Introduction to linear models:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Beverly Hills [u.a.]
Sage
1984
|
| Ausgabe: | 1. print. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | 357 S. graph. Darst. |
| ISBN: | 0803921756 |
Internformat
MARC
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| 245 | 1 | 0 | |a Introduction to linear models |c George H. Dunteman |
| 250 | |a 1. print. | ||
| 264 | 1 | |a Beverly Hills [u.a.] |b Sage |c 1984 | |
| 300 | |a 357 S. |b graph. Darst. | ||
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| 650 | 4 | |a Analyse de régression | |
| 650 | 7 | |a Lineaire modellen |2 gtt | |
| 650 | 4 | |a Modèles linéaires (Statistique) | |
| 650 | 4 | |a Linear models (Statistics) | |
| 650 | 4 | |a Regression analysis | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents Preface 9 Introduction 11 Basic Statistical Concepts 15 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 Introduction Probability Random Variables Univariate Frequency Distributions Bivariate Frequency Distributions Marginal Distributions Conditional Distributions Regression and Correlation Normal Distribution Sampling Distribution of the Mean Confidence Interval for Sample Mean Hypothesis Testing Involving Means Testing Hypotheses Concerning ß Problems 15 16 22 24 27 29 30 33 43 52 55 60 68 73 Matrix Algebra 77 Introduction Vectors and Matrices Characteristics of Vectors Vector Operations Geometrical Representation of Vectors and Related Characteristics Linear Independence of Vectors 3.6 3.7 Basis of a Vector Space Vector Representation of Statistical Models 3.8 3.9 Characteristics of Matrices 3.10 Matrix Operations 3.11 Trace of a Matrix 3.12 Partitioned Matrices 3.13 Matrix Inversion 77 77 81 82 3.1 3.2 3.3 3.4 3.5 87 90 93 99 102 104 113 114 118
3.14 Simultaneous Linear Equations 3.15 Quadratic Forms 3.16 Latent Roots and Vectors 3.17 Problems 4. Multiple Regression Analysis 120 124 125 125 129 Introduction Basic Assumptions of Multiple Regression Least-Squares Estimation of the Regression Parameters Solving the Normal Equations for ß Multiple Regression with Deviation Scores Multiple Regression with Standardized Scores Properties of ß Estimation of a2 and a1 (X X)՜1 Partitioning the Total Sum of Squares in the Multiple Regression Model Multiple Correlation Hypothesis Testing of ß Generalizations of the Classical Regression Model Nonlinear Models Multiple Regression on a Computer Example Problems 129 134 136 139 146 152 157 163 5. Linear Regression with One Categorical Independent Variable 191 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 Introduction The Model Estimable Functions of Parameters Solving the Normtd Equations Partitioning and Computing Sums of Squares Hypothesis Testing One-Way Analysis of Variance Other Ways to Solve the Normal Equations Use of Computers Problems 6. Linear Regression with Two Categorical Independent Variables 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Introduction Two-Factor Model with Unbalanced Data Normal Equations Estimable Functions of Parameters Computing Sums of Squares Testing Specific Hypotheses General Procedures for Testing Hypotheses Use of Computers Example Problems 165 166 169 176 179 180 183 184 191 192 197 202 206 209 211 213 217 221 223 223 227 230 234 237 249 247 251 254 255
7. Regression Models with Interaction 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Introduction The Concept of Interaction in Multiple Regression Interaction in the Case of Categorical Independent Variables A Balanced Factorial Design with Interactions Analysis of Variance for Factorial Experiments Creating a Full Rank Design Matrix An Interaction Model with Unbalanced Data Use of Computers Problems 8. Analysis of Covariance 8.1 8.2 8.3 8.4 8.5 8.6 8.7 259 259 260 261 267 285 288 293 299 301 303 Introduction Analysis of Covariance Models Solving the Normal Equations An Example Use of Computers Applied Example Problems 303 304 305 305 321 322 324 9. Analysis Considerations andModel Extensions 327 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Introduction Experimental Versus Survey Data Survey Sample Designs and Statistical Models Nonresponse Bias Missing Data Data Editing Ridge Estimation Logistic Regression Analysis 327 327 330 332 333 334 335 336 Appendix 343 References 353 Index 355 About the Author 359
