Linear Regression Diagnostic Plots Using Python A Medium

Leo Migdal

-Dec 4, 2025, 7:12 AM

linear regression diagnostic plots using python a medium

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. While linear regression is a pretty simple task, there are several assumptions for the model that we may want to validate. I follow the regression diagnostic here, trying to justify four principal assumptions, namely LINE in Python:

I learnt this abbreviation of linear regression assumptions when I was taking a course on correlation and regression taught by Walter Vispoel at UIowa. Really helped me to remember these four little things! In fact, statsmodels itself contains useful modules for regression diagnostics. In addition to those, I want to go with somewhat manual yet very simple ways for more flexible visualizations. Let’s go with the depression data. More toy datasets can be found here.

For simplicity, I randomly picked 3 columns. Linear regression is simple, with statsmodels. We are able to use R style regression formula. 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. Dear Freedium users, We recently experienced downtime due to a trademark infringement complaint filed by Bolster Inc. on behalf of Canva.

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Your support helps us maintain this service: The success of any statistical model to analyse a dataset depends on how closely the data satisfy the underlying assumptions of the model. Quite often it is very difficult to verify the assumptions. In the article, we will examine the assumptions related to a linear regression model and how quickly we can verify some of them using visula techniques or plots. For a dataset of the form (𝑥𝑖1,𝑥𝑖2,…,𝑥𝑖𝑝,𝑦𝑖) for 𝑖=1,…,𝑛 with 𝑦 being the response variable and 𝑥1,𝑥2,…,𝑥𝑝 being the predictor variables, the linear regression model can be stated as follows: In this model, 𝛽0,𝛽1,…,𝛽𝑝 are the regression coefficients or parameters and 𝜖𝑖𝜖𝑖 is the random error term.

We make the following assumptions. Quite often, instead of the assumptions 2 and 3 above, we assume: Discover content by tools and technology Python, with its rich ecosystem of libraries like NumPy, statsmodels, and scikit-learn, has become the go-to language for data scientists. Its ease of use and versatility make it perfect for both understanding the theoretical underpinnings of linear regression and implementing it in real-world scenarios. In this guide, I'll walk you through everything you need to know about linear regression in Python.

We'll start by defining what linear regression is and why it's so important. Then, we'll look into the mechanics, exploring the underlying equations and assumptions. You'll learn how to perform linear regression using various Python libraries, from manual calculations with NumPy to streamlined implementations with scikit-learn. We'll cover both simple and multiple linear regression, and I'll show you how to evaluate your models and enhance their performance. Linear regression is a statistical method used to model the relationship between a dependent variable (target) and one or more independent variables (predictors). The objective is to find a linear equation that best describes this relationship.

Linear regression is widely used for predictive modeling, inferential statistics, and understanding relationships in data. Its applications include forecasting sales, assessing risk, and analyzing the impact of different variables on a target outcome. There are many ways to do linear regression in Python. We have already used the heavyweight Statsmodels library, so we will continue to use it here. It has much more functionality than we need, but it provides nicely-formatted output similar to SAS Enterprise Guide. The method we will use to create linear regression models in the Statsmodels library is OLS().

OLS stands for “ordinary least squares”, which means the algorithm finds the best fit line my minimizing the squared residuals (this is “least squares”). The “ordinary” part of the name gives us the sense that the type of linear regression we are seeing here is just the tip of the methodological iceberg. There is a whole world of non-ordinary regression techniques out there intended to address this or that methodological problem or circumstance. But since this is a basic course, we will stick with ordinary least squares. Recall the general format of the linear regression equation: \(Y = \beta_0 + \beta_1 X_1 + ... + \beta_n X_n\), where \(Y\) is the value of the response variable and \(X_i\) is the value of the explanatory variable(s).

If we think about this equation in matrix terms, we see that Y is a 1-dimensional matrix: it is just a single column (or array or vector) of numbers. In our case, this vector corresponds to the compressive strength of different batches of concrete measured in megapascals. The right-hand side of the equation is actually a 2-dimensional matrix: there is one column for our X variable and another column for the constant. We don’t often think about the constant as a column of data, but the Statsmodels library does, which is why we are talking about it. Creating a linear regression model in Statsmodels thus requires the following steps:

Linear Regression Diagnostic Plots Using Python A Medium

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