Fitting equations to data: computer analysis of multifactor data
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1980
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in probability and mathematical statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 458 S. graph. Darst. |
| ISBN: | 0471053708 |
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| 245 | 1 | 0 | |a Fitting equations to data |b computer analysis of multifactor data |c Cuthbert Daniel ; Fred S. Wood |
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| 264 | 1 | |a New York [u.a.] |b Wiley |c 1980 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Fitting equations to data
Autor: Daniel, Cuthbert
Jahr: 1980
Contents Chapter 1 Introduction 1.1 Flow diagram of procedure used, 1 1.2 Role of computer, 1 1.3 Sequence of subjects discussed, 3 Chapter 2 Assumptions and Methods of Fitting Equations 2.1 Assumptions, 5 2.2 Methods of fitting equations. 6 2.3 Least squares, 6 2.4 Linear least-squares estimation, 9 2.5 Nonlinear least-squares estimation, 9 Appendix 2A Linear least-squares estimates—one independent variable, 10 2A.1 Assumptions, 10 2A.2 Basic idea and derivation, 10 2A.3 Confidence regions, 12 Appendix 2B Linear least-squares estimates—general case, 13 2B.1 Estimates of coefficients, 13 2B.2 Variance and standard errors of coefficients, 15 2B.3 Computer computations, 16 2B.4 Partitioning sums of squares, 16 2B.5 Multiple correlation coefficient squared, R y 2 , 17 2B.6 F-value, 17 2B.7 Bias and random error, 17 2B.8 Residual mean square, 17 2B.9 Residual root mean square, 18
XIV CONTENTS Chapter 3 One Independent Variable 19 3.1 Plotting data and selecting form of equation, 19 3.2 Plots of linearizable equations, 19 3.3 Plots of nonlinearizable equations, 22 3.4 Statistical independence and clusters of dependent variable, 24 3.5 Allocation of data points, 25 3.6 Outliers, 25 3.7 Use of computer program, 26 3.8 Study of residuals, 27 3.9 Dealing with error in the independent variable, 32 3.10 Example of fitting a straight line to data—one independent variable, 32 Appendix 3A Cumulative distribution plots of random normal deviates, 33 Appendix 3B Example of fitting a straight line to data— one independent variable, 33 Chapter 4 Two or More Independent Variables 50 4.1 Inadequacies of x-y plots with two or more independent variables, 50 4.2 Equation forms and transformations, 53 4.3 Variances of estimated coefficients, bi, and fitted values, Yj, 55 4.4 Use of indicator variables for discontinuous or qualitative classifications, 56 One qualitative factor at two levels One qualitative two-level factor and one quantitative (continuous) factor Discrete factors at more than two levels Discrete factors interacting with continuous factors 4.5 Allocation of data in factor space, 57 Linear dependences among the x t The outermost points in data space Nested data Chapter 5 Fitting an Equation in Three Independent Variables 60 5.1 Introduction, 60 5.2 First trials, 60 5.3 Possible causes of disturbance, 61
CONTENTS XV 5.4 Outlier or logged response or squared independent variable, 65 5.5 Random error estimated from near neighbors, 72 5.6 Independence of observations, 73 5.7 Systematic examination of alternatives discovered sequentially, 75 5.8 Remote points in factor space, 77 5.9 Equation using “lined-out” data, 77 5.10 Conclusions on stack loss problem, 81 5.11 General conclusions, 82 Chapter 6 Selection of Independent Variables 83 6.1 Introduction, 83 Assumptions Obvious imperfections 2 K possible equations from K candidate variables On stepwise regression E-test All 2 K equations and fractions 6.2 Total squared error as a criterion for goodness of fit—C p , 86 Definition Derivation of the C P statistic Mallows’ graphical method of comparing fitted equations 6.3 A four-variable example, 89 6.4 Disposition of data in factor space, 91 6.5 A six-variable example, 95 a. Search for all 2 K equations b. t Kt [-directed search c. Fractional replicates Appendix 6A Computer printouts of four-variable example, 104 Appendix 6B Computer printouts of six-variable example, 104 Appendix 6C Fractional replication for 2 K equations, 104 Chapter 7 Some Consequences of the Disposition of the Data Points 121 7.1 Introduction, 121 7.2 Description of example with ten independent variables, 122 First steps
