Understanding Residual Plots in Linear Regression Models: A Comprehensive Guide with Examples

Linear regression is a widely used statistical method for analyzing the relationship between a dependent variable and one or more independent variables. The primary goal of linear regression is to create a model that can predict the dependent variable based on the independent variables, minimizing the difference between the predicted and actual values. A residual plot is a graphical representation that helps assess the quality of a linear regression model by illustrating the differences between observed and predicted values. In this comprehensive guide, we will explore the concept of residual plots, their importance in linear regression models, and practical examples to help you better understand their application in real-world scenarios.

What is a Residual Plot?

A residual plot is a graphical representation of the residuals (errors) in a linear regression model. Residuals are the differences between the observed values of the dependent variable and the predicted values obtained from the linear regression model. In simple terms, a residual plot shows how far off the predictions are from the actual data points.

The residual plot is created by plotting the residuals on the vertical axis against the predicted values or…