Contents Preface 9 Introduction 11 Basic Statistical Concepts 15 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 Introduction Probability Random Variables Univariate Frequency Distributions Bivariate Frequency Distributions Marginal Distributions Conditional Distributions Regression and Correlation Normal Distribution Sampling Distribution of the Mean Confidence Interval for Sample Mean Hypothesis Testing Involving Means Testing Hypotheses Concerning ß Problems 15 16 22 24 27 29 30 33 43 52 55 60 68 73 Matrix Algebra 77 Introduction Vectors and Matrices Characteristics of Vectors Vector Operations Geometrical Representation of Vectors and Related Characteristics Linear Independence of Vectors 3.6 3.7 Basis of a Vector Space Vector Representation of Statistical Models 3.8 3.9 Characteristics of Matrices 3.10 Matrix Operations 3.11 Trace of a Matrix 3.12 Partitioned Matrices 3.13 Matrix Inversion 77 77 81 82 3.1 3.2 3.3 3.4 3.5 87 90 93 99 102 104 113 114 118
3.14 Simultaneous Linear Equations 3.15 Quadratic Forms 3.16 Latent Roots and Vectors 3.17 Problems 4. Multiple Regression Analysis 120 124 125 125 129 Introduction Basic Assumptions of Multiple Regression Least-Squares Estimation of the Regression Parameters Solving the Normal Equations for ß Multiple Regression with Deviation Scores Multiple Regression with Standardized Scores Properties of ß Estimation of a2 and a1 (X X)՜1 Partitioning the Total Sum of Squares in the Multiple Regression Model Multiple Correlation Hypothesis Testing of ß Generalizations of the Classical Regression Model Nonlinear Models Multiple Regression on a Computer Example Problems 129 134 136 139 146 152 157 163 5. Linear Regression with One Categorical Independent Variable 191 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 Introduction The Model Estimable Functions of Parameters Solving the Normtd Equations Partitioning and Computing Sums of Squares Hypothesis Testing One-Way Analysis of Variance Other Ways to Solve the Normal Equations Use of Computers Problems 6. Linear Regression with Two Categorical Independent Variables 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Introduction Two-Factor Model with Unbalanced Data Normal Equations Estimable Functions of Parameters Computing Sums of Squares Testing Specific Hypotheses General Procedures for Testing Hypotheses Use of Computers Example Problems 165 166 169 176 179 180 183 184 191 192 197 202 206 209 211 213 217 221 223 223 227 230 234 237 249 247 251 254 255
7. Regression Models with Interaction 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Introduction The Concept of Interaction in Multiple Regression Interaction in the Case of Categorical Independent Variables A Balanced Factorial Design with Interactions Analysis of Variance for Factorial Experiments Creating a Full Rank Design Matrix An Interaction Model with Unbalanced Data Use of Computers Problems 8. Analysis of Covariance 8.1 8.2 8.3 8.4 8.5 8.6 8.7 259 259 260 261 267 285 288 293 299 301 303 Introduction Analysis of Covariance Models Solving the Normal Equations An Example Use of Computers Applied Example Problems 303 304 305 305 321 322 324 9. Analysis Considerations andModel Extensions 327 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Introduction Experimental Versus Survey Data Survey Sample Designs and Statistical Models Nonresponse Bias Missing Data Data Editing Ridge Estimation Logistic Regression Analysis 327 327 330 332 333 334 335 336 Appendix 343 References 353 Index 355 About the Author 359
Contents Preface 9 Introduction 11 Basic Statistical Concepts 15 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2.10 2.11 2.12 2.13 2.14 Introduction Probability Random Variables Univariate Frequency Distributions Bivariate Frequency Distributions Marginal Distributions Conditional Distributions Regression and Correlation Normal Distribution Sampling Distribution of the Mean Confidence Interval for Sample Mean Hypothesis Testing Involving Means Testing Hypotheses Concerning ß Problems 15 16 22 24 27 29 30 33 43 52 55 60 68 73 Matrix Algebra 77 Introduction Vectors and Matrices Characteristics of Vectors Vector Operations Geometrical Representation of Vectors and Related Characteristics Linear Independence of Vectors 3.6 3.7 Basis of a Vector Space Vector Representation of Statistical Models 3.8 3.9 Characteristics of Matrices 3.10 Matrix Operations 3.11 Trace of a Matrix 3.12 Partitioned Matrices 3.13 Matrix Inversion 77 77 81 82 3.1 3.2 3.3 3.4 3.5 87 90 93 99 102 104 113 114 118
