A first Course in linear regression:
Gespeichert in:
| Vorheriger Titel: | Younger, Marys S. Handbook for linear regression |
|---|---|
| 1. Verfasser: | |
| Format: | Buch |
| Sprache: | Undetermined |
| Veröffentlicht: |
Boston
Duxbury Pr.
1985
|
| Ausgabe: | 2. ed. |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 703 S. |
| ISBN: | 0871508656 |
Internformat
MARC
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| 100 | 1 | |a Younger, Mary S. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A first Course in linear regression |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boston |b Duxbury Pr. |c 1985 | |
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| 780 | 0 | 0 | |i 1. Aufl. |a Younger, Marys S. |t Handbook for linear regression |
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Datensatz im Suchindex
| _version_ | 1804140615756152832 |
|---|---|
| adam_text | Titel: A first course in linear regression
Autor: Younger, Mary S
Jahr: 1985
CONTENTS O s~ N E L I N E A l.l Introduction 1 1.2 What Is Regression? Exercises 7 1.3 Scatter Diagrams Exercises 15 1.4 The Model 19 Exercises 23 1.5 Summary 23 E O N 1 T R W T H E LEA S T S Q U A R E G R E S S I 0 N E Q U A T I O 2.1 Introduction 24 2.2 Criteria for the “Best” Line 24 2.3 The Method of Least Squares and Normal Equations Exercises 40 2.4 Shortcut Formula 43 Exercise 49 2.5 Effects of Transformations of the A -Values 50 Exercises 57 2.6 Summary 59 S N 30 24 O ix
X CONTENTS T H R E E THE MATRIX APPROACH 60 3.1 A Brief Introduction to Matrices 60 3.2 Some Definitions 61 Exercises 64 3.3 Matrix Operations 66 Exercises 71 3.4 Determinants 73 Exercises 79 3.5 Inverses 81 Exercises 85 3.6 Application to Solving Simultaneous Equations 86 Exercises 92 3.7 Application to Simple Linear Regression 93 Exercises 102 3.8 Summary 103 THE USE OF COMPUTER PROGRAMS IN SIMPLE REGRESSION 104 4.1 Introduction 104 4.2 Biomedical (BMD) P-Series Packages 105 Exercises 112 4.3 Minitab 113 Exercises 122 4.4 Statistical Analysis System (SAS) 123 Exercises 131 4.5 Statistical Package for the Social Sciences (SPSS X ) 133 Exercises 142 4.6 Inverting a Matrix 142 Exercises 149 4.7 Choice of a Package 150 4.8 Summary 151 F O U R
CONTENTS xi five A N D T INTE H R E P R U E S T E A T I O N O F THE R E GRES S I O N E Q U A T I O N 152 5.1 Introduction 152 5.2 Predicting an Average 152 5.3 Predicting the Average in a Designed Experiment 156 5.4 Meaning of the Intercept 158 5.5 Meaning of the Slope 162 5.6 Relationships and Causal Relationships 165 Exercises 169 5.7 Summary 176 S_I_X MEASURING ERROR IN ESTIMATION 177 6.1 Introduction 177 6.2 Assumptions 177 Exercise 183 6.3 Calculating a Formula for the Standard Error of Estimate 183 6.4 Interpretation of the Standard Error of Estimate 188 Exercises 190 6.5 Interval Estimates: A Review 191 6.6 The t Distribution 197 Exercise 199 6.7 Confidence Intervals on a Mean Response 200 Exercises 203 6.8 Confidence Interval for an Individual Response 204 Exercises 205 6.9 Finding the Standard Error of Estimate on Computer Printout 206 6.10 Summary 210
xii CONTENTS s _E_V_E_N NFERENCES CONCERNING THE REGRESSION COEFFICIENTS 211 7.1 Introduction 211 7.2 Can We Be Confident That a Relationship Exists? 211 7.3 Hypothesis Tests on the Regression Coefficient 213 Exercises 223 7.4 Tests on the Regression Constant 225 Exercises 227 7.5 The Attained Significance Level (/5-Value) 227 Exercises 229 7.6 Analysis of Variance Using Matrices 230 Exercises 237 7.7 Confidence Intervals on the Parameters in the Model 239 Exercises 241 7.8 Testing for Significance Using the Computer 242 Exercises 245 7.9 Summary 245 E_I_ G _H_T CORRELATION 247 8.1 Introduction 247 8.2 The Coefficient of Determination 248 Exercises 255 8.3 The Correlation Coefficient 255 8.4 Test of Significance 257 Exercises 260 8.5 Correlation Using the Computer 261 Exercises 263 8.6 Summary 263 N I N I appropriateness OF THE MODEL 264 9.1 Introduction 264 9.2 The Assumption of Uniform Scatter 264 Exercises 279
