Applied regression analysis and experimental design:
Gespeichert in:
Hauptverfasser: | , |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
New York [u.a.]
Dekker
1985
|
Ausgabe: | 1. print. |
Schriftenreihe: | Statistics
62 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | VII, 237 S. graph. Darst. |
ISBN: | 0824772520 |
Internformat
MARC
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245 | 1 | 0 | |a Applied regression analysis and experimental design |c Richard J. Brook ; Gregory C. Arnold |
250 | |a 1. print. | ||
264 | 1 | |a New York [u.a.] |b Dekker |c 1985 | |
300 | |a VII, 237 S. |b graph. Darst. | ||
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337 | |b n |2 rdamedia | ||
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490 | 1 | |a Statistics |v 62 | |
650 | 4 | |a Analyse de régression | |
650 | 4 | |a Diseño de experimentos | |
650 | 7 | |a Onderzoeksontwerp |2 gtt | |
650 | 4 | |a Plan d'expérience | |
650 | 7 | |a Regressieanalyse |2 gtt | |
650 | 4 | |a Experimental design | |
650 | 4 | |a Regression analysis | |
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Datensatz im Suchindex
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---|---|
adam_text | CONTENTS
Preface iii
1. Fitting a Model to Data 1
1.1 Introduction 1
1.2 How to Fit a Line 3
1.3 Residuals 10
1.4 Transformations to Obtain Linearity 12
1 .5 Fitting a Model Using Vectors and Matrices 16
1.6 Deviations from Means 21
1.7 An Example Value of a Postage Stamp over Time 24
Problems 28
2. Goodness of Fit of the Model 30
2.1 Introduction 30
2.2 Coefficient Estimates for Univariate Regression 31
2.3 Coefficient Estimates for Multivariate Regression 32
2.4 ANOVA Tables 33
2.5 The F Test 35
2.6 The Coefficient of Determination 36
2.7 Predicted Values of Y and Confidence Intervals 37
2.8 Residuals 41
2.9 Reduced Models 45
2.10 Pure Error and Lack of Fit 48
2.11 Example Lactation Curve 50
Problems 53
3. Which Variables Should Be Included in the Model 56
3.1 Introduction 56
3.2 Orthogonal Predictor Variables 57
3.3 Linear Transformations of the Predictor Variables 60
3.4 Adding Nonorthogonal Variables Sequentially 61
v
vi CONTENTS
3.5 Correlation Form 64
3.6 Variable Selection All Possible Regressions 68
3.7 Variable Selection Sequential Methods 71
3.8 Qualitative (Dummy) Variables 74
3.9 Aggregation of Data 78
Problems 81
4. Peculiarities of Observations 84
4.1 Introduction 84
4.2 Sensitive, or High Leverage, Points 85
4.3 Outliers 86
4.4 Weighted Least Squares 87
4.5 More on Transformations 91
4.6 Eigenvalues and Principal Components 93
4.7 Ridge Regression 96
4.8 Prior Information 100
4.9 Cleaning up Data 101
Problems 103
5. The Experimental Design Model 106
5.1 Introduction 106
5.2 What Makes an Experiment 107
5.3 The Linear Model 112
5.4 Tests of Hypothesis 118
5.5 Testing the Assumptions 120
Problems 123
6. Assessing the Treatment Means 126
6.1 Introduction 126
6.2 Specific Hypothesis 127
6.3 Contrasts 133
6.4 Factorial Analysis 139
6.5 Unpredicted Effects 144
6.6 Conclusion 150
Problems 151
7. Blocking 153
7.1 Introduction 153
7.2 Structure of Experimental Units 154
7.3 Balanced Incomplete Block Designs 159
7.4 Confounding 165
7.5 Miscellaneous Tricks 173
Problems 176
8. Extensions to the Model 182
8.1 Introduction 182
8.2 Hierarchic Designs 182
8.3 Repeated Measures 190
8.4 Covariance Analysis 192
8.5 Unequal Replication 198
8.6 Modelling the Data 204
Problems 207
CONTENTS Vii
Appendix A. Review of Vectors and Matrices 212
A.1 Some Properties of Vectors 212
A.2 Some Properties of Vector Spaces 215
A.3 Some Properties of Matrices 217
Appendix B. Expectation, Linear and Quadratic Forms ?19
