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Preface | |

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Introduction | |

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Simple Linear Regression Model | |

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Multiple Linear Regression Model | |

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Analysis-of-Variance Models | |

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Matrix Algebra | |

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Matrix and Vector Notation | |

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Matrices, Vectors, and Scalars | |

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Matrix Equality | |

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Transpose | |

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Matrices of Special Form | |

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Operations | |

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Sum of Two Matrices or Two Vectors | |

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Product of a Scalar and a Matrix | |

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Product of Two Matrices or Two Vectors | |

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Hadamard Product of Two Matrices or Two Vectors | |

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Partitioned Matrices | |

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Rank | |

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Inverse | |

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Positive Definite Matrices | |

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Systems of Equations | |

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Generalized Inverse | |

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Definition and Properties | |

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Generalized Inverses and Systems of Equations | |

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Determinants | |

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Orthogonal Vectors and Matrices | |

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Trace | |

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Eigenvalues and Eigenvectors | |

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Definition | |

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Functions of a Matrix | |

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Products | |

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Symmetric Matrices | |

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Positive Definite and Semidefinite Matrices | |

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Idempotent Matrices | |

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Vector and Matrix Calculus | |

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Derivatives of Functions of Vectors and Matrices | |

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Derivatives Involving Inverse Matrices and Determinants | |

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Maximization or Minimization of a Function of a Vector | |

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Random Vectors and Matrices | |

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Introduction | |

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Means, Variances, Covariances, and Correlations | |

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Mean Vectors and Covariance Matrices for Random Vectors | |

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Mean Vectors | |

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Covariance Matrix | |

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Generalized Variance | |

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Standardized Distance | |

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Correlation Matrices | |

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Mean Vectors and Covariance Matrices for Partitioned Random Vectors | |

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Linear Functions of Random Vectors | |

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Means | |

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Variances and Covariances | |

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Multivariate Normal Distribution | |

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Univariate Normal Density Function | |

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Multivariate Normal Density Function | |

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Moment Generating Functions | |

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Properties of the Multivariate Normal Distribution | |

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Partial Correlation | |

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Distribution of Quadratic Forms in y | |

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Sums of Squares | |

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Mean and Variance of Quadratic Forms | |

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Noncentral Chi-Square Distribution | |

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Noncentral F and t Distributions | |

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Noncentral F Distribution | |

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Noncentral t Distribution | |

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Distribution of Quadratic Forms | |

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Independence of Linear Forms and Quadratic Forms | |

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Simple Linear Regression | |

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The Model | |

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Estimation of [beta subscript 0], [beta subscript 1], and [sigma superscript 2] | |

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Hypothesis Test and Confidence Interval for [beta subscript 1] | |

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Coefficient of Determination | |

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Multiple Regression: Estimation | |

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Introduction | |

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The Model | |

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Estimation of [beta] and [sigma superscript 2] | |

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Least-Squares Estimator for [beta] | |

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Properties of the Least-Squares Estimator [beta] | |

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An Estimator for [sigma superscript 2] | |

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Geometry of Least-Squares | |

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Parameter Space, Data Space, and Prediction Space | |

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Geometric Interpretation of the Multiple Linear Regression Model | |

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The Model in Centered Form | |

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Normal Model | |

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Assumptions | |

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Maximum Likelihood Estimators for [beta] and [sigma superscript 2] | |

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Properties of [beta] and [sigma superscript 2] | |

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R[superscript 2] in Fixed-x Regression | |

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Generalized Least-Squares: cov(y) = [sigma superscript 2]V | |

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Estimation of [beta] and [sigma superscript 2] when cov(y) = [sigma superscript 2]V | |

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Misspecification of the Error Structure | |

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Model Misspecification | |

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Orthogonalization | |

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Multiple Regression: Tests of Hypotheses and Confidence Intervals | |

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Test of Overall Regression | |

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Test on a Subset of the [beta] Values | |

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F Test in Terms of R[superscript 2] | |

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The General Linear Hypothesis Tests for H[subscript 0]: C[beta] = 0 and H[subscript 0]: C[beta] = t | |

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The Test for H[subscript 0]: C[beta] = 0 | |

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The Test for H[subscript 0]: C[beta] = t | |

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Tests on [beta subscript j] and a' [beta] | |

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Testing One [beta subscript j] or One a' [beta] | |

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Testing Several [beta subscript j] or a'[subscript i beta] Values | |

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Confidence Intervals and Prediction Intervals | |

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Confidence Region for [beta] | |

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Confidence Interval for [beta subscript j] | |

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Confidence Interval for a'[beta] | |

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Confidence Interval for E(y) | |

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Prediction Interval for a Future Observation | |

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Confidence Interval for [sigma superscript 2] | |

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Simultaneous Intervals | |

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Likelihood Ratio Tests | |

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Multiple Regression: Model Validation and Diagnostics | |

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Residuals | |

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The Hat Matrix | |

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Outliers | |

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Influential Observations and Leverage | |

