Linear Regression Diagnostic Plots Using Python A Comprehensive Guide

Leo Migdal

-Dec 4, 2025, 7:46 AM

linear regression diagnostic plots using python a comprehensive guide

Regression analysis helps us understand the relationship between variables. However, after fitting a model, we need to check if it meets key assumptions. Diagnostic plots help us assess these assumptions visually. These plots check for patterns in residuals, normality, and influential points. In this article, we will learn how to create diagnostic plots using the statsmodels library in Python. Diagnostic plots are used to evaluate the validity of regression models by checking assumptions such as:

First, ensure you have the necessary libraries installed. You can install them using: We will use NumPy, pandas, statsmodels, Matplotlib, and Seaborn: In real-life, relation between response and target variables are seldom linear. Here, we make use of outputs of statsmodels to visualise and identify potential problems that can occur from fitting linear regression model to non-linear relation. Primarily, the aim is to reproduce visualisations discussed in Potential Problems section (Chapter 3.3.3) of An Introduction to Statistical Learning (ISLR) book by James et al., Springer.

Firstly, let us load the Advertising data from Chapter 2 of ISLR book and fit a linear model to it. In the following first we present a base code that we will later use to generate following diagnostic plots: now we generate diagnostic plots one by one. Graphical tool to identify non-linearity. Making the switch to Python after having used R for several years, I noticed there was a lack of good base plots for evaluating ordinary least squares (OLS) regression models in Python. From using R, I had familiarized myself with debugging and tweaking OLS models with the built-in diagnostic plots, but after switching to Python I didn’t know how to get the original plots from R...

So, I did what most people in my situation would do - I turned to Google for help. After trying different queries, I eventually found this excellent resource that was helpful in recreating these plots in a programmatic way. This post will leverage a lot of that work and at the end will wrap it all in a function that anyone can cut and paste into their code to reproduce these plots regardless... In short, diagnostic plots help us determine visually how our model is fitting the data and if any of the basic assumptions of an OLS model are being violated. We will be looking at four main plots in this post and describe how each of them can be used to diagnose issues in an OLS model. Each of these plots will focus on the residuals - or errors - of a model, which is mathematical jargon for the difference between the actual value and the predicted value, i.e., r_i =...

These 4 plots examine a few different assumptions about the model and the data: Communities for your favorite technologies. Explore all Collectives Stack Overflow for Teams is now called Stack Internal. Bring the best of human thought and AI automation together at your work. Bring the best of human thought and AI automation together at your work.

Learn more Find centralized, trusted content and collaborate around the technologies you use most. Bring the best of human thought and AI automation together at your work. Sarah Lee AI generated Llama-4-Maverick-17B-128E-Instruct-FP8 8 min read · June 13, 2025 Linear regression is a widely used statistical technique for modeling the relationship between a dependent variable and one or more independent variables. However, the validity of the model relies on certain assumptions being met.

In this article, we will explore how diagnostic plots can be used to visualize and validate linear regression models, detect potential issues, and improve model performance. Linear regression is based on several key assumptions: Diagnostic plots can be used to validate these assumptions and detect potential issues. To understand the importance of diagnostic plots, let's first review the assumptions of linear regression. Python Library providing Diagnostic Plots for Linear Regression Models. (Like plot.lm in R.)

I built this, because I missed the diagnostics plots of R for a university project. There are some substitutions in Python for individual charts, but they are spread over different libraries and sometimes don't show the exact same. My implementation tries to copycat the R-plots, but I didn't reimplement the R-code: The charts are just based on available documentation. lmdiag generates plots for fitted linear regression models from statsmodels, linearmodels and scikit-learn. You can find some usage examples in this jupyter notebook. Print description to aid plot interpretation:

Regression analysis is a common method used to predict continuous values, like sales or prices. Building a regression model is easy, but the results are only reliable if the model’s assumptions are met. Diagnostics help identify issues like multicollinearity, heteroscedasticity, non-linearity, or outliers that can distort predictions. Python provides libraries such as statsmodels, scikit-learn, and matplotlib to visualize and assess these aspects. In this article, we’ll explore how to interpret common regression diagnostics in Python and use them to refine model performance. We’ll use the Diabetes dataset and fit a regression model:

Diagnostics help verify whether the assumptions of linear regression are satisfied. Let’s look at the main plots. The Residuals vs. Fitted Values plot shows whether residuals are randomly scattered around zero. Patterns suggest non-linearity or heteroscedasticity (unequal variance).

Linear Regression Diagnostic Plots Using Python A Comprehensive Guide

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