Applied Linear Models with SAS

by Daniel Zelterman

• ISBN13: 9780521761598
• ISBN10: 052176159X
• Edition: 1st
• Format: Hardcover
• Copyright: 2010-05-10
• Publisher: Cambridge University Press

Summary

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.

Author Biography

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	p. ix
Acknowledgments	p. xiii
Introduction	p. 1
What Is Statistics?	p. 1
Statistics in the News: The Weather Map	p. 4
Mathematical Background	p. 6
Calculus	p. 7
Calculus in the News: New Home Sales	p. 9
Statistics in the News: IMF Loans and Tuberculosis	p. 11
Exercises	p. 13
Principles of Statistics	p. 21
Binomial Distribution	p. 21
Confidence Intervals and the Hubble Constant	p. 25
Normal Distribution	p. 26
Hypothesis Tests	p. 30
The Student t-Test	p. 34
The Chi-Squared Test and 2 × 2 Tables	p. 42
What Are Degrees of Freedom?	p. 47
SAS, in a Nutshell	p. 49
Survey of the Rest of the Book	p. 51
Exercises	p. 52
Introduction to Linear Regression	p. 58
Low-Birth-Weight Infants	p. 58
The Least Squares Regression Line	p. 59
Regression in SAS	p. 63
Statistics in the News: Future Health Care Costs	p. 65
Exercises	p. 66
Assessing the Regression	p. 75
Correlation	p. 75
Statistics in the News: Correlations of the Global Economy	p. 77
Analysis of Variance	p. 78
Model Assumptions and Residual Plots	p. 81
Exercises	p. 84
Multiple Linear Regression	p. 90
Introductory Example: Maximum January Temperatures	p. 90
Graphical Displays of Multivariate Data	p. 94
Leverage and the Hat Matrix Diagonal	p. 96
Jackknife Diagnostics	p. 99
Partial Regression Plots and Correlations	p. 102
Model-Building Strategies	p. 105
Exercises	p. 110
Indicators, Interactions, and Transformations	p. 120
Indicator Variables	p. 120
Synergy in the News: Airline Mergers	p. 127
Interactions of Explanatory Variables	p. 128
Transformations	p. 132
Additional Topics: Longitudinal Data	p. 137
Exercises	p. 138
Nonparametric Statistics	p. 150
A Test for Medians	p. 150
Statistics in the News: Math Achievement Scores	p. 153
Rank Sum Test	p. 155
Nonparametric Methods in SAS	p. 156
Ranking and the Healthiest State	p. 157
Nonparametric Regression: LOESS	p. 160
Exercises	p. 163
Logistic Regression	p. 169
Example	p. 169
The Logit Transformation	p. 170
Logistic Regression in SAS	p. 173
Statistics in the News: The New York Mets	p. 177
Key Points	p. 178
Exercises	p. 179
Diagnostics for Logistic Regression	p. 187
Some Syntax for proc logistic	p. 188
Residuals for Logistic Regression	p. 190
Influence in Logistic Regression	p. 193
Exercises	p. 197
Poisson Regression	p. 204
Statistics in the News: Lottery Winners	p. 204
Poisson Distribution Basics	p. 204
Regression Models for Poisson Data	p. 206
Statistics in the News: Attacks in Iraq	p. 208
Poisson Regression in SAS	p. 209
Exercises	p. 215
Survival Analysis	p. 225
Censoring	p. 225
The Survival Curve and Its Estimate	p. 227
The Log-Rank Test and SAS Program	p. 232
Exercises	p. 235
Proportional Hazards Regression	p. 237
The Hazard Function	p. 237
The Model of Proportional Hazards Regression	p. 239
Proportional Hazards Regression in SAS	p. 241
Exercises	p. 243
Review of Methods	p. 247
The Appropriate Method	p. 247
Other Review Questions	p. 249
Appendix: Statistical Tables	p. 255
Normal Distribution	p. 255
Chi-squared Tables	p. 257
References	p. 259
Selected Solutions and Hints	p. 263
Index	p. 269
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