Theory of Linear Models

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Summary

This book provides a self-contained exposition of the theory of linear models, including practical aspects of residuals and data analysis.

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Preface
Simple Linear Regression
The linear regression model	p. 1
Parameter estimation	p. 4
Properties of the estimators	p. 8
Residuals	p. 14
Parameter inference	p. 16
Writing statistical reports	p. 20
Analysis of the spinach data	p. 21
The General Linear Model
Linear models and linear algebra	p. 25
Maximum likelihood estimation	p. 29
The likelihood ratio test	p. 32
Simple linear regression revisited	p. 37
Distribution theory	p. 39
The relationship between the t- and F-tests	p. 43
Affine hypotheses and confidence regions	p. 46
Sufficiency	p. 50
Non-central distributions	p. 53
One-Sample and One-Factor Analysis of Variance
The one-sample model	p. 68
Paired observations	p. 72
Analysis of variance with one factor	p. 75
Parameterization of linear models	p. 89
Testing for homogeneity of variances	p. 94
Multiple Regression Models
Regression with replications	p. 105
Comparing regression lines	p. 113
Multiple regression	p. 124
Polynomial regression	p. 139
Prediction intervals	p. 144
Weighted linear models	p. 149
Analysis of Residuals
Residuals and the hat matrix	p. 156
Studentized residuals	p. 162
The non-null distribution of residuals	p. 166
The elements of residual analysis	p. 173
Analysis of Variance With Two or Three Factors
The two-factor model	p. 184
Pairwise comparisons	p. 201
A two-factor random effects model	p. 203
The latin square	p. 205
Three-factor analysis of variance	p. 209
References and Bibliography	p. 221
Index	p. 223
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