An introduction to computational statistics: regression analysis
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ
Prentice Hall
1995
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 364 S. graph. Darst. |
| ISBN: | 0134548108 |
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MARC
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| 100 | 1 | |a Jennrich, Robert I. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An introduction to computational statistics |b regression analysis |c Robert I. Jennrich |
| 264 | 1 | |a Englewood Cliffs, NJ |b Prentice Hall |c 1995 | |
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| adam_text | AN INTRODUCTION TO COMPUTATIONAL STATISTICS REGRESSION ANALYSIS ROBERT I
. JENNRICH PREFACE XII I CHAPTER 1 : A QUICK LOOK AT A TYPICA L
REGRESSION PROGRAM 1 1.1 INTRODUCTION 1 1.2 SOME CONCEPTS AND
TERMINOLOGY 1 1.3 PROBLEM SPECIFICATION 4 1.4 THE OUTPUT 8 1.5 PROBLEM
SPECIFICATION USING OTHER SYSTEMS 12 1.6 PROBLEMS 15 CHAPTER 2: SIMPLE
LINEAR REGRESSION 1 8 2.1 THE SIMPLE LINEAR REGRESSION MODEL 18 2.2
LEAST SQUARES FITTING 19 2 .2.1 OBSERVATION SPACE REPRESENTATION 1 9 2
.2.2 VARIABLE SPACE REPRESENTATION 2 0 2 .2.3 NORMAL EQUATIONS 2 1 2.3
STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATES 25 2 .3.1 UNBIASED
ERRORS 2 6 2 .3.2 UNCORRELATED CONSTANT VARIANCE ERRORS 2 6 2 .3.3
NORMALLY DISTRIBUTED ERRORS 2 9 2.4 CONFIDENCE AND PREDICTION INTERVALS
30 2 .4.1 CONFIDENCE INTERVALS FOR A AND /3 31 2.4.2 CONFIDENCE
INTERVALS FOR THE EXPECTED RESPONSE 3 2 2 .4.3 PREDICTING ANEW RESPONSE
3 3 2 .4.4 TESTING HYPOTHESES 34 2.5 RANDOM REGRESSORS 36 2.6 A
NONSTANDARD APPLICATION : THE TWO-SAMPLE T-TEST 37 2.7 SOME POTENTIAL
PROBLEMS IN APPLYING REGRESSION 39 2.8 THE REGRESSION PHENOMENON 44 2.9
PROBLEMS 46 CHAPTER 3: APPLYING SIMPLE LINEAR REGRESSION 5 1 3.1
TRANSFORMING A GIVEN MODEL TO A LINEAR MODEL 5 1 3.2 CORRELATION AND THE
COEFFICIENT OF DETERMINATION 53 3.3 RESIDUAL ANALYSIS 56 3 .3.1 PLOTS OF
E ON Y 56 3 .3.2 NORMAL PROBABILITY PLOTS 6 1 3 .3 .3 PLOTS ON EXTERNAL
VARIABLES 67 3.4 WEIGHTED REGRESSION 67 3.5 STRUCTURE OF THE POWER
TRANSFORMS 71 3.6 SOME REMEDIAL ACTIONS 74 3.6.1 OUTLIERS 74 3.6.2
SEARCHING FOR A LINEARIZING TRANSFORM 7 5 3.6.3 TRANSFORMING TO
STABILIZE VARIANCE 7 9 3.6.4 THE RELATION BETWEEN WEIGHTING AND
TRANSFORMING 82 3.6.5 NONNORMALITY - 8 3 3.6.6 HOW DOES ONE PROCEED? 8 4
3.7 CORRELATED ERRORS 85 3.7.1 THE EFFECT OF CORRELATED ERRORS 8 5 3.7.2
DETECTING CORRELATION 8 6 3 .7.3 TRANSFORMING TO REDUCE AUTOCORRELATION
8 8 3.7.4 CONFOUNDING OF CORRELATION AND BIAS 90 3.8 PROBLEMS 92 CHAPTER
4: MULTIPLE LINEAR REGRESSION 97 4.1 THE MULTIPLE LINEAR REGRESSION
MODEL 97 4.2 LEAST SQUARES FITTING 98 4.2.1 OBSERVATION AND VARIABLE
SPACE REPRESENTATIONS 9 8 4.2.2 NORMAL EQUATIONS 9 9 4.2.3 MULTIPLE
