套用線性統計模型上冊（英文影印版·原書第5版）

《套用線性統計模型上冊（英文影印版·原書第5版）》是2016年4月機械工業出版社出版的圖書，作者是麥可H.庫特納。

基本介紹

• 中文名：套用線性統計模型上冊（英文影印版·原書第5版）
• 作者：麥可H.庫特納
• 出版時間：2016年4月
• 出版社：機械工業出版社
• ISBN：9787111490685
• 定價：98 元
• 開本：16 開
• 裝幀：平裝

內容簡介

本書從McGrawHill出版公司引進，共分三部分，內容包括：第 一部分：簡單線性回歸：一元預測函式的線性回歸，回歸影響和相關分析，診斷及補救措施，即時推斷和回歸分析的其它幾個專題，簡單線性回歸分析中的矩陣方法；第二部分：多元線性回歸：多元回歸Ⅰ，多元回歸2，定性回歸模型和定量預測，建立線性回歸模型Ⅰ：模型選擇及有效性，建立線性回歸模型Ⅱ：診斷，建立線性回歸模型Ⅲ：補救措施，時間序列數據中的自相關；第三部分：非線性回歸：非線性回歸和神經網路方法。

圖書目錄

Contents

preface

PART ONE

SIMPLE LINEAR REGRESSION 1

Chapter 1

Linear Regression with One Predictor

Variable 2

1.1 Relations between Variables 2

Functional Relation between Two

Variables 2

Statistical Relation between Two Variables 3

1.2 Regression Models and Their Uses 5

Historical Origins 5

Basic Concepts 5

Construction of Regression Models 7

Uses of Regression Analysis 8

Regression and Causality 8

Use of Computers 9

1.3 Simple Linear Regression Model

with Distribution of Error Terms

Unspecified 9

Formal Statement of Model 9

Important Features of Model 9

Meaning of Regression Parameters 11

Alternative Versions of Regression Model 12

1.4 Data for Regression Analysis 12

Observational Data 12

Experimental Data 13

Completely Randomized Design 13

1.5 Overview of Steps in Regression

Analysis 13

1.6 Estimation of Regression Function 15

Method of Least Squares 15

Point Estimation of Mean Response 21

Residuals 22

Properties of Fitted Regression Line 23

1.7 Estimation of Error Terms Variance ·2 24

Point Estimator of ·2 24

1.8 Normal Error Regression Model 26

Model 26

Estimation of Parameters by Method

of Maximum Likelihood 27

Cited References 33

Problems 33

Exercises 37

Projects 38

Chapter 2

Inferences in Regression and Correlation

Analysis 40

2.1 Inferences Concerning ·1 40

Sampling Distribution of b1 41

Sampling Distribution of (b1 -·1)/s{b1} 44

Confidence Interval for ·1 45

Tests Concerning ·1 47

2.2 Inferences Concerning ·0 48

Sampling Distribution of b0 48

Sampling Distribution of (b0 -·0)/s{b0} 49

Confidence Interval for ·0 49

2.3 Some Considerations on Making Inferences

Concerning ·0 and ·1 50

Effects of Departures from Normality 50

Interpretation of Confidence Coefficient

and Risks of Errors 50

Spacing of the X Levels 50

Power of Tests 50

2.4 Interval Estimation of E{Yh} 52

Sampling Distribution of ˆY

h 52

Sampling Distribution of

( ˆYh - E{Yh})/s{ ˆYh} 54

Confidence Interval for E{Yh} 54

2.5 Prediction of New Observation 55

Prediction Interval for Yh(new) when

Parameters Known 56

Prediction Interval for Yh(new) when

Parameters Unknown 57

Prediction of Mean of m New Observations

for Given Xh 60

2.6 Confidence Band for Regression Line 61

2.7 Analysis of Variance Approach

to Regression Analysis 63

Partitioning of Total Sum of Squares 63

Breakdown of Degrees of Freedom 66

x

Contents xi

Mean Squares 66

Analysis of Variance Table 67

Expected Mean Squares 68

F Test of ·1 = 0 versus ·1 _= 0 69

2.8 General Linear Test Approach 72

Full Model 72

Reduced Model 72

Test Statistic 73

Summary 73

2.9 Descriptive Measures of Linear Association

between X and Y 74

Coefficient of Determination 74

Limitations of R2 75

Coefficient of Correlation 76

2.10 Considerations in Applying Regression

Analysis 77

2.11 Normal Correlation Models 78

Distinction between Regression and

Correlation Model 78

Bivariate Normal Distribution 78

Conditional Inferences 80

Inferences on Correlation Coefficients 83

Spearman Rank Correlation Coefficient 87

Cited References 89

Problems 89

Exercises 97

Projects 98

Chapter 3

