Applied Multivariate Data Analysis

"On the whole, this volume is an excellent compendium on the subject of statistics to serve as a textbook for a number of courses." (Zentralblatt fuer Mathematik)

• 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.