Linear Regression Models

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Linear Models in Statistics

Alvin C. Rencher,G. Bruce Schaalje
Linear Models in Statistics Book PDF

Author : Alvin C. Rencher,G. Bruce Schaalje
Publisher : John Wiley & Sons
Page : 690 pages
File Size : 45,8 Mb
Release : 2008-01-07
Category : Mathematics
ISBN : 9780470192603

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Linear Models in Statistics by Alvin C. Rencher,G. Bruce Schaalje Pdf

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.

Linear Regression Models

John P. Hoffmann
Linear Regression Models Book PDF

Author : John P. Hoffmann
Publisher : CRC Press
Page : 436 pages
File Size : 49,7 Mb
Release : 2021-09-12
Category : Mathematics
ISBN : 9781000437966

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Linear Regression Models by John P. Hoffmann Pdf

Research in social and behavioral sciences has benefited from linear regression models (LRMs) for decades to identify and understand the associations among a set of explanatory variables and an outcome variable. Linear Regression Models: Applications in R provides you with a comprehensive treatment of these models and indispensable guidance about how to estimate them using the R software environment. After furnishing some background material, the author explains how to estimate simple and multiple LRMs in R, including how to interpret their coefficients and understand their assumptions. Several chapters thoroughly describe these assumptions and explain how to determine whether they are satisfied and how to modify the regression model if they are not. The book also includes chapters on specifying the correct model, adjusting for measurement error, understanding the effects of influential observations, and using the model with multilevel data. The concluding chapter presents an alternative model—logistic regression—designed for binary or two-category outcome variables. The book includes appendices that discuss data management and missing data and provides simulations in R to test model assumptions. Features Furnishes a thorough introduction and detailed information about the linear regression model, including how to understand and interpret its results, test assumptions, and adapt the model when assumptions are not satisfied. Uses numerous graphs in R to illustrate the model’s results, assumptions, and other features. Does not assume a background in calculus or linear algebra, rather, an introductory statistics course and familiarity with elementary algebra are sufficient. Provides many examples using real-world datasets relevant to various academic disciplines. Fully integrates the R software environment in its numerous examples. The book is aimed primarily at advanced undergraduate and graduate students in social, behavioral, health sciences, and related disciplines, taking a first course in linear regression. It could also be used for self-study and would make an excellent reference for any researcher in these fields. The R code and detailed examples provided throughout the book equip the reader with an excellent set of tools for conducting research on numerous social and behavioral phenomena. John P. Hoffmann is a professor of sociology at Brigham Young University where he teaches research methods and applied statistics courses and conducts research on substance use and criminal behavior.

Beyond Multiple Linear Regression

Paul Roback,Julie Legler
Beyond Multiple Linear Regression Book PDF

Author : Paul Roback,Julie Legler
Publisher : CRC Press
Page : 436 pages
File Size : 42,8 Mb
Release : 2021-01-14
Category : Mathematics
ISBN : 9781439885406

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Beyond Multiple Linear Regression by Paul Roback,Julie Legler Pdf

Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R is designed for undergraduate students who have successfully completed a multiple linear regression course, helping them develop an expanded modeling toolkit that includes non-normal responses and correlated structure. Even though there is no mathematical prerequisite, the authors still introduce fairly sophisticated topics such as likelihood theory, zero-inflated Poisson, and parametric bootstrapping in an intuitive and applied manner. The case studies and exercises feature real data and real research questions; thus, most of the data in the textbook comes from collaborative research conducted by the authors and their students, or from student projects. Every chapter features a variety of conceptual exercises, guided exercises, and open-ended exercises using real data. After working through this material, students will develop an expanded toolkit and a greater appreciation for the wider world of data and statistical modeling. A solutions manual for all exercises is available to qualified instructors at the book’s website at www.routledge.com, and data sets and Rmd files for all case studies and exercises are available at the authors’ GitHub repo (https://github.com/proback/BeyondMLR)

Regression Analysis and Linear Models

Richard B. Darlington,Andrew F. Hayes
Regression Analysis and Linear Models Book PDF

