A one-stop guide for public health students and practitioners learning regression analysis and statistical methods This book is written for public health professionals and students interested in applying regression models in the field of public health. A one-stop guide for public health students and practitioners learning the applications of classical regression models in epidemiology This book is written for public health professionals and students interested in applying regression models in the field of epidemiology. Dedication About the Author Preface Acknowledgements  Chapter 1: Basic concepts for Statistical Modeling 1.1 Introduction 1.2 Parameter versus statistic 1.3 Probability definition 1.4 Conditional probability 1.5 Concepts of prevalence and incidence 1.6 Random variables 1.7 Probability distributions 1.8 Centrality and dispersion parameters of a random variable 1.9 Independence and dependence of random variables 1.10 Special probability distribution 1.11 Hypothesis testing 1.12 Confidence intervals 1.13 Clinical significance versus statistical significance 1.14 Data management         1.15 What to do when detecting a data issue 1.16 Impact of data issues and how to proceed 1.17 Concept of causality References Chapter 2: Introduction to Simple Linear Regression Models 2.1 Introduction 2.2 Specific objectives 2.3 Model definition 2.4 Model assumptions 2.5 Graphic representation 2.6 Geometry of the simple regression model 2.7 Estimation of parameters 2.8 Variance of estimators 2.9 Hypothesis testing about the slope of the regression line  2.10 Coefficient of determination R2 2.11 Pearson correlation coefficient 2.12 Estimation of regression line values and prediction   2.13 Example 2.14 Predictions   2.15 Conclusions 2.16 Practice Exercise Reference Chapter 3 : Matrix Representation of the Linear Regression Model 3.1 Introduction 3.2 Specific objectives 3.3 Definition 3.4 Matrix representation of a SLRM 3.5 Matrix arithmetic 3.6 Matrix multiplication 3.7 Special matrices 3.8 Linear dependence 3.9 Rank of a matrix 3.10 Inverse matrix [A-1] 3.11 Application of an inverse matrix in a SLRM 3.12 Estimation of Ò parameters in a SLRM 3.13 Multiple linear regression model (MLRM) 3.14 Interpretation of the coefficients in a MLRM 3.15 ANOVA in a MLRM 3.16 Using indicator variables (Dummy Variables) 3.17 Polynomial regression models 3.18 Centering 3.19 Multicollinearity 3.20 Interaction terms 3.21 Conclusion 3.22 Practice Exercise Reference Chapter 4 : Evaluation of Partial Tests of Hypotheses in a MLRM 4.1 Introduction 4.2 Specific objectives 4.3 Definition of partial hypothesis 4.4 Evaluation process of partial hypotheses 4.5 Special situations 4.6 Examples 4.7 Conclusion 4.8 Practice exercise Reference Chapter 5 : Selection of Variables in a Multiple Linear Regression Model 5.1 Introduction 5.2 Specific Objectives 5.3 Selection of variables according to the study objectives 5.4 Criteria for selecting the best regression model 5.5 Stepwise method in regression 5.6 Limitations of stepwise methods 5.7 Conclusion 5.8 Practice exercise References Chapter 6 : Correlation Analysis 6.1 Introduction 6.2 Specific objectives 6.3 Main correlation coefficients based on SLRM 6.4 Major correlation coefficients based on MLRM 6.5 Partial correlation coefficient 6.6 Significance Tests 6.7 Suggested Correlations 6.8 Example 6.9 Conclusion 6.10 Practice Exercise Reference Chapter 7 : Strategies for assessing the adequacy of the Linear Regression Model 7.1 Introduction 7.2 Specific objectives 7.3 Residual definition 7.4 Initial exploration 7.5 Initial considerations 7.6 Standardized residual 7.7 Jackknife residuals (R-Student residuals) 7.8 Normality of the errors 7.9 Correlation of Errors 7.10 Criteria for detecting outliers, leverage, and influential points 7.11 Leverage values 7.12 Cook s distance 7.13 COV RATIO 7.14 DFBETAS 7.15 DFFITS 7.16 Summary of the results 7.17 Multicollinearity 7.18 Transformation of variables 7.19 Conclusion 7.20 Practice Exercise Reference Chapter 8 : Weighted Least Squares Linear Regression 8.1 Introduction 8.2 Specific objectives 8.3 Regression model with transformation into the original scale of Y 8.4 Matrix Notation of the Weighted Linear Regression Model 8.5 Application of the WLS model with unequal number of subjects 8.6 Applications of the WLS model when variance increases 8.7 Conclusions 8.8 Practice Exercise Reference Chapter 9 : Generalized Linear Models  9.1 Introduction 9.2 Specific objectives 9.3 Exponential Family of Probability Distributions   9.4 Exponential Family of Probability Distributions with Dispersion 9.5 Mean and Variance in EF and EDF 9.6 Definition of a Generalized Linear Model  9.7 Estimation Methods  9.8 Deviance calculation 9.9 Hypothesis Evaluation 9.10 Analysis of Residuals 9.11 Model Selection 9.12 Bayesian Models 9.13 Conclusions Reference Chapter 10 : Poisson Regression Models for Cohort Studies 10.1 Introduction 10.2 Specific Objectives 10.3 Incidence Measures 10.4 Confounding variable 10.5 Stratified analysis 10.6 Poisson regression model 10.7 Definition of Adjusted Relative Risk 10.8 Interaction assessment 10.9 Relative Risk Estimation 10.10 Implementation of the Poisson regression model 10.11 Conclusion 10.12 Practice Exercise Reference Chapter 11 : Logistic Regression in Case-Control Studies 11.1 Introduction 11.2 Specific Objectives 11.3 Graphical Representation 11.4 Definition of the Odds Ratio 11.5 Confounding assessment 11.6 Effect Modification 11.7 Stratified analysis 11.8 Unconditional Logistic Regression Model 11.9 Types of logistic regression models 11.10 Computing the ORcrude 11.11 Computing the adjusted OR 11.12 Inference on OR 11.13 Example of the application of ULR model-binomial case 11.14 Conditional logistic regression model 11.15 Conclusions 11.16 Practice Exercise Reference Chapter 12 : Regression models in a cross-sectional study 12.1 Introduction 12.2 Specific Objectives 12.3 Prevalence estimation using the normal approach 12.4 Definition of the magnitude of the association 12.5 POR Estimation 12.6 Prevalence Ratio 12.7 Stratified analysis 12.8 Logistic Regression Model        12.9 Conclusions 12.10 Practice Exercise Reference Chapter 13 :  Solutions to Practice Exercises Chapter II: Practice exercise Chapter III: Practice exercise Chapter IV: Practice exercise Chapter V: Practice exercise Chapter VI: Practice exercise Chapter VII: Practice exercise Chapter VIII: Practice exercise Chapter X: Practice exercise Chapter XI: Practice exercise Chapter XII: Practice exercise Index