Introduction to Simple Linear Regression

Author

Dr. Gia Elise Barboza-Salerno

Week 4: January 27, 2025

Today’s Reading

  • Diez et al., Chapter 8, pp. 304-340. Intro to linear regression. Be sure to check out the embedded videos.

Simple Linear Regression – Introduction to the Topic

This week, we will delve into Simple Linear Regression, a foundational tool in statistical analysis that allows us to model relationships between two variables. Students will learn how to interpret the slope, intercept, and residuals, and use regression output to draw meaningful conclusions about data. Through this process, students will develop a deeper understanding of how regression can be used to predict outcomes and test hypotheses in social work research.

In this unit we will learn to quantify the relationship between two numerical variables, as well as modeling numerical response variables using a numerical or categorical explanatory variable.


What will students learn this week?

  • The fundamental components of a simple linear regression model (slope, intercept, and residuals).
  • How to interpret regression output, including unstandardized and standardized coefficients.
  • The practical steps to fit a simple linear regression model in R using lm().
  • How to visualize regression results and residuals using ggplot2.

Why is this topic important?

Simple Linear Regression serves as the building block for more advanced statistical methods, such as multiple regression, moderation, and mediation analysis. It allows social work researchers to identify relationships between variables, predict outcomes, and inform data-driven decision-making. Mastering this concept is essential for understanding more complex techniques later in the course.


How does it relate to previous or future content?

  • Ties to previous content: Builds upon last week’s review of descriptive statistics and introduces the concept of relationships between variables.
  • Prepares for future topics: Provides a foundation for upcoming topics like multiple regression (Week 5), where we will expand from one predictor to multiple predictors, and interaction effects (Week 9), where regression will be used to explore moderating relationships.

This session emphasizes the practical and theoretical importance of regression analysis, helping students connect statistical techniques to real-world social work applications.

Class Files

Lecture Notes

R Code

Resources

  • Here is my annotated file for correlation and SLR
  • Here is the data I used if you want to replicate it in SPSS

Today’s Reading

R Lab Files

Additional Notes

  • Remain calm