# Applied Multivariate Statistics with SAS Software

#### Chapter 1: Multivariate Analysis Concepts

• Introduction
• Random Vectors, Means, Variances, and Covariances
• Multivariate Normal Distribution
• Sampling from Multivariate Normal Populations
• Some Important Sample Statistics and Their Distributions
• Tests for Multivariate Normality
• Random Vector and Matrix Generation

#### Chapter 2: Graphical Representation of Multivariate Data

• Introduction
• Scatter Plots
• Profile Plots
• Andrews Function Plots
• Biplots: Plotting Observations and Variables Together
• Q-Q Plots for Assessing Multivariate Normality
• Plots for Detection of Multivariate Outliers
• Bivariate Normal Distribution
• SAS/INSIGHT Software
• Concluding Remarks

#### Chapter 3: Multivariate Regression

• Introduction
• Statistical Background
• Least Squares Estimation
• ANOVA Partitioning
• Testing Hypotheses: Linear Hypotheses
• Simultaneous Confidence Intervals
• Multiple Response Surface Modeling
• General Linear Hypotheses
• Variance and Bias Analyses for Calibration Problems
• Regression Diagnostics
• Concluding Remarks

#### Chapter 4: Multivariate Analysis of Experimental Data

• Introduction
• Balanced and Unbalanced Data
• One-Way Classification
• Two-Way Classification
• Blocking
• Fractional Factorial Experiments
• Analysis of Covariance
• Concluding Remarks

#### Chapter 5: Analysis of Repeated Measures Data

• Introduction
• Single Population
• k Populations
• Factorial Designs
• Analysis in the Presence of Covariates
• The Growth Curve Models
• Crossover Designs
• Concluding Remarks

#### Chapter 6: Analysis of Repeated Measures Using Mixed Models

• Introduction
• The Mixed Effects Linear Model
• An Overview of the MIXED Procedure
• Statistical Tests for Covariance Structures
• Models with Only Fixed Effects
• Analysis in the Presence of Covariates
• A Random Coefficient Model
• Multivariate Repeated Measures Data
• Concluding Remarks

#### Appendix A: A Brief Introduction to the IML Procedure

• The First SAS Statement
• Scalars
• Matrices
• Printing of Matrices
• Algebra of Matrices
• Transpose
• Inverse
• Finding the Number of Rows and Columns
• Trace and Determinant
• Eigenvalues and Eigenvectors
• Square Root of a Symmetric Nonnegative Definite Matrix
• Generalized Inverse of a Matrix
• Singular Value Decomposition
• Symmetric Square Root of a Symmetric Nonnegative Definite Matrix
• Kronecker Product
• Augmenting Two or More Matrices
• Construction of a Design Matrix
• Checking the Estimability of a Linear Function p' B
• Creating a Matrix from a SAS Data Set
• Creating a SAS Data Set from a Matrix
• Generation of Normal Random Numbers
• Computation of Cumulative Probabilities
• Computation of Percentiles and Cut Off Points