Regression analysis and linear models: concepts, applications, and implementation
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
New York ; London
Guilford Press
[2017]
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| Series: | Methodology and the social sciences
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xxvi, 661 Seiten Illustrationen, Diagramme |
| ISBN: | 9781462521135 |
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MARC
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| 100 | 1 | |a Darlington, Richard B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Regression analysis and linear models |b concepts, applications, and implementation |c Richard B. Darlington, Andrew F. Hayes |
| 264 | 1 | |a New York ; London |b Guilford Press |c [2017] | |
| 300 | |a xxvi, 661 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a Methodology and the social sciences | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Sozialwissenschaften | |
| 650 | 4 | |a Regression analysis | |
| 650 | 4 | |a Linear models (Statistics) | |
| 650 | 4 | |a Psychology |x Statistical methods | |
| 650 | 4 | |a Social sciences |x Statistical methods | |
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Contents
List of Symbols and Abbreviations
1 • Statistical Control and Linear Models
1.1 Statistical Control / 1
1.1.1 The Need for Control /1
1.1.2 Five Methods of Control / 2
1.1.3 Examples of Statistical Control / 4
1.2 An Overview of Linear Models / 8
1.2.1 What You Should Know Already 111
1.2.2 Statistical Software for Linear Modeling and Statistical Control 111
1.2.3 About Formulas /14
1.2.4 On Symbolic Representations /15
1.3 Chapter Summary / 16
2 • The Simple Regression Model
2.1 Scatterplots and Conditional Distributions / 17
2.1.1 Scatterplots /17
2.1.2 A Line through Conditional Means /18
2.1.3 Errors of Estimate / 21
2.2 The Simple Regression Model / 23
2.2.1 The Regression Line /23
2.2.2 Variance, Covariance, and Correlation / 24
2.2.3 Finding the Regression Line / 25
2.2.4 Example Computations / 26
2.2.5 Linear Regression Analysis by Computer / 28
2.3 The Regression Coefficient versus the Correlation Coefficient / 31
2.3.1 Properties of the Regression and Correlation Coefficients / 32
2.3.2 Uses of the Regression and Correlation Coefficients / 34
2.4 Residuals / 35
2.4.1 The Three Components of Y135
2.4.2 Algebraic Properties of Residuals / 36
2.4.3 Residuals as Y Adjusted for Differences in XI37
2.4.4 Residual Analysis / 37
2.5 Chapter Summary / 41
3 • Partial Relationship and the Multiple Regression Model
3.1 Regression .Analysis with More Than One Predictor Variable / 43
3.1.1 An Example/43
3.1.2 Regressors / 46
XX
Contents
3.1.3 Models/47
3.1.4 Representing a Model Geometrically / 49
3.1.5 Model Errors / 50
3.1.6 An Alternative View of the Model / 52
3.2 The Best-Fitting Model / 55
3.2.1 Model Estimation with Computer Software / 55
3.2.2 Partial Regression Coefficients / 58
3.2.3 The Regression Constant / 63
3.2.4 Problems with Three or More Regressors / 64
3.2.5 Tfe? Multiple Correlation R/68
3.3 Scale-Free Measures of Partial Association / 70
3.3.1 Semipartial Correlation / 70
3.3.2 Partial Correlation / 71
3.3.3 Tfte Standardized Regression Coefficient / 73
3.4 Some Relations among Statistics / 75
3.4.1 Relations among Simple, Multiple, Partial, and Semipartial Correlations / 75
3.4.2 Venn Diagrams / 73
3.4.3 Partial Relationships and Simple Relationships May Have Different Signs / 30
3.4.4 How Covariates Affect Regression Coefficients / 81
3.4.5 Formulas for by pry, sfy and R/82
3.5 Chapter Summary / 83
4 • Statistical Inference in Regression 85
