Introduction to Probability and Statistics Using R

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Description

Contents

Reviews

Language

English

ISBN

978-0-557-24979-4

Contents

Preface

List of Figures

List of Tables

1 An Introduction to Probability and Statistics

1.1 Probability

1.2 Statistics

Chapter Exercises

2 An Introduction to R

2.1 Downloading and Installing R

2.2 Communicating with R

2.3 Basic R Operations and Concepts

2.4 Getting Help

2.5 External Resources

2.6 Other Tips

Chapter Exercises

3 Data Description

3.1 Types of Data

3.2 Features of Data Distributions

3.3 Descriptive Statistics

3.4 Exploratory Data Analysis

3.5 Multivariate Data and Data Frames

3.6 Comparing Populations

Chapter Exercises

4 Probability

4.1 Sample Spaces

4.2 Events

4.3 Model Assignment

4.4 Properties of Probability

4.5 Counting Methods

4.6 Conditional Probability

4.7 Independent Events

4.8 Bayes' Rule

4.9 Random Variables

Chapter Exercises

5 Discrete Distributions

5.1 Discrete Random Variables

5.2 The Discrete Uniform Distribution

5.3 The Binomial Distribution

5.4 Expectation and Moment Generating Functions

5.5 The Empirical Distribution

5.6 Other Discrete Distributions

5.7 Functions of Discrete Random Variables

Chapter Exercises

6 Continuous Distributions

6.1 Continuous Random Variables

6.2 The Continuous Uniform Distribution

6.3 The Normal Distribution

6.4 Functions of Continuous Random Variables

6.5 Other Continuous Distributions

Chapter Exercises

7 Multivariate Distributions

7.1 Joint and Marginal Probability Distributions

7.2 Joint and Marginal Expectation

7.3 Conditional Distributions

7.4 Independent Random Variables

7.5 Exchangeable Random Variables

7.6 The Bivariate Normal Distribution

7.7 Bivariate Transformations of Random Variables

7.8 Remarks for the Multivariate Case

7.9 The Multinomial Distribution

Chapter Exercises

8 Sampling Distributions

8.1 Simple Random Samples

8.2 Sampling from a Normal Distribution

8.3 The Central Limit Theorem

8.4 Sampling Distributions of Two-Sample Statistics

8.5 Simulated Sampling Distributions

Chapter Exercises

9 Estimation

9.1 Point Estimation

9.2 Confidence Intervals for Means

9.3 Confidence Intervals for Differences of Means

9.4 Confidence Intervals for Proportions

9.5 Confidence Intervals for Variances

9.6 Fitting Distributions

9.7 Sample Size and Margin of Error

9.8 Other Topics

Chapter Exercises

10 Hypothesis Testing

10.1 Introduction

10.2 Tests for Proportions

10.3 One Sample Tests for Means and Variances

10.4 Two-Sample Tests for Means and Variances

10.5 Other Hypothesis Tests

10.6 Analysis of Variance

10.7 Sample Size and Power

Chapter Exercises

11 Simple Linear Regression

11.1 Basic Philosophy

11.2 Estimation

11.3 Model Utility and Inference

11.4 Residual Analysis

11.5 Other Diagnostic Tools

Chapter Exercises

12 Multiple Linear Regression

12.1 The Multiple Linear Regression Model

12.2 Estimation and Prediction

12.3 Model Utility and Inference

12.4 Polynomial Regression

12.5 Interaction

12.6 Qualitative Explanatory Variables

12.7 Partial F Statistic

12.8 Residual Analysis and Diagnostic Tools

12.9 Additional Topics

Chapter Exercises

13 Resampling Methods

13.1 Introduction

13.2 Bootstrap Standard Errors

13.3 Bootstrap Confidence Intervals

13.4 Resampling in Hypothesis Tests

Chapter Exercises

14 Categorical Data Analysis

15 Nonparametric Statistics

16 Time Series

A R Session Information

B GNU Free Documentation License

C History

D Data

D.1 Data Structures

D.2 Importing Data

D.3 Creating New Data Sets

D.4 Editing Data

D.5 Exporting Data

D.6 Reshaping Data

E Mathematical Machinery

E.1 Set Algebra

E.2 Differential and Integral Calculus

E.3 Sequences and Series

E.4 The Gamma Function

E.5 Linear Algebra

E.6 Multivariable Calculus

F Writing Reports with R

F.1 What to Write

F.2 How to Write It with R

F.3 Formatting Tables

F.4 Other Formats

G Instructions for Instructors

G.1 Generating This Document

G.2 How to Use This Document

G.3 Ancillary Materials

G.4 Modifying This Document

H RcmdrTestDrive Story

Bibliography

Index

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