book

The Statistics and Machine Learning with R Workshop

Name: The Statistics and Machine Learning with R Workshop
Author: Liu Peng
ISBN: 9781803240305

by Liu Peng

October 2023

Beginner

516 pages

12h 12m

English

Packt Publishing

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The Statistics and Machine Learning with R Workshop
ContributorsAbout the authorAbout the reviewer
Preface
Who this book is forWhat this book coversTo get the most out of this bookDownload the example code filesConventions usedGet in touchShare your thoughtsDownload a free PDF copy of this book
Part 1:Statistics Essentials
Chapter 1: Getting Started with R
Technical requirementsIntroducing RCovering the R and RStudio basicsCommon data types in RCommon data structures in RVectorMatrixData frameListControl logic in RRelational operatorsLogical operatorsConditional statementsLoopsExploring functions in RSummary
Chapter 2: Data Processing with dplyr
Technical requirementsIntroducing tidyverse and dplyrData transformation with dplyrSlicing the dataset using the filter() functionSorting the dataset using the arrange() functionAdding or changing a column using the mutate() functionSelecting columns using the select() functionSelecting the top rows using the top_n() functionCombining the five verbsIntroducing other verbsData aggregation with dplyrCounting observations using the count() functionAggregating data via group_by() and summarize()Data merging with dplyrCase study – working with the Stack Overflow datasetSummary
Chapter 3: Intermediate Data Processing
Technical requirementsTransforming categorical and numeric variablesRecoding categorical variablesCreating variables using case_when()Binning numeric variables using cut()Reshaping the DataFrameConverting from long format into wide format using spread()Converting from wide format into long format using gather()Manipulating string dataCreating stringsConverting numbers into stringsConnecting stringsWorking with stringrBasics of stringrPattern matching in a stringSplitting a stringReplacing a stringPutting it togetherIntroducing regular expressionsWorking with tidy text miningConverting text into tidy data using unnest_tokens()Working with a document-term matrixSummary
Chapter 4: Data Visualization with ggplot2
Technical requirementsIntroducing ggplot2Building a scatter plotUnderstanding the grammar of graphicsGeometries in graphicsUnderstanding geometry in scatter plotsIntroducing bar chartsIntroducing line plotsControlling themes in graphicsAdjusting themesExploring ggthemesSummary
Chapter 5: Exploratory Data Analysis
Technical requirementsEDA fundamentalsAnalyzing categorical dataSummarizing categorical variables using countsConverting counts into proportionsMarginal distribution and faceted bar chartsAnalyzing numerical dataVisualization in higher dimensionsMeasuring the central concentrationMeasuring variabilityWorking with skewed distributionsEDA in practiceObtaining the stock price dataUnivariate analysis of individual stock pricesCorrelation analysisSummary
Chapter 6: Effective Reporting with R Markdown
Technical requirementsFundamentals of R MarkdownGetting started with R MarkdownGetting to know the YAML headerFormatting textual informationWriting R codeGenerating a financial analysis reportGetting and displaying the dataPerforming data analysisAdding plots to the reportAdding tables to the reportConfiguring code chunksCustomizing R Markdown reportsAdding a table of contentsCreating a report with parametersCustomizing the report styleSummary
Part 2:Fundamentals of Linear Algebra and Calculus in R

