Applied Regression Analysis and Experimental Design

Richard J. Brook, Gregory C. Arnold

• Publisher: CRC Press
• Year: 2018
• eBook ISBN: 9781351465885
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

For a solid foundation of important statistical methods, the concise, single-source text unites linear regression with analysis of experiments and provides students with the practical understanding needed to apply theory in real data analysis problems.

Stressing principles while keeping computational and theoretical details at a manageable level, Applied Regression Analysis and Experimental Design features an emphasis on vector geometry and least squares to unify and provide an intuitive basis for most topics covered… abundant examples and exercises using real-life data sets clearly illustrating practical of data analysis…essential exposure to MINITAB and GENSTAT computer packages , including computer printouts…and important background material such as vector and matrix properties and the distributional properties of quadratic forms.

Designed to make theory work for students, this clearly written, easy-to-understand work serves as the ideal texts for courses Regression, Experimental Design, and Linear Models in a broad range of disciplines. Moreover, applied statisticians will find the book a useful reference for the general application of the linear model.

1

FITTING A MODEL TO DATA

1.1 INTRODUCTION

The title of this chapter could well be the title of this book. In the first four chapters, we consider problems associated with fitting a regression model and in the last four we consider experimental designs. Mathematically, the two topics use the same model. The term regression is used when the model is fitted to observational data, and experimental design is used when the data is carefully organized to give the model special properties. For some data, the distinction may not be at all clear or, indeed, relevant. We shall consider sets of data consisting of observations of a variable of interest which we shall call y, and we shall assume that these observations are a random sample from a population, usually infinite, of possible values. It is this population which is of primary interest, and not the sample, for in trying to fit models to the data we are really trying to fit models to the population from which the sample is drawn. For each observation, y, the model will be of the form

$\text{observed y = population mean + deviation}$

(1.1.1)

The population mean may depend on the corresponding values of a predictor variable which we often label as x. For this reason, y is called the dependent variable. The deviation term indicates the individual peculiarity of the observation, y, which makes it differ from the population mean.

As an example, $y could be the price paid for a house in a certain city. The population mean could be thought of as the mean price paid for houses in that city, presumably in a given time period. In this case the deviation term could be very large as house prices would vary greatly depending on a number of factors such as the size and condition of the house as well as its position in the city. In New Zealand, each house is given a government valuation, GV, which is reconsidered on a fi...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1. Fitting a Model to Data
• 2. Goodness of Fit of the Model
• 3. Which Variables Should Be Included in the Model
• 4. Peculiarities of Observations
• 5. The Experimental Design Model
• 6. Assessing the Treatment Means
• 7. Blocking
• 8. Extensions to the Model
• Appendix A. Review of Vectors and Matrices
• Appendix B. Expectation, Linear and Quadratic Forms
• Appendix C. Data Sets
• References
• Index