Diagnostics and Remedial Measures 100

3.1 Diagnostics for Predictor Variable 100

3.2 Residuals 102

Properties of Residuals 102

Semistudentized Residuals 103

Departures from Model to Be Studied by

Residuals 103

3.3 Diagnostics for Residuals 103

Nonlinearity of Regression Function 104

Nonconstancy of Error Variance 107

Presence of Outliers 108

Nonindependence of Error Terms 108

Nonnormality of Error Terms 110

Omission of Important Predictor

Variables 112

Some Final Comments 114

3.4 Overview of Tests Involving

Residuals 114

Tests for Randomness 114

Tests for Constancy of Variance 115

Tests for Outliers 115

Tests for Normality 115

3.5 Correlation Test for Normality 115

3.6 Tests for Constancy of Error

Variance 116

Brown-Forsythe Test 116

Breusch-Pagan Test 118

3.7 F Test for Lack of Fit 119

Assumptions 119

Notation 121

Full Model 121

Reduced Model 123

Test Statistic 123

ANOVA Table 124

3.8 Overview of Remedial Measures 127

Nonlinearity of Regression

Function 128

Nonconstancy of Error Variance 128

Nonindependence of Error Terms 128

Nonnormality of Error Terms 128

Omission of Important Predictor

Variables 129

Outlying Observations 129

3.9 Transformations 129

Transformations for Nonlinear

Relation Only 129

Transformations for Nonnormality

and Unequal Error Variances 132

Box-Cox Transformations 134

3.10 Exploration of Shape of Regression

Function 137

Lowess Method 138

Use of Smoothed Curves to Confirm Fitted

Regression Function 139

3.11 Case Example—Plutonium

Measurement 141

Cited References 146

Problems 146

Exercises 151

Projects 152

Case Studies 153

xii Contents

Chapter 4

Simultaneous Inferences and Other

Topics in Regression Analysis 154

4.1 Joint Estimation of ·0 and ·1 154

Need for Joint Estimation 154

Bonferroni Joint Confidence Intervals 155

4.2 Simultaneous Estimation of Mean

Responses 157

Working-Hotelling Procedure 158

Bonferroni Procedure 159

4.3 Simultaneous Prediction Intervals

for New Observations 160

4.4 Regression through Origin 161

Model 161

Inferences 161

Important Cautions for Using Regression

through Origin 164

4.5 Effects of Measurement Errors 165

Measurement Errors in Y 165

Measurement Errors in X 165

Berkson Model 167

4.6 Inverse Predictions 168

4.7 Choice of X Levels 170

Cited References 172

Problems 172

Exercises 175

Projects 175

Chapter 5

Matrix Approach to Simple

Linear Regression Analysis 176

5.1 Matrices 176

Definition of Matrix 176

Square Matrix 178

Vector 178

Transpose 178

Equality of Matrices 179

5.2 Matrix Addition and Subtraction 180

5.3 Matrix Multiplication 182

Multiplication of a Matrix by a Scalar 182

Multiplication of a Matrix by a Matrix 182

5.4 Special Types of Matrices 185

Symmetric Matrix 185

Diagonal Matrix 185

Vector and Matrix with All Elements

Unity 187

Zero Vector 187

5.5 Linear Dependence and Rank

of Matrix 188

Linear Dependence 188

Rank of Matrix 188

5.6 Inverse of a Matrix 189

Finding the Inverse 190

Uses of Inverse Matrix 192

5.7 Some Basic Results for Matrices 193

5.8 Random Vectors and Matrices 193

Expectation of Random Vector or Matrix 193

Variance-Covariance Matrix

of Random Vector 194

Some Basic Results 196

Multivariate Normal Distribution 196

5.9 Simple Linear Regression Model

in Matrix Terms 197

5.10 Least Squares Estimation

of Regression Parameters 199

Normal Equations 199

Estimated Regression Coefficients 200

5.11 Fitted Values and Residuals 202

Fitted Values 202

Residuals 203

5.12 Analysis of Variance Results 204

Sums of Squares 204

Sums of Squares as Quadratic

Forms 205

