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A Primer on Linear Models presents a unified, thorough, and rigorous development of the theory behind the statistical methodology of regression and analysis of variance (ANOVA). It seamlessly incorporates these concepts using non-full-rank design matrices and emphasizes the exact, finite sample theory supporting common statistical methods.
In a conversational tone, Regression & Linear Modeling provides conceptual, user-friendly coverage of the generalized linear model (GLM). Readers will become familiar with applications of ordinary least squares (OLS) regression, binary and multinomial logistic regression, ordinal regression, Poisson regression, and loglinear models. Author Jason W. Osborne returns to certain themes throughout the text, such as testing assumptions, examining data quality, and, where appropriate, nonlinear and non-additive effects modeled within different types of linear models.
The essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
Peter Vik's Regression, ANOVA, and the General Linear Model: A Statistics Primer demonstrates basic statistical concepts from two different perspectives, giving the reader a conceptual understanding of how to interpret statistics and their use. The two perspectives are (1) a traditional focus on the t-test, correlation, and ANOVA, and (2) a model-comparison approach using General Linear Models (GLM). This book juxtaposes the two approaches by presenting a traditional approach in one chapter, followed by the same analysis demonstrated using GLM. By so doing, students will acquire a theoretical and conceptual appreciation for data analysis as well as an applied practical understanding as to how these two approaches are alike.
This textbook for students in the health and social sciences covers the basics of linear model methods with a minimum of mathematics, assuming only a pre-calculus background. Numerous examples drawn from the news and current events with an emphasis on health issues, illustrate the concepts in an immediately accessible way. Methods covered include linear regression models, Poisson regression, logistic regression, proportional hazards regression, survival analysis, and nonparametric regression. The author emphasizes interpretation of computer output in terms of the motivating example. All of the R code is provided and carefully explained, allowing readers to quickly apply the methods to their own data. Plenty of exercises help students think about the issues involved in the analysis and its interpretation. Code and datasets are available for download from the book's website at www.cambridge.org/zelterman
Master linear regression techniques with a new edition of a classic text Reviews of the Second Edition: "I found it enjoyable reading and so full of interesting material that even the well-informed reader will probably find something new . . . a necessity for all of those who do linear regression." —Technometrics, February 1987 "Overall, I feel that the book is a valuable addition to the now considerable list of texts on applied linear regression. It should be a strong contender as the leading text for a first serious course in regression analysis." —American Scientist, May–June 1987 Applied Linear Regression, Third Edition has been thoroughly updated to help students master the theory and applications of linear regression modeling. Focusing on model building, assessing fit and reliability, and drawing conclusions, the text demonstrates how to develop estimation, confidence, and testing procedures primarily through the use of least squares regression. To facilitate quick learning, the Third Edition stresses the use of graphical methods in an effort to find appropriate models and to better understand them. In that spirit, most analyses and homework problems use graphs for the discovery of structure as well as for the summarization of results. The Third Edition incorporates new material reflecting the latest advances, including: Use of smoothers to summarize a scatterplot Box-Cox and graphical methods for selecting transformations Use of the delta method for inference about complex combinations of parameters Computationally intensive methods and simulation, including the bootstrap method Expanded chapters on nonlinear and logistic regression Completely revised chapters on multiple regression, diagnostics, and generalizations of regression Readers will also find helpful pedagogical tools and learning aids, including: More than 100 exercises, most based on interesting real-world data Web primers demonstrating how to use standard statistical packages, including R, S-Plus®, SPSS®, SAS®, and JMP®, to work all the examples and exercises in the text A free online library for R and S-Plus that makes the methods discussed in the book easy to use With its focus on graphical methods and analysis, coupled with many practical examples and exercises, this is an excellent textbook for upper-level undergraduates and graduate students, who will quickly learn how to use linear regression analysis techniques to solve and gain insight into real-life problems.
• Exercises and solutions are included throughout, from both the first and second volume • Includes coverage of additional topics not covered in the first volume • Highly valuable as a reference book for graduate students or researchers
This innovative, intermediate-level statistics text fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the author's introduces students to the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models A First Course in Linear Model Theory systematically presents the basic theory behind linear statistical models with motivation from an algebraic as well as a geometric perspective. Through the concepts and tools of matrix and linear algebra and distribution theory, it provides a framework for understanding classical and contemporary linear model theory. It does not merely introduce formulas, but develops in students the art of statistical thinking and inspires learning at an intuitive level by emphasizing conceptual understanding. The authors' fresh approach, methodical presentation, wealth of examples, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.
Given the importance of linear models in statistical theory and experimental research, a good understanding of their fundamental principles and theory is essential. Supported by a large number of examples, Linear Model Methodology provides a strong foundation in the theory of linear models and explores the latest developments in data analysis.After
This is the first book on linear algebra written specifically for social scientists. It deals only with those aspects of the subject applicable in the social sciences and provides a thorough understanding of linear algebra for those who wish to use it as a tool in the design, execution, and interpretation of research. Linear mathematical models play an important role in all of the social sciences. This book provides a step-by-step introduction to those parts of linear algebra which are useful in such model building. It illustrates some of the applications of linear analysis and helps the reader learn how to convert his formulation of a social science problem into algebraic terms. The author covers matrix algebra, computational methods, linear models involving discrete variables, and clear, complete explanations of necessary mathematical concepts. Prior knowledge of calculus is not required since no use is made of calculus or of complex numbers. A novel feature of the mathematical content of the book is the treatment of models expressed in terms of variables which must be whole numbers (integers). The book is distinguished by a step-by-step exposition that allows the reader to grasp quickly and fully the principles of linear algebra. All of the examples used to illustrate the text are drawn from the social sciences, enabling the reader to relate the subject to concrete problems in his field. Exercises are included as a necessary part of the text to develop points not covered in the text and to provide practice in the algebraic formulation of applied problems. An appendix gives solutions (or hints) for selected exercises.