Applied Statistics with R - GitHub Pages

1 Applied Statistics with RDavid Dalpiaz2 Contents1 About This Book.. Conventions.. Acknowledgements.. License..142 Introduction Getting Started.. Basic Calculations.. Getting Help.. Installing Packages..183 Data and Data Types.. Data Structures.. Vectors.. Vectorization.. Logical Operators.. More Vectorization.. Matrices.. Lists.. Data Frames.. Programming Basics.. Control Flow.. Functions..534 Summarizing Summary Statistics .. Plotting.. Histograms.. Barplots.. Boxplots.. Scatterplots..645 Probability and Statistics Probability inR.. Distributions.. Hypothesis Tests inR.

2 One Sample t-Test: Review.. One Sample t-Test: Example.. Two Sample t-Test: Review.. Two Sample t-Test: Example.. Simulation.. Paired Differences.. Distribution of a Sample Mean.. Beginner Tutorials and References.. Intermediate References.. Advanced References.. Quick Comparisons to Other Languages.. RStudio and RMarkdown Videos.. RMarkdown Template..87 CONTENTS57 Simple Linear Modeling.. Simple Linear Regression Model.. Least Squares Approach.. Making Predictions.. Residuals.. Variance Estimation.. Decomposition of Variation.. Coe icient of Determination.. ThelmFunction.

3 Maximum Likelihood Estimation (MLE) Approach.. Simulating SLR.. History..1228 Inference for Simple Linear Gauss Markov Theorem.. Sampling Distributions.. Simulating Sampling Distributions.. Standard Errors.. Confidence Intervals for Slope and Intercept.. Hypothesis Tests.. Tests inR.. Significance of Regression, t-Test.. Confidence Intervals inR.. Confidence Interval for Mean Response.. Prediction Interval for New Observations.. Confidence and Prediction Bands.. Significance of Regression, F-Test..1516 CONTENTS9 Multiple Linear Matrix Approach to Regression.. Sampling Distribution.

4 Single Parameter Tests.. Confidence Intervals.. Confidence Intervals for Mean Response.. Prediction Intervals.. Significance of Regression.. Nested Models.. Simulation..18410 Model Family, Form, and Fit.. Fit.. Form.. Family.. Assumed Model, Fitted Model.. Explanation versus Prediction.. Explanation.. Prediction.. Summary..19411 Categorical Predictors and Dummy Variables.. Interactions.. Factor Variables.. Factors with More Than Two Levels.. Parameterization.. Building Larger Models..229 CONTENTS712 Analysis of Experiments.. Two-Sample t-Test.. One-Way ANOVA.. Factor Variables.. Some Simulation.

5 Power.. Post Hoc Testing.. Two-Way ANOVA..25913 Model Model Assumptions.. Checking Assumptions.. Fitted versus Residuals Plot.. Breusch-Pagan Test.. Histograms.. Q-Q Plots.. Shapiro-Wilk Test.. Unusual Observations.. Leverage.. Outliers.. Influence.. Data Analysis Examples.. Good Diagnostics.. Suspect Diagnostics..3018 CONTENTS14 Response Transformation.. Variance Stabilizing Transformations.. Box-Cox Transformations.. Predictor Transformation.. Polynomials.. A Quadratic Model.. Overfitting and Extrapolation.. Comparing Polynomial Models.. ()Function and Orthogonal Polynomials.. Inhibit Function.

6 Data Example..36315 Exact Collinearity.. Collinearity.. Variance Inflation .. Simulation..38216 Variable Selection and Model Quality Criterion.. Akaike Information Criterion.. Bayesian Information Criterion.. Adjusted R-Squared.. Cross-Validated RMSE.. Selection Procedures.. Backward Search.. Forward Search.. Stepwise Search.. Exhaustive Search.. Higher Order Terms.. Explanation versus Prediction.. Explanation.. Prediction..41617 Logistic Generalized Linear Models.. Binary Response.. Fitting Logistic Regression.. Fitting Issues.. Simulation Examples.. Working with Logistic Regression.. Testing with GLMs.

7 Wald Test.. Likelihood-Ratio Test.. Confidence Intervals.. Confidence Intervals for Mean Response.. Formula Syntax.. Deviance.. Classification.. Evaluating Classifiers..45318 What s Next.. RStudio.. Tidy Data.. Visualization.. Web Applications.. Experimental Design.. Machine Learning.. Deep Learning.. Time Series.. Bayesianism.. Performance Computing..45819 Appendix459 Chapter 1 IntroductionWelcome to Applied Statistics with R! About This BookThis book was originally (and currently) designed for use withSTAT 420,Methods of Applied Statistics , at the University of Illinois may certainly be used elsewhere, but any references to this course in thisbook specifically refer to STAT book is under active development.

8 When possible, it would be best toalways access the text online to be sure you are using the most up-to-dateversion. Also, the html version provides additional features such as changingtext size, font, and colors. If you are in need of a local copy, apdf versionis continuously maintained, however, because a pdf uses Pages , the formattingmay not be as functional. (In other words, the author needs to go back andspend some time working on the pdf formatting.)Since this book is under active development you may encounter errors rangingfrom typos, to broken code, to poorly explained topics. If you do, please let usknow! Simply send an email and we will make the changes as soon as possible.

9 (dalpiaz2 AT illinois DOT edu) Or, if you know RMarkdown and are famil-iar with GitHub ,make a pull request and fix an issue yourself!This process ispartially automated by the edit button in the top-left corner of the html your suggestion or fix becomes part of the book, you will be added to the listat the end of this chapter. We ll also link to your GitHub account, or personalwebsite upon text usesMathJaxto render mathematical notation for the web. Occa-sionally, but rarely, a JavaScript error will prevent MathJax from rendering1112 CHAPTER 1. INTRODUCTION correctly. In this case, you will see the code instead of the expected math-ematical equations.

10 From experience, this is almost always fixed by simplyrefreshing the page. You ll also notice that if you right-click any equation youcan obtain the MathML Code (for copying into Microsoft Word) or the TeXcommand used to generate the equation. 2+ 2= ConventionsRcode will be typeset using amonospacefont which is syntax =3b =4sqrt(a^2+b^2)Routput lines, which would appear in the console will begin with##. They willgenerally not be syntax highlighted.## [1] 5We use the quantity to refer to the number of parameters in a linear model,notthe number of predictors. Don t worry if you don t know what this meansyet! AcknowledgementsMaterial in this book was heavily influenced by: Alex Stepanov Longtime instructor of STAT 420 at the University of Illinois atUrbana-Champaign.