5.13 Inferences in Regression Analysis 206

Regression Coefficients 207

Mean Response 208

Prediction of New Observation 209

Cited Reference 209

Problems 209

Exercises 212

PART TWO

MULTIPLE LINEAR

REGRESSION 213

Chapter 6

Multiple Regression I 214

6.1 Multiple Regression Models 214

Contents xiii

Need for Several Predictor Variables 214

First-Order Model with Two Predictor

Variables 215

First-Order Model with More than Two

Predictor Variables 217

General Linear Regression Model 217

6.2 General Linear Regression Model in Matrix

Terms 222

6.3 Estimation of Regression Coefficients 223

6.4 Fitted Values and Residuals 224

6.5 Analysis of Variance Results 225

Sums of Squares and Mean Squares 225

F Test for Regression Relation 226

Coefficient of Multiple Determination 226

Coefficient of Multiple Correlation 227

6.6 Inferences about Regression

Parameters 227

Interval Estimation of ·k 228

Tests for ·k 228

Joint Inferences 228

6.7 Estimation of Mean Response and

Prediction of New Observation 229

Interval Estimation of E{Yh} 229

Confidence Region for Regression

Surface 229

Simultaneous Confidence Intervals for Several

Mean Responses 230

Prediction of New Observation Yh(new) 230

Prediction of Mean of m New Observations

at Xh 230

Predictions of g New Observations 231

Caution about Hidden Extrapolations 231

6.8 Diagnostics and Remedial Measures 232

Scatter Plot Matrix 232

Three-Dimensional Scatter Plots 233

Residual Plots 233

Correlation Test for Normality 234

Brown-Forsythe Test for Constancy of Error

Variance 234

Breusch-Pagan Test for Constancy of Error

Variance 234

F Test for Lack of Fit 235

Remedial Measures 236

6.9 An Example—Multiple Regression with

Two Predictor Variables 236

Setting 236

Basic Calculations 237

Estimated Regression Function 240

Fitted Values and Residuals 241

Analysis of Appropriateness of Model 241

Analysis of Variance 243

Estimation of Regression Parameters 245

Estimation of Mean Response 245

Prediction Limits for New Observations 247

Cited Reference 248

Problems 248

Exercises 253

Projects 254

Chapter 7

Multiple Regression II 256

7.1 Extra Sums of Squares 256

Basic Ideas 256

Definitions 259

Decomposition of SSR into Extra Sums

of Squares 260

ANOVA Table Containing Decomposition

of SSR 261

7.2 Uses of Extra Sums of Squares in Tests for

Regression Coefficients 263

Test whether a Single ·k = 0 263

Test whether Several ·k = 0 264

7.3 Summary of Tests Concerning Regression

Coefficients 266

Test whether All ·k = 0 266

Test whether a Single ·k = 0 267

Test whether Some ·k = 0 267

Other Tests 268

7.4 Coefficients of Partial Determination 268

Two Predictor Variables 269

General Case 269

Coefficients of Partial Correlation 270

7.5 Standardized Multiple Regression

Model 271

Roundoff Errors in Normal Equations

Calculations 271

Lack of Comparability in Regression

Coefficients 272

Correlation Transformation 272

Standardized Regression Model 273

X_X Matrix for Transformed Variables 274

xiv Contents

Estimated Standardized Regression

Coefficients 275

7.6 Multicollinearity and Its Effects 278

Uncorrelated Predictor Variables 279

Nature of Problem when Predictor Variables

Are Perfectly Correlated 281

Effects of Multicollinearity 283

Need for More Powerful Diagnostics for

Multicollinearity 289

Cited Reference 289

Problems 289

Exercise 292

Projects 293

Chapter 8

Regression Models for Quantitative

and Qualitative Predictors 294

8.1 Polynomial Regression Models 294

Uses of Polynomial Models 294

One Predictor Variable—Second Order 295

