Applied Linear Models with SAS

"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"--Provided by publisher. "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"--Provided by publisher. Cover......Page 1 Half-title......Page 3 Title......Page 5 Copyright......Page 6 Contents......Page 7 Preface......Page 11 Acknowledgments......Page 15 1.1 What Is Statistics?......Page 17 1.2 Statistics in the News: The Weather Map......Page 20 1.3 Mathematical Background......Page 22 1.4 Calculus......Page 23 1.5 Calculus in the News: New Home Sales......Page 25 1.6 Statistics in the News: IMF Loans and Tuberculosis......Page 27 1.7 Exercises......Page 29 1.7.1 Motorcycle Accidents......Page 30 1.7.2 Olympic Records......Page 31 1.7.4 Statistics in the News: China Buys U.S. Debt......Page 32 1.7.5 U.S. Presidents and Stock Market Returns......Page 33 2.1 Binomial Distribution......Page 37 2.2 Confidence Intervals and the Hubble Constant......Page 41 2.3 Normal Distribution......Page 42 2.4 Hypothesis Tests......Page 46 2.5 The Student t-Test......Page 50 2.6 The Chi-Squared Test and 2 x 2 Tables......Page 58 2.7 What Are Degrees of Freedom?......Page 63 2.8 SAS, in a Nutshell......Page 65 2.9 Survey of the Rest of the Book......Page 67 2.10 Exercises......Page 68 2.10.1 Maintaining Balance......Page 70 2.10.2 Reading Scores......Page 71 2.10.3 A Helium-Filled Football......Page 72 3.1 Low-Birth-Weight Infants......Page 74 3.2 The Least Squares Regression Line......Page 75 3.3 Regression in SAS......Page 79 3.4 Statistics in the News: Future Health Care Costs......Page 81 3.5 Exercises......Page 82 3.5.1 Statistics in the News: Savings for Medicare......Page 84 3.5.2 Arsenic in Drinking Water......Page 85 3.5.3 Statistics in the News: Dermatologists' Fees......Page 87 3.5.4 Breast Cancer Survival and Climate......Page 89 3.5.5 Vital Rates......Page 90 4.1 Correlation......Page 91 4.2 Statistics in the News: Correlations of the Global Economy......Page 93 4.3 Analysis of Variance......Page 94 4.4 Model Assumptions and Residual Plots......Page 97 4.5 Exercises......Page 100 4.5.1 Statistics in the News: Food Imports......Page 102 4.5.2 Statistics in the News: Women Managers......Page 103 4.5.3 Statistics Is More Than Just Numbers......Page 104 5.1 Introductory Example: Maximum January Temperatures......Page 106 5.2 Graphical Displays of Multivariate Data......Page 110 5.3 Leverage and the Hat Matrix Diagonal......Page 112 5.4 Jackknife Diagnostics......Page 115 5.5 Partial Regression Plots and Correlations......Page 118 5.6 Model-Building Strategies......Page 121 5.7.1 University Endowments......Page 126 5.7.2 Maximum January Temperatures......Page 127 5.7.3 Statistics in the News: Heart Surgery Mortality......Page 128 5.7.4 Characteristics of Cars, 1974......Page 130 5.7.5 Statistics in Advertising: Wine Prices......Page 131 5.7.6 Statistics in Finance: Mutual Fund Returns......Page 132 6.1 Indicator Variables......Page 136 6.2 Synergy in the News: Airline Mergers......Page 143 6.3 Interactions of Explanatory Variables......Page 144 6.4 Transformations......Page 148 6.5 Additional Topics: Longitudinal Data......Page 153 6.6 Exercises......Page 154 6.6.2 Statistics in the News: Nicotine Levels in Cigarettes......Page 156 6.6.3 The Speed of a Reaction......Page 157 6.6.4 Tumor Growth in Mice......Page 158 6.6.5 Statistics in Advertising: Used Car Prices......Page 159 6.6.6 Percent Body Fat......Page 160 6.6.7 Fertility Rates in Switzerland......Page 161 6.6.8 ELISA......Page 163 7.1 A Test for Medians......Page 166 7.2 Statistics in the News: Math Achievement Scores......Page 169 7.3 Rank Sum Test......Page 171 7.4 Nonparametric Methods in SAS......Page 172 7.5 Ranking and the Healthiest State......Page 173 7.6 Nonparametric Regression: LOESS......Page 176 7.7 Exercises......Page 179 7.7.2 Prices of Beanie Babies......Page 181 7.7.3 The Cracker Diet......Page 183 8.1 Example......Page 185 8.2 The Logit Transformation......Page 186 8.3 