[PDF] Mathematical Algorithms For Linear Regression eBook

Author : Helmuth Späth
Publisher : Academic Press
Page : 338 pages
File Size : 35,73 MB
Release : 2014-05-10
Category : Mathematics
ISBN : 1483264548

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Mathematical Algorithms for Linear Regression discusses numerous fitting principles related to discrete linear approximations, corresponding numerical methods, and FORTRAN 77 subroutines. The book explains linear Lp regression, method of the lease squares, the Gaussian elimination method, the modified Gram-Schmidt method, the method of least absolute deviations, and the method of least maximum absolute deviation. The investigator can determine which observations can be classified as outliers (those with large errors) and which are not by using the fitting principle. The text describes the elimination of outliers and the selection of variables if too many or all of them are given by values. The clusterwise linear regression accounts if only a few of the relevant variables have been collected or are collectible, assuming that their number is small in relation to the number of observations. The book also examines linear Lp regression with nonnegative parameters, the Kuhn-Tucker conditions, the Householder transformations, and the branch-and-bound method. The text points out the method of least squares is mainly used for models with nonlinear parameters or for orthogonal distances. The book can serve and benefit mathematicians, students, and professor of calculus, statistics, or advanced mathematics.

Author : George A. F. Seber
Publisher : Wiley-Interscience
Page : 494 pages
File Size : 38,27 MB
Release : 1977-01-27
Category : Mathematics
ISBN :

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This book explains the theory and application of research techniques used in linar regression analysis. Dr. Seber gives a full discussion on the assumptions underlying regression models, and presents a variety of graphic and computational techniques for investigating these assumptions. His geometric approach enables the reader to deal with full rank and less than full rank models at the same time, and he varies the material by using the theory of generalized inverses to explain other approaches. Seber gives special attention to cases in straight-line and polynomial regression, analysis of variance and co-variance models associated with experimental designs in a theoretical framework. He also includes a number of topics which are usually omitted from most books, but are important in this area: optimal design, ridge estimators, two-phase regression, spline functions, and missing observations-with up-to-date sources of the literature available in these areas. Over 200 carefully selected problems, outline solutions, a reference bibliography, and appendices make this one of the most useful and informative books available on the subject of linear regression.

Author : Douglas C. Montgomery
Publisher : John Wiley & Sons
Page : 679 pages
File Size : 38,64 MB
Release : 2015-06-29
Category : Mathematics
ISBN : 1119180171

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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.

Author : Marc Peter Deisenroth
Publisher : Cambridge University Press
Page : 392 pages
File Size : 21,69 MB
Release : 2020-04-23
Category : Computers
ISBN : 1108569323

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The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

Author : Steven M. Kay
Publisher : Pearson Education
Page : 496 pages
File Size : 38,60 MB
Release : 2013
Category : Technology & Engineering
ISBN : 013280803X

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"For those involved in the design and implementation of signal processing algorithms, this book strikes a balance between highly theoretical expositions and the more practical treatments, covering only those approaches necessary for obtaining an optimal estimator and analyzing its performance. Author Steven M. Kay discusses classical estimation followed by Bayesian estimation, and illustrates the theory with numerous pedagogical and real-world examples."--Cover, volume 1.

Author : Xin Yan
Publisher : World Scientific
Page : 349 pages
File Size : 40,88 MB
Release : 2009
Category : Mathematics
ISBN : 9812834117

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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 methods and techniques described in the book. It covers the fundamental theories in linear regression analysis and is extremely useful for future research in this area. The examples of regression analysis using the Statistical Application System (SAS) are also included. This book is suitable for graduate students who are either majoring in statistics/biostatistics or using linear regression analysis substantially in their subject fields.

Author : Farebrother
Publisher : Routledge
Page : 320 pages
File Size : 40,51 MB
Release : 2018-05-02
Category : Mathematics
ISBN : 1351435264

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Presenting numerous algorithms in a simple algebraic form so that the reader can easilytranslate them into any computer language, this volume gives details of several methodsfor obtaining accurate least squares estimates. It explains how these estimates may beupdated as new information becomes available and how to test linear hypotheses.Linear Least Squares Computations features many structured exercises that guidethe reader through the available algorithms, plus a glossary of commonly used terms anda bibliography of supplementary reading ... collects "ancient" and modem results onlinear least squares computations in a convenient single source . . . develops the necessarymatrix algebra in the context of multivariate statistics . .. only makes peripheral use ofconcepts such as eigenvalues and partial differentiation .. . interprets canonical formsemployed in computation ... discusses many variants of the Gauss, Laplace-Schmidt,Givens, and Householder algorithms ... and uses an empirical approach for the appraisalof algorithms.Linear Least Squares Computations serves as an outstanding reference forindustrial and applied mathematicians, statisticians, and econometricians, as well as atext for advanced undergraduate and graduate statistics, mathematics, and econometricscourses in computer programming, linear regression analysis, and applied statistics.

Author : J. C. Misra
Publisher : Alpha Science Int'l Ltd.
Page : 540 pages
File Size : 12,47 MB
Release : 2003
Category : Computers
ISBN : 9788173194900

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This comprehensive volume introduces educational units dealing with important topics in Mathematics, Modelling and Algorithms. Key Features: Illustrative examples and exercises Comprehensive bibliography

Author : George A. F. Seber
Publisher : John Wiley & Sons
Page : 596 pages
File Size : 13,25 MB
Release : 2003-02-05
Category : Mathematics
ISBN : 0471415405

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Concise, mathematically clear, and comprehensive treatment of the subject. * Expanded coverage of diagnostics and methods of model fitting. * Requires no specialized knowledge beyond a good grasp of matrix algebra and some acquaintance with straight-line regression and simple analysis of variance models. * More than 200 problems throughout the book plus outline solutions for the exercises. * This revision has been extensively class-tested.