4.1 Concepts in Statistical Inference / 85
4.1.1 Statistics and Parameters / 35
4.1.2 Assumptions for Proper Inference / 38
4.1.3 Expected Values and Unbiased Estimation / 91
4.2 The ANOVA Summary Table / 92
4.2.1 Data = Model + Error / 95
4.2.2 Total and Regression Sums of Squares / 97
4.2.3 Degrees of Freedom / 99
4.2.4 Mean Squares /100
4.3 Inference about the Multiple Correlation / 102
4.3.1 Biased and Less Biased Estimation of rRz f 102
4.3.2 Testing a Hypothesis about TR /104
4.4 The Distribution of and Inference about a Partial
Regression Coefficient / 105
4.4.1 Testing a Null Hypothesis about Tbj /105
4.4.2 Interval Estimates for Tb;- /106
4.4.3 Factors Affecting the Standard Error of bj /107
4.4.4 Tolerance /109
4.5 Inferences about Partial Correlations / 112
4.5.1 Testing a Null Hypothesis about Tprj and Tsr;- /112
4.5.2 Other Inferences about Partial Correlations /113
4.6 Inferences about Conditional Means / 116
4.7 Miscellaneous Issues in Inference / 118
4.7.1 Hozv Great a Drawback Is Collinearity? /118
4.7.2 Contradicting Inferences /119
4.7.3 Sample Size and Nonsignificant Covariates /121
4.7.4 Inference in Simple Regression (When k~l)/121
4.8 Chapter Summary / 122
5 • Extending Regression Analysis Principles 125
5.1 Dichotomous Regressors / 125
5.1.1 Indicator or Dummy Variables /125
5.1.2 Estimates of Y Are Group Means /126
5.1.3 The Regression Coefficient for an Indicator Is a Difference /128
Contents
XXI
5.1.4 A Graphic Representation /129
5.1.5 A Caution about Standardized Regression Coefficients
for Dichotomous Regressors /130
5.1.6 Artificial Categorization of Numerical Variables /132
5.2 Regression to the Mean / 135
5.2.1 How Regression Got Its Name /135
5.2.2 The Phenomenon /135
5.2.3 Versions of the Phenomenon /138
5.2.4 Misconceptions and Mistakes Fostered by Regression to the Mean /140
5.2.5 Accounting for Regression to the Mean Using Linear Models /141
5.3 Multidimensional Sets / 144
5.3.1 The Partial and Semipartial Multiple Correlation /145
5.3.2 What It Means IfPR = 0 or SR = 0/148
5.3.3 Inference Concerning Sets of Variables /148
5.4 A Glance at the Big Picture / 152
5.4.1 Further Extensions of Regression /153
5.4.2 Some Difficulties and Limitations j 153
5.5 Chapter Summary / 155
6 • Statistical versus Experimental Control 157
6.1 Why Random Assignment? / 158
6.1.1 Limitations of Statistical Control /158
6.1.2 The Advantage of Random Assignment /159
6.1.3 The Meaning of Random Assignment /160
6.2 Limitations of Random Assignment / 162
6.2.1 Limitations Common to Statistical Control and Random Assignment /162
6.2.2 Limitations Specific to Random Assignment /165
6.2.3 Correlation and Causation /166
6.3 Supplementing Random Assignment with Statistical Control / 169
6.3.1 Increased Precision and Power /169
6.3.2 Invulnerability to Chance Differences between Groups /174
6.3.3 Quantifying and Assessing Indirect Effects f 175
6.4 Chapter Summary / 176
7 • Regression for Prediction 177
7.1 Mechanical Prediction and Regression / 177
7.1.1 The Advantages of Mechanical Prediction /177
7.1.2 Regression as a Mechanical Prediction Method /178
7.1.3 A Focus on R Rather Than on the Regression Weights /180
7.2 Estimating True Validity / 181
7.2.1 Shrunken versus Adjusted Rf 181
7.2.2 Estimating TRS /183
7.2.3 Shrunken R Using Statistical Software f 186
7.3 Selecting Predictor Variables / 188
7.3.1 Stepwise Regression /189
7.3.2 All Subsets Regression /192
7.3.3 How Do Variable Selection Methods Perform? f 192
7.4 Predictor Variable Configurations / 195
7.4.1 Partial Redundancy (the Standard Configuration) /196
7.4.2 Complete Redundancy /198
7.4.3 Independence /199
