Real Python: 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:

• Linear regression is a statistical method for modeling the relationship between a dependent variable and one or more independent variables by fitting a linear equation.
• Implementing linear regression in Python involves using libraries like scikit-learn and statsmodels to fit models and make predictions.
• The formula for linear regression is 𝑦 = 𝛽₀ + 𝛽₁𝑥₁ + ⋯ + 𝛽ᵣ𝑥ᵣ + 𝜀, representing the linear relationship between variables.
• Simple linear regression involves one independent variable, whereas multiple linear regression involves two or more.
• The scikit-learn library provides a convenient and efficient interface for performing linear regression in Python.

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.

Take the Quiz: Test your knowledge with our interactive “Linear Regression in Python” quiz. You’ll receive a score upon completion to help you track your learning progress:

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Interactive Quiz

Linear Regression in Python

In this quiz, you'll test your knowledge of linear regression in Python. Linear regression is one of the fundamental statistical and machine learning techniques, and Python is a popular choice for machine learning.

Regression

Regression analysis is one of the most important fields in statistics and machine learning. There are many regression methods available. Linear regression is one of them.

What Is Regression?

Regression searches for relationships among variables. For example, you can observe several employees of some company and try to understand how their salaries depend on their features, such as experience, education level, role, city of employment, and so on.

This is a regression problem where data related to each employee represents one observation. The presumption is that the experience, education, role, and city are the independent features, while the salary depends on them.

Similarly, you can try to establish the mathematical dependence of housing prices on area, number of bedrooms, distance to the city center, and so on.

Generally, in regression analysis, you consider some phenomenon of interest and have a number of observations. Each observation has two or more features. Following the assumption that at least one of the features depends on the others, you try to establish a relation among them.

In other words, you need to find a function that maps some features or variables to others sufficiently well.

The dependent features are called the dependent variables, outputs, or responses. The independent features are called the independent variables, inputs, regressors, or predictors.

Regression problems usually have one continuous and unbounded dependent variable. The inputs, however, can be continuous, discrete, or even categorical data such as gender, nationality, or brand.

It’s a common practice to denote the outputs with 𝑦 and the inputs with 𝑥. If there are two or more independent variables, then they can be represented as the vector 𝐱 = (𝑥₁, …, 𝑥ᵣ), where 𝑟 is the number of inputs.

When Do You Need Regression?

Typically, you need regression to answer whether and how some phenomenon influences the other or how several variables are related. For example, you can use it to determine if and to what extent experience or gender impacts salaries.

Regression is also useful when you want to forecast a response using a new set of predictors. For example, you could try to predict electricity consumption of a household for the next hour given the outdoor temperature, time of day, and number of residents in that household.

Regression is used in many different fields, including economics, computer science, and the social sciences. Its importance rises every day with the availability of large amounts of data and increased awareness of the practical value of data.

Linear Regression

Linear regression is probably one of the most important and widely used regression techniques. It’s among the simplest regression methods. One of its main advantages is the ease of interpreting results.

Problem Formulation

When implementing linear regression of some dependent variable 𝑦 on the set of independent variables 𝐱 = (𝑥₁, …, 𝑥ᵣ), where 𝑟 is the number of predictors, you assume a linear relationship between 𝑦 and 𝐱: 𝑦 = 𝛽₀ + 𝛽₁𝑥₁ + ⋯ + 𝛽ᵣ𝑥ᵣ + 𝜀. This equation is the regression equation. 𝛽₀, 𝛽₁, …, 𝛽ᵣ are the regression coefficients, and 𝜀 is the random error.