Applied Regression Analysis

Norman R. Draper, Harry Smith

• Publisher: Wiley-Interscience
• Year: 2014
• Print ISBN: 9780471170822
• eBook ISBN: 9781118625682
• Edition: 3
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

An outstanding introduction to the fundamentals of regression analysis-updated and expanded The methods of regression analysis are the most widely used statistical tools for discovering the relationships among variables. This classic text, with its emphasis on clear, thorough presentation of concepts and applications, offers a complete, easily accessible introduction to the fundamentals of regression analysis. Assuming only a basic knowledge of elementary statistics, Applied Regression Analysis, Third Edition focuses on the fitting and checking of both linear and nonlinear regression models, using small and large data sets, with pocket calculators or computers. This Third Edition features separate chapters on multicollinearity, generalized linear models, mixture ingredients, geometry of regression, robust regression, and resampling procedures. Extensive support materials include sets of carefully designed exercises with full or partial solutions and a series of true/false questions with answers. All data sets used in both the text and the exercises can be found on the companion disk at the back of the book. For analysts, researchers, and students in university, industrial, and government courses on regression, this text is an excellent introduction to the subject and an efficient means of learning how to use a valuable analytical tool. It will also prove an invaluable reference resource for applied scientists and statisticians.

CHAPTER 1
Fitting a Straight Line by Least Squares

1.0. INTRODUCTION: THE NEED FOR STATISTICAL ANALYSIS

In today’s industrial processes, there is no shortage of “information.” No matter how small or how straightforward a process may be, measuring instruments abound. They tell us such things as input temperature, concentration of reactant, percent catalyst, steam temperature, consumption rate, pressure, and so on, depending on the characteristics of the process being studied. Some of these readings are available at regular intervals, every five minutes perhaps or every half hour; others are observed continuously. Still other readings are available with a little extra time and effort. Samples of the end product may be taken at intervals and, after analysis, may provide measurements of such things as purity, percent yield, glossiness, breaking strength, color, or whatever other properties of the end product are important to the manufacturer or user.

In research laboratories, experiments are being performed daily. These are usually small, carefully planned studies and result in sets of data of modest size. The objective is often a quick yet accurate analysis, enabling the experimenter to move on to “better” experimental conditions, which will produce a product with desirable characteristics. Additional data can easily be obtained if needed, however, if the decision is initially unclear.

A Ph.D. researcher may travel into an African jungle for a one-year period of intensive data-gathering on plants or animals. She will return with the raw material for her thesis and will put much effort into analyzing the data she has, searching for the messages that they contain. It will not be easy to obtain more data once her trip is completed, so she must carefully analyze every aspect of what data she has.

Regression analysis is a technique that can be used in any of these situations. Our purpose in this book is to explain in some detail something of the technique of extracting, from data of the types just mentioned, the main features of the relationships hidden or implied in the tabulated figures. (Nevertheless, the study of regres...

Table of contents

• Cover
• Table of Contents
• Preface to the Third Edition
• CHAPTER 0: Basic Prerequisite Knowledge
• CHAPTER 1: Fitting a Straight Line by Least Squares
• CHAPTER 2: Checking the Straight Line Fit
• CHAPTER 3: Fitting Straight Lines: Special Topics
• CHAPTER 4: Regression in Matrix Terms: Straight Line Case
• CHAPTER 5: The General Regression Situation
• CHAPTER 6: Extra Sums of Squares and Tests for Several Parameters Being Zero
• CHAPTER 7: Serial Correlation in the Residuals and the Durbin-Watson Test
• CHAPTER 8: More on Checking Fitted Models
• CHAPTER 9: Multiple Regression: Special Topics
• CHAPTER 10: Bias in Regression Estimates, and Expected Values of Mean Squares and Sums of Squares
• CHAPTER 11: On Worthwhile Regressions, Big F’s, and R2
• CHAPTER 12: Models Containing Functions of the Predictors, Including Polynomial Models
• CHAPTER 13: Transformation of the Response Variable
• CHAPTER 14: “Dummy” Variables
• CHAPTER 15: Selecting the “Best” Regression Equation
• CHAPTER 16: Ill-Conditioning in Regression Data
• CHAPTER 17: Ridge Regression
• CHAPTER 18: Generalized Linear Models (GLIM)
• CHAPTER 19: Mixture Ingredients as Predictor Variables
• CHAPTER 20: The Geometry of Least Squares
• CHAPTER 21: More Geometry of Least Squares
• CHAPTER 22: Orthogonal Polynomials and Summary Data
• CHAPTER 23: Multiple Regression Applied to Analysis of Variance Problems
• CHAPTER 24: An Introduction to Nonlinear Estimation
• CHAPTER 25: Robust Regression
• CHAPTER 26: Resampling Procedures (Bootstrapping)
• Bibliography
• True/False Questions
• Answers to Exercises
• Tables
• Index of Authors Associated with Exercises
• Index
• End User License Agreement