Fitting of Segmented Scheffe Models to Freezing-Point Data from a Two-Component System | |
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| Biplot Displays for Multiple Responses | |
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| A Five-Response Plastics-Compounding Example | |
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| Optimizing Several Responses Simultaneously | |
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| Recalling the Three-Component Propellant Example of Section 5.13 | |
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| Summary | |
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| References and Recommended Reading | |
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| Questions | |
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| The Modified L-Pseudocomponent Model and the Centered and Scaled Intercept Model | |
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| Expressing the Coefficients in the Scheffe Quadratic Model As Functions of the Coefficients in the L-Pseudocomponent, Modified L-Pseudocomponent, and Centered and Scaled Intercept Models | |
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| Matrix Algebra, Least Squares, and the Analysis of Variance | |
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| Matrix Algebra | |
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| Some Fundamental Definitions | |
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| A Review of Least Squares | |
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| The Analysis of Variance | |
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| A Numerical Example: Modeling the Texture of Fish Patties | |
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| The Adjusted Multiple Correlation Coefficient | |
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| The Press Statistic and Studentized Residuals | |
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| Testing Hypotheses About the Form of the Model: Tests of Significance | |
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| References and Recommended Reading | |
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| Data Sets from Mixture Experiments with Partial Solutions | |
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| Experiment One: Fruit Punch Experiment | |
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| Experiment Two: Chick Feeding Experiment | |
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| Experiment Three: Concrete Batches | |
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| Experiment Four: Surface Resistivity of Paper Coatings | |
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| Experiments Five, Six, and Seven: Estimating Solubilities of Multisolvent Systems | |
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| References and Recommended Reading | |
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| CONVRT Program Listing for Calculating the Coordinates of the Extreme Vertices of a Constrained Region | |
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| CONAEV Program Listing for Calculating the Coordinates of the Centroids (Approximate) of the Boundaries of a Constrained Region | |
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| Listings of Subroutines Called by CONVRT and CONAEV | |
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| Bibliography and Index of Authors | |
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| Answers to Selected Questions | |
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| Appendix | |
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| Index | |