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1. Statistical Control and Linear Models 1.1 Statistical Control 1.1.1 The Need for Control 1.1.2 Five Methods of Control 1.1.3 Examples of Statistical Control 1.2 An Overview of Linear Models 1.2.1 What You Should Know Already 1.2.2 Statistical Software for Linear Modeling and Statistical Control 1.2.3 About Formulas 1.2.4 On Symbolic Representations 1.3 Chapter Summary 2. The Simple Regression Model 2.1 Scatterplots and Conditional Distributions 2.1.1 Scatterplots 2.1.2 A Line through Conditional Means 2.1.3 Errors of Estimate 2.2 The Simple Regression Model 2.2.1 The Regression Line 2.2.2 Variance, Covariance, and Correlation 2.2.3 Finding the Regression Line 2.2.4 Example Computations 2.2.5 Linear Regression Analysis by Computer 2.3 The Regression Coefficient versus the Correlation Coefficient 2.3.1 Properties of the Regression and Correlation Coefficients 2.3.2 Uses of the Regression and Correlation Coefficients 2.4 Residuals 2.4.1 The Three Components of Y 2.4.2 Algebraic Properties of Residuals 2.4.3 Residuals as Y Adjusted for Differences in X 2.4.4 Residual Analysis 2.5 Chapter Summary 3. Partial Relationship and the Multiple Regression Model 3.1 Regression Analysis with More Than One Predictor Variable 3.1.1 An Example 3.1.2 Regressors 3.1.3 Models 3.1.4 Representing a Model Geometrically 3.1.5 Model Errors 3.1.6 An Alternative View of the Model 3.2 The Best-Fitting Model 3.2.1 Model Estimation with Computer Software 3.2.2 Partial Regression Coefficients 3.2.3 The Regression Constant 3.2.4 Problems with Three or More Regressors 3.2.5 The Multiple Correlation R 3.3 Scale-Free Measures of Partial Association 3.3.1 Semipartial Correlation 3.3.2 Partial Correlation 3.3.3 The Standardized Regression Coefficient 3.4 Some Relations among Statistics 3.4.1 Relations among Simple, Multiple, Partial, and Semipartial Correlations 3.4.2 Venn Diagrams 3.4.3 Partial Relationships and Simple Relationships May Have Different Signs 3.4.4 How Covariates Affect Regression Coefficients 3.4.5 Formulas for bj, prj, srj, and R 3.5 Chapter Summary 4. Statistical Inference in Regression 4.1 Concepts in Statistical Inference 4.1.1 Statistics and Parameters 4.1.2 Assumptions for Proper Inference 4.1.3 Expected Values and Unbiased Estimation 4.2 The ANOVA Summary Table 4.2.1 Data = Model + Error 4.2.2 Total and Regression Sums of Squares 4.2.3 Degrees of Freedom 4.2.4 Mean Squares 4.3 Inference about the Multiple Correlation 4.3.1 Biased and Less Biased Estimation of TR2 4.3.2 Testing a Hypothesis about TR 4.4 The Distribution of and Inference about a Partial Regression Coefficient 4.4.1 Testing a Null Hypothesis about Tbj 4.4.2 Interval Estimates for Tbj 4.4.3 Factors Affecting the Standard Error of bj 4.4.4 Tolerance 4.5 Inferences about Partial Correlations 4.5.1 Testing a Null Hypothesis about Tprj and Tsrj 4.5.2 Other Inferences about Partial Correlations 4.6 Inferences about Conditional Means 4.7 Miscellaneous Issues in Inference 4.7.1 How Great a Drawback Is Collinearity? 4.7.2 Contradicting Inferences 4.7.3 Sample Size and Nonsignificant Covariates 4.7.4 Inference in Simple Regression (When k = 1) 4.8 Chapter Summary 5. Extending Regression Analysis Principles 5.1 Dichotomous Regressors 5.1.1 Indicator or Dummy Variables 5.1.2 Y Is a Group Mean 5.1.3 The Regression Coefficient for an Indicator Is a Difference 5.1.4 A Graphic Representation 5.1.5 A Caution about Standardized Regression Coefficients for Dichotomous Regressors 5.1.6 Artificial Categorization of Numerical Variables 5.2 Regression to the Mean 5.2.1 How Regression Got Its Name 5.2.2 The Phenomenon 5.2.3 Versions of the Phenomenon 5.2.4 Misconceptions and Mistakes Fostered by Regression to the Mean 5.2.5 Accounting for Regression to the Mean Using Linear Models 5.3 Multidimensional Sets 5.3.1 The Partial and Semipartial Multiple Correlation 5.3.2 What It Means If PR = 0 or SR = 0 5.3.3 Inference Concerning Sets of Variables 5.4 A Glance at the Big Picture 5.4.1 Further Extensio
Richard B. Darlington, PhD, is Emeritus Professor of Psychology at Cornell University. He is a Fellow of the American Association for the Advancement of Science and has published extensively on regression and related methods, the cultural bias of mental tests, the long-term effects of preschool programs, and, most recently, the neuroscience of brain development and evolution. Andrew F. Hayes, PhD, is Professor of Quantitative Psychology at The Ohio State University. His research and writing on data analysis has been published widely, and he is the author of Introduction to Mediation, Moderation, and Conditional Process Analysis and Statistical Methods for Communication Science, as well as coauthor, with Richard B. Darlington, of Regression Analysis and Linear Models. Dr. Hayes teaches data analysis, primarily at the graduate level, and frequently conducts workshops on statistical analysis throughout the world. His website is www.afhayes.com.