7.4.4 Complementarity /199
7.4.5 Suppression / 200
7.4.6 How These Configurations Relate to the Correlation between Predictors /201
7A.7 Configurations of Three or More Predictors f 205
7.5 Revisiting the Value of Human Judgment / 205
7.6 Chapter Summary / 207
Contents
XXII
8 • Assessing the Importance of Regressors 209
8.1 What Does It Mean for a Variable to Be Important? / 210
8.1.1 Variable Importance in Substantive or Applied Terms / 210
8.1.2 Variable Importance in Statistical Terms /211
8.2 Should Correlations Be Squared? / 212
8.2.1 Decision Theory / 213
8.2.2 Small Squared Correlations Can Reflect Noteworthy Effects / 217
8.2.3 Pearson's r as the Ratio of a Regression Coefficient to Its Maximum
Possible Value f 218
8.2.4 Proportional Reduction in Estimation Error / 220
8.2.5 When the Standard Is Perfection / 222
8.2.6 Summary/223 *
8.3 Determining the Relative Importance of Regressors in a Single
Regression Model / 223
8.3.1 The Limitations of the Standardized Regression Coefficient / 224
8.3.2 The Advantage of the Semipartial Correlation / 225
8.3.3 Some Equivalences among Measures / 226
8.3.4 Eta-Squared, Partial Eta-Squared, and Cohen's f-Squared / 227
8.3.5 Comparing Two Regression Coefficients in the Same Model / 229
8.4 Dominance Analysis / 233
8.4.1 Complete and Partial Dominance / 235
8.4.2 Example Computations / 236
8.4.3 Dominance Analysis Using a Regression Program / 237
8.5 Chapter Summary / 240
9 • Multicategorical Regressors 243
9.1 Multicategorical Variables as Sets / 244
9.1.1 Indicator (Dummy) Coding/245
9.1.2 Constructing Indicator Variables ( 249
9.1.3 The Reference Category / 250
9.1.4 Testing the Equality of Several Means f 252
9.1.5 Parallels with Analysis of Variance / 254
9.1.6 Interpreting Estimated Y and the Regression Coefficients /255
9.2 Multicategorical Regressors as or with Covariates / 258
9.2.1 Multicategorical Variables as Covariates / 258
9.2.2 Comparing Groups and Statistical Control / 260
9.2.3 Interpretation of Regression Coefficients / 264
9.2.4 Adjusted Means / 266
9.2.5 Parallels with ANCOVA /268
9.2.6 More Than One Covariate / 271
9.3 Chapter Summary / 273
10 • More on Multicategorical Regressors 275
10.1 Alternative Coding Systems / 276
10.1.1 Sequential (Adjacent or Repeated Categories) Coding / 277
10.1.2 Helmert Coding / 283
10.1.3 Effect Coding / 287
10.2 Comparisons and Contrasts / 289
10.2.1 Contrasts / 289
10.2.2 Computing the Standard Error of a Contrast / 291
10.2.3 Contrasts Using Statistical Software / 292
10.2.4 Covariates and the Comparison of Adjusted Means / 294
10.3 Weighted Group Coding and Contrasts / 298
10.3.1 Weighted Effect Coding / 298
10.3.2 Weighted Helmert Coding / 300
Contents
10.3.3 Weighted Contrasts / 304
10.3.4 Application to Adjusted Means / 308
10.4 Chapter Summary / 308
11 • Multiple Tests
11.1 The Multiple Test Problem / 312
11.1.1 An Illustration through Simulation / 312
11.1.2 The Problem Defined/315
11.1.3 The Role of Sample Size / 316
11.1.4 The Generality of the Problem / 317
11.1.5 Do Omnibus Tests Offer "Protection"? /319
11.1.6 Should You Be Concerned about the Midtiple Test Problem? /319
11.2 The Bonferroni Method / 320
11.2.1 Independent Tests / 321
11.2.2 The Bonferroni Method for Nonindependent Tests / 322
11.2.3 Revisiting the Illustration / 324
11.2.4 Bonferroni Layering / 324
11.2.5 Finding an "Exact" p-Value / 325
11.2.6 Nonsense Values ¡327
11.2.7 Flexibility of the Bonferroni Method / 327
11.2.8 Power of the Bonferroni Method / 328
11.3 Some Basic Issues Surrounding Multiple Tests / 328
11.3.1 Why Correct for Multiple Tests at All? j 329
