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Linear Regression With Python Statsmodels Assumptions And

Leo Migdal
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linear regression with python statsmodels assumptions and

Linear regression is a powerful and widely used statistical tool for modeling the relationship between a dependent variable and one or more independent variables. However, its reliability hinges on certain underlying assumptions being met. Ignoring these assumptions can lead to misleading results, incorrect inferences, and ultimately, poor decisions. In this post, we”ll dive deep into checking the crucial assumptions of linear regression using Python”s powerful statsmodels library. Understanding and validating these assumptions is a critical step in building robust and trustworthy predictive models. Before interpreting your model”s coefficients or making predictions, it”s vital to ensure that your data aligns with the requirements of linear regression.

Here are the key assumptions: Let”s begin by importing the necessary libraries and generating some synthetic data to work with. This will allow us to demonstrate the assumption checks effectively. With our data ready, let”s fit a simple Ordinary Least Squares (OLS) model using statsmodels. We”ll then extract the residuals, which are central to checking most assumptions. I’ve built dozens of regression models over the years, and here’s what I’ve learned: the math behind linear regression is straightforward, but getting it right requires understanding what’s happening under the hood.

That’s where statsmodels shines. Unlike scikit-learn, which optimizes for prediction, statsmodels gives you the statistical framework to understand relationships in your data. Let’s work through linear regression in Python using statsmodels, from basic implementation to diagnostics that actually matter. Statsmodels is a Python library that provides tools for estimating statistical models, including ordinary least squares (OLS), weighted least squares (WLS), and generalized least squares (GLS). Think of it as the statistical counterpart to scikit-learn. Where scikit-learn focuses on prediction accuracy, statsmodels focuses on inference: understanding which variables matter, quantifying uncertainty, and validating assumptions.

The library gives you detailed statistical output including p-values, confidence intervals, and diagnostic tests. This matters when you’re not just predicting house prices but explaining to stakeholders why square footage matters more than the number of bathrooms. Start with the simplest case: one predictor variable. Here’s a complete example using car data to predict fuel efficiency: Let’s say you are a real estate agent and want to know the price of houses based on their characteristics. You will need records of available homes, their features and prices, and you will use this data to estimate the price of a house based on those features.

This technique is known as regression analysis, and this article will focus specifically on linear regression. You will also learn about the requirements your data should meet, before you can perform a linear regression analysis using the Python library statsmodels , how to conduct the linear regression analysis, and interpret... Linear regression is a statistical technique used to model the relationship between a continuous dependent variable(outcome) and one or more independent variables (predictors) by fitting a linear equation to the observed data. This allows us to understand how the outcome variable changes to the predictor variables. We have various types of linear regression. Before conducting a linear regression, our data should meet some assumptions:

In this article, we will discuss how to use statsmodels using Linear Regression in Python. Linear regression analysis is a statistical technique for predicting the value of one variable(dependent variable) based on the value of another(independent variable). The dependent variable is the variable that we want to predict or forecast. In simple linear regression, there's one independent variable used to predict a single dependent variable. In the case of multilinear regression, there's more than one independent variable. The independent variable is the one you're using to forecast the value of the other variable.

The statsmodels.regression.linear_model.OLS method is used to perform linear regression. Linear equations are of the form: Syntax: statsmodels.regression.linear_model.OLS(endog, exog=None, missing='none', hasconst=None, **kwargs) Return: Ordinary least squares are returned. Importing the required packages is the first step of modeling. The pandas, NumPy, and stats model packages are imported.

Linear models with independently and identically distributed errors, and for errors with heteroscedasticity or autocorrelation. This module allows estimation by ordinary least squares (OLS), weighted least squares (WLS), generalized least squares (GLS), and feasible generalized least squares with autocorrelated AR(p) errors. See Module Reference for commands and arguments. \(Y = X\beta + \epsilon\), where \(\epsilon\sim N\left(0,\Sigma\right).\) Depending on the properties of \(\Sigma\), we have currently four classes available: GLS : generalized least squares for arbitrary covariance \(\Sigma\)

Checking model assumptions is like commenting code. Everybody should be doing it often, but it sometimes ends up being overlooked in reality. A failure to do either can result in a lot of time being confused, going down rabbit holes, and can have pretty serious consequences from the model not being interpreted correctly. Linear regression is a fundamental tool that has distinct advantages over other regression algorithms. Due to its simplicity, it’s an exceptionally quick algorithm to train, thus typically makes it a good baseline algorithm for common regression scenarios. More importantly, models trained with linear regression are the most interpretable kind of regression models available - meaning it’s easier to take action from the results of a linear regression model.

However, if the assumptions are not satisfied, the interpretation of the results will not always be valid. This can be very dangerous depending on the application. This post contains code for tests on the assumptions of linear regression and examples with both a real-world dataset and a toy dataset. For our real-world dataset, we’ll use the Boston house prices dataset from the late 1970’s. The toy dataset will be created using scikit-learn’s make_regression function which creates a dataset that should perfectly satisfy all of our assumptions. One thing to note is that I’m assuming outliers have been removed in this blog post.

This is an important part of any exploratory data analysis (which isn’t being performed in this post in order to keep it short) that should happen in real world scenarios, and outliers in particular... See Anscombe’s Quartet for examples of outliers causing issues with fitting linear regression models. 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. If you are looking for how to run code jump to the next section or if you would like some theory/refresher then start with this section. Linear regression is used to test the relationship between independent variable(s) and a continous dependent variable. The overall regression model needs to be significant before one looks at the individual coeffiecients themselves. The model's signifance is measured by the F-statistic and a corresponding p-value.

If the overall F-statistic is not significant, it indicates that the current model is no better than using the mean value of the dependent variable at predicting the outcome. Regression models are useful because it allows one to see which variable(s) are important while taking into account other variables that could influence the outcome as well. Furthermore, once a regression model is decided on, there is a good amount of additional post-estimation work that can be done to further explore the relationship(s) that may be present. Since linear regression is a parametric test it has the typical parametric testing assumptions. In addition to this, there is an additional concern of multicollinearity. While multicollinearity is not an assumption of the regression model, it's an aspect that needs to be checked.

Multicollinearity occurs when an independent variable is able to be predicted, with good accuracy, by another independent variable in the same model. Multicollinearity is a concern because it weakens significance of independent variables. How to test for this will be demonstrated later on. For this demonstration, the conventional p-value of 0.05 will be used. The test statistic is the F-statistic and compares the regression mean square ($MS_R$) to the error mean square ($MS_E$). $MS_R$ is also known as the model's mean square.

This F-statistic can be calculated using the following formula: Before the decision is made to accept or reject the null hypothesis the assumptions need to be checked. See this page on how to check the parametric assumptions in detail - how to check the assumptions for this example will be demonstrated near the end. Don't forget to check the assumptions before interpreting the results! First to load the libraries and data needed. Below, Pandas, Researchpy, StatsModels and the data set will be loaded.

Let's look at the variables in the data set. Python is popular for statistical analysis because of the large number of libraries. One of the most common statistical calculations is linear regression. statsmodels offers some powerful tools for regression and analysis of variance. Here's how to get started with linear models. statsmodels is a Python library for running common statistical tests.

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