CORRELATION AND THE COEFFICIENT OF DETERMINATION 10 1 4.3 STATISTICAL
PROPERTIES OF LEAST SQUARES ESTIMATORS 10 2 4 .3 .1 UNBIASED ERRORS 103
4.3.2 UNCORRELATED CONSTANT VARIANCE ERRORS 103 4.3.3 NORMALLY
DISTRIBUTED ERRORS 104 4.4 USING THE COMPUTER 104 4.5 CONFIDENCE AND
PREDICTION INTERVALS 106 4 .5.1 STUDENT T-STATISTICS 107 4 .5.2
CONFIDENCE INTERVALS 108 4 .5.3 PREDICTION INTERVALS 11 1 4.6 GOODNESS
OF FIT AND OTHER HYPOTHESES 112 4.6.1 THE GENERAL LINEAR HYPOTHESIS TEST
112 4 .6.2 GOODNESS OF FIT USING REPLICATE OBSERVATIONS 115 4.6.3
ROBUSTNESS TO NONNORMALITY 11 8 4.7 COLLINEARITY 119 4.7.1 TOLERANCE AND
VARIANCE INFLATION 119 4 .7 .2 POLYNOMIAL REGRESSION 122 4 .7 .3
STEPWISE AND RIDGE REGRESSION 12 3 4.8 REGRESSION DIAGNOSTICS 125 4.8.1
MAHALANOBIS DISTANCE 12 5 4 .8 .2 LEVERAGE 12 7 4 .8 .3 STUDENTIZED
RESIDUALS AND DETECTING OUTLIERS 13 1 4.8.4 INFLUENCE 13 5 4.8.5 PARTIAL
RESIDUAL PLOTS AND PARTIAL REGRESSION PLOTS 14 0 4.9 PROBLEMS 143
CHAPTER 5: COMPUTER ASSISTED MODEL BUILDING 15 1 5.1 INTRODUCTION 151
5.2 BIAS VERSUS VARIANCE 152 5.3 STEPWISE METHODS 152 5 .3 .1 FORWARD
SELECTION AND BACKWARD ELIMINATION 15 3 5 .3 .2 STEPWISE REGRESSION 15 4
5.4 BEST SUBSET REGRESSION 158 5.5 CRITERIA FOR EVALUATING SUBSETS 160
5.6 HOW DOES ONE PROCEED? 167 5.7 A NONSTANDARD APPLICATION 168 5.8
PROBLEMS 169 CHAPTER 6: THE GENERAL LINEAR MODEL 173 61 INTRODUCTION 17
3 62 MEAN VECTORS AND COVARIANCE MATRICES 174 63 THE MULTIVARIATE NORMAL
DISTRIBUTION 175 6.4 PROJECTIONS 176 65 THE X2-THEOREM 180 6.6 THE
GENERAL LINEAR MODEL 18 1 6 .6.1 LEAST SQUARES ESTIMATES 18 1 6.6.2
STATISTICAL PROPERTIES 182 67 THE LINEAR REGRESSION MODEL 18 4 6.8 THE
FUNDAMENTAL F-TEST 186 6.9 THE GAUSS-MARKOV THEOREM 187 610 GENERALIZED
LEAST SQUARES AND WEIGHTED REGRESSION 188 6.11 PROBLEMS 19 0 CHAPTER 7:
ANALYSIS OF VARIANCE AND COVARIANCE 196 7.1 INTRODUCTION 196 7.2 THE
ONE=WAY MODEL 197 7.3 DUMMY VARIABLES 202 7.4 THE SIMPLE TWO-WAY
ADDITIVE MODEL 203 7.5 THE GENERAL TWO-WAY ADDITIVE MODEL 208 7.6 THE
GENERAL TWO-WAY MODEL 214 7.7 HIGHER ORDER MODELS 22 1 7.8 ANALYSIS OF
COVARIANCE 223 7.9 TRANSFORMATION AND MODEL DIAGNOSTICS 230 7.10
PROBLEMS 234 CHAPTER 8: NONLINEAR REGRESSION 23 8 8.1 WHY NONLINEAR
MODELS? 238 8.2 OVERVIEW OF A NONLINEAR REGRESSION PROGRAM 239 8 .2.1
PROBLEM SPECIFICATION 240 8 .2.2 OUTPUT 24 1 8.3 THE NONLINEAR
REGRESSION MODEL 245 8.4 NONLINEAR LEAST SQUARES FITTING 246 8.4.1
OBSERVATION AND VARIABLE SPACE REPRESENTATIONS 24 6 8 .4.2 NORMAL
EQUATIONS 24 8 8.5 THE GAUSS-NEWTON ALGORITHM 248 8 :5 .1 THE ALGORITHM
24 9 8 .5 .2 CONVERGENCE OF THE UNMODIFIED ALGORITHM 250 8 .5 .3
STANDARD MODIFICATIONS 25 1 8 .5 .4 DERIVATIVE FREE VERSIONS 25 5 8.6
USING THE COMPUTER; GROWTH CURVES 25 8 8.7 STATISTICAL PROPERTIES 266