Logistic Regression in SAS......Page 189 8.4 Statistics in the News: The New York Mets......Page 193 8.5 Key Points......Page 194 8.6.1 A Phase I Clinical Trial in Cancer......Page 195 8.6.2 Toxoplasmosis in El Salvador......Page 197 8.6.3 Estimation of the ED01......Page 198 8.6.4 Super Bowl XXXVIII......Page 200 9 Diagnostics for Logistic Regression......Page 203 9.1 Some Syntax for proc logistic......Page 204 9.2 Residuals for Logistic Regression......Page 206 9.3 Influence in Logistic Regression......Page 209 9.4 Exercises......Page 213 9.4.1 Statistics in the News: Sex and Violins......Page 214 9.4.2 Glove Use Among Nurses......Page 216 9.4.3 Statistics in Sports: Pittsburgh Steelers Rushing Game......Page 217 10.2 Poisson Distribution Basics......Page 220 10.3 Regression Models for Poisson Data......Page 222 10.4 Statistics in the News: Attacks in Iraq......Page 224 10.5.1 Basic Output for Poisson Regression......Page 225 10.5.2 The obstats Output......Page 227 10.5.3 The offset Option......Page 229 10.6.1 Coronary Bypass Mortality, Revisited......Page 231 10.6.2 Cases of Mental Illness......Page 232 10.6.4 Lottery Winners......Page 233 10.6.5 Species on the Galapagos Islands......Page 234 10.6.6 Statistics in the News: Pro Bowl Appearances......Page 236 10.6.7 Cancer Rates in Japan......Page 237 10.6.8 Tourette's Syndrome......Page 238 11.1 Censoring......Page 241 11.2 The Survival Curve and Its Estimate......Page 243 11.3 The Log-Rank Test and SAS Program......Page 248 11.4.2 Survival of Centenarians......Page 251 12.1 The Hazard Function......Page 253 12.2 The Model of Proportional Hazards Regression......Page 255 12.3 Proportional Hazards Regression in SAS......Page 257 12.4.1 Survival of Halibut......Page 259 12.4.3 Primary Biliary Cirrhosis......Page 260 12.4.4 Multiple Myeloma......Page 261 13.1 The Appropriate Method......Page 263 13.2 Other Review Questions......Page 265 A.1 Normal Distribution......Page 271 A.2 Chi-squared Tables......Page 273 References......Page 275 Selected Solutions and Hints......Page 279 Index......Page 285 Cover 1 Half-title 3 Title 5 Copyright 6 Contents 7 Preface 11 Acknowledgments 15 1 Introduction 17 1.1 What Is Statistics? 17 1.2 Statistics in the News: The Weather Map 20 1.3 Mathematical Background 22 1.4 Calculus 23 1.5 Calculus in the News: New Home Sales 25 1.6 Statistics in the News: IMF Loans and Tuberculosis 27 1.7 Exercises 29 1.7.1 Motorcycle Accidents 30 1.7.2 Olympic Records 31 1.7.3 Gasoline Consumption 32 1.7.4 Statistics in the News: China Buys U.S. Debt 32 1.7.5 U.S. Presidents and Stock Market Returns 33 2 Principles of Statistics 37 2.1 Binomial Distribution 37 2.2 Confidence Intervals and the Hubble Constant 41 2.3 Normal Distribution 42 2.4 Hypothesis Tests 46 2.5 The Student t-Test 50 2.6 The Chi-Squared Test and 2 x 2 Tables 58 2.7 What Are Degrees of Freedom? 63 2.8 SAS, in a Nutshell 65 2.9 Survey of the Rest of the Book 67 2.10 Exercises 68 2.10.1 Maintaining Balance 70 2.10.2 Reading Scores 71 2.10.3 A Helium-Filled Football 72 3 Introduction to Linear Regression 74 3.1 Low-Birth-Weight Infants 74 3.2 The Least Squares Regression Line 75 3.3 Regression in SAS 79 3.4 Statistics in the News: Future Health Care Costs 81 3.5 Exercises 82 3.5.1 Statistics in the News: Savings for Medicare 84 3.5.2 Arsenic in Drinking Water 85 3.5.3 Statistics in the News: Dermatologists' Fees 87 3.5.4 Breast Cancer Survival and Climate 89 3.5.5 Vital Rates 90 4 Assessing the Regression 91 4.1 Correlation 91 4.2 Statistics in the News: Correlations of the Global Economy 93 4.3 Analysis of Variance 94 4.4 Model Assumptions and Residual Plots 97 4.5 Exercises 100 4.5.1 Statistics in the News: Food Imports 102 4.5.2 Statistics in the News: Women Managers 103 4.5.3 Statistics Is More Than Just Numbers 104 5 Multiple Linear Regression 106 5.1 Introductory Example: Maximum January Temperatures 106 5.2 Graphical Displays of Multivariate Data 110 5.3 Leverage and the Hat Matrix