XVI CONTENTS 7.3 Interior analysis I. “Component effects” table, 123 7.4 Interior analysis II. Component and component-plus-residual plots, 124 7.5 Search of all 2 K possible subset equations, 126 7.6 ¿-directed search, 126 7.7 Test for an outlier, 127 7.8 Interior analysis III. Weighted-squared-standardized- distance to look for far-out points of influential variables, 129 7.9 Interior analysis IV. Variance ratio to look for far-out points of uninfluential variables, 131 7.10 Interior analysis V. Error estimation from near neighbors, 133 7.11 Cross verification, 136 7.12 Other examples of error estimation from near neighbors, 137 Six-variable example of Chapter 6 Stack loss example of Chapter 5 7.13 Additional examples of using component and component-plus-residual plots, 139 Example of the use of plots in choosing the form of equation Distribution of observations over each independent variable Four-variable example—Distribution of independent variables Eleven-variable example—Inner and outer observations 7.14 Other conditions identified by component and component-plus-residual plots, 145 7.15 Summary, 146 Appendix 7A Appendix 7B Appendix 7C Appendix 7D Appendix 7E 0 Appendix 7F Computer printouts of ten-variable example, 150 Computer printout of six-variable example, 199 Computer printouts of stack loss example, 200 Computer printouts of four-variable octane example, 207 Computer printouts of eleven-variable example, 218 Critical values for studentized residual to test for single outlier, 232
CONTENTS XVll Chapter 8 Selection of Variables in Nested Data 234 8.1 Background of example, 234 8.2 Fitting equation, 236 8.3 Recognition of nested data, 236 8.4 Data identification and entry, 236 8.5 Fitting equation to nested data, 236 Use of indicator (dummy) variables Test for significance of added variables, “individual” versus “common” slopes 8.6 Fitting equation among sets of nested data, 240 8.7 Selecting variables based on total error, recognizing bias and random error, 243 8.8 Properties of final equation, 244 8.9 Comparison of equations, 247 Appendix 8A Data preparation and computer printouts of example, 248 Chapter 9 Nonlinear Least Squares, a Complex Example 267 9.1 Introduction, 267 9.2 Background of example, 268 9.3 Replicates, 271 9.4 Potential equations, 273 9.5 Nonlinear fit—observations of individual cements versus time, 276 9.6 Fit with indicator variables, 277 9.7 Fit with composition, 280 9.8 Possible nesting within cements, 293 9.9 Comparison with previous linear least-square fits, 295 9.10 Fit using composition in mol percents, 296 9.11 Conclusions, 299 Appendix 9A Computer printout of nonlinear example, 300 Glossary 338 Conventions, 338 Symbols, 338 Computer terms, 343
xvin CONTENTS LINWOOD User’s Manual 354 LINWOOD, a computer linear least-squares curve-fitting program Abstract, 354 General information, 355 Input, 356 Control card entry, 356 Standard data card entry, 366 Problems using transformation option, 367 Order of cards, 374 Sample problem, 376 Example of weighted observations, 381 Example to measure the precision of calculations, 396 Example of using plots in choosing the form of equation, 406 Execution time, 415 Summary of control cards, 418 Summary of order of cards, 419 NONLINWOOD, a computer nonlinear least-squares curve-fitting program Abstract, 420 General information, 421 Input, 422 Control card, 422 Format card, 424 Starting values of coefficients, 424 Data cards, 424 Order of cards, 425 Control and data card entry forms, 425 Equation subroutine, 425 Example of transformations, 427 Example 1, 2 coefficients, 2 variables, 428 Example 2, 43 coefficients, 16 variables, 442 Example 3, 19 coefficients, 7 variables, 444 Summary of control cards, 446 Example of subroutine model, 447 Summary of order of cards, 447 NONLINWOOD User’s Manual 420 Bibliography 449 Index 453
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| genre | 1\p (DE-588)4151278-9 Einführung gnd-content |
| genre_facet | Einführung |
| id | DE-604.BV001942287 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:37:37Z |
| institution | BVB |
| isbn | 0471053708 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001265938 |
| oclc_num | 886204699 |
| open_access_boolean | |
| owner | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-N2 DE-945 DE-19 DE-BY-UBM DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-91 DE-BY-TUM DE-91G DE-BY-TUM DE-384 DE-N2 DE-945 DE-19 DE-BY-UBM DE-83 DE-11 DE-188 |
| physical | XVIII, 458 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and mathematical statistics |
