Linear models with R / Julian J. Faraway.

Format:

Book

Author/Creator:

Faraway, Julian James, author.

Contributor:

ProQuest ebook central.

Series:

Texts in statistical science

Chapman & Hall/CRC texts in statistical science series

Language:

English

Subjects (All):

Analysis of variance.

Regression analysis.

R (Computer program language)--Mathematical models.

R (Computer program language).

Mathematical models.

Physical Description:

1 online resource (xii, 274 pages) : illustrations.

Edition:

Second edition.

Place of Publication:

Boca Raton : CRC Press, Taylor & Francis Group, [2015]

System Details:

text file

Summary:

Part of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition. New to the Second Edition, Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality, Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates, Extensive use of the ggplot2 graphics package in addition to base graphics, Like its widley praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R. Features, Demonstrates the flexibility of linear models in many examples, Assumes basic knowledge of R and statistics, Emphasizes intuition over rigorous proofs, Presents exercises at the end of each chapter, Includes datasets and R commands Book jacket.

Contents:

1 Introduction 1

1.1 Before You Start 1

1.2 Initial Data Analysis 2

1.3 When to Use Linear Modeling 7

1.4 History 8

2 Estimation 13

2.1 Linear Model 13

2.2 Matrix Representation 14

2.3 Estimating β 15

2.4 Least Squares Estimation 16

2.5 Examples of Calculating β 17

2.6 Example 17

2.7 QR Decomposition 20

2.8 Gauss-Markov Theorem 22

2.9 Goodness of Fit 23

2.10 Identifiability 26

2.11 Orthogonality 28

3 Inference 33

3.1 Hypothesis Tests to Compare Models 33

3.2 Testing Examples 35

3.3 Permutation Tests 40

3.4 Sampling 42

3.5 Confidence Intervals for β 43

3.5 Bootstrap Confidence Intervals 46

4 Prediction 51

4.1 Confidence Intervals for Predictions 51

4.2 Predicting Body Fat 52

4.3 Autoregression 54

4.4 What Can Go Wrong with Predictions? 56

5 Explanation 59

5.1 Simple Meaning 59

5.2 Causality 61

5.3 Designed Experiments 62

5.4 Observational Data 63

5.5 Matching 65

5.6 Covariate Adjustment 68

5.7 Qualitative Support for Causation 69

6 Diagnostics 73

6.1 Checking Error Assumptions 73

6.1.1 Constant Variance 73

6.1.2 Normality 78

6.1.3 Correlated Errors 81

6.2 Finding Unusual Observations 83

6.2.1 Leverage 83

6.2.2 Outliers 85

6.2.3 Influential Observations 89

6.3 Checking the Structure of the Model 92

6.4 Discussion 96

7 Problems with the Predictors 99

7.1 Errors in the Predictors 99

7.2 Changes of Scale 103

7.3 Collinearity 106

8 Problems with the Error 113

8.1 Generalized Least Squares 113

8.2 Weighted Least Squares 116

8.3 Testing for Lack of Fit 119

8.4 Robust Regression 123

8.4.1 M-Estimation 123

8.4.2 Least Trimmed Squares 126

9 Transformation 133

9.1 Transforming the Response 133

9.2 Transforming the Predictors 137

9.3 Broken Stick Regression 137

9.4 Polynomials 139

9.5 Splines 141

9.6 Additive Models 144

9.7 More Complex Models 145

10 Model Selection 149

10.1 Hierarchical Models 150

10.2 Testing-Based Procedures 151

10.3 Criterion-Based Procedures 153

10.4 Summary 159

11 Shrinkage Methods 161

11.1 Principal Components 161

11.2 Partial Least Squares 172

11.3 Ridge Regression 174

11.4 Lasso 177

12 Insurance Redlining-A Complete Example 183

12.1 Ecological Correlation 183

12.2 Initial Data Analysis 185

12.3 Full Model and Diagnosics 188

12.4 Sensitivity Analysis 190

12.5 Discussion 194

13 Missing Data 197

13.1 Types of Missing Data 197

13.2 Deletion 198

13.3 Single Imputation 200

13.4 Multiple Imputation 202

14 Categorical Predictors 205

14.1 A Two-Level Factor 205

14.2 Factors and Quantitative Predictors 209

14.3 Interpretation with Interaction Terms 212

14.4 Factors With More Than Two Levels 213

14.5 Alternative Codings of Qualitative Predictors 219

15 One Factor Models 223

15.1 The Model 223

15.2 An Example 224

15.3 Diagnostics 227

15.4 Pairwise Comparisons 228

15.5 False Discovery Rate 230

16 Models with Several Factors 235

16.1 Two Factors with No Replication 235

16.2 Two Factors with Replication 239

16.3 Two Factors with an Interaction 243

16.4 Larger Factorial Experiments 246

17 Experiments with Blocks 251

17.1 Randomized Block Design 252

17.2 Latin Squares 256

17.3 Balanced Incomplete Block Design 259.

Notes:

"A CRC title."

Includes bibliographical references (pages 267-270) and index.

Electronic reproduction. Ann Arbor, MI Available via World Wide Web.

Description based on print version record.

ISBN:

9781439887349

1439887349

Publisher Number:

99973226838

Access Restriction:

Restricted for use by site license.