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Overview
This bestseller will help you learn regressionanalysis methods that you can apply to reallife problems. It highlights the role of the computer in contemporary statistics with numerous printouts and exercises that you can solve using the computer. The authors continue to emphasize model development, the intuitive logic and assumptions that underlie the techniques covered, the purposes, advantages, and disadvantages of the techniques, and valid interpretations of those techniques.
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Table of Contents
1. CONCEPTS AND EXAMPLES OF RESEARCH. Concepts. Examples. Concluding Remarks. References. 2. CLASSIFICATION OF VARIABLES AND THE CHOICE OF ANALYSIS. Classification of Variables. Overlapping of Classification Schemes. Choice of Analysis. References. 3. BASIC STATISTICS: A REVIEW. Preview. Descriptive Statistics. Random Variables and Distributions. Sampling Distributions of t, ƒÓ2, and F. Statistical Inference: Estimation. Statistical Inference: Hypothesis Testing. Error Rate, Power, and Sample Size. Problems. References. 4. INTRODUCTION TO REGRESSION ANALYSIS. Preview. Association versus Causality. Statistical versus Deterministic Models. Concluding Remarks. References. 5. STRAIGHTLINE REGRESSION ANALYSIS. Preview. Regression with a Single Independent Variable. Mathematical Properties of a Straight Line. Statistical Assumptions for a Straightline Model. Determining the Bestfitting Straight Line. Measure of the Quality of the Straightline Fit and Estimate ƒã2. Inferences About the Slope and Intercept. Interpretations of Tests for Slope and Intercept. Inferences About the Regression Line ƒÝYX = ƒÒ0 + ƒÒ1X . Prediction of a New Value of Y at X0. Problems. References. 6. THE CORRELATION COEFFICIENT AND STRAIGHTLINE REGRESSION ANALYSIS. Definition of r. r as a Measure of Association. The Bivariate Normal Distribution. r and the Strength of the Straightline Relationship. What r Does Not Measure. Tests of Hypotheses and Confidence Intervals for the Correlation Coefficient. Testing for the Equality of Two Correlations. Problems. References. 7. THE ANALYSISOFVARIANCE TABLE. Preview. The ANOVA Table for Straightline Regression. Problems. 8. MULTIPLE REGRESSION ANALYSIS: GENERAL CONSIDERATIONS. Preview. Multiple Regression Models. Graphical Look at the Problem. Assumptions of Multiple Regression. Determining the Best Estimate of the Multiple Regression Equation. The ANOVA Table for Multiple Regression. Numerical Examples. Problems. References. 9. TESTING HYPOTHESES IN MULTIPLE REGRESSION. Preview. Test for Significant Overall Regression. Partial F Test. Multiple Partial F Test. Strategies for Using Partial F Tests. Tests Involving the Intercept. Problems. References. 10. CORRELATIONS: MULTIPLE, PARTIAL, AND MULTIPLE PARTIAL. Preview. Correlation Matrix. Multiple Correlation Coefficient. Relationship of RYX1, X2, KXk to the Multivariate Normal Distribution. Partial Correlation Coefficient. Alternative Representation of the Regression Model. Multiple Partial Correlation. Concluding Remarks. Problems. References. 11. CONFOUNDING AND INTERACTION IN REGRESSION. Preview. Overview. Interaction in Regression. Confounding in Regression. Summary and Conclusions. Problems. References. 12. DUMMY VARIABLES IN REGRESSION. Preview. Definitions. Rule for Defining Dummy Variables. Comparing Two Straightline Regression Equations: An Example. Questions for Comparing Two Straight Lines. Methods of Comparing Two Straight Lines. Method I: Using Separate Regression Fits to Compare Two Straight Lines. Method II: Using a Single Regression Equation to Compare Two Straight Lines. Comparison of Methods I and II. Testing Strategies and Interpretation: Comparing Two Straight Lines. Other Dummy Variable Models. Comparing Four Regression Equations. Comparing Several Regression Equations Involving Two Nominal Variables. Problems. References. 13. ANALYSIS OF COVARIANCE AND OTHER METHODS FOR ADJUSTING CONTINUOUS DATA. Preview. Adjustment Problem. Analysis of Covariance. Assumption of Parallelism: A Potential Drawback. Analysis of Covariance: Several Groups and Several Covariates. Comments and Cautions. Summary Problems. Reference. 14. REGRESSION DIAGNOSTICS. Preview. Simple Approaches to Diagnosing Problems in Data. Residual Analysis: Detecting Outliers and Violations of Model Assumptions. Strategies of Analysis. Collinearity. Scaling Problems. Diagnostics Example. An Important Caution. Problems. References. 