| spelling | Daniel, Cuthbert 1904-1997 Verfasser (DE-588)14001036X aut Fitting equations to data computer analysis of multifactor data Cuthbert Daniel ; Fred S. Wood 2. ed. New York [u.a.] Wiley 1980 XVIII, 458 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics Analyse multivariée - Informatique Courbes empiriques - Informatique Curve fitting gtt Kleinste-kwadratenmethode gtt Moindres carrés - Informatique Multivariate analyse gtt Datenverarbeitung Curve fitting Data processing Least squares Data processing Multivariate analysis Data processing Statistik (DE-588)4056995-0 gnd rswk-swf Multivariate Daten (DE-588)4195680-1 gnd rswk-swf Faktorenanalyse (DE-588)4016338-6 gnd rswk-swf Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Datenauswertung (DE-588)4131193-0 gnd rswk-swf Datenverarbeitung (DE-588)4011152-0 gnd rswk-swf Kurvenanpassung (DE-588)4727564-9 gnd rswk-swf Computerunterstütztes Verfahren (DE-588)4139030-1 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Multivariate Analyse (DE-588)4040708-1 s Datenverarbeitung (DE-588)4011152-0 s DE-604 Faktorenanalyse (DE-588)4016338-6 s Statistik (DE-588)4056995-0 s Computerunterstütztes Verfahren (DE-588)4139030-1 s Multivariate Daten (DE-588)4195680-1 s 2\p DE-604 Kurvenanpassung (DE-588)4727564-9 s 3\p DE-604 Datenauswertung (DE-588)4131193-0 s 4\p DE-604 Wood, Fred S. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001265938&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 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Daniel, Cuthbert 1904-1997 Wood, Fred S. Fitting equations to data computer analysis of multifactor data Analyse multivariée - Informatique Courbes empiriques - Informatique Curve fitting gtt Kleinste-kwadratenmethode gtt Moindres carrés - Informatique Multivariate analyse gtt Datenverarbeitung Curve fitting Data processing Least squares Data processing Multivariate analysis Data processing Statistik (DE-588)4056995-0 gnd Multivariate Daten (DE-588)4195680-1 gnd Faktorenanalyse (DE-588)4016338-6 gnd Multivariate Analyse (DE-588)4040708-1 gnd Datenauswertung (DE-588)4131193-0 gnd Datenverarbeitung (DE-588)4011152-0 gnd Kurvenanpassung (DE-588)4727564-9 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd |
| subject_GND | (DE-588)4056995-0 (DE-588)4195680-1 (DE-588)4016338-6 (DE-588)4040708-1 (DE-588)4131193-0 (DE-588)4011152-0 (DE-588)4727564-9 (DE-588)4139030-1 (DE-588)4151278-9 |
| title | Fitting equations to data computer analysis of multifactor data |
| title_auth | Fitting equations to data computer analysis of multifactor data |
| title_exact_search | Fitting equations to data computer analysis of multifactor data |
| title_full | Fitting equations to data computer analysis of multifactor data Cuthbert Daniel ; Fred S. Wood |
| title_fullStr | Fitting equations to data computer analysis of multifactor data Cuthbert Daniel ; Fred S. Wood |
| title_full_unstemmed | Fitting equations to data computer analysis of multifactor data Cuthbert Daniel ; Fred S. Wood |
| title_short | Fitting equations to data |
| title_sort | fitting equations to data computer analysis of multifactor data |
| title_sub | computer analysis of multifactor data |
| topic | Analyse multivariée - Informatique Courbes empiriques - Informatique Curve fitting gtt Kleinste-kwadratenmethode gtt Moindres carrés - Informatique Multivariate analyse gtt Datenverarbeitung Curve fitting Data processing Least squares Data processing Multivariate analysis Data processing Statistik (DE-588)4056995-0 gnd Multivariate Daten (DE-588)4195680-1 gnd Faktorenanalyse (DE-588)4016338-6 gnd Multivariate Analyse (DE-588)4040708-1 gnd Datenauswertung (DE-588)4131193-0 gnd Datenverarbeitung (DE-588)4011152-0 gnd Kurvenanpassung (DE-588)4727564-9 gnd Computerunterstütztes Verfahren (DE-588)4139030-1 gnd |
| topic_facet | Analyse multivariée - Informatique Courbes empiriques - Informatique Curve fitting Kleinste-kwadratenmethode Moindres carrés - Informatique Multivariate analyse Datenverarbeitung Curve fitting Data processing Least squares Data processing Multivariate analysis Data processing Statistik Multivariate Daten Faktorenanalyse Multivariate Analyse Datenauswertung Kurvenanpassung Computerunterstütztes Verfahren Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001265938&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT danielcuthbert fittingequationstodatacomputeranalysisofmultifactordata AT woodfreds fittingequationstodatacomputeranalysisofmultifactordata |