Multivariate Data Analysis: An Introduction to Multivariate Analysis

This book provides an introduction to the analysis of multivariate data. It should be suitable for statisticians and other research workers who are familiar with basic probability theory and elementary inference, and also have a basic grounding in matrix algebra. The book should also be suitable as a text for undergraduate and postgraduate statistics courses on multivariate analysis. The book covers a wider range oftopics than some other books in this area. It deals with preliminary data analysis, principal component and factor analysis and traditional normal-theory material. It also covers cluster analysis and scaling techniques. In writing the book, we have tried to provide a reasonable blend of theory and practice, in contrast to much of the existing literature which concentrates on one or other aspect. Enough theory is given to introduce the concepts and to make the topics mathematically interesting.

Multivariable analysis is an important subject for mathematicians, both pure and applied. Apart from mathematicians, we expect that physicists, mechanical engi­ neers, electrical engineers, systems engineers, mathematical biologists, mathemati­ cal economists, and statisticians engaged in multivariate analysis will find this book extremely useful. The material presented in this work is fundamental for studies in differential geometry and for analysis in N dimensions and on manifolds. It is also of interest to anyone working in the areas of general relativity, dynamical systems, fluid mechanics, electromagnetic phenomena, plasma dynamics, control theory, and optimization, to name only several. An earlier work entitled An Introduction to Analysis: from Number to Integral by Jan and Piotr Mikusinski was devoted to analyzing functions of a single variable. As indicated by the title, this present book concentrates on multivariable analysis and is completely self-contained. Our motivation and approach to this useful subject are discussed below. A careful study of analysis is difficult enough for the average student; that of multi variable analysis is an even greater challenge. Somehow the intuitions that served so well in dimension I grow weak, even useless, as one moves into the alien territory of dimension N. Worse yet, the very useful machinery of differential forms on manifolds presents particular difficulties; as one reviewer noted, it seems as though the more precisely one presents this machinery, the harder it is to understand.

This book contains several new sections that provide even more in-depth knowledge on the topics. New content on the classical least-squares model, which shows its advantages and limitations in greater detail, was added. Additionally, the book contains a new section on the inverse least-squares model, which explains how it differs from the classical model and its applications in chemometrics. Furthermore, a new chapter on principal component analysis, which covers the concept in greater detail and its applications in chemometrics, is added. This book also includes several real-world examples to help you better understand the topic. Overall, this book provides the reader with even more comprehensive knowledge on chemometrics and multivariate calibration, making it an essential resource for students and professionals alike.

"Chemometrics with R" offers readers an accessible introduction to the world of multivariate statistics in the life sciences, providing a complete description of the general data analysis paradigm, from exploratory analysis to modeling to validation. Several more specific topics from the area of chemometrics are included in a special section. The corresponding R code is provided for all the examples in the book; scripts, functions and data are available in a separate, publicly available R package. For researchers working in the life sciences, the book can also serve as an easy-to-use primer on R.

This book contains several new sections that provide even more in-depth knowledge on the topics. New content on the classical least-squares model, which shows its advantages and limitations in greater detail, was added. Additionally, the book contains a new section on the inverse least-squares model, which explains how it differs from the classical model and its applications in chemometrics. Furthermore, a new chapter on principal component analysis, which covers the concept in greater detail and its applications in chemometrics, is added. This book also includes several real-world examples to help you better understand the topic. Overall, this book provides the reader with even more comprehensive knowledge on chemometrics and multivariate calibration, making it an essential resource for students and professionals alike.