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.
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.
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
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