Types of Residual Plots
Residual plots provide valuable insights into the adequacy of regression models by visualizing the differences between observed and predicted values. Two common types of residual patterns are:
- Random Pattern
- U-Shaped Pattern
Random Pattern
A random pattern in residual plots indicates that the residuals scatter randomly around the horizontal axis. It suggests that the regression model adequately captures the variability in the data.
- Residuals are evenly spread around the horizontal axis with no discernible trend or pattern.
- Points in the residual plot are randomly scattered, showing no systematic deviation from the axis.
- Absence of a clear pattern suggests that the regression model is a good fit for the data.
- A random pattern indicates that the assumptions of linearity, independence, and constant variance are likely met.
- It is the desired outcome in residual analysis, indicating the validity of the regression model.
U-Shaped Pattern
A U-shaped pattern in residual plots appears when the residuals exhibit a systematic curvature, resembling the shape of the letter U.
- Residuals tend to cluster around the ends of the plot, forming a U-shaped curve.
- Curvature indicates that the regression model may not adequately capture the relationship between the variables.
- In a U-shaped pattern, the residuals systematically deviate from the horizontal axis, suggesting model inadequacy.
- This pattern may occur when the relationship between the variables is nonlinear or when influential data points are present.
- Detecting a U-shaped pattern prompts further investigation into potential nonlinearities or outliers in the data.
Residual Analysis
Residual analysis is a powerful statistical technique used to assess the accuracy of regression models. By examining the differences between observed and predicted values, residual analysis provides information about the adequacy of the model fit. Researchers and analysts need this technique to make better decisions about the validity and reliability of their statistical models.
In this article, we will learn about Residual Analysis in detail.
Table of Content
- What is Residual Analysis?
- Residuals in Regression Analysis
- Residual Plots
- Types of Residual Plots
- ANOVA Residuals
- Residual Plot Analysis
- Assumptions Regarding Residuals in Linear Regression
- Software for Calculating Residual Analysis