Author : Richard B. Darlington,Andrew F. Hayes
Publisher : Guilford Publications
Page : 689 pages
File Size : 52,8 Mb
Release : 2016-08-22
Category : Social Science
ISBN : 9781462527984

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Regression Analysis and Linear Models by Richard B. Darlington,Andrew F. Hayes Pdf

Emphasizing conceptual understanding over mathematics, this user-friendly text introduces linear regression analysis to students and researchers across the social, behavioral, consumer, and health sciences. Coverage includes model construction and estimation, quantification and measurement of multivariate and partial associations, statistical control, group comparisons, moderation analysis, mediation and path analysis, and regression diagnostics, among other important topics. Engaging worked-through examples demonstrate each technique, accompanied by helpful advice and cautions. The use of SPSS, SAS, and STATA is emphasized, with an appendix on regression analysis using R. The companion website (www.afhayes.com) provides datasets for the book's examples as well as the RLM macro for SPSS and SAS. Pedagogical Features: *Chapters include SPSS, SAS, or STATA code pertinent to the analyses described, with each distinctively formatted for easy identification. *An appendix documents the RLM macro, which facilitates computations for estimating and probing interactions, dominance analysis, heteroscedasticity-consistent standard errors, and linear spline regression, among other analyses. *Students are guided to practice what they learn in each chapter using datasets provided online. *Addresses topics not usually covered, such as ways to measure a variable’s importance, coding systems for representing categorical variables, causation, and myths about testing interaction.

Applied Linear Statistical Models

Michael H. Kutner
Applied Linear Statistical Models Book PDF

Author : Michael H. Kutner
Publisher : McGraw-Hill Education
Page : 1396 pages
File Size : 41,9 Mb
Release : 2005
Category : Analysis of variance
ISBN : 0071122214

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Applied Linear Statistical Models by Michael H. Kutner Pdf

Applied Linear Statistical Models 5e is the long established leading authoritative text and reference on statistical modeling. For students in most any discipline where statistical analysis or interpretation is used, ALSM serves as the standard work. The text includes brief introductory and review material, and then proceeds through regression and modeling for the first half, and through ANOVA and Experimental Design in the second half. All topics are presented in a precise and clear style supported with solved examples, numbered formulae, graphic illustrations, and "Notes" to provide depth and statistical accuracy and precision. Applications used within the text and the hallmark problems, exercises, and projects are drawn from virtually all disciplines and fields providing motivation for students in virtually any college. The Fifth edition provides an increased use of computing and graphical analysis throughout, without sacrificing concepts or rigor. In general, the 5e uses larger data sets in examples and exercises, and where methods can be automated within software without loss of understanding, it is so done.

Interpretable Machine Learning

Christoph Molnar
Interpretable Machine Learning Book PDF

Author : Christoph Molnar
Publisher : Lulu.com
Page : 320 pages
File Size : 55,7 Mb
Release : 2020
Category : Artificial intelligence
ISBN : 9780244768522

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Interpretable Machine Learning by Christoph Molnar Pdf

This book is about making machine learning models and their decisions interpretable. After exploring the concepts of interpretability, you will learn about simple, interpretable models such as decision trees, decision rules and linear regression. Later chapters focus on general model-agnostic methods for interpreting black box models like feature importance and accumulated local effects and explaining individual predictions with Shapley values and LIME. All interpretation methods are explained in depth and discussed critically. How do they work under the hood? What are their strengths and weaknesses? How can their outputs be interpreted? This book will enable you to select and correctly apply the interpretation method that is most suitable for your machine learning project.

Linear Regression Analysis

Xin Yan,Xiaogang Su
Linear Regression Analysis Book PDF

Author : Xin Yan,Xiaogang Su
Publisher : World Scientific
Page : 349 pages
File Size : 42,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812834102

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Linear Regression Analysis by Xin Yan,Xiaogang Su Pdf

"This volume presents in detail the fundamental theories of linear regression analysis and diagnosis, as well as the relevant statistical computing techniques so that readers are able to actually model the data using the techniques described in the book. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject area." --Book Jacket.

