Linear Regression Models: Applications in R


Categories: , Tag: GTIN: 9780367753689
Linear Regression Models: Applications in R
Size: 4 MB (3849618 bytes) Extension: pdf
Author(s): John P. Hoffmann

Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

Publisher: Chapman and Hall/CRC, Year: 2021

ISBN: 0367753685,9780367753689

Research in social and behavioral sciences has benefited from linear regression models (LRMs) for decades to identify and understand the associations among a set of explanatory variables and an outcome variable. Linear Regression Models: Applications in R provides you with a comprehensive treatment of these models and indispensable guidance about how to estimate them using the R software environment.


After furnishing some background material, the author explains how to estimate simple and multiple LRMs in R, including how to interpret their coefficients and understand their assumptions. Several chapters thoroughly describe these assumptions and explain how to determine whether they are satisfied and how to modify the regression model if they are not. The book also includes chapters on specifying the correct model, adjusting for measurement error, understanding the effects of influential observations, and using the model with multilevel data. The concluding chapter presents an alternative model―logistic regression―designed for binary or two-category outcome variables. The book includes appendices that discuss data management and missing data and provides simulations in R to test model assumptions.




  • Furnishes a thorough introduction and detailed information about the linear regression model, including how to understand and interpret its results, test assumptions, and adapt the model when assumptions are not satisfied.
  • Uses numerous graphs in R to illustrate the model’s results, assumptions, and other features.
  • Does not assume a background in calculus or linear algebra, rather, an introductory statistics course and familiarity with elementary algebra are sufficient.
  • Provides many examples using real-world datasets relevant to various academic disciplines.
  • Fully integrates the R software environment in its numerous examples.

The book is aimed primarily at advanced undergraduate and graduate students in social, behavioral, health sciences, and related disciplines, taking a first course in linear regression. It could also be used for self-study and would make an excellent reference for any researcher in these fields. The R code and detailed examples provided throughout the book equip the reader with an excellent set of tools for conducting research on numerous social and behavioral phenomena.


John P. Hoffmann is a professor of sociology at Brigham Young University where he teaches research methods and applied statistics courses and conducts research on substance use and criminal behavior.

Table of contents :
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Author Biography
Chapter 1 Introduction
Our Doubts are Traitors and Make Us Lose the Good We Oft Might Win
Best Statistical Practices
Statistical Software
Chapter 2 Review of Elementary Statistical Concepts
Measures of Central Tendency
Measures of Dispersion
Samples and Populations
Sampling Error and Standard Errors
Significance Tests
Unbiasedness and Efficiency
The Standard Normal Distribution and Z-Scores
Covariance and Correlation
Comparing Means from Two Groups
Examples Using R
Chapter Summary
Chapter Exercises
Chapter 3 Simple Linear Regression Models
Assumptions of Simple LRMs
An Example of an LRM Using R
Formulas for the Slope Coefficient and Intercept
Hypothesis Tests for the Slope Coefficient
Chapter Summary
Chapter Exercises
Chapter 4 Multiple Linear Regression Models
An Example of a Multiple LRM
Comparing Slope Coefficients
Assumptions of Multiple LRMs
Some Important Characteristics of Multiple LRMs
Chapter Summary
Chapter Exercises
Chapter 5 The ANOVA Table and Goodness-of-Fit Statistics
Another Example of a Multiple LRM
Chapter Summary
Chapter Exercises
Chapter 6 Comparing Linear Regression Models
The Partial F-Test and Multiple Partial F-Test
Evaluating Model Fit with Information Criterion Measures
Confounding Variables
Chapter Summary
Chapter Exercises
Chapter 7 Indicator Variables in Linear Regression Models
Indicator Variables in Multiple LRMs
LRMs with Indicator and Continuous Explanatory Variables
Chapter Summary
Chapter Exercises
Chapter 8 Independence
Determining Dependence
Example of Adjustment for Clustering
LRM with No Adjustment for Clustering
LRM That Adjusts for Clustering
Serial Correlation
Linear Regression Model
Solutions for Serial Correlation
Linear Regression Model (OLS)
Prais–Winsten Regression Model
Generalized Estimating Equations for Longitudinal Data
Linear Regression Model (OLS)
General Estimating Equation (GEE) Model with AR(1) Pattern
General Estimating Equation (GEE) Model with Unstructured Pattern
Spatial Autocorrelation
Chapter Summary
Chapter Exercises
Chapter 9 Homoscedasticity
Assessing Homoscedasticity in Multiple LRMs
What to Do About Heteroscedasticity
Chapter Summary
Chapter Exercises
Chapter 10 Collinearity and Multicollinearity
How to Detect Collinearity and Multicollinearity
What to Do About Collinearity and Multicollinearity
Chapter Summary
Chapter Exercises
Chapter 11 Normality, Linearity, and Interaction Effects
Are the Errors of Prediction Normally Distributed?
Testing for Nonlinearities in LRMs
Incorporating Nonlinear Associations in LRMs
Interaction Effects
Interaction Effects with Continuous Explanatory Variables
Classification and Regression Trees (CART)
A Cautionary Note about Interaction Effects
Chapter Summary
Chapter Exercises
Chapter 12 Model Specification
Variable Selection
Overfitting—or the Case of Irrelevant Variables
Underfitting—or the Case of the Absent Variables
Endogeneity Bias
Selection Bias
How Do We Assess Specification Error and What Do We Do about It?
What to Do about Selection Bias?
Variable Selection Procedures
Chapter Summary
Chapter Exercises
Chapter 13 Measurement Errors
The Outcome Variable Is Measured with Error
The Explanatory Variables Are Measured with Error
What Should We Do about Measurement Error?
Latent Variables as a Solution to Measurement Error
Chapter Summary
Chapter Exercises
Chapter 14 Influential Observations: Leverage Points and Outliers
Detecting Influential Observations
An Example of Using Diagnostic Methods to Identify Influential Observations
What to Do about Influential Observations
Chapter Summary
Chapter Exercises
Chapter 15 Multilevel Linear Regression Models
The Basics of Multilevel Regression Models
The Multilevel LRM
Examining Assumptions of the Model
Group-Level Variables and Cross-Level Interactions
Chapter Summary
Chapter Exercises
Chapter 16 A Brief Introduction to Logistic Regression
An Alternative to the LRM: Logistic Regression
Extending the Logistic Regression Model
Chapter Summary
Chapter Exercises
Chapter 17 Conclusions
Sampling Weights
Establishing Causal Associations
Final Words
Linear Regression Modeling: A Summary
Appendix A: Data Management
Appendix B: Using Simulations to Examine Assumptions of Linear Regression Models
Appendix C: Selected Formulas
Appendix D: User-Written R Packages Employed in the Examples

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