3.14 Simultaneous Linear Equations 3.15 Quadratic Forms 3.16 Latent Roots and Vectors 3.17 Problems 4. Multiple Regression Analysis 120 124 125 125 129 Introduction Basic Assumptions of Multiple Regression Least-Squares Estimation of the Regression Parameters Solving the Normal Equations for ß Multiple Regression with Deviation Scores Multiple Regression with Standardized Scores Properties of ß Estimation of a2 and a1 (X X)՜1 Partitioning the Total Sum of Squares in the Multiple Regression Model Multiple Correlation Hypothesis Testing of ß Generalizations of the Classical Regression Model Nonlinear Models Multiple Regression on a Computer Example Problems 129 134 136 139 146 152 157 163 5. Linear Regression with One Categorical Independent Variable 191 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 Introduction The Model Estimable Functions of Parameters Solving the Normtd Equations Partitioning and Computing Sums of Squares Hypothesis Testing One-Way Analysis of Variance Other Ways to Solve the Normal Equations Use of Computers Problems 6. Linear Regression with Two Categorical Independent Variables 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 6.10 Introduction Two-Factor Model with Unbalanced Data Normal Equations Estimable Functions of Parameters Computing Sums of Squares Testing Specific Hypotheses General Procedures for Testing Hypotheses Use of Computers Example Problems 165 166 169 176 179 180 183 184 191 192 197 202 206 209 211 213 217 221 223 223 227 230 234 237 249 247 251 254 255
7. Regression Models with Interaction 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Introduction The Concept of Interaction in Multiple Regression Interaction in the Case of Categorical Independent Variables A Balanced Factorial Design with Interactions Analysis of Variance for Factorial Experiments Creating a Full Rank Design Matrix An Interaction Model with Unbalanced Data Use of Computers Problems 8. Analysis of Covariance 8.1 8.2 8.3 8.4 8.5 8.6 8.7 259 259 260 261 267 285 288 293 299 301 303 Introduction Analysis of Covariance Models Solving the Normal Equations An Example Use of Computers Applied Example Problems 303 304 305 305 321 322 324 9. Analysis Considerations andModel Extensions 327 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Introduction Experimental Versus Survey Data Survey Sample Designs and Statistical Models Nonresponse Bias Missing Data Data Editing Ridge Estimation Logistic Regression Analysis 327 327 330 332 333 334 335 336 Appendix 343 References 353 Index 355 About the Author 359
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| spelling | Dunteman, George H. 1935- Verfasser (DE-588)143244620 aut Introduction to linear models George H. Dunteman 1. print. Beverly Hills [u.a.] Sage 1984 357 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse de régression Lineaire modellen gtt Modèles linéaires (Statistique) Linear models (Statistics) Regression analysis Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf Lineares Regressionsmodell (DE-588)4127971-2 s DE-604 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002291762&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002291762&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002291762&sequence=000005&line_number=0003&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dunteman, George H. 1935- Introduction to linear models Analyse de régression Lineaire modellen gtt Modèles linéaires (Statistique) Linear models (Statistics) Regression analysis Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| subject_GND | (DE-588)4127971-2 |
| title | Introduction to linear models |
| title_auth | Introduction to linear models |
| title_exact_search | Introduction to linear models |
| title_full | Introduction to linear models George H. Dunteman |
| title_fullStr | Introduction to linear models George H. Dunteman |
| title_full_unstemmed | Introduction to linear models George H. Dunteman |
| title_short | Introduction to linear models |
| title_sort | introduction to linear models |
| topic | Analyse de régression Lineaire modellen gtt Modèles linéaires (Statistique) Linear models (Statistics) Regression analysis Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| topic_facet | Analyse de régression Lineaire modellen Modèles linéaires (Statistique) Linear models (Statistics) Regression analysis Lineares Regressionsmodell |
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