11.3.2 Why Not Correct for the Whole History of Science? / 330
11.3.3 Plausibility and Logical Independence of Hypotheses / 331
11.3.4 Planned versus Unplanned Tests / 335
11.3.5 Summary of the Basic Issues / 338
11.4 Chapter Summary / 338
12 • Nonlinear Relationships
12.1 Linear Regression Can Model Nonlinear Relationships / 341
12.1.1 When Must Curves Be Fitted? / 342
12.1.2 The Graphical Display of Curvilinearity / 344
12.2 Polynomial Regression / 347
12.2.1 Basic Principles / 347
12.2.2 An Example / 350
12.2.3 The Meaning of the Regression Coefficients
for Lower-Order Regressors / 352
12.2.4 Centering Variables in Polynomial Regression / 354
12.2.5 Finding a Parabola's Maximum or Minimum /356
12.3 Spline Regression / 357
12.3.1 Linear Spline Regression / 358
12.3.2 Implementation in Statistical Software / 363
12.3.3 Polynomial Spline Regression / 364
12.3.4 Covariates, Weak Curvilinearity, and Choosing Joints / 368
12.4 Transformations of Dependent Variables or Regressors / 369
12.4.1 Logarithmic Transformation / 370
12.4.2 The Box-Cox Transformation ¡372
12.5 Chapter Summary / 374
13 • Linear Interaction
13.1 Interaction Fundamentals / 377
13.1.1 Interaction as a Difference in Slope / 377
13.1.2 Interaction between Two Numerical Regressors / 378
13.1.3 Interaction versus Intercorrelation / 379
13.1.4 Simple Linear Interaction / 380
xxiii
311
341
377
XXIV
Contents
13.1.5 Representing Simple Linear Interaction with a Cross-Product / 381
13.1.6 The Symmetry of Interaction / 382
13.1.7 Interaction as a Warped Surface / 384
13.1.8 Covariates in a Regression Model with an Interaction / 385
13.1.9 The Meaning of the Regression Coefficients / 385
13.1.10 An Example with Estimation Using Statistical Software / 386
13.2 Interaction Involving a Categorical Regressor / 390
13.2.1 Interaction between a Dichotomous and a Numerical Regressor / 390
13.2.2 The Meaning of the Regression Coefficients / 392
13.2.3 Interaction Involving a Multicategorical and a Numerical Regressor / 394
13.2.4 Inference When Interaction Requires More Than One
Regression Coefficient / 397 t
13.2.5 A Substantive Example / 398
13.2.6 Interpretation of the Regression Coefficients / 402
13.3 Interaction between Two Categorical Regressors / 404
13.3.1 The 2x2 Design / 404
13.3.2 Interaction between a Dichotomous and a Multicategorical Regressor /407
13.3.3 Interaction between Two Multicategorical Regressors / 408
13.4 Chapter Summary / 408
14 • Probing Interactions and Various Complexities 411
14.1 Conditional Effects as Functions / 411
14.1.1 When the Interaction Involves Dichotomous or Numerical Variables / 412
14.1.2 When the Interaction Involves a Multicategorical Variable / 414
14.2 Inference about a Conditional Effect / 415
14.2.1 When the Focal Predictor and Moderator Are Numerical or Dichotomous / 415
14.2.2 When the Focal Predictor or Moderator Is Multicategorical / 419
14.3 Probing an Interaction / 422
14.3.1 Examining Conditional Effects at Various Values of the Moderator / 423
14.3.2 The ]ohnson-Neyman Technique / 425
14.3.3 Testing versus Probing an Interaction 1427
14.3.4 Comparing Coyiditional Effects / 428
14.4 Complications and Confusions in the Study of Interactions / 429
14.4.1 The Difficulty of Detecting Interactions / 429
14.4.2 Confusing Interaction with Curvilinearity / 430
14.4.3 How the Scaling of Y Affects Interaction /432
14.4.4 The Interpretation of Lower-Order Regression Coefficients When
a Cross-Product Is Present 1433
14.4.5 Some Myths about Testing Interaction / 435
14.4.6 Interaction and Nonsignificant Linear Terms / 437
14.4.7 Homogeneity of Regression in ANCOVA / 437
14.4.8 Multiple, Higher-Order; and Curvilinear Interactions / 438
