Hay-Jahans C. An R Companion to Linear Statistical Models

CRC Press – 2011, 365 p.
ISBN10: 1439873658Focusing on user-developed programming, An R Companion to Linear Statistical Models serves two audiences: those who are familiar with the theory and applications of linear statistical models and wish to learn or enhance their skills in R; and those who are enrolled in an R-based course on regression and analysis of variance. For those who have never used R, the book begins with a self-contained introduction to R that lays the foundation for later chapters.
This book includes extensive and carefully explained examples of how to write programs using the R programming language. These examples cover methods used for linear regression and designed experiments with up to two fixed-effects factors, including blocking variables and covariates. It also demonstrates applications of several pre-packaged functions for complex computational procedures.Getting StartedStarting up R
Searching for Help
Managing Objects in the Workspace
Installing and Loading Packages from CRAN
Attaching R Objects
Saving Graphics Images from R
Viewing and Saving Session History
Citing R and Packages from CRAN
The R Script Editor
Working with NumbersElementary Operators and Functions
Sequences of Numbers
Common Probability Distributions
User Defined Functions
Working with Data StructuresNaming and Initializing Data Structures
Classifications of Data within Data Structures
Basics with Univariate Data
Basics with Multivariate Data
Descriptive Statistics
For the Curious
Basic Plotting FunctionsThe Graphics Window
Boxplots
Histograms
Density Histograms and Normal Curves
Stripcharts
QQ Normal Probability Plots
Half-Normal Plots
Time-Series Plots
Scatterplots
Matrix Scatterplots
Bells and Whistles
For the Curious
Automating Flow in ProgramsLogical Variables, Operators, and Statements
Conditional Statements
Loops
Programming Examples
Some Programming TipsLinear Regression Models
Simple Linear RegressionExploratory Data Analysis
Model Construction and Fit
Diagnostics
Estimating Regression Parameters
Confidence Intervals for the Mean Response
Prediction Intervals for New Observations
For the Curious
Simple Remedies for Simple RegressionImproving Fit
Normalizing Transformations
Variance Stabilizing Transformations
Polynomial Regression
Piecewise Defined Models
Introducing Categorical Variables
For the Curious
Multiple Linear RegressionExploratory Data Analysis
Model Construction and Fit
Diagnostics
Estimating Regression Parameters
Confidence Intervals for the Mean Response
Prediction Intervals for New Observations
For the Curious
Additional Diagnostics for Multiple RegressionDetection of Structural Violations
Diagnosing Multicollinearity
Variable Selection
Model Selection Criteria
For the Curious
Simple Remedies for Multiple RegressionImproving Fit
Normalizing Transformations
Variance Stabilizing Transformations
Polynomial Regression
Adding New Explanatory Variables
What if None of the Simple Remedies Help?
For the Curious: Box — Tidwell RevisitedLinear Models with Fixed-Effects Factors
One-Factor ModelsExploratory Data Analysis
Model Construction and Fit
Diagnostics
Pairwise Comparisons of Treatment Effects
Testing General Contrasts
Alternative Variable Coding Schemes
For the Curious
One-Factor Models with CovariatesExploratory Data Analysis
Model Construction and Fit
Diagnostics
Pairwise Comparisons of Treatment Effects
Models with Two or More Covariates
For the Curious
One-Factor Models with a Blocking VariableExploratory Data Analysis
Model Construction and Fit
Diagnostics
Pairwise Comparisons of Treatment Effects
Tukey’s Nonadditivity Test
For the Curious
Two-Factor ModelsExploratory Data Analysis
Model Construction and Fit
Diagnostics
Pairwise Comparisons of Treatment Effects
What if Interaction Effects Are Significant?
Data with Exactly One Observation per Cell
Two-Factor Models with Covariates
For the Curious: Scheffe’s F-Tests
Simple Remedies for Fixed-Effects ModelsIssues with the Error Assumptions
Missing Variables
Issues Specific to Covariates
For the Curious