CONTENTS xiii T AND E_ M U 9.3 The Assumption of the Simple Linear Model 280 Exercises 286 9.4 Independence of Errors 288 9.5 The Assumption of Normality 302 9.6’ Summary 305 E N E X P O N E N T I A L POL Y N O M I A L M O 10.1 Introduction 306 10.3 Alternatives to the Straight-Line Model: Exponential Models 307 Exercises 327 10.4 Alternatives to the Straight-Line Model: Polynomial Models 330 10.5 Using the Computer To Fit Polynomial Models 343 Exercises 368 10.6 Summary 370 L _E_V_E_N LTIPLE REGRESSION 372 11.1 Introduction 372 11.2 The Multiple Linear Regression Model 372 11.3 Normal Equations 374 Exercises 382 11.4 Using the Computer To Perform Multiple Regression 387 Exercise 401 11.5 Interpretation and Use of the Multiple Regression Equation 402 Exercises 404 11.6 Multicollinearity 405 Exercises 416 11.7 The Standard Error of Estimate 417 Exercises 422 11.8 More Complicated Multiple Regression Models 423 Exercises 424 11.9 Summary 424
XIV CONTENTS I _W_ E _L_V_ CORRELATION IN MULTIPLE REGRESSION 425 12.1 Introduction 425 12.2 Correlations Between Pairs of Variables 425 Exercises 426 12.3 Multiple Coefficient of Determination 427 Exercises 429 12.4 Partial Correlation 429 Exercises 434 12.5 Summary 434 T H I R T E E T E S T S 0 F SIGNIFICA N C E I N M U L T I P LE REGRESS ION 43 13.1 Introduction 435 13.2 The General Test of Significance of the Regression 435 Exercise 439 13.3 Individual Tests: General 439 13.4 Individual Tests: Uncorrelated Predictors 441 Exercise 446 13.5 Individual Tests: Correlated Predictors 447 Exercises 455 13.6 Confidence Intervals on Net Regression Coefficients 455 Exercise 456 13.7 Summary 457 F O U RTE E DUMMY VARIABLES 458 14.1 Introduction 458 14.2 The Use of Dummy Variables 459 Exercises 467
CONTENTS XV 14.3 Interactions When Variables Are Not Dummy Variables 470 Exercises 476 14.4 Summary 477 F_I_F_T_E_E_N SOME VARIABLE-SELECTION PROCEDURES 479 15.1 Analysis of a Larger Problem 479 Exercise 486 15.2 Selecting a Subset of Predictors 487 15.3 Selection Procedures 488 15.4 BMD Selection Procedures 491 Exercises 509 15.5 Minitab Selection Procedures 510 Exercises 519 15.6 SAS Selection Procedures 519 Exercises 544 15.7 SPSS X Selection Procedures 545 Exercises 556 15.8 Other Techniques for Selecting Variables 557 Exercises 572 15.9 Summary 572 I X T E E A N A L Y s I s OF R E S I DUALS M U L T I P L E R E G R E S S I O N 574 16.1 Introduction 574 16.2 Examination of Residuals in Multiple Regression 575 Exercises 581 16.3 Two-Model Selection Criteria 582 Exercises 596 16.4 Summary 597
xvi CONTENTS s E L E C T E D R E F E R E N C E S A N D S U G G E S T I O N s F O R F U R T H E R R E A D I N G APPENDICES Appendix A: Appendix B: Appendix C: Appendix D: Appendix E: Appendix F: Appendix G: Appendix H: Appendix I: Appendix J: Appendix K: Appendix L: The Algebra of Summation Notation 601 Minimization of L = , (T - Y) 2 603 Formatting for the Computer 605 The Binary Number System 608 Orthogonal Polynomials 611 Fitting the Regression Line Through the Origin 614 A Large Data Set 615 Table of Critical Values of the Student’s t Distribution Table of Critical Values of the F Distribution 626 Table of Dixon Criteria 629 Table of Durbin-Watson Test Bounds 630 Analyses of Data Set 632 6 ANSWERS TO SELECTED EXERCISES 666 INDEX 697
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| id | DE-604.BV024601323 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:02:48Z |
| institution | BVB |
| isbn | 0871508656 |
| language | Undetermined |
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| publishDate | 1985 |
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| publisher | Duxbury Pr. |
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| spelling | Younger, Mary S. Verfasser aut A first Course in linear regression 2. ed. Boston Duxbury Pr. 1985 703 S. txt rdacontent n rdamedia nc rdacarrier 1. Aufl. Younger, Marys S. Handbook for linear regression HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018574599&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Younger, Mary S. A first Course in linear regression |
| title | A first Course in linear regression |
| title_auth | A first Course in linear regression |
| title_exact_search | A first Course in linear regression |
| title_full | A first Course in linear regression |
| title_fullStr | A first Course in linear regression |
| title_full_unstemmed | A first Course in linear regression |
| title_old | Younger, Marys S. Handbook for linear regression |
| title_short | A first Course in linear regression |
| title_sort | a first course in linear regression |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018574599&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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