An R Companion to Linear Statistical Models

An R Companion to Linear Statistical Models

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Features

  • Demonstrates the use of pre-packaged functions from the Comprehensive R Archive Network (CRAN), and how to create user-defined functions and programs
  • Shows examples of generating "grass-roots" code, which help remove the "black box" image of many pre-packaged functions
  • Applies methods to user-generated data, providing illustrations on how to create and test code for use on actual data
  • Provides detailed interpretations and explanations on computed model parameter estimates, and associated tests
  • Limits statistical theory to only that which is necessary for computations; common "rules of thumb" used in interpreting graphs and computational outputs are provided

Summary

Focusing 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.

Table of Contents

Background
Getting Started
Introduction
Starting 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 Numbers
Introduction
Elementary Operators and Functions
Sequences of Numbers
Common Probability Distributions
User Defined Functions
Working with Data Structures
Introduction
Naming 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 Functions
Introduction
The 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 Programs
Introduction
Logical Variables, Operators, and Statements
Conditional Statements
Loops
Programming Examples
Some Programming Tips

Linear Regression Models
Simple Linear Regression
Introduction
Exploratory 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 Regression
Introduction
Improving Fit
Normalizing Transformations
Variance Stabilizing Transformations
Polynomial Regression
Piecewise Defined Models
Introducing Categorical Variables
For the Curious
Multiple Linear Regression
Introduction
Exploratory 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 Regression
Introduction
Detection of Structural Violations
Diagnosing Multicollinearity
Variable Selection
Model Selection Criteria
For the Curious
Simple Remedies for Multiple Regression
Introduction
Improving 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 Revisited

Linear Models with Fixed-Effects Factors
One-Factor Models
Introduction
Exploratory 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 Covariates
Introduction
Exploratory 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 Variable
Introduction
Exploratory Data Analysis
Model Construction and Fit
Diagnostics
Pairwise Comparisons of Treatment Effects
Tukey’s Nonadditivity Test
For the Curious
Two-Factor Models
Introduction
Exploratory 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 Models
Introduction
Issues with the Error Assumptions
Missing Variables
Issues Specific to Covariates
For the Curious
Bibliography
Index

Author Bio(s)

Christopher Hay-Jahans received his Doctor of Arts in mathematics from Idaho State University in 1999. After spending three years at University of South Dakota, he moved to Juneau, Alaska, in 2002 where he has taught a wide range of undergraduate courses at University of Alaska Southeast. Each year, since 2004, he has also been teaching a course on regression and analysis of variance. Students enrolling in this course have included UAS undergraduates, masters and doctoral students from the Juneau Campus of the University of Alaska Fairbanks School of Fisheries and Ocean Sciences, as well as area professionals in the applied sciences. This work was developed as a supplement for his regression and analysis of variance course and is geared to cover topics from a wide range of textbooks, as well as address the interests, needs, and abilities of a fairly diverse group of students.

Downloads Updates

Resource OS Platform Updated Description Instructions
K13410_RFiles.zip Cross Platform October 10, 2011 Final Source Files and R Script Files
Errata.pdf Cross Platform December 18, 2012 Errata

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