One Predictor Variable—Third Order 296

One Predictor Variable—Higher Orders 296

Two Predictor Variables—Second Order 297

Three Predictor Variables—Second

Order 298

Implementation of Polynomial Regression

Models 298

Case Example 300

Some Further Comments on Polynomial

Regression 305

8.2 Interaction Regression Models 306

Interaction Effects 306

Interpretation of Interaction Regression

Models with Linear Effects 306

Interpretation of Interaction Regression

Models with Curvilinear Effects 309

Implementation of Interaction Regression

Models 311

8.3 Qualitative Predictors 313

Qualitative Predictor with Two

Classes 314

Interpretation of Regression Coefficients 315

Qualitative Predictor with More than Two

Classes 318

Time Series Applications 319

8.4 Some Considerations in Using Indicator

Variables 321

Indicator Variables versus Allocated

Codes 321

Indicator Variables versus Quantitative

Variables 322

Other Codings for Indicator Variables 323

8.5 Modeling Interactions between Quantitative

and Qualitative Predictors 324

Meaning of Regression Coefficients 324

8.6 More Complex Models 327

More than One Qualitative Predictor

Variable 328

Qualitative Predictor Variables Only 329

8.7 Comparison of Two or More Regression

Functions 329

Soap Production Lines Example 330

Instrument Calibration Study Example 334

Cited Reference 335

Problems 335

Exercises 340

Projects 341

Case Study 342

Chapter 9

Building the Regression Model I:

Model Selection and Validation 343

9.1 Overview of Model-Building Process 343

Data Collection 343

Data Preparation 346

Preliminary Model Investigation 346

Reduction of Explanatory Variables 347

Model Refinement and Selection 349

Model Validation 350

9.2 Surgical Unit Example 350

9.3 Criteria for Model Selection 353

R2

p or SSEp Criterion 354

R2

a,p or MSEp Criterion 355

Mallows’ Cp Criterion 357

AICp and SBCp Criteria 359

PRESSp Criterion 360

9.4 Automatic Search Procedures for Model

Selection 361

“Best” Subsets Algorithm 361

Stepwise Regression Methods 364

Contents xv

Forward Stepwise Regression 364

Other Stepwise Procedures 367

9.5 Some Final Comments on Automatic

Model Selection Procedures 368

9.6 Model Validation 369

Collection of New Data to Check

Model 370

Comparison with Theory, Empirical

Evidence, or Simulation Results 371

Data Splitting 372

Cited References 375

Problems 376

Exercise 380

Projects 381

Case Studies 382

Chapter 10

Building the Regression Model II:

Diagnostics 384

10.1 Model Adequacy for a Predictor

Variable—Added-Variable Plots 384

10.2 Identifying Outlying Y Observations—

Studentized Deleted Residuals 390

Outlying Cases 390

Residuals and Semistudentized

Residuals 392

Hat Matrix 392

Studentized Residuals 394

Deleted Residuals 395

Studentized Deleted Residuals 396

10.3 Identifying Outlying X Observations—Hat

Matrix Leverage Values 398

Use of Hat Matrix for Identifying Outlying

X Observations 398

Use of Hat Matrix to Identify Hidden

Extrapolation 400

10.4 Identifying Influential Cases—DFFITS,

Cook’s Distance, and DFBETAS

Measures 400

Influence on Single Fitted

Value—DFFITS 401

Influence on All Fitted Values—Cook’s

Distance 402

Influence on the Regression

Coefficients—DFBETAS 404

Influence on Inferences 405

Some Final Comments 406

10.5 Multicollinearity Diagnostics—Variance

Inflation Factor 406

Informal Diagnostics 407

Variance Inflation Factor 408

10.6 Surgical Unit Example—Continued 410

Cited References 414

Problems 414

Exercises 419

Projects 419

Case Studies 420

Chapter 11

Building the Regression Model III:

