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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.
BackgroundGetting StartedIntroductionStarting up R Searching for HelpManaging Objects in the WorkspaceInstalling and Loading Packages from CRANAttaching R ObjectsSaving Graphics Images from RViewing and Saving Session HistoryCiting R and Packages from CRANThe R Script EditorWorking with NumbersIntroductionElementary Operators and FunctionsSequences of NumbersCommon Probability DistributionsUser Defined FunctionsWorking with Data StructuresIntroductionNaming and Initializing Data StructuresClassifications of Data within Data StructuresBasics with Univariate DataBasics with Multivariate DataDescriptive StatisticsFor the CuriousBasic Plotting FunctionsIntroductionThe Graphics WindowBoxplotsHistogramsDensity Histograms and Normal CurvesStripchartsQQ Normal Probability PlotsHalf-Normal PlotsTime-Series PlotsScatterplotsMatrix ScatterplotsBells and WhistlesFor the CuriousAutomating Flow in ProgramsIntroductionLogical Variables, Operators, and StatementsConditional StatementsLoopsProgramming ExamplesSome Programming TipsLinear Regression ModelsSimple Linear RegressionIntroductionExploratory Data AnalysisModel Construction and FitDiagnosticsEstimating Regression ParametersConfidence Intervals for the Mean ResponsePrediction Intervals for New ObservationsFor the CuriousSimple Remedies for Simple RegressionIntroductionImproving FitNormalizing TransformationsVariance Stabilizing TransformationsPolynomial RegressionPiecewise Defined ModelsIntroducing Categorical VariablesFor the CuriousMultiple Linear RegressionIntroductionExploratory Data AnalysisModel Construction and FitDiagnosticsEstimating Regression ParametersConfidence Intervals for the Mean ResponsePrediction Intervals for New ObservationsFor the CuriousAdditional Diagnostics for Multiple RegressionIntroductionDetection of Structural ViolationsDiagnosing MulticollinearityVariable SelectionModel Selection CriteriaFor the CuriousSimple Remedies for Multiple RegressionIntroductionImproving FitNormalizing TransformationsVariance Stabilizing TransformationsPolynomial RegressionAdding New Explanatory VariablesWhat if None of the Simple Remedies Help?For the Curious: Box-Tidwell RevisitedLinear Models with Fixed-Effects FactorsOne-Factor ModelsIntroductionExploratory Data AnalysisModel Construction and FitDiagnosticsPairwise Comparisons of Treatment EffectsTesting General ContrastsAlternative Variable Coding SchemesFor the CuriousOne-Factor Models with CovariatesIntroductionExploratory Data AnalysisModel Construction and FitDiagnosticsPairwise Comparisons of Treatment EffectsModels with Two or More CovariatesFor the CuriousOne-Factor Models with a Blocking VariableIntroductionExploratory Data AnalysisModel Construction and FitDiagnosticsPairwise Comparisons of Treatment EffectsTukey's Nonadditivity TestFor the CuriousTwo-Factor ModelsIntroductionExploratory Data AnalysisModel Construction and FitDiagnosticsPairwise Comparisons of Treatment EffectsWhat if Interaction Effects Are Significant?Data with Exactly One Observation per CellTwo-Factor Models with CovariatesFor the Curious: Scheffe's F-TestsSimple Remedies for Fixed-Effects ModelsIntroductionIssues with the Error AssumptionsMissing VariablesIssues Specific to CovariatesFor the CuriousBibliographyIndex
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