Statistical Methods The Geometric Approach [Paperback]

A novel exposition of the analysis of variance and regression. The key feature here is that these tools are viewed in their natural mathematical setting - the geometry of finite dimensions. This is because geometry clarifies the basic statistics and unifies the many aspects of analysing variance and regression.This book is a novel exposition of the traditional workhorses of statistics: analysis of variance and regression. The key feature is that these tools are viewed in their natural mathematical setting, the geometry of finite dimensions. The Authors To introduce ourselves, Dave Saville is a practicing statistician working in agricultural research; Graham Wood is a university lecturer involved in the teaching of statistical methods. Each of us has worked for sixteen years in our current field. Features of the Book People like pictures. One picture can present a set of ideas at a glance, while a series of pictures, each building on the last, can unify a wealth of ideas. Such a series we present in this text by means of a systematic geometric approach to the presentation of the theory of basic statistical methods. This approach fills the void between the traditional extremes of the cookbook approach and the matrix algebra approach, providing an elementary but at the same time rigorous view of the subject. It combines the virtues of the traditional methods, while avoiding their vices.I Basic Ideas.- 1 Introduction.- 1.1 Why Use Geometry?.- 1.2 A Simple Illustration.- 1.3 Tradition and Practice.- 1.4 How to Read This Book.- Exercise.- 2 The Geometric Tool Kit.- 2.1 Introducing Vectors.- 2.2 Putting Vectors Together.- 2.3 Angles Between Vectors.- 2.4 Projections.- 2.5 Sums of Squares.- Exercises.- Solutions to the Reader Exercises.- 3 The Statistical Tool Kit.- 3.1 Basic Ideas.- 3.2 Combining Variables.- 3.3 Estimation.- 3.4 Reference Distributions.- Solutions to the Reader Exercises.- 4 Tool Kits At Work.- 4.1 The Scientific Method.- 4.2 Statistical Analysis.- Exelc¶