About the Book
An easy to read survey of data analysis, linear regression models and analysis of variance. The extensive development of the linear model includes the use of the linear model approach to analysis of variance provides a strong link to statistical software packages, and is complemented by a thorough overview of theory. It is assumed that the reader has the background equivalent to an introductory book in statistical inference. Can be read easily by those who have had brief exposure to calculus and linear algebra. Intended for first year graduate students in business, social and the biological sciences. Provides the student with the necessary statistics background for a course in research methodology. In addition, undergraduate statistics majors will find this text useful as a survey of linear models and their applications.
Table of Contents:
1 Introduction.- 1.1 Multivariate Data Analysis, Data Matrices and Measurement Scales.- 1.2 The Setting.- 1.3 Review of Statistical Inference for Univariate Distributions.- Exercises for Chapter 1.- Questions for Chapter 1.- 2 Univariate Data Analysis.- 2.1 Data Analysis for Univariate Samples.- 2.2 Characteristics of Sample Distributions.- 2.3 Outliers.- 2.4 Assessing Normality.- 2.5 Transformations.- Cited Literature for Chapter 2.- Exercises for Chapter 2.- Questions for Chapter 2.- 3 Bivariate Analysis for Qualitative Random Variables.- 3.1 Joint Distributions.- 3.2 Statistical Inference for Bivariate Random Variables.- 3.3 The Simple Linear Regression Model.- 3.4 Regression and Correlation in a Multivariate Setting.- Cited Literature for Chapter 3.- Exercises for Chapter 3.- Questions for Chapter 3.- 4 Multiple Linear Regression.- 4.1 The Multiple Linear Regression Model.- 4.2 Variable Selection.- 4.3 Multicollinearity and Biased Regression.- 4.4 Residuals, Influence, Outliers andModel Validation.- 4.5 Qualitative Explanatory Variables.- 4.6 Additional Topics in Linear Regression.- Cited Literature and Additional References for Chapter 4.- Exercises for Chapter 4.- Questions for Chapter 4.- 5 Analysis of Variance and Experimental Design.- 5.1 One-Way Analysis of Variance.- 5.2 Two-Way Analysis of Variance.- 5.3 Analysis of Covariance.- 5.4 Some Three-Way Analysis of Variance Models.- 5.5 Some Basics of Experimental Design.- 5.6 Multifactor Factorials, Fractional Replication Confounding and Incomplete Blocks.- 5.7 Random Effects Models and Variance Components.- 5.8 Repeated Measures and Split Plots Designs.- Cited Literature for Chapter 5.- Exercises for Chapter 5.- Questions for Chapter 5.- 1. Matrix Algebra.- 1.1 Matrices.- Matrix, Transpose of a Matrix, Row Vector and Column Vector, Square Matrix, Symmetric Matrix, Diagonal Elements, Trace of a Matrix, Null or Zero Matrix, Identity Matrix, Diagonal Matrix, Submatrix.- 1.2 Matrix Operations.- Equality of Matrices, Addition of Matrices, Additive Inverse, Scalar Multiplication of a Matrix, Product of Two Matrices, Multiplicative Inverse, Idempotent Matrix, Kronecker Product.- 1.3 Determinants and Rank.- Determinant, Nonsingular, Relation Between Inverse and Determinant, Rank of a Matrix.- 1.4 Quadratic Forms and Positive Definite Matrices.- Quadratic Form, Congruent Matrix, Positive Definite, Positive Semidefinite, Negative Definite, Non-negative Definite.- 1.5 Partitioned Matrices.- Product of Partitioned Matrices, Inverse of a Partitioned Matrix, Determinant of a Partitioned Matrix.- 1.6 Expectations of Random Matrices.- 1.7 Derivatives of Matrix Expressions.- 2. Linear Algebra.- 2.1 Geometric Representation for Vectors.- 2.2 Linear Dependence And Linear Transformations.- 2.3 Systems of Equations.- Solution Vector for a System of Equations, Homogeneous Equations — Trivial and Nontrivial Solutions.- 2.4 Column Spaces, Projection Operators and Least Squares.- Column Space, Orthogonal Complement, Projection, Ordinary Least Squares Solution Vector, Idempotent Matrix — Projection Operator.- 3. Eigenvalue Structure and Singular Value Decomposition.- 3.1 Eigenvalue Structure for Square Matrices.- Eigenvalues and Eigenvectors, Characteristic Polynomial, Characteristic Roots, Latent Roots, Eigenvalues, Eigenvalues and Eigenvectors for Real Symmetric Matrices and Some Properties, Spectral Decomposition, Matrix Approximation, Eigenvalues for Nonnegative Definite Matrices.- 3.2 Singular Value Decomposition.- Left and Right Singular Vectors, Complete Singular Value Decomposition, Generalized Singular Value Decomposition, Relationship to Spectral Decomposition and Eigenvalues.- Data Appendix for Volume I.- Data Set D1, Data Set D2, Data Set D3, Data Set D4, Data Set D5, Data Set D6, Data Set D7, Data Set D8, Data Set D.- Table D1.- Table D2.- Table D3.- Table D4.- Table D5.- Table D6.- Table D7.- Table D8.- Table D9.- Table Appendix.- Table 1 The Cumulative Distribution Function forthe Standard Normal.- Table 3 Critical Values for the Chi-Square Distribution.- Table 5 Critical Values for the Studentized Range Distribution.- Author Index.