Chapter 7: Linear Algebra in R
Technical requirementsIntroducing linear algebraWorking with vectorsWorking with matricesMatrix vector multiplicationMatrix multiplicationThe identity matrixTransposing a matrixInverting a matrixSolving a system of linear equationsSystem of linear equationsThe solution to matrix-vector equationsGeometric interpretation of solving a system of linear equationsObtaining a unique solution to a system of linear equationsOverdetermined and underdetermined systems of linear equationsSummary
Chapter 8: Intermediate Linear Algebra in R
Technical requirementsIntroducing the matrix determinantInterpreting the determinantConnection to the matrix rankIntroducing the matrix traceSpecial properties of the matrix traceUnderstanding the matrix normUnderstanding the vector normCalculating the L 1-norm of a vectorCalculating the L 2-norm of a vectorCalculating the L ∞-norm of a vectorUnderstanding the matrix normCalculating the L 1-norm of a matrixCalculating the Frobenius norm of a matrixCalculating the infinity norm of a matrixGetting to know eigenvalues and eigenvectorsUnderstanding scalar-vector multiplicationDefining eigenvalues and eigenvectorsComputing eigenvalues and eigenvectorsIntroducing principal component analysisUnderstanding the variance-covariance matrixConnecting to PCAPerforming PCASummary
Chapter 9: Calculus in R
Technical requirementsIntroducing calculusDifferential and integral calculusMore on functionsVertical line testFunctional symmetryIncreasing and decreasing functionsSlope of a functionFunction compositionCommon functionsUnderstanding limitsInfinite limitLimit at infinityIntroducing derivativesCommon derivativesCommon properties and rules of derivativesIntroducing integral calculusIndefinite integralsIndefinite integrals of basic functionsProperties of indefinite integralsIntegration by partsDefinite integralsWorking with calculus in RPlotting basic functionsWorking with derivativesUsing symbolic parametersWorking with the second derivativeWorking with partial derivativesWorking with integration in RMore on antiderivativesEvaluating the definite integralSummary
Part 3:Fundamentals of Mathematical Statistics in R
Chapter 10: Probability Basics
Technical requirementsIntroducing probability distributionExploring common discrete probability distributionsThe Bernoulli distributionThe binomial distributionThe Poisson distributionPoisson approximation to binomial distributionThe geometric distributionComparing different discrete probability distributionsDiscovering common continuous probability distributionsThe normal distributionThe exponential distributionUniform distributionGenerating normally distributed random samplesUnderstanding common sampling distributionsCommon sampling distributionsUnderstanding order statisticsExtracting order statisticsCalculating the value at riskSummary
Chapter 11: Statistical Estimation
Statistical inference for categorical dataStatistical inference for a single parameterIntroducing the General Social Survey datasetCalculating the sample proportionCalculating the confidence intervalInterpreting the confidence interval of the sample proportionHypothesis testing for the sample proportionInference for the difference in sample proportionsType I and Type II errorsTesting the independence of two categorical variablesIntroducing the contingency tableApplying the chi-square test for independence between two categorical variablesStatistical inference for numerical dataGenerating a bootstrap distribution for the medianConstructing the bootstrapped confidence intervalRe-centering a bootstrap distributionIntroducing the central limit theorem used in t-distributionConstructing the confidence interval for the population mean using the t-distributionPerforming hypothesis testing for two meansIntroducing ANOVASummary
Chapter 12: Linear Regression in R
Introducing linear regressionUnderstanding simple linear regressionIntroducing multiple linear regressionSeeking a higher coefficient of determinationMore on adjusted R 2Developing an MLR modelIntroducing Simpson’s ParadoxWorking with categorical variablesIntroducing the interaction termHandling nonlinear termsMore on the logarithmic transformationWorking with the closed-form solutionDealing with multicollinearityDealing with heteroskedasticityIntroducing penalized linear regressionWorking with ridge regressionWorking with lasso regressionSummary
Chapter 13: Logistic Regression in R
Technical requirementsIntroducing logistic regressionUnderstanding the sigmoid functionGrokking the logistic regression modelComparing logistic regression with linear regressionMaking predictions using the logistic regression modelMore on log odds and odds ratioIntroducing the cross-entropy lossEvaluating a logistic regression modelDealing with an imbalanced datasetPenalized logistic regressionExtending to multi-class classificationSummary
Chapter 14: Bayesian Statistics
Technical requirementsIntroducing Bayesian statisticsA first look into the Bayesian theoremUnderstanding the generative modelUnderstanding prior distributionsIntroducing the likelihood functionIntroducing the posterior modelDiving deeper into Bayesian inferenceIntroducing the normal-normal modelIntroducing MCMCThe full Bayesian inference procedureBayesian linear regression with a categorical variableSummary
Index
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Content preview from The Statistics and Machine Learning with R Workshop

8 Intermediate Linear Algebra in R

The previous chapter covered the basics of linear algebra and its calculations in R. This chapter will go a step further by extending to intermediate linear algebra and cover topics such as the determinant, rank, and trace of a matrix, eigenvalues and eigenvectors, and principal component analysis (PCA). Besides providing an intuitive understanding of these abstract yet important mathematical concepts, we’ll cover the practical implementations of calculating these quantities in R.

By the end of this chapter, you will have grasped important matrix properties, such as determinant and rank, and gained hands-on experience in calculating these quantities.

In this chapter, we will cover the following topics:

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The Statistics and Machine Learning with R Workshop

by Liu Peng

8

Intermediate Linear Algebra in R

Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
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