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More About This Textbook
Overview
This textbook for a second course in basic statistics for undergraduates or first-year graduate students introduces linear regression models and describes other linear models including Poisson regression, logistic regression, proportional hazards regression, and nonparametric regression. Numerous examples drawn from the news and current events with an emphasis on health issues illustrate these concepts. Assuming only a pre-calculus background, the author keeps equations to a minimum and demonstrates all computations using SAS. Most of the programs and output are displayed in a self-contained way, with an emphasis on the interpretation of the output in terms of how it relates to the motivating example. Plenty of exercises conclude every chapter. All of the datasets and SAS programs are available from the book’s Web site, along with other ancillary material.
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Meet the Author
Dr Daniel Zelterman is Professor of Epidemiology and Public Health in the Division of Biostatistics at Yale University. His application areas include work in genetics, HIV, and cancer. Before moving to Yale in 1995, he was on the faculty of the University of Minnesota and at the State University of New York at Albany. He is an elected Fellow of the American Statistical Association. He serves as associate editor of Biometrics and other statistical journals. He is the author of Models for Discrete Data (1999), Advanced Log-Linear Models Using SAS (2002), Discrete Distributions: Application in the Health Sciences (2004), and Models for Discrete Data, 2nd edition (2006).
Table of Contents
Preface
Acknowledgments
1 Introduction 1
1.1 What Is Statistics? 1
1.2 Statistics in the News: The Weather Map 4
1.3 Mathematical Background 6
1.4 Calculus 7
1.5 Calculus in the News: New Home Sales 9
1.6 Statistics in the News: IMF Loans and Tuberculosis 11
1.7 Exercises 13
2 Principles of Statistics 21
2.1 Binomial Distribution 21
2.2 Confidence Intervals and the Hubble Constant 25
2.3 Normal Distribution 26
2.4 Hypothesis Tests 30
2.5 The Student t-Test 34
2.6 TheChi-SquaredTestand2 - 2Tables 42
2.7 What Are Degrees of Freedom? 47
2.8 SAS, in a Nutshell 49
2.9 Survey of the Rest of the Book 51
2.10 Exercises 52
3 Introduction to Linear Regression 58
3.1 Low-Birth-Weight Infants 58
3.2 The Least Squares Regression Line 59
3.3 Regression in SAS 63
3.4 Statistics in the News: Future Health Care Costs 65
3.5 Exercises 66
4 Assessing the Regression 75
4.1 Correlation 75
4.2 Statistics in the News: Correlations of the Global Economy 77
4.3 Analysis of Variance 78
4.4 Model Assumptions and Residual Plots 81
4.5 Exercises 84
5 Multiple Linear Regression 90
5.1 Introductory Example: Maximum January Temperatures 90
5.2 Graphical Displays of Multivariate Data 94
5.3 Leverage and the Hat Matrix Diagonal 96
5.4 Jackknife Diagnostics 99
5.5 Partial Regression Plots and Correlations 102
5.6 Model-Building Strategies 105
5.7 Exercises 110
6 Indicators, Interactions, and Transformations 120
6.1 Indicator Variables 120
6.2 Synergy in the News: Airline Mergers 127
6.3 Interactions of Explanatory Variables 128
6.4 Transformations 132
6.5 Additional Topics: Longitudinal Data 137
6.6 Exercises 138
7 Nonparametric Statistics 150
7.1 A Test for Medians 150
7.2 Statistics in the News: Math Achievement Scores 153
7.3 Rank Sum Test 155
7.4 Nonparametric Methods in SAS 156
7.5 Ranking and the Healthiest State 157
7.6 Nonparametric Regression: LOESS 160
7.7 Exercises 163
8 Logistic Regression 169
8.1 Example 169
8.2 The Logit Transformation 170
8.3 Logistic Regression in SAS 173
8.4 Statistics in the News: The New York Mets 177
8.5 Key Points 178
8.6 Exercises 179
9 Diagnostics for Logistic Regression 187
9.1 Some Syntax for proc logistic 188
9.2 Residuals for Logistic Regression 190
9.3 Influence in Logistic Regression 193
9.4 Exercises 197
10 Poisson Regression 204
10.1 Statistics in the News: Lottery Winners 204
10.2 Poisson Distribution Basics 204
10.3 Regression Models for Poisson Data 206
10.4 Statistics in the News: Attacks in Iraq 208
10.5 Poisson Regression in SAS 209
10.6 Exercises 215
11 Survival Analysis 225
11.1 Censoring 225
11.2 The Survival Curve and Its Estimate 227
11.3 The Log-Rank Test and SAS Program 232
11.4 Exercises 235
12 Proportional Hazards Regression 237
12.1 The Hazard Function 237
12.2 The Model of Proportional Hazards Regression 239
12.3 Proportional Hazards Regression in SAS 241
12.4 Exercises 243
13 Review of Methods 247
13.1 The Appropriate Method 247
13.2 Other Review Questions 249
Appendix: Statistical Tables 255
A.1 Normal Distribution 255
A.2 Chi-squared Tables 257
References 259
Selected Solutions and Hints 263
Index 269