14.4.9 Artificial Categorization ofContinua / 441
14.5 Organizing Tests on Interaction / 441
14.5.1 Three Approaches to Managing Complications / 442
14.5.2 Broad versus Narrow Tests / 443
14.6 Chapter Summary / 445
15 • Mediation and Path Analysis 447
15.1 Path Analysis and Linear Regression / 448
15.1.1 Direct, Indirect, and Total Effects / 448
15.1.2 The Regression Algebra of Path Analysis / 452
15.1.3 Covariates / 454
15.1.4 Inference about the Total and Direct Effects / 455
15.1.5 Inference about the Indirect Effect / 455
15.1.6 Implementation in Statistical Software } 458
Contents
xxv
15.2 Multiple Mediator Models / 464
15.2.1 Path Analysis for a Parallel Multiple Mediator Model / 464
15.2.2 Path Analysis for a Serial Multiple Mediator Model / 467
15.3 Extensions, Complications, and Miscellaneous Issues / 469
15.3.1 Causality and Causal Order / 469
15.3.2 The Causal Steps Approach / 471
15.3.3 Mediation of a Nonsignificant Total Effect / 472
15.3.4 Multicategorical Independent Variables / 473
15.3.5 Fixing Direct Effects to Zero / 474
15.3.6 Nonlinear Effects / 475
15.3.7 Moderated Mediation f 475
15.4 Chapter Summary / 476
16 • Detecting and Managing Irregularities
16.1 Regression Diagnostics / 480
16.1.1 Shortcomings of Eyeballing the Data / 481
16.1.2 Types of Extreme Cases / 482
16.1.3 Quantifying Leverage, Distance, and Influence / 484
16.1.4 Using Diagnostic Statistics / 490
16.1.5 Generating Regression Diagnostics with Computer Software / 494
16.2 Detecting Assumption Violations / 495
16.2.1 Detecting Nonlinearity / 496
16.2.2 Detecting Non-Normality / 498
16.2.3 Detecting Heteroscedasticity f 499
16.2.4 Testing Assumptions as a Set / 505
16.2.5 What about Nonindependence? / 506
16.3 Dealing with Irregularities / 509
16.3.1 Heteroscedasticity-Consistent Standard Errors / 511
16.3.2 The Jackknife / 512
16.3.3 Bootstrapping / 512
16.3.4 Permutation Tests /513
16.4 Inference without Random Sampling / 514
16.5 Keeping the Diagnostic Analysis Manageable / 516
16.6 Chapter Summary / 517
17 • Power, Measurement Error, and Various Miscellaneous Topics
17.1 Power and Precision of Estimation / 519
17.1.1 Factors Determining Desirable Sample Size / 520
17.1.2 Revisiting the Standard Error of a Regression Coefficient / 521
17.1.3 On the Effect of Unnecessary Covariates / 524
17.2 Measurement Error / 525
17.2.1 What Is Measurement Error? / 525
17.2.2 Measurement Error in Y / 526
17.2.3 Measurement Error in Independent Variables / 527
17.2.4 The Biggest Weakness of Regression: Measurement Error in Covariates / 527
17.2.5 Summary: The Effects of Measurement Error f 528
17.2.6 Managing Measurement Error f 530
17.3 An Assortment of Problems / 532
17.3.1 Violations of the Basic Assumptions / 532
17.3.2 Collinearity / 532
17.3.3 Singularity / 534
17.3.4 Specification Error and Overcontrol / 538
17.3.5 Noninterval Scaling / 541
17.3.6 Missing Data / 543
17.3.7 Rounding Error / 546
17.4 Chapter Summary / 548
479
519
XXVI
Contents
18 • Logistic Regression and Other Linear Models 551
18.1 Logistic Regression / 551
18.1.1 Measuring a Model's Fit to Data/552
18.1.2 Odds and Logits/554
18.1.3 The Logistic Regression Equation / 556
18.1.4 An Example with a Single Regressor /557
18.1.5 Interpretation of and Inference about the Regression Coefficients / 560
18.1.6 Multiple Logistic Regression and Implementation in Computing
Software/ 562
18.1.7 Measuring and Testing the Fit of the Model / 565
18.1.8 Further Extensions / 568
18.1.9 Discriminant Function Analysis / 568
18.1.10 Using OLS Regression with a Dichotomous Y / 569
18.2 Other Linear Modeling Methods / 570