Linear Regression

David J. Olive
Linear Regression Book PDF

Author : David J. Olive
Publisher : Springer
Page : 494 pages
File Size : 45,8 Mb
Release : 2017-04-18
Category : Mathematics
ISBN : 9783319552521

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Linear Regression by David J. Olive Pdf

This text covers both multiple linear regression and some experimental design models. The text uses the response plot to visualize the model and to detect outliers, does not assume that the error distribution has a known parametric distribution, develops prediction intervals that work when the error distribution is unknown, suggests bootstrap hypothesis tests that may be useful for inference after variable selection, and develops prediction regions and large sample theory for the multivariate linear regression model that has m response variables. A relationship between multivariate prediction regions and confidence regions provides a simple way to bootstrap confidence regions. These confidence regions often provide a practical method for testing hypotheses. There is also a chapter on generalized linear models and generalized additive models. There are many R functions to produce response and residual plots, to simulate prediction intervals and hypothesis tests, to detect outliers, and to choose response transformations for multiple linear regression or experimental design models. This text is for graduates and undergraduates with a strong mathematical background. The prerequisites for this text are linear algebra and a calculus based course in statistics.

Applied Regression Analysis and Generalized Linear Models

John Fox
Applied Regression Analysis and Generalized Linear Models Book PDF

Author : John Fox
Publisher : SAGE Publications
Page : 612 pages
File Size : 44,8 Mb
Release : 2015-03-18
Category : Social Science
ISBN : 9781483321318

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Applied Regression Analysis and Generalized Linear Models by John Fox Pdf

Combining a modern, data-analytic perspective with a focus on applications in the social sciences, the Third Edition of Applied Regression Analysis and Generalized Linear Models provides in-depth coverage of regression analysis, generalized linear models, and closely related methods, such as bootstrapping and missing data. Updated throughout, this Third Edition includes new chapters on mixed-effects models for hierarchical and longitudinal data. Although the text is largely accessible to readers with a modest background in statistics and mathematics, author John Fox also presents more advanced material in optional sections and chapters throughout the book. Accompanying website resources containing all answers to the end-of-chapter exercises. Answers to odd-numbered questions, as well as datasets and other student resources are available on the author′s website. NEW! Bonus chapter on Bayesian Estimation of Regression Models also available at the author′s website.

Learning Statistics with R

Daniel Navarro
Learning Statistics with R Book PDF

Author : Daniel Navarro
Publisher : Lulu.com
Page : 617 pages
File Size : 46,7 Mb
Release : 2013-01-13
Category : Psychology
ISBN : 9781326189723

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Learning Statistics with R by Daniel Navarro Pdf

"Learning Statistics with R" covers the contents of an introductory statistics class, as typically taught to undergraduate psychology students, focusing on the use of the R statistical software and adopting a light, conversational style throughout. The book discusses how to get started in R, and gives an introduction to data manipulation and writing scripts. From a statistical perspective, the book discusses descriptive statistics and graphing first, followed by chapters on probability theory, sampling and estimation, and null hypothesis testing. After introducing the theory, the book covers the analysis of contingency tables, t-tests, ANOVAs and regression. Bayesian statistics are covered at the end of the book. For more information (and the opportunity to check the book out before you buy!) visit http://ua.edu.au/ccs/teaching/lsr or http://learningstatisticswithr.com

Regression

N. H. Bingham,John M. Fry
Regression Book PDF

Author : N. H. Bingham,John M. Fry
Publisher : Springer Science & Business Media
Page : 293 pages
File Size : 54,8 Mb
Release : 2010-09-17
Category : Mathematics
ISBN : 9781848829695

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Regression by N. H. Bingham,John M. Fry Pdf

