Contents

Introduction

Chapter 1: Basic Data Analysis

R Programming Conventions

Generation of Random Numbers and Patterns

• Random Numbers
• Patterns

Case Study: Distribution Diagnostics

• Distribution Functions
• Histogram and Related Plots; Barcharts
• Statistics of Distribution Functions; Kolmogorov-Smirnov Tests; Monte Carlo Confidence Bands
• Statistics of Histograms and Related Plots; χ²-Tests

Moments and Quantiles

R Complements

• Random Numbers
• Graphical Comparisons
• Functions
• Enhancing Graphical Displays
• R Internals: Parse, Eval, Print, Executing Files
• Packages

Statistical Summary

Chapter 2: Regression

General Regression Model

Linear Model

• Factors
• Least Squares Estimation
• More Examples for Linear Models
• Model Formulae
• Gauss-Markov Estimator

Variance Decomposition and Analysis of Variance

Simultaneous Inference

• Scheffé's Confidence Bands
• Tukey's Confidence Intervals; Case Study: Titre Plates

Beyond Linear Regression

• Transformations
• Generalised Linear Models
• Local Regression

R Complements

• Discretisation
• External Data
• Testing Software
• R Data Types
• Classes and Polymorphic Functions
• Extractor Functions

Statistical Summary

Chapter 3: Comparisons

Shift/Scale Families, and Stochastic Order

QQ plot, PP plot, and Comparison of Distributions

• Kolmogorov-Smirnov Tests
• Tests for Shift Alternatives

A Road Map

Power and Confidence

• Theoretical Power and Confidence
• Simulated Power and Confidence
• Quantile Estimation by Simulation

Qualitative Features of Distributions

Statistical Summary

Chapter 4: Dimensions 1, 2, 3, …, ∞

R Complements

Dimensions

Selections

Projections

• Marginal Distributions and Scatter Plot Matrices
• Projection Pursuit
• Projections for Dimensions 1, 2, 3, …, 7
• Parallel Coordinates

Sections, Conditional Distributions and Coplots

Transformations and Dimension Reduction

Higher Dimensions

• Linear Case
• Partial Residuals and Added Variable Plots
• Non-linear Case; Example: Cusp Non-linearity
• Case Study: Melbourne Temperature Data
• ``Curse of Dimensionality"
• Case Study: Body Fat

High Dimensions

Statistical Summary

Appendix: R as a Programming Language and Environment

• Help and Information
• Names and Search Paths
• Administation and Customisation
• Basic Data Types
• Output for Objects
• Object Inspection
• System Inspection
• Complex Data Types
• Accessing Components
• Data Manipulation
• Operators
• Functions
• Debugging and Profiling
• Control Structures
• Input and Output to Data Streams; External Data
• Libraries, Packages
• Mathematical Operators and Functions; Linear Algebra
• Model Descriptions
• Graphic Functions
• High Level Graphics
• Low Level Graphics
• Annotations and Legends
• Graphic Parameters and Layout
• Basic Statistical Functions
• Distributions, Random Numbers, Densities, ...
• Computing on the Language

References

Functions and Variables by Topic

Function and Variable Index

Index