18.2.1 Ordered Logistic and Probit Regression / 570
18.2.2 Poisson Regression and Related Models of Count Outcomes / 572
18.2.3 Time Series Analysis / 573
18.2.4 Survival Analysis / 573
18.2.5 Structural Equation Modeling / 574
18.2.6 Multilevel Modeling / 575
18.2.7 Other Resources / 577
18.3 Chapter Summary / 578
Appendices
A. The RLM Macro for SPSS and SAS 581
B. Linear Regression Analysis Using R 603
C. Statistical Tables 611
D. The Matrix Algebra of Linear Regression Analysis 621
References 627
Author Index 637
Subject Index 641
About the Authors
661 |
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| author | Darlington, Richard B. Hayes, Andrew F. |
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| discipline | Allgemeines Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV043764068 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T07:21:45Z |
| institution | BVB |
| isbn | 9781462521135 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029175346 |
| oclc_num | 961158631 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-384 DE-1043 DE-N2 DE-355 DE-BY-UBR DE-739 DE-11 DE-29 DE-20 DE-634 DE-19 DE-BY-UBM DE-862 DE-BY-FWS DE-824 |
| owner_facet | DE-473 DE-BY-UBG DE-384 DE-1043 DE-N2 DE-355 DE-BY-UBR DE-739 DE-11 DE-29 DE-20 DE-634 DE-19 DE-BY-UBM DE-862 DE-BY-FWS DE-824 |
| physical | xxvi, 661 Seiten Illustrationen, Diagramme |
| publishDate | 2017 |
| publishDateSearch | 2017 |
| publishDateSort | 2017 |
| publisher | Guilford Press |
| record_format | marc |
| series2 | Methodology and the social sciences |
| spellingShingle | Darlington, Richard B. Hayes, Andrew F. Regression analysis and linear models concepts, applications, and implementation Sozialwissenschaften Regression analysis Linear models (Statistics) Psychology Statistical methods Social sciences Statistical methods Regressionsanalyse (DE-588)4129903-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| subject_GND | (DE-588)4129903-6 (DE-588)4127971-2 |
| title | Regression analysis and linear models concepts, applications, and implementation |
| title_auth | Regression analysis and linear models concepts, applications, and implementation |
| title_exact_search | Regression analysis and linear models concepts, applications, and implementation |
| title_full | Regression analysis and linear models concepts, applications, and implementation Richard B. Darlington, Andrew F. Hayes |
| title_fullStr | Regression analysis and linear models concepts, applications, and implementation Richard B. Darlington, Andrew F. Hayes |
| title_full_unstemmed | Regression analysis and linear models concepts, applications, and implementation Richard B. Darlington, Andrew F. Hayes |
| title_short | Regression analysis and linear models |
| title_sort | regression analysis and linear models concepts applications and implementation |
| title_sub | concepts, applications, and implementation |
| topic | Sozialwissenschaften Regression analysis Linear models (Statistics) Psychology Statistical methods Social sciences Statistical methods Regressionsanalyse (DE-588)4129903-6 gnd Lineares Regressionsmodell (DE-588)4127971-2 gnd |
| topic_facet | Sozialwissenschaften Regression analysis Linear models (Statistics) Psychology Statistical methods Social sciences Statistical methods Regressionsanalyse Lineares Regressionsmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029175346&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT darlingtonrichardb regressionanalysisandlinearmodelsconceptsapplicationsandimplementation AT hayesandrewf regressionanalysisandlinearmodelsconceptsapplicationsandimplementation |