B.1 Expectation 219
B.2 Linear Forms 219
B.3 Quadratic Forms 220
B.I) The F Statistic 220
Appendix C. Data Sets 221
C.1 Ultra Sound Measurements of Horses Hearts 221
C.2 Ph Measurement of Leaf Protein 222
C.3 Lactation Records of Cows 223
C.4 Sports Cars 224
C.5 House Price Data 225
C.6 Computer Teaching Data
C.7 Weedicide Data 227
References 229
Index 231
|
adam_txt |
CONTENTS
Preface iii
1. Fitting a Model to Data 1
1.1 Introduction 1
1.2 How to Fit a Line 3
1.3 Residuals 10
1.4 Transformations to Obtain Linearity 12
1 .5 Fitting a Model Using Vectors and Matrices 16
1.6 Deviations from Means 21
1.7 An Example Value of a Postage Stamp over Time 24
Problems 28
2. Goodness of Fit of the Model 30
2.1 Introduction 30
2.2 Coefficient Estimates for Univariate Regression 31
2.3 Coefficient Estimates for Multivariate Regression 32
2.4 ANOVA Tables 33
2.5 The F Test 35
2.6 The Coefficient of Determination 36
2.7 Predicted Values of Y and Confidence Intervals 37
2.8 Residuals 41
2.9 Reduced Models 45
2.10 Pure Error and Lack of Fit 48
2.11 Example Lactation Curve 50
Problems 53
3. Which Variables Should Be Included in the Model 56
3.1 Introduction 56
3.2 Orthogonal Predictor Variables 57
3.3 Linear Transformations of the Predictor Variables 60
3.4 Adding Nonorthogonal Variables Sequentially 61
v
vi CONTENTS
3.5 Correlation Form 64
3.6 Variable Selection All Possible Regressions 68
3.7 Variable Selection Sequential Methods 71
3.8 Qualitative (Dummy) Variables 74
3.9 Aggregation of Data 78
Problems 81
4. Peculiarities of Observations 84
4.1 Introduction 84
4.2 Sensitive, or High Leverage, Points 85
4.3 Outliers 86
4.4 Weighted Least Squares 87
4.5 More on Transformations 91
4.6 Eigenvalues and Principal Components 93
4.7 Ridge Regression 96
4.8 Prior Information 100
4.9 Cleaning up Data 101
Problems 103
5. The Experimental Design Model 106
5.1 Introduction 106
5.2 What Makes an Experiment 107
5.3 The Linear Model 112
5.4 Tests of Hypothesis 118
5.5 Testing the Assumptions 120
Problems 123
6. Assessing the Treatment Means 126
6.1 Introduction 126
6.2 Specific Hypothesis 127
6.3 Contrasts 133
6.4 Factorial Analysis 139
6.5 Unpredicted Effects 144
6.6 Conclusion 150
Problems 151
7. Blocking 153
7.1 Introduction 153
7.2 Structure of Experimental Units 154
7.3 Balanced Incomplete Block Designs 159
7.4 Confounding 165
7.5 Miscellaneous Tricks 173
Problems 176
8. Extensions to the Model 182
8.1 Introduction 182
8.2 Hierarchic Designs 182
8.3 Repeated Measures 190
8.4 Covariance Analysis 192
8.5 Unequal Replication 198
8.6 Modelling the Data 204
Problems 207
CONTENTS Vii
Appendix A. Review of Vectors and Matrices 212
A.1 Some Properties of Vectors 212
A.2 Some Properties of Vector Spaces 215
A.3 Some Properties of Matrices 217
Appendix B. Expectation, Linear and Quadratic Forms ?19
B.1 Expectation 219
B.2 Linear Forms 219
B.3 Quadratic Forms 220
B.I) The F Statistic 220
Appendix C. Data Sets 221
C.1 Ultra Sound Measurements of Horses' Hearts 221
C.2 Ph Measurement of Leaf Protein 222
C.3 Lactation Records of Cows 223
C.4 Sports Cars 224
C.5 House Price Data 225
C.6 Computer Teaching Data
C.7 Weedicide Data 227
References 229
Index 231 |
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author | Brook, Richard J. Arnold, Gregory C. |
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callnumber-subject | QA - Mathematics |
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ctrlnum | (OCoLC)11784346 (DE-599)BVBBV022156914 |
dewey-full | 519.5/36 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics |
dewey-raw | 519.5/36 |
dewey-search | 519.5/36 |
dewey-sort | 3519.5 236 |
dewey-tens | 510 - Mathematics |
