Handbook of Regression Analysis With Applications in R

Samprit Chatterjee, Jeffrey S. Simonoff

• Publisher: Wiley
• Year: 2020
• Print ISBN: 9781119392378
• eBook ISBN: 9781119392484
• Edition: 2
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Handbook and reference guide for students and practitioners of statistical regression-based analyses in R

Handbook of Regression Analysis with Applications in R, Second Edition is a comprehensive and up-to-date guide to conducting complex regressions in the R statistical programming language. The authors' thorough treatment of "classical" regression analysis in the first edition is complemented here by their discussion of more advanced topics including time-to-event survival data and longitudinal and clustered data.

The book further pays particular attention to methods that have become prominent in the last few decades as increasingly large data sets have made new techniques and applications possible. These include:

• Regularization methods
• Smoothing methods
• Tree-based methods

In the new edition of the Handbook, the data analyst's toolkit is explored and expanded. Examples are drawn from a wide variety of real-life applications and data sets. All the utilized R code and data are available via an author-maintained website.

Of interest to undergraduate and graduate students taking courses in statistics and regression, the Handbook of Regression Analysis will also be invaluable to practicing data scientists and statisticians.

PART ONE
The Multiple Linear Regression Model

CHAPTER ONE
Multiple Linear Regression

1. 1.1 Introduction
2. 1.2 Concepts and Background Material
   1. 1.2.1 The Linear Regression Model
   2. 1.2.2 Estimation Using Least Squares
   3. 1.2.3 Assumptions
3. 1.3 Methodology
   1. 1.3.1 Interpreting Regression Coefficients
   2. 1.3.2 Measuring the Strength of the Regression Relationship
   3. 1.3.3 Hypothesis Tests and Confidence Intervals for β
   4. 1.3.4 Fitted Values and Predictions
   5. 1.3.5 Checking Assumptions Using Residual Plots
4. 1.4 Example—Estimating Home Prices
5. 1.5 Summary

1.1 Introduction

This is a book about regression modeling, but when we refer to regression models, what do we mean? The regression framework can be characterized in the following way:

1. We have one particular variable that we are interested in understanding or modeling, such as sales of a particular product, sale price of a home, or voting preference of a particular voter. This variable is called the target, response, or dependent variable, and is usually represented by
   
   .
2. We have a set of
   
   other variables that we think might be useful in predicting or modeling the target variable (the price of the product, the competitor's price, and so on; or the lot size, number of bedrooms, number of bathrooms of the home, and so on; or the gender, age, income, party membership of the voter, and so on). These are called the predicting, or independent variables, and are usually represented by
   
   ,
   
   , etc.

Typically, a regression analysis is used for one (or more) of three purposes:

1. modeling the relationship between
   
   and
   
   ;
2. prediction of the target variable (forecasting);
3. and testing of hypotheses.

In this chapter, we introduce the basic multiple linear regression model, and discuss how this model can be used for these three purposes. Specifically, we discuss the interpretations of the estimates of different regression parameters, the assumptions underlying the model, measures of the strength of the relationship between the target and predictor variables, the construction of tests of hypotheses and intervals related to regression parameters, and the checking of assumptions using diagnostic plots.

1.2 Concepts and Background Material

1.2.1 THE LINEAR REGRESSION MODEL

The data consist of

observations, which are sets of observed values

that represent a random sample from a larger population. It is assumed that these observations satisfy a linear relationship,

(1.1)

where the

coefficients are unknown parameters, and the

are random error terms. By a linear model, it is meant that the model is linear in the para...

Table of contents

• Cover
• Table of Contents
• Preface to the Second Edition
• Preface to the First Edition
• PART ONE: The Multiple Linear Regression Model
• PART TWO: Addressing Violations of Assumptions
• PART THREE: Categorical Predictors
• PART FOUR: Non‐Gaussian Regression Models
• PART FIVE: Other Regression Models
• PART SIX: Nonparametric and Semiparametric Models
• Bibliography
• Index
• End User License Agreement