15. POLYNOMIAL REGRESSION. Preview. Polynomial Models. Leastsquares Procedure for Fitting a Parabola. ANOVA Table for Secondorder Polynomial Regression. Inferences Associated with Secondorder Polynomial Regression. Example Requiring a Secondorder Model. Fitting and Testing Higherorder Model. Lackoffit Tests. Orthogonal Polynomials. Strategies for Choosing a Polynomial Model. Problems. 16. SELECTING THE BEST REGRESSION EQUATION. Preview. Steps in Selecting the Best Regression Equation. Step 1: Specifying the Maximum Model. Step 2: Specifying a Criterion for Selecting a Model. Step 3: Specifying a Strategy for Selecting Variables. Step 4: Conducting the Analysis. Step 5: Evaluating Reliability with Split Samples. Example Analysis of Actual Data. Issues in Selecting the Most Valid Model. Problems. References. 17. ONEWAY ANALYSIS OF VARIANCE. Preview. Oneway ANOVA: The Problem, Assumptions, and Data Configuration. for Oneway Fixedeffects ANOVA. Regression Model for Fixedeffects Oneway ANOVA Fixedeffects Model for Oneway ANOVA. Randomeffects Model for Oneway ANOVA. comparison Procedures for Fixedeffects Oneway ANOVA. a Multiplecomparison Technique. Orthogonal Contrasts and Partitioning an ANOVA Sum of Squares. Problems. References. 18. RANDOMIZED BLOCKS: SPECIAL CASE OF TWOWAY ANOVA. Preview. Equivalent Analysis of a Matchedpairs Experiment. Principle of Blocking. Analysis of a Randomizedblocks Experiment. ANOVA Table for a Randomizedblocks Experiment. Models for a Randomizedblocks Experiment. Fixedeffects ANOVA Model for a Randomizedblocks Experiment. Problems. References. 19. TWOWAY ANOVA WITH EQUAL CELL NUMBERS. Preview. Using a Table of Cell Means. General Methodology. F Tests for Twoway ANOVA. Regression Model for Fixedeffects Twoway ANOVA. Interactions in Twoway ANOVA. Random and Mixedeffects Twoway ANOVA Models. Problems. References. 20. TWOWAY ANOVA WITH UNEQUAL CELL NUMBERS. Preview. Problem with Unequal Cell Numbers: Nonorthogonality. Regression Approach for Unequal Cell Sample Sizes. Higherway ANOVA. Problems. References. 21. THE METHOD OF MAXIMUM LIKELIHOOD. Preview. The Principle of Maximum Likelihood. Statistical Inference Using Maximum Likelihood. Summary. Problems. 22. LOGISTIC REGRESSION ANALYSIS. Preview. The Logistic Model. Estimating the Odds Ratio Using Logistic Regression. A Numerical Example of Logistic Regression. Theoretical Considerations. An Example of Conditional ML Estimation Involving Pairmatched Data with Unmatched Covariates. Summary. Problems. References. 23. POLYTOMOUS AND ORDINAL LOGISTIC REGRESSION. Preview. Why Not Use Binary Regression? An Example of Polytomous Logistic Regression: One Predictor, Three Outcome Categories. An Example: Extending the Polytomous Logistic Model to Several Predictors. Ordinal Logistic Regression: Overview. A "Simple" Hypothetical Example: Three Ordinal Categories and One Dichotomous Exposure Variable. Ordinal Logistic Regression Example Using Real Data with Four Ordinal Categories and Three Predictor Variables. Summary. Problems. References. 24. POISSON REGRESSION ANALYSIS. Preview. The Poisson Distribution. Example of Poisson Regression. Poisson Regression: General Considerations. Measures of Goodness of Fit. Continuation of Skin Cancer Data Example. A Second Illustration of Poisson Regression Analysis. Summary. Problems. References. 25. ANALYSIS OF CORRELATED DATA PART 1: THE GENERAL LINEAR MIXED MODEL. Preview. Examples. General Linear Mixed Model Approach. Example: Study of Effects of an Air Polluion Episode on FEV1 Levels. SummaryXAnalysis of Correlated Data: Part 1. Problems. References. 26. ANALYSIS OF CORRELATED DATA PART 2: RANDOM EFFECTS AND OTHER ISSUES. Preview. Random Effects Revisited. Results for Random Effects Models Applied to Air Pollution Study Data. Second ExampleXAnalysis of Posture Measurement Data. Recommendations about Choice of Correlation Structure. Analysis of Data for Discrete Outcomes. Problems. References. 27. SAMPLE SIZE PLANNING FOR LINEAR AND LOGISTIC REGRESSION AND ANALYSIS OF VARIANCE. Preview. Review: Sample Size Calculations for Comparisons of Means and Proportions. Sample Size Planning for Linear Regression. Sample Size Planning for Logistic Regression. Power and Sample Size Determination for Linear Models: A General Approach. Sample Size Determination for Matched Casecontrol Studies with a Dichotomous Outcome. Practical Considerations and Cautions. Problems. References. Appendix A. Appendix B. Appendix C. Solutions to Exercises. Index.