The theory of linear models:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Chapman & Hall
1993
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| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 226 S. Illustrationen |
| ISBN: | 0412042614 |
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MARC
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| 100 | 1 | |a Jørgensen, Bent |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The theory of linear models |c Bent Jørgensen |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a New York, NY [u.a.] |b Chapman & Hall |c 1993 | |
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Contents
Preface xi
Chapter 1—Simple Linear Regression 1
§1.1 The linear regression model 1
§1.2 Parameter estimation 4
§1.3 Properties of the estimators 8
1.3.1 Sufficiency 8
1.3.2 The regression coefficients 9
1.3.3 The variance parameter 12
§1.4 Residuals 14
§1.5 Parameter inference 16
§1.6 Writing statistical reports 20
§1.7 Analysis of the spinach data 21
§1.8 Exercises 24
Chapter 2 The General Linear Model 25
§2.1 Linear models and linear algebra 25
§2.2 Maximum likelihood estimation 29
2.2.1 A matrix expression for the projection 30
§2.3 The likelihood ratio test 32
§2.4 Simple linear regression revisited 37
§2.5 Distribution theory 39
2.5.1 General results 39
2.5.2 The parameter estimators 41
2.5.3 The F test 42
§2.6 The relationship between the t and F tests 43
§2.7 Affine hypotheses and confidence regions 46
2.7.1 Confidence ellipsoids 46
2.7.2 Confidence intervals 48
2.7.3 Affine hypotheses 49
§2.8 Sufficiency 50
§2.9 Non central distributions 53
2.9.1 The non central ^ distribution 53
2.9.2 The non central F and 2 distributions 56
2.9.3 The power of F and i tests 57
§2.10 Exercises 61
viii CONTENTS
Chapter 3 One Sample and One Factor Analysis of Variance 68
§3.1 The one sample model 68
§3.2 Paired observations 72
§3.3 Analysis of variance with one factor 75
3.3.1 The model 75
3.3.2 Checking the model 78
3.3.3 Testing for equal means 80
3.3.4 Example: Bilirubin data 83
§3.4 Parameterization of linear models 89
3.4.1 Contrasts 89
3.4.2 The Wilkinson and Rogers notation 91
§3.5 Testing for homogeneity of variances 94
§3.6 Exercises 96
Chapter 4 Multiple Regression Models 105
§4.1 Regression with replications 105
4.1.1 The model 105
4.1.2 Example: Tensile strength of cement 109
§4.2 Comparing regression lines 113
4.2.1 Theory 113
4.2.2 Example: UFFI data 120
§4.3 Multiple regression 124
4.3.1 General 124
4.3.2 Example: Trees data 126
4.3.3 Further aspects of multiple regression 134
§4.4 Polynomial regression 139
4.4.1 Polynomials in one variable 139
4.4.2 Orthogonal polynomials 140
4.4.3 Two variables 143
§4.5 Prediction intervals 144
4.5.1 Simple linear Regression 144
4.5.2 Multiple regression 147
§4.6 Weighted linear models 149
§4.7 Exercises 151
Chapter 5—Analysis of Residuals 156
§5.1 Residuals and the hat matrix 156
5.1.1 The raw residuals and their distribution 156
5.1.2 Standardized residuals 158
5.1.3 Leverage 160
§5.2 Studentized residuals 162
§5.3 The non null distribution of residuals 166
5.3.1 General theory 166
5.3.2 Stabilizing the variance 168
CONTENTS ix
5.3.3 Partial residual plots 169
§5.4 The elements of residual analysis 173
5.4.1 General discussion 173
5.4.2 Example: Production of flax 174
§5.5 Exercises 182
Chapter 6—Analysis of Variance With Two or Three Factors 184
§6.1 The two factor model 184
6.1.1 Introduction 184
6.1.2 The projections 187
6.1.3 Wilkinson and Rogers formulae 191
6.1.4 Analysis of the two factor model 192
6.1.5 Example: Permeability of a building material . . 195
§6.2 Pairwise comparisons 201
§6.3 A two factor random effects model 203
§6.4 The latin square 205
§6.5 Three factor analysis of variance 209
6.5.1 General discussion 209
6.5.2 Analysis of the three factor model 211
6.5.3 Projections and effects 213
6.5.4 Example: Steel rods 215
§6.6 Exercises 217
References and Bibliography 221
Index 223 |
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| illustrated | Illustrated |
| indexdate | 2025-04-04T14:02:03Z |
| institution | BVB |
| isbn | 0412042614 |
| language | English |
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| spelling | Jørgensen, Bent Verfasser aut The theory of linear models Bent Jørgensen 1. publ. New York, NY [u.a.] Chapman & Hall 1993 XIII, 226 S. Illustrationen txt rdacontent n rdamedia nc rdacarrier Lineaire modellen gtt Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd rswk-swf Lineares Modell (DE-588)4134827-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006341198&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jørgensen, Bent The theory of linear models Lineaire modellen gtt Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd |
| subject_GND | (DE-588)4134827-8 |
| title | The theory of linear models |
| title_auth | The theory of linear models |
| title_exact_search | The theory of linear models |
| title_full | The theory of linear models Bent Jørgensen |
| title_fullStr | The theory of linear models Bent Jørgensen |
| title_full_unstemmed | The theory of linear models Bent Jørgensen |
| title_short | The theory of linear models |
| title_sort | the theory of linear models |
| topic | Lineaire modellen gtt Linear models (Statistics) Lineares Modell (DE-588)4134827-8 gnd |
| topic_facet | Lineaire modellen Linear models (Statistics) Lineares Modell |
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