Linear Statistical Models, 2nd Edition

1 Linear Algebra, Projections.

1.1 Introduction.

1.2 Vectors, Inner Products, Lengths.

1.3 Subspaces, Projections.

1.4 Examples.

1.5 Some History.

1.6 Projection Operators.

1.7 Eigenvalues and Eigenvectors.

2 Random Vectors.

2.1 Covariance Matrices.

2.2 Expected Values of Quadratic Forms.

2.3 Projections of Random Variables.

2.4 The Multivariate Normal Distribution.

2.5 The χ2, F, and t Distributions.

3 The Linear Model.

3.1 The Linear Hypothesis.

3.2 Confidence Intervals and Tests on η = c₁ß₁ + . . . + c_kß_k.

3.3 The Gauss-Markov Theorem.

3.4 The Gauss-Markov Theorem For The General Case.

3.5 Interpretation of Regression Coefficients.

3.6 The Multiple Correlation Coefficient.

3.7 The Partial Correlation Coefficient.

3.8 Testing H₀ : θ ε V₀ С V.

3.9 Further Decomposition of Subspaces.

3.10 Power of the F-Test.

3.11 Confidence and Prediction Intervals.

3.12 An Example from SAS.

3.13 Another Example: Salary Data.

4 Fitting of Regression Models.

4.1 Linearizing Transformations.

4.2 Specification Error.

4.3 Generalized Least Squares.

4.4 Effects of Additional or Fewer Observations.

4.5 Finding the "Best" Set of Regressors.

4.6 Examination of Residuals.

4.7 Collinearity.

4.8 Asymptotic Normality.

4.9 Spline Functions.

4.10 Nonlinear Least Squares.

4.11 Robust Regression.

4.12 Bootstrapping in Regression.

4.13 Quantile Regression.

5 Simultaneous Confidence Intervals.

5.1 Bonferroni Confidence Intervals.

5.2 Scheffé Simultaneous Confidence Intervals.

5.3 Tukey Simultaneous Confidence Intervals.

5.4 Comparison of Lengths.

5.5 Bechhofer's Method.

6 Two-and Three-Way Analyses of Variance.

6.1 Two-Way Analysis of Variance.

6.2 Unequal Numbers of Observations Per Cell.

6.3 Two-Way Analysis of Variance, One Observation Per Cell.

6.4 Design of Experiments.

6.5 Three-Way Analysis of Variance.

6.6 The Analysis of Covariance.

7 Miscellaneous Other Models.

7.1 The Random Effects Model.

7.2 Nesting.

7.3 Split Plot Designs.

7.4 Mixed Models.

7.5 Balanced Incomplete Block Designs.

8 Analysis of Frequency Data.

8.1 Examples.

8.2 Distribution Theory.

8.3 Conf. Ints. on Poisson and Binomial Parameters.

8.4 Log-Linear Models.

8.5 Estimation for the Log-Linear Model.

8.6 Chi-Square Goodness-of-Fit Statistics.

8.7 Limiting Distributions of the Estimators.

8.8 Logistic Regression.

The Statistical Language R.

Answers.

Index.