Synopses & Reviews
A comprehensive and up-to-date introduction to the fundamentals of regression analysisThe Fourth Edition of Introduction to Linear Regression Analysis describes both the conventional and less common uses of linear regression in the practical context of today's mathematical and scientific research. This popular book blends both theory and application to equip the reader with an understanding of the basic principles necessary to apply regression model-building techniques in a wide variety of application environments. It assumes a working knowledge of basic statistics and a familiarity with hypothesis testing and confidence intervals, as well as the normal, t, x2, and F distributions.
Illustrating all of the major procedures employed by the contemporary software packages MINITAB®, SAS®, and S-PLUS®, the Fourth Edition begins with 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 discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. Subsequent chapters discuss:
- Indicator variables and the connection between regression and analysis-of-variance models
- Variable selection and model-building techniques and strategies
- The multicollinearity problem—its sources, effects, diagnostics, and remedial measures
- Robust regression techniques such as M-estimators, and properties of robust estimators
- The basics of nonlinear regression
- Generalized linear models
- Using SAS® for regression problems
This book is a robust resource that offers solid methodology for statistical practitioners and professionals in the fields of engineering, physical and chemical sciences, economics, management, life and biological sciences, and the social sciences. Both the accompanying FTP site, which contains data sets, extensive problem solutions, software hints, and PowerPoint® slides, as well as the book's revised presentation of topics in increasing order of complexity, facilitate its use in a classroom setting.
With its new exercises and structure, this book is highly recommended for upper-undergraduate and beginning graduate students in mathematics, engineering, and natural sciences. Scientists and engineers will find the book to be an excellent choice for reference and self-study.
Review
"This book represents a very competent and very comprehensive monograph on regression analysis. It can highly be recommended to anyone who wants to perform a regression analysis for a given set of data." (Stat Papers, 2010)
"As with previous editions, the authors have produced a leading textbook on regression." (Journal of the American Statistical Association, December 2007)
"…written by the best in the field and I strongly recommend it both as a textbook and as a handy reference…" (Technometrics, May 2007)
"…an excellent reference and…self-teaching text for anyone with a basic level of statistical knowledge." (MAA Reviews, August 21, 2006)
Synopsis
Often, algebra & trigonometry students leave class believing that they understand a concept but are unable to apply that understanding when they get home and attempt their homework problems. This mainstream yet innovative text is written by an experienced professor who has identified this gap as one of the biggest challenges that algebra & trigonometry professors face. She uses a clear, voice that speaks directly to students- similar to how instructors communicate to them in class. Students learning from this text will overcome common barriers to learning algebra & trigonometry and will build confidence in their ability to do mathematics.
Synopsis
Anyone trying to learn algebra and trigonometry may think they understand a concept but then are unable to apply that understanding when they attempt to complete exercises. This innovative book helps them overcome common barriers to learning the concepts and builds confidence in their ability to do mathematics. The second edition presents new sections on modeling at the end of each chapter as well as new material on Limits and Early Functions. Numerous examples are also included that provide more detailed annotations using everyday language. This approach gives them the skills to understand and apply algebra and trigonometry.
About the Author
Cynthia Young received her BA in Math Education from UNC in 1990, has two masters, one in Mathematical Sciences from UCF in 1993 and a second in Electrical Engineering from the University of Washington in 1997. Finally, she received a PhD in Applied Mathematics from the University of Washington in 1996. She is already a tenured professor at UCF and is very actively involved in the supervision of UCF's graduate and undergraduate research assistants. Before becoming an award-winning Associate Professor at UCF, Cynthia taught High School. Cynthia received numerous grants and was named the principal investigator on six military and academic research projects. She has been an administrator/advisor to the Florida Space Institute at the Kennedy Space Center since 1998. Cynthia is a veteran presenter at conferences and conventions and has published over a dozen journal articles. In addition, she has been a contributor to several texts, including a College Algebra workbook for McGraw-Hill. Lastly, she edited the Marcel Decker's Optical Engineering Encyclopedia.