Regression is the branch of Statistics in which a dependent variable of interest is modelled as a linear combination of one or more predictor variables, together with a random error. The subject is inherently two- or higher- dimensional, thus an understanding of Statistics in one dimension is essential. Regression: Linear Models in Statistics fills the gap between introductory statistical theory and more specialist sources of information. In doing so, it provides the reader with a number of worked examples, and exercises with full solutions. The book begins with simple linear regression (one predictor variable), and analysis of variance (ANOVA), and then further explores the area through inclusion of topics such as multiple linear regression (several predictor variables) and analysis of covariance (ANCOVA). The book concludes with special topics such as non-parametric regression and mixed models, time series, spatial processes and design of experiments. Aimed at 2nd and 3rd year undergraduates studying Statistics, Regression: Linear Models in Statistics requires a basic knowledge of (one-dimensional) Statistics, as well as Probability and standard Linear Algebra. Possible companions include John Haigh’s Probability Models, and T. S. Blyth & E.F. Robertsons’ Basic Linear Algebra and Further Linear Algebra.

Introduction to Linear Regression Analysis

Douglas C. Montgomery,Elizabeth A. Peck,G. Geoffrey Vining
Introduction to Linear Regression Analysis Book PDF

Author : Douglas C. Montgomery,Elizabeth A. Peck,G. Geoffrey Vining
Publisher : John Wiley & Sons
Page : 679 pages
File Size : 40,7 Mb
Release : 2015-06-29
Category : Mathematics
ISBN : 9781119180173

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Introduction to Linear Regression Analysis by Douglas C. Montgomery,Elizabeth A. Peck,G. Geoffrey Vining Pdf

Praise for the Fourth Edition "As with previous editions, the authors have produced a leading textbook on regression." —Journal of the American Statistical Association A comprehensive and up-to-date introduction to the fundamentals of regression analysis Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences. Following a general introduction to regression modeling, including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics, including: A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model Tests on individual regression coefficients and subsets of coefficients Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition. Numerous exercises have been added throughout, allowing readers to test their understanding of the material. Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences.

Linear Models with R

Julian J. Faraway
Linear Models with R Book PDF

Author : Julian J. Faraway
Publisher : CRC Press
Page : 284 pages
File Size : 53,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781439887349

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Linear Models with R by Julian J. Faraway Pdf

A Hands-On Way to Learning Data AnalysisPart of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models

Regression Modeling Strategies

Frank E. Harrell
Regression Modeling Strategies Book PDF

Author : Frank E. Harrell
Publisher : Springer Science & Business Media
Page : 583 pages
File Size : 51,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475734621

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Regression Modeling Strategies by Frank E. Harrell Pdf

Many texts are excellent sources of knowledge about individual statistical tools, but the art of data analysis is about choosing and using multiple tools. Instead of presenting isolated techniques, this text emphasizes problem solving strategies that address the many issues arising when developing multivariable models using real data and not standard textbook examples. It includes imputation methods for dealing with missing data effectively, methods for dealing with nonlinear relationships and for making the estimation of transformations a formal part of the modeling process, methods for dealing with "too many variables to analyze and not enough observations," and powerful model validation techniques based on the bootstrap. This text realistically deals with model uncertainty and its effects on inference to achieve "safe data mining".

Applied Linear Regression Models

John Neter,William Wasserman,Michael H. Kutner
Applied Linear Regression Models Book PDF

Author : John Neter,William Wasserman,Michael H. Kutner
Publisher : Irwin Professional Publishing
Page : 694 pages
File Size : 46,8 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015027296568

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Applied Linear Regression Models by John Neter,William Wasserman,Michael H. Kutner Pdf

Applied Linear Regression Models was listed in the newsletter of the Decision Sciences Institute as a classic in its field and a text that should be on every member's shelf. The third edition continues this tradition. It is a successful blend of theory and application. The authors have taken an applied approach, and emphasize understanding concepts; this text demonstrates their approach trough worked-out examples. Sufficient theory is provided so that applications of regression analysis can be carried out with understanding. John Neter is past president of the Decision Science Institute, and Michael Kutner is a top statistician in the health and life sciences area. Applied Linear Regression Models should be sold into the one-term course that focuses on regression models and applications. This is likely to be required for undergraduate and graduate students majoring in allied health, business, economics, and life sciences.