Introduction

Abstract

Regression is the most popular and commonly used statistical methodology for analyzing empirical problems in social sciences, economics, and life sciences. Correspondingly, there exist a large variety of models and inferential tools, ranging from conventional linear models to modern non- and semiparametric regression. Currently available textbooks mostly focus on particular classes of regression models, however, strongly varying in style, mathematical level, and orientation towards theory or application. Why then another book on regression? Several introductory textbooks are available for students and practitioners in diverse fields of applications, but they deal almost exclusivelywith linear regression. On the other hand, most texts concentrating onmodern non- and semiparametricmethods primar- ily address readers with strong theoretical interest and methodological background, presupposing a correspondingly high-level mathematical basis. They are therefore less accessible to readers from applied fields who need to employ these methods. The aimof this book is an applied and unified introduction into parametric, non-, and semiparametric regression that closes the gap between theory and application. The most important models and methods in regression are presented on a solid formal basis, and their appropriate application is shown through many real data examples and case studies. Availability of (user-friendly) software has been amajor criterion for the methods selected and presented. In our view, the interplay and balance between theory and application are essential for progress in substantive disciplines, as well as for the development of statistical methodology, motivated and stimulated through newchallenges arising frommultidisciplinary collaboration. A similar goal, but with somewhat different focus, has been pursued in the book Semiparametric Regression by Ruppert,Wand, and Carroll (2003). Thus, our book primarily targets an audience that includes students, teachers, and practitioners in social, economic, and life sciences, as well as students and teachers in statistics programs and mathematicians and computer scientists with interests in statistical modeling and data analysis. It is written at an intermediate mathematical level and assumes only knowledge of basic probability, calculus, and statistics. Short parts in the text dealing with more complex details or providing additional information start with the symbol and end with . These parts may be omitted in a first reading without loss of continuity. The most important definitions and statements are concisely summarized in boxes. Two appendices describe required matrix algebra, as well as elements of probability calculus and statistical inference.