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Preface | |

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Examples and Limits of the GLM | |

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Motivation | |

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A Review of Basic Statistical Ideas | |

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GLM Definition | |

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GLM Examples | |

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Student Goals | |

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Homework Exercises | |

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Statement of the Model, Estimation, and Testing | |

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Motivation | |

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Statement of the Model | |

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Least Squares Assumptions | |

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Discussion of Homogeneity | |

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Gaussian Errors Assumption | |

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Estimation of the GLM | |

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Hypothesis Testing for the GLM | |

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Homework Exercises | |

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Some Distributions for the GLM | |

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Motivation | |

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A Full-Rank Basis for Less-than-Full-Rank Models | |

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Definitions and Theorems | |

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GLM Distributions | |

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Definitions and Properties of Residuals | |

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Homework Exercises | |

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Multiple Regression: General Considerations | |

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Motivation | |

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Definitions of Basic Sums of Squares | |

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The Nature of the Intercept | |

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Models that Span but May Not Include an Intercept | |

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Corrected SS | |

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Intercept-Only Model | |

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Null Model | |

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Overall ANOVA Table for Multiple Regression | |

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Usual ("Corrected") Overall Test for Regression | |

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"Uncorrected" Overall Test for Regression | |

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Strength of Association | |

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Homework Exercises | |

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Testing Hypotheses in Multiple Regression | |

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Motivation | |

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Choosing an Error Term | |

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Review of GLH Concepts | |

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Model Pools | |

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Test Class 1: Overall | |

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Test Class 2: Addition of One Variable | |

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Test Class 3: Tests of the Intercept | |

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Test Class 4: Addition of a Group of Variables | |

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Test Class 5: GLH Tests | |

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The Multiple Testing Issue | |

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Interaction | |

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Homework Exercises | |

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Correlations | |

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Motivation | |

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Interpreting [rho superscript 2] | |

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Correlation Formulas | |

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Partial Correlation | |

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Semipartial Correlation | |

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Relating Semipartial Correlations to Standardized Regression Coefficients | |

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Multiple Partial Correlation | |

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Multiple Semipartial Correlation | |

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Hypothesis Tests for Correlations | |

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Relating Multiple Partials and Semipartials to Regression Coefficient Tests | |

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Using Correlations to Interpret Added-in-Order Tests | |

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Computing Partial Correlations | |

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Some Useful Properties of Correlations | |

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The Importance and Utility of Correlations | |

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Homework Exercises | |

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GLM Assumption Diagnostics | |

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Motivation | |

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The First Step: Get to Know Your Data | |

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Residual Analysis | |

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Outliers | |

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Homework Exercises | |

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GLM Computation Diagnostics | |

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Motivation | |

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Single Variable Problems and Solutions | |

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Collinearity Definitions and Concepts | |

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Matrices of Interest | |

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Models Corresponding to Cross-Products Matrices | |

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Eigenanalysis | |

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R[superscript 2 subscript j], Tolerance and VIF | |

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Detecting Numerical Inaccuracy | |

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Treating Regression Problems | |

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Homework Exercises | |

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Polynomial Regression | |

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Motivation | |

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Polynomial Models of Most Interest | |

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Examples | |

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Lack-of-Fit Tests | |

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Limitations of Natural Polynomials | |

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Orthogonal Polynomials | |

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Strategies for Accurate Computations with Polynomials | |

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Strategy for Choosing a Model | |

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Polynomial Interactions and Response Surfaces | |

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Homework Exercises | |

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Transformations | |

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Motivation | |

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General Principles | |

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Power Transformation of the Response | |

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Other Comments | |

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Transformations of Predictors | |

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Pitfalls | |

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Homework Exercises | |

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Selecting the Best Model | |

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Motivation | |

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Overview of Solution Strategies | |

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Step 1: Specify the Maximum Model | |

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Step 2: Specify a Criterion | |

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Step 3: Specify a Strategy | |

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Step 4: Conduct the Analysis | |

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Step 5: Evaluate the Reliability | |

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Overall Implementation | |

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Homework Exercises | |

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Coding Schemes for Regression | |

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Motivation | |

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Reference Cell Coding | |

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Cell Mean Coding | |

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Classical ANOVA Coding | |

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Effect Coding | |

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Polynomial Coding | |

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The Essence Matrix | |

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Comments on Coding Schemes | |

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Relationships among Coding Schemes | |

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Homework Exercises | |

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One-Way ANOVA | |

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Motivation | |

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Specification of the Model | |

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(Usual) Overall Test | |

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Defining and Estimating Cell Means | |

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Which Means Are Different? | |

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Contrasts | |

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Conducting Multiple Comparisons | |

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Homework Exercises | |

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Complete, Two-Way Factorial ANOVA | |

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Motivation | |

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Model Concepts | |

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Coding Schemes | |

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Generating Cell Means | |

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Computing Estimates and Tests | |

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Contrast Matrices for Marginal Means | |

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Choosing and Interpreting Tests | |

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Step-Down Tests | |

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Missing Data | |

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Homework Exercises | |

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Special Cases of Two-Way ANOVA and Random Effects Basics | |

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Motivation | |

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Blocking Variables and Block Designs | |

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Fixed Block Design | |

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Introduction to Random Effects Models | |

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The Classical Approach to a Random Block Design | |

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Role of Nonindependence of Observations | |

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Computations for Mixed Models | |

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Review Comments | |

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Homework Exercises | |

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The Full Model in Every Cell (ANCOVA as a Special Case) | |

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Motivation | |

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Cell Mean Style Coding of Full Model | |

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Properties of the Model | |

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Testing Strategies | |

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Implementing Strategy 1, Adjusted ANOVA | |

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Implementing Strategy 2, GLM Testing | |

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Models of Interest | |

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Implementing Strategy 3: Backwards Groupwise | |

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Difference Scores: A Special Case of ANCOVA | |

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Other Contrasts of Interest in ANCOVA | |

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Other Tests of Interest in the Full Model | |

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Regression (Reference Cell) Style Coding | |

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Effect Style Coding | |

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Modeling a Baseline Covariate | |

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Comparing Coding Schemes | |

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Generalizations | |

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Homework Exercises | |

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Understanding and Computing Power for the GLM | |

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Motivation | |

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GLM Theory | |

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Factors in Choosing a Design | |

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Using Parameter Estimates in Power Analysis | |

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Example Power Analysis | |

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Reporting Power | |

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Tables and Software | |

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How Much To Do? | |

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Benefits | |

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Homework Exercises | |

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Matrix Algebra for Linear Models | |

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Basics | |

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Matrix Properties and Decompositions | |

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Principal Components (Basics) | |

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Homework Exercises in Matrix Arithmetic | |

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Homework Exercises for a Matrix Language | |

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Statistical Tables | |

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Study Guide for Linear Model Theory | |

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Homework and Example Data | |

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Introduction to SAS/IML | |

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A Brief Manual for LINMOD | |

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SAS/IML Power Program User's Guide | |

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Regression Model Selection Data | |

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References | |

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Index | |