8.7.1 STANDARD ERRORS 26 8 8 .7 .2 FUNCTIONS OF PARAMETERS 27 0 8.7.3
GOODNESS OF FIT AND OTHER HYPOTHESES 27 6 8.8 PROBLEMS 278 CHAPTER 9:
MAXIMUM LIKELIHOOD ANALYSIS AND ROBUST ESTIMATION 284 9.1 FITTING
EXPECTATIONS USING ITERATIVE REWEIGHTING 284 9.2 MAXIMUM LIKELIHOOD
ANALYSIS 285 9.2.1 GENERAL RESULTS FOR THE EXPONENTIAL FAMILY 287 9.2.2
POISSON MODELS 28 8 9.2.3 BINOMIAL MODELS 29 3 9.2.4 MULTINOMIAL MODELS
297 9.2.5 EXPONENTIAL SURVIVAL MODELS 304 9.3 ROBUST ESTIMATION 306 9
.3.1 THE LOCATION PROBLEM 30 6 9 .3.2 ROBUST REGRESSION 30 8 9.4
PROBLEMS 313 APPENDIX A: STATISTICAL TABLES 32 1 TABLE I NORMAL CURVE
AREAS 322 TABLE II CRITICAL VALUES OF T 323 TABLE III CRITICAL VALUES OF
X 324 TABLE IV PERCENTAGE POINTS OF THE F-DISTRIBUTION, A = .05 32 6
TABLE V PERCENTAGE POINTS OF THE F-DISTRIBUTION, A = .01 328 APPENDIX B:
PARTIAL ANSWERS TO SELECTED PROBLEMS 33 0 APPENDIX C: REFERENCES 348
INDEX 355
|
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| language | English |
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| spelling | Jennrich, Robert I. Verfasser aut An introduction to computational statistics regression analysis Robert I. Jennrich Englewood Cliffs, NJ Prentice Hall 1995 XVI, 364 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analise de regressao e de correlacao larpcal Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 s Regressionsanalyse (DE-588)4129903-6 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006872904&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jennrich, Robert I. An introduction to computational statistics regression analysis Analise de regressao e de correlacao larpcal Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4011152-0 |
| title | An introduction to computational statistics regression analysis |
| title_auth | An introduction to computational statistics regression analysis |
| title_exact_search | An introduction to computational statistics regression analysis |
| title_full | An introduction to computational statistics regression analysis Robert I. Jennrich |
| title_fullStr | An introduction to computational statistics regression analysis Robert I. Jennrich |
| title_full_unstemmed | An introduction to computational statistics regression analysis Robert I. Jennrich |
| title_short | An introduction to computational statistics |
| title_sort | an introduction to computational statistics regression analysis |
| title_sub | regression analysis |
| topic | Analise de regressao e de correlacao larpcal Regressieanalyse gtt Regression analysis Regressionsanalyse (DE-588)4129903-6 gnd Datenverarbeitung (DE-588)4011152-0 gnd |
| topic_facet | Analise de regressao e de correlacao Regressieanalyse Regression analysis Regressionsanalyse Datenverarbeitung |
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