Remedial Measures 421

11.1 Unequal Error Variances Remedial

Measures—Weighted Least Squares 421

Error Variances Known 422

Error Variances Known up to

Proportionality Constant 424

Error Variances Unknown 424

11.2 Multicollinearity Remedial

Measures—Ridge Regression 431

Some Remedial Measures 431

Ridge Regression 432

11.3 Remedial Measures for Influential

Cases—Robust Regression 437

Robust Regression 438

IRLS Robust Regression 439

11.4 Nonparametric Regression: Lowess

Method and Regression Trees 449

Lowess Method 449

Regression Trees 453

11.5 Remedial Measures for Evaluating

Precision in Nonstandard

Situations—Bootstrapping 458

General Procedure 459

Bootstrap Sampling 459

Bootstrap Confidence Intervals 460

11.6 Case Example—MNDOT Traffic

Estimation 464

The AADT Database 464

Model Development 465

Weighted Least Squares Estimation 468

xvi Contents

Cited References 471

Problems 472

Exercises 476

Projects 476

Case Studies 480

Chapter 12

Autocorrelation in Time

Series Data 481

12.1 Problems of Autocorrelation 481

12.2 First-Order Autoregressive Error

Model 484

Simple Linear Regression 484

Multiple Regression 484

Properties of Error Terms 485

12.3 Durbin-Watson Test for

Autocorrelation 487

12.4 Remedial Measures for

Autocorrelation 490

Addition of Predictor Variables 490

Use of Transformed Variables 490

Cochrane-Orcutt Procedure 492

Hildreth-Lu Procedure 495

First Differences Procedure 496

Comparison of Three Methods 498

12.5 Forecasting with Autocorrelated Error

Terms 499

Cited References 502

Problems 502

Exercises 507

Projects 508

Case Studies 508

PART THREE

NONLINEAR REGRESSION 509

Chapter 13

Introduction to Nonlinear Regression

and Neural Networks 510

13.1 Linear and Nonlinear Regression

Models 510

Linear Regression Models 510

Nonlinear Regression Models 511

Estimation of Regression Parameters 514

13.2 Least Squares Estimation in Nonlinear

Regression 515

Solution of Normal Equations 517

Direct Numerical Search—Gauss-Newton

Method 518

Other Direct Search Procedures 525

13.3 Model Building and Diagnostics 526

13.4 Inferences about Nonlinear Regression

Parameters 527

Estimate of Error Term Variance 527

Large-Sample Theory 528

When Is Large-Sample Theory

Applicable? 528

Interval Estimation of a Single ·k 531

Simultaneous Interval Estimation

of Several ·k 532

Test Concerning a Single ·k 532

Test Concerning Several ·k 533

13.5 Learning Curve Example 533

13.6 Introduction to Neural Network

Modeling 537

Neural Network Model 537

Network Representation 540

Neural Network as Generalization of Linear

Regression 541

Parameter Estimation: Penalized Least

Squares 542

Example: Ischemic Heart Disease 543

Model Interpretation and

Prediction 546

Some Final Comments on Neural Network

Modeling 547

Cited References 547

Problems 548

Exercises 552

Projects 552

Case Studies 554

Chapter 14

Logistic Regression, Poisson Regression,

and Generalized Linear Models 555

14.1 Regression Models with Binary Response

Variable 555

Meaning of Response Function when

Outcome Variable Is Binary 556

Contents xvii

Special Problems when Response Variable

Is Binary 557

14.2 Sigmoidal Response Functions

for Binary Responses 559

Probit Mean Response Function 559

Logistic Mean Response Function 560

Complementary Log-Log Response

Function 562

14.3 Simple Logistic Regression 563

Simple Logistic Regression Model 563

Likelihood Function 564

Maximum Likelihood Estimation 564

Interpretation of b1 567

Use of Probit and Complementary Log-Log

Response Functions 568

Repeat Observations—Binomial

Outcomes 568

14.4 Multiple Logistic Regression 570

Multiple Logistic Regression Model 570

Fitting of Model 571

Polynomial Logistic Regression 575

14.5 Inferences about Regression

Parameters 577

Test Concerning a Single ·k: Wald

Test 578

Interval Estimation of a Single ·k 579

Test whether Several ·k = 0: Likelihood

Ratio Test 580

14.6 Automatic Model Selection

Methods 582

Model Selection Criteria 582

Best Subsets Procedures 583

Stepwise Model Selection 583

14.7 Tests for Goodness of Fit 586

Pearson Chi-Square Goodness

of Fit Test 586

Deviance Goodness of Fit Test 588

Hosmer-Lemeshow Goodness

of Fit Test 589

14.8 Logistic Regression Diagnostics 591

Logistic Regression Residuals 591

Diagnostic Residual Plots 594

Detection of Influential

Observations 598

14.9 Inferences about

Mean Response 602

Point Estimator 602

Interval Estimation 602

Simultaneous Confidence Intervals for

Several Mean Responses 603

14.10 Prediction of a New Observation 604

Choice of Prediction Rule 604

Validation of Prediction Error Rate 607

14.11 Polytomous Logistic Regression for

Nominal Response 608

Pregnancy Duration Data

with Polytomous Response 609

J - 1 Baseline-Category Logits for

Nominal Response 610

Maximum Likelihood Estimation 612

14.12 Polytomous Logistic Regression

for Ordinal Response 614

14.13 Poisson Regression 618

Poisson Distribution 618

Poisson Regression Model 619

Maximum Likelihood Estimation 620

Model Development 620

Inferences 621

14.14 Generalized Linear Models 623

Cited References 624

Problems 625

Exercises 634

Projects 635

Case Studies 640

Appendix A

Some Basic Results in Probability

and Statistics

Appendix B

Tables

Appendix C

Data Sets

Appendix D

Selected Bibliography

Index