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Multiple Regression: Random x's | |

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Multivariate Normal Regression Model | |

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Estimation and Testing in Multivariate Normal Regression | |

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Standardized Regression Coefficients | |

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R[superscript 2] in Multivariate Normal Regression | |

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Tests and Confidence Intervals for R[superscript 2] | |

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Effect of Each Variable on R[superscript 2] | |

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Prediction for Multivariate Normal or Nonnormal Data | |

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Sample Partial Correlations | |

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Multiple Regression: Bayesian Inference | |

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Elements of Bayesian Statistical Inference | |

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A Bayesian Multiple Linear Regression Model | |

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A Bayesian Multiple Regression Model with a Conjugate Prior | |

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Marginal Posterior Density of [beta] | |

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Marginal Posterior Densities of [tau] and [sigma superscript 2] | |

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Inference in Bayesian Multiple Linear Regression | |

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Bayesian Point and Interval Estimates of Regression Coefficients | |

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Hypothesis Tests for Regression Coefficients in Bayesian Inference | |

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Special Cases of Inference in Bayesian Multiple Regression Models | |

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Bayesian Point and Interval Estimation of [sigma superscript 2] | |

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Bayesian Inference through Markov Chain Monte Carlo Simulation | |

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Posterior Predictive Inference | |

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Analysis-of-Variance Models | |

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Non-Full-Rank Models | |

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One-Way Model | |

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Two-Way Model | |

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Estimation | |

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Estimation of [beta] | |

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Estimable Functions of [beta] | |

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Estimators | |

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Estimators of [lambda]'[beta] | |

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Estimation of [sigma superscript 2] | |

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Normal Model | |

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Geometry of Least-Squares in the Overparameterized Model | |

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Reparameterization | |

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Side Conditions | |

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Testing Hypotheses | |

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Testable Hypotheses | |

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Full-Reduced-Model Approach | |

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General Linear Hypothesis | |

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An Illustration of Estimation and Testing | |

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Estimable Functions | |

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Testing a Hypothesis | |

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Orthogonality of Columns of X | |

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One-Way Analysis-of-Variance: Balanced Case | |

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The One-Way Model | |

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Estimable Functions | |

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Estimation of Parameters | |

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Solving the Normal Equations | |

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An Estimator for [sigma superscript 2] | |

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Testing the Hypothesis H[subscript 0]: [mu subscript 1] = [mu subscript 2] = ... = [mu subscript k] | |

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Full-Reduced-Model Approach | |

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General Linear Hypothesis | |

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Expected Mean Squares | |

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Full-Reduced-Model Approach | |

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General Linear Hypothesis | |

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Contrasts | |

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Hypothesis Test for a Contrast | |

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Orthogonal Contrasts | |

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Orthogonal Polynomial Contrasts | |

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Two-Way Analysis-of-Variance: Balanced Case | |

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The Two-Way Model | |

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Estimable Functions | |

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Estimators of [lambda]'[beta] and [sigma superscript 2] | |

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Solving the Normal Equations and Estimating [lambda]'[beta] | |

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An Estimator for [sigma superscript 2] | |

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Testing Hypotheses | |

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Test for Interaction | |

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Tests for Main Effects | |

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Expected Mean Squares | |

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Sums-of-Squares Approach | |

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Quadratic Form Approach | |

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Analysis-of-Variance: The Cell Means Model for Unbalanced Data | |

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Introduction | |

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One-Way Model | |

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Estimation and Testing | |

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Contrasts | |

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Two-Way Model | |

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Unconstrained Model | |

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Constrained Model | |

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Two-Way Model with Empty Cells | |

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Analysis-of-Covariance | |

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Introduction | |

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Estimation and Testing | |

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The Analysis-of-Covariance Model | |

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Estimation | |

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Testing Hypotheses | |

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One-Way Model with One Covariate | |

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The Model | |

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Estimation | |

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Testing Hypotheses | |

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Two-Way Model with One Covariate | |

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Tests for Main Effects and Interactions | |

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Test for Slope | |

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Test for Homogeneity of Slopes | |

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One-Way Model with Multiple Covariates | |

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The Model | |

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Estimation | |

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Testing Hypotheses | |

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Analysis-of-Covariance with Unbalanced Models | |

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Linear Mixed Models | |

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Introduction | |

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The Linear Mixed Model | |

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Examples | |

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Estimation of Variance Components | |

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Inference for [beta] | |

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An Estimator for [beta] | |

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Large-Sample Inference for Estimable Functions of [beta] | |

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Small-Sample Inference for Estimable Functions of [beta] | |

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Inference for the a[subscript i] Terms | |

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Residual Diagnostics | |

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Additional Models | |

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Nonlinear Regression | |

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Logistic Regression | |

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Loglinear Models | |

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Poisson Regression | |

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Generalized Linear Models | |

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Answers and Hints to the Problems | |

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References | |

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Index | |