discipline | Mathematik Wirtschaftswissenschaften |
discipline_str_mv | Mathematik Wirtschaftswissenschaften |
edition | 1. print. |
format | Book |
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illustrated | Illustrated |
index_date | 2024-07-02T16:18:33Z |
indexdate | 2024-07-09T20:51:31Z |
institution | BVB |
isbn | 0824772520 |
language | English |
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physical | VII, 237 S. graph. Darst. |
publishDate | 1985 |
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series | Statistics |
series2 | Statistics |
spelling | Brook, Richard J. Verfasser aut Applied regression analysis and experimental design Richard J. Brook ; Gregory C. Arnold 1. print. New York [u.a.] Dekker 1985 VII, 237 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics 62 Analyse de régression Diseño de experimentos Onderzoeksontwerp gtt Plan d'expérience Regressieanalyse gtt Experimental design Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Entwurf (DE-588)4121208-3 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Experiment (DE-588)4015999-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 s DE-604 Regressionsanalyse (DE-588)4129903-6 s Versuchsplanung (DE-588)4078859-3 s 1\p DE-604 Experiment (DE-588)4015999-1 s Entwurf (DE-588)4121208-3 s 2\p DE-604 Arnold, Gregory C. Verfasser aut Statistics 62 (DE-604)BV000003265 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015371576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
spellingShingle | Brook, Richard J. Arnold, Gregory C. Applied regression analysis and experimental design Statistics Analyse de régression Diseño de experimentos Onderzoeksontwerp gtt Plan d'expérience Regressieanalyse gtt Experimental design Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Entwurf (DE-588)4121208-3 gnd Versuchsplanung (DE-588)4078859-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Experiment (DE-588)4015999-1 gnd |
subject_GND | (DE-588)4129903-6 (DE-588)4121208-3 (DE-588)4078859-3 (DE-588)4114528-8 (DE-588)4015999-1 |
title | Applied regression analysis and experimental design |
title_auth | Applied regression analysis and experimental design |
title_exact_search | Applied regression analysis and experimental design |
title_exact_search_txtP | Applied regression analysis and experimental design |
title_full | Applied regression analysis and experimental design Richard J. Brook ; Gregory C. Arnold |
title_fullStr | Applied regression analysis and experimental design Richard J. Brook ; Gregory C. Arnold |
title_full_unstemmed | Applied regression analysis and experimental design Richard J. Brook ; Gregory C. Arnold |
title_short | Applied regression analysis and experimental design |
title_sort | applied regression analysis and experimental design |
topic | Analyse de régression Diseño de experimentos Onderzoeksontwerp gtt Plan d'expérience Regressieanalyse gtt Experimental design Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Entwurf (DE-588)4121208-3 gnd Versuchsplanung (DE-588)4078859-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Experiment (DE-588)4015999-1 gnd |
topic_facet | Analyse de régression Diseño de experimentos Onderzoeksontwerp Plan d'expérience Regressieanalyse Experimental design Regression analysis Regressionsanalyse Entwurf Versuchsplanung Mathematisches Modell Experiment |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015371576&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
volume_link | (DE-604)BV000003265 |
work_keys_str_mv | AT brookrichardj appliedregressionanalysisandexperimentaldesign AT arnoldgregoryc appliedregressionanalysisandexperimentaldesign |