Table of Contents
CHAPTER 0 PREREQUISITES AND REVIEW
0.1 Real Numbers
0.2 Integer Exponents and Scientific Notation
0.3 Polynomials: Basic Operations
0.4 Factoring Polynomials
0.5 Rational Expressions
0.6 Rational Exponents and Radicals
0.7 Complex Numbers
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 1 EQUATIONS AND INEQUALITIES
1.1 Linear Equations
1.2 Applications Involving Linear Equations
1.3 Quadratic Equations
1.4 Other Types of Equations
1.5 Linear Inequalities
1.6 Polynomial and Rational Inequalities
1.7 Absolute Value Equations and Inequalities
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 2 GRAPHS
2.1 Basic Tools: Cartesian Plane, Distance, and Midpoint
2.2 Graphing Equations: Point-Plotting, Intercepts and Symmetry
2.3 Lines
2.4 Circles
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 3 FUNCTIONS AND THEIR GRAPHS
3.1 Functions
3.2 Graphs of Functions; Piecewise-Defined Functions; Increasing and Decreasing Functions; Average Rate of Change
3.3 Graphing Techniques: Transformations
3.4 Operation on Functions and Composition of Functions
3.5 One-to-One Functions and Inverse Functions
3.6 Modeling Functions Using Variation
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 4 POLYNOMIAL AND RATIONAL FUNCTIONS
4.1 Quadratic Functions
4.2 Polynomial Functions of Higher Degree
4.3 Dividing Polynomials: Long Division and Synthetic Division
4.4 The Real Zeros of a Polynomial Function
4.5 Complex Zeros; The Fundamental Theorem of Algebra
4.6 Rational Functions
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
5.1 Exponential Functions and Their Graphs
5.2 Exponential Functions and Their Graphs
5.3 Properties of Logarithms
5.4 Exponential and Logarithmic Equations
5.5 Exponential and Logarithmic Models
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 6 TRIGONOMETRIC FUNCTIONS
6.1 Angles, Degrees and Triangles
6.2 Definition 1 of Trigonometric Functions: Right Triangle Ratios
6.3 Applications of Right Triangle Trigonometry: Solving Right Triangles
6.4 Definition 2 of Trigonometric Functions: Cartesian Plane
6.5 Trigonometric Functions of Non-Acute Angles
6.6 Radian Measure and Applications
6.7 Definition 3 of Trigonometric Functions: Unit Circle Approach
6.8 Graphs of Sine and Cosine Functions
6.9 Graphs of Other Trigonometric Functions
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 7 ANALYTIC TRIGONOMETRY
7.1 Basic Trigonometric Identities
7.2 Verifying Trigonometric Identities
7.3 Sum and Difference Identities
7.4 Double-Angle Identities
7.5 Half-Angle Identities
7.6 Product-to-Sum and Sum-to-Product Identities
7.7 Inverse Trigonometric Functions
7.8 Trigonometric Equations
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 8 ADDITIONAL TOPIC IN TRIGONOMETRY
8.1 Oblique Triangles and The Law of Sines
8.2 The Law of Cosines
8.3 Area of a Triangle
8.4 Vectors
8.5 Dot Product
8.6 Polar (Trigonometric) Form of Complex Numbers
8.7 Products, Quotients, Powers and Roots of Complex Numbers
8.8 Polar Equations and Graphs
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 9 SYSTEMS OF LINEAR EQUATIONS AND INEQUALITIES
9.1 Systems of Linear Equations in Two Variables
9.2 Systems of Linear Equations in Three Variables
9.3 Partial Fractions
9.4 Systems of Linear Inequalities in Two Variables
9.5 The Linear Programming Model
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 10 MATRICES
10.1 Matrices and Systems of Linear Equations
10.2 Matrix Algebra
10.3 Matrix Equations; The Inverse of a Square Matrix
10.4 The Determinant of a Square Matrix and Cramer's Rule
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 11 ANALYTIC GEOMETRY
11.1 Conic Basics
11.2 The Parabola
11.3 The Ellipse
11.4 The Hyperbola
11.5 Systems of Nonlinear Equations
11.6 Systems of Nonlinear Inequalities
11.7 Rotation of Axes
11.8 Polar Equations of Conics
11.9 Parametric Equations and Graphs
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test
CHAPTER 12 SEQUENCES, SERIES, AND PROBABILITY
12.1 Sequences and Series
12.2 Arithmetic Sequences and Series
12.3 Geometric Sequences and Series
12.4 Mathematical Induction
12.5 Binomial Theorem
12.6 Counting, Permutations, and Combinations
12.7 Probability
Modeling Your World
Review
Review Exercises
Practice Test
Cumulative Test