Python Linear Regression A Complete Guide With Example

Leo Migdal

-Dec 4, 2025, 6:03 AM

python linear regression a complete guide with example

Recommended Video CourseStarting With Linear Regression in Python Watch Now This tutorial has a related video course created by the Real Python team. Watch it together with the written tutorial to deepen your understanding: Starting With Linear Regression in Python Linear regression is a foundational statistical tool for modeling the relationship between a dependent variable and one or more independent variables. It’s widely used in data science and machine learning to predict outcomes and understand relationships between variables. In Python, implementing linear regression can be straightforward with the help of third-party libraries such as scikit-learn and statsmodels.

By the end of this tutorial, you’ll understand that: To implement linear regression in Python, you typically follow a five-step process: import necessary packages, provide and transform data, create and fit a regression model, evaluate the results, and make predictions. This approach allows you to perform both simple and multiple linear regressions, as well as polynomial regression, using Python’s robust ecosystem of scientific libraries. A complete hands-on guide to simple linear regression, including formulas, intuitive explanations, worked examples, and Python code. Learn how to fit, interpret, and evaluate a simple linear regression model from scratch. This article is part of the free-to-read Data Science Handbook

Choose your expertise level to adjust how many terms are explained. Beginners see more tooltips, experts see fewer to maintain reading flow. Hover over underlined terms for instant definitions. Simple linear regression is the foundation of predictive modeling in data science and machine learning. It's a statistical method that models the relationship between a single independent variable (feature) and a dependent variable (target) by fitting a straight line to observed data points. Think of it as finding a straight line that passes through or near your data points on a scatter plot.

Simple linear regression offers simplicity and interpretability. When you have two variables that seem to have a linear relationship, this method helps you understand how one variable changes with respect to the other. For example, you might want to predict house prices based on square footage, or understand how study hours relate to test scores. Simple linear regression models the relationship between a dependent variable and a single independent variable. In this article, we will explore simple linear regression and it's implementation in Python using libraries such as NumPy, Pandas, and scikit-learn. Simple Linear Regression aims to describe how one variable i.e the dependent variable changes in relation with reference to the independent variable.

For example consider a scenario where a company wants to predict sales based on advertising expenditure. By using simple linear regression the company can determine if an increase in advertising leads to higher sales or not. The below graph explains the relationship between advertising expenditure and sales using simple linear regression: The relationship between the dependent and independent variables is represented by the simple linear equation: In this equation m signifies the slope of the line indicating how much y changes for a one-unit increase in x, a positive m suggests a direct relationship while a negative m indicates an... Linear regression is one of the first algorithms you’ll add to your statistics and data science toolbox.

It helps model the relationship between one more independent variables and a dependent variable. In this tutorial, we’ll review how linear regression works and build a linear regression model in Python. You can follow along with this Google Colab notebook if you like. Linear regression aims to fit a linear equation to observed data given by: As you might already be familiar, linear regression finds the best-fitting line through the data points by estimating the optimal values of β1 and β0 that minimize the sum of the squared residuals—the differences... When there are multiple independent variables, the multiple linear regression model is given by:

In the real world, events often follow patterns. A person with a high BMI is more likely to have a high blood sugar level. Similarly, a company’s stock prices depend on its profits, order book value, and liabilities. By identifying and modeling these patterns, we can predict outcomes that will help us make better decisions across domains. To achieve this, we can build a linear regression model using the sklearn module in Python. In this article, we will discuss linear regression and how it works.

We will also implement linear regression models using the sklearn module in Python to predict the disease progression of diabetic patients using features like BMI, blood pressure, and age. Finally, we will discuss the assumptions and use cases for linear regression models that will help you decide whether to use linear regression for a given dataset or not. In statistics and machine learning, regression is the process of modeling the relationship between independent and dependent variables. Linear regression is a supervised machine learning algorithm that models the relationship between independent and dependent variables, assuming that the dependent variable is a linear combination of the input features. For example, we can model the relationship between age and blood sugar level of a given population as follows: Here, we have assumed that people’s blood sugar levels are linearly dependent on their age.

According to the formula, a newborn child will have a blood sugar level in the 70s, and a 20-year-old person will have a blood sugar level of 110. Now, suppose we have other population features, such as body mass index (BMI), blood pressure, and age. In that case, we can model the relationship between the features and the blood sugar level of a given population as follows: Data Science, linear regression, machine learning, pandas, predictive modeling, python, python tutorial, Regression Analysis, statistics, statsmodels The field of statistics provides a robust framework for quantifying complex relationships within data. Central to this discipline is linear regression, a foundational modeling technique.

It is used universally across economics, engineering, and data science to formally establish and predict the linear relationship between a scalar response variable (or dependent variable) and one or more predictor variables (or independent... Mastering this technique is essential for anyone seeking to transition from correlation to causal modeling in their analysis. This comprehensive, expert-level guide is designed to walk you through the entire lifecycle of building, executing, and rigorously interpreting a multiple linear regression model. We focus specifically on the high-performance Python programming environment, utilizing its most powerful statistical libraries. This approach ensures not only computational efficiency but also the generation of robust and scientifically sound model outputs, crucial for reliable inference. We will leverage the industry-standard tools: Pandas for data manipulation and the powerful Statsmodels library for advanced statistical fitting and summary generation.

By the end of this tutorial, you will possess a deep understanding of how to apply multiple linear regression to real-world problems and correctly diagnose the resulting statistical metrics. To effectively illustrate the methodology of multiple linear regression, we will employ a classic scenario drawn from educational research. Our objective is to rigorously determine which factors significantly influence a student’s final performance on a standardized examination. This type of analysis moves beyond simple bivariate relationships, allowing us to test the simultaneous impact of several factors. Machine learning > Linear Models > Regression > Linear Regression Linear Regression is a fundamental machine learning algorithm used for predicting a continuous target variable based on one or more predictor variables.

This tutorial provides a detailed explanation of linear regression, along with Python code examples to illustrate its implementation and application. We will cover the core concepts, mathematical foundations, and practical considerations for using linear regression effectively. Linear Regression aims to model the relationship between a dependent variable (Y) and one or more independent variables (X) by fitting a linear equation to observed data. A simple linear regression has one independent variable, while multiple linear regression has multiple independent variables. The goal is to find the best-fitting line (or hyperplane in the case of multiple variables) that minimizes the difference between the predicted and actual values. The equation for simple linear regression is: Y = β₀ + β₁X + ε, where:

Python Linear Regression A Complete Guide With Example

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