Diagonal 112 5.4 Jackknife Diagnostics 115 5.5 Partial Regression Plots and Correlations 118 5.6 Model-Building Strategies 121 5.7 Exercises 126 5.7.1 University Endowments 126 5.7.2 Maximum January Temperatures 127 5.7.3 Statistics in the News: Heart Surgery Mortality 128 5.7.4 Characteristics of Cars, 1974 130 5.7.5 Statistics in Advertising: Wine Prices 131 5.7.6 Statistics in Finance: Mutual Fund Returns 132 6 Indicators, Interactions, and Transformations 136 6.1 Indicator Variables 136 6.2 Synergy in the News: Airline Mergers 143 6.3 Interactions of Explanatory Variables 144 6.4 Transformations 148 6.5 Additional Topics: Longitudinal Data 153 6.6 Exercises 154 6.6.1 More on Wine Prices 156 6.6.2 Statistics in the News: Nicotine Levels in Cigarettes 156 6.6.3 The Speed of a Reaction 157 6.6.4 Tumor Growth in Mice 158 6.6.5 Statistics in Advertising: Used Car Prices 159 6.6.6 Percent Body Fat 160 6.6.7 Fertility Rates in Switzerland 161 6.6.8 ELISA 163 7 Nonparametric Statistics 166 7.1 A Test for Medians 166 7.2 Statistics in the News: Math Achievement Scores 169 7.3 Rank Sum Test 171 7.4 Nonparametric Methods in SAS 172 7.5 Ranking and the Healthiest State 173 7.6 Nonparametric Regression: LOESS 176 7.7 Exercises 179 7.7.1 Cloth Run-up 181 7.7.2 Prices of Beanie Babies 181 7.7.3 The Cracker Diet 183 8 Logistic Regression 185 8.1 Example 185 8.2 The Logit Transformation 186 8.3 Logistic Regression in SAS 189 8.4 Statistics in the News: The New York Mets 193 8.5 Key Points 194 8.6 Exercises 195 8.6.1 A Phase I Clinical Trial in Cancer 195 8.6.2 Toxoplasmosis in El Salvador 197 8.6.3 Estimation of the ED01 198 8.6.4 Super Bowl XXXVIII 200 9 Diagnostics for Logistic Regression 203 9.1 Some Syntax for proc logistic 204 9.2 Residuals for Logistic Regression 206 9.3 Influence in Logistic Regression 209 9.4 Exercises 213 9.4.1 Statistics in the News: Sex and Violins 214 9.4.2 Glove Use Among Nurses 216 9.4.3 Statistics in Sports: Pittsburgh Steelers Rushing Game 217 10 Poisson Regression 220 10.1 Statistics in the News: Lottery Winners 220 10.2 Poisson Distribution Basics 220 10.3 Regression Models for Poisson Data 222 10.4 Statistics in the News: Attacks in Iraq 224 10.5 Poisson Regression in SAS 225 10.5.1 Basic Output for Poisson Regression 225 10.5.2 The obstats Output 227 10.5.3 The offset Option 229 10.6 Exercises 231 10.6.1 Coronary Bypass Mortality, Revisited 231 10.6.2 Cases of Mental Illness 232 10.6.3 Statistics in the News: Airlines Bump Passengers 233 10.6.4 Lottery Winners 233 10.6.5 Species on the Galapagos Islands 234 10.6.6 Statistics in the News: Pro Bowl Appearances 236 10.6.7 Cancer Rates in Japan 237 10.6.8 Tourette's Syndrome 238 11 Survival Analysis 241 11.1 Censoring 241 11.2 The Survival Curve and Its Estimate 243 11.3 The Log-Rank Test and SAS Program 248 11.4 Exercises 251 11.4.1 Cancer of the Bile Duct 251 11.4.2 Survival of Centenarians 251 12 Proportional Hazards Regression 253 12.1 The Hazard Function 253 12.2 The Model of Proportional Hazards Regression 255 12.3 Proportional Hazards Regression in SAS 257 12.4 Exercises 259 12.4.1 Survival of Halibut 259 12.4.2 Stanford Heart Transplant Survival 260 12.4.3 Primary Biliary Cirrhosis 260 12.4.4 Multiple Myeloma 261 13 Review of Methods 263 13.1 The Appropriate Method 263 13.2 Other Review Questions 265 Appendix: Statistical Tables 271 A.1 Normal Distribution 271 A.2 Chi-squared Tables 273 References 275 Selected Solutions and Hints 279 Index 285

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.

Machine generated contents note: 1. Introduction; 2. Principles of statistics; 3. Introduction to linear regression; 4. Assessing the regression; 5. Multiple linear regression; 6. Indicators, interactions, and transformations; 7. Nonparametric statistics; 8. Logistic regression; 9. Diagnostics for logistic regression; 10. Poisson regression; 11. Survival analysis; 12. Proportional hazards regression; 13. Review of methods; Appendix: statistical tables.