Regression models: a concise tutorial with theory and real-life examples

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In this tutorial, we will discuss seven regression models with their respective mathematical equations and real-life examples.

What is regression?

Regression is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. Sometimes, independent variables are also known as explanatory variables.

The goal of regression is to fit a line (or a more complex mathematical model) that best captures the underlying relationship between the variables.

Regression can be used to make predictions about the value of the dependent variable based on new values of the independent variables. For example, a regression can be used to predict the price of a house based on its square footage, number of bedrooms, location, etc.

How do we explain regression models mathematically?

At a high level, regression is a statistical technique for modeling the relationship between a dependent variable and one or more independent variables. The goal of regression is to fit a mathematical equation to the data that best captures the underlying relationship between the variables.

The most basic form of regression is simple linear regression, which involves a single independent variable and a single dependent variable. The equation for a simple linear regression model is given by:

y = β₀ + β₁x

where y is the dependent variable, x is the independent variable, β₀ is the y-intercept, and β₁ is the slope of the line. The goal is to determine the values of β₀ and β₁ that best fit the data.

In multiple linear regression, the equation is slightly more complex, involving multiple independent variables:

y = β₀ + β₁x₁ + β₂x₂ + … + βₚxₚ

where x₁, x₂, …, xₚ are the independent variables, and β₁, β₂, …, βₚ are the corresponding coefficients.

The values of the coefficients are typically estimated using a method such as least squares, which finds the values of the coefficients that minimize the sum of the squared differences between the observed…