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Different Types of Regression Models

P
Prashant Last Updated : 10 Oct, 2024
7 min read

Introduction

Regression analysis is a cornerstone of machine learning, crucial for modeling relationships between variables and making predictions. This article explores various types of linear regression and regression models, offering insights into their applications and distinctions. From the simplicity of linear regression to the complexities of ridge and lasso regression, understanding these models is essential for data-driven decision-making across diverse fields.

This article will cover about the regression models, variations of regression, and diverse forms of regression. Regression models is comprehension of the relationship between two or more factors. There are different forms of regression, each fulfilling distinct functions. Understanding the various forms of regression can assist in selecting the most suitable model for your data and inquiries.you will explore the different types of regression in machine learning, including various types of regression models.

Regression Models

Learning Outcomes

  • Understand the fundamental concepts of regression analysis and its importance in machine learning.
  • Differentiate between various types of linear regression models, including simple linear regression and multiple linear regression.
  • Identify the characteristics and applications of different regression models such as logistic regression, polynomial regression, and ridge regression.
  • Gain insights into advanced regression techniques like lasso regression, quantile regression, Bayesian linear regression and different types of regression.
  • Apply regression analysis to model and predict continuous outcomes based on relationships between variables.

This article was published as a part of the Data Science Blogathon.

Table of contents

What is a Regression Model/Analysis?

A regression model establishes a mathematical function that illustrates the connection between one or more independent variables and a dependent, response, or target variable.

You can use predictive modeling techniques such as regression models/analysis to determine the relationship between a dataset’s dependent (goal) and independent variables. Use these techniques widely when the dependent and independent variables are linked in a linear or non-linear fashion, and the target variable has a set of continuous values. Thus, regression analysis approaches help establish causal relationships between variables, modelling time series, and forecasting. Different types of regression, for example, is the best way to examine the relationship between sales and advertising expenditures for a corporation.

Also Read: What is Linear Regression?

What is the purpose of a Regression Models?

Use regression analysis for one of two purposes: predict the value of the dependent variable when you know the independent variables or predict the effect of an independent variable on the dependent variable.

Types of Regression Models

There are numerous regression analysis approaches available for making predictions. Various parameters, including the number of independent variables, the form of the regression line, and the type of dependent variable, determine the choice of technique.

Let us examine several of the most often utilized regression analysis techniques:

1. Linear Regression

The most extensively used modelling technique is linear regression, which assumes a linear connection between a dependent variable (Y) and an independent variable (X). It employs a regression line, also known as a best-fit line. The linear connection is defined as Y = c+m*X + e, where ‘c’ denotes the intercept, ‘m’ denotes the slope of the line, and ‘e’ is the error term.

The linear regression model can be simple (with only one dependent and one independent variable) or complex (with numerous dependent and independent variables) (with one dependent variable and more than one independent variable).

Linear Regression

2. Logistic Regression

When the dependent variable is discrete, the logistic regression technique is applicable. In other words, this technique is used to compute the probability of mutually exclusive occurrences such as pass/fail, true/false, 0/1, and so forth. Thus, the target variable can take on only one of two values, and a sigmoid curve represents its connection to the independent variable, and probability has a value between 0 and 1.

Logistic Regression | Regression Models

3. Polynomial Regression

Polynomial regression analysis represents a non-linear relationship between dependent and independent variables. This technique is a variant of the multiple linear regression model, but the best fit line is curved rather than straight.

Polynomial Regression

4. Ridge Regression

When data exhibits multicollinearity, that is, the ridge regression technique is applied when the independent variables are highly correlated. While least squares estimates are unbiased in multicollinearity, their variances are significant enough to cause the observed value to diverge from the actual value. Ridge regression reduces standard errors by biassing the regression estimates.

The lambda (λ) variable in the ridge regression equation resolves the multicollinearity problem.

Log Lambda, types of regression

5. Lasso Regression

As with ridge regression, the lasso (Least Absolute Shrinkage and Selection Operator) technique penalizes the absolute magnitude of the regression coefficient. Additionally, the lasso regression technique employs variable selection, which leads to the shrinkage of coefficient values to absolute zero.

Lasso Regression , types of regression models

6. Quantile Regression

The quantile regression approach is a subset of the linear regression technique. Statisticians and econometricians employ quantile regression when linear regression requirements are not met or when the data contains outliers.

Quantile Regression

7. Bayesian Linear Regression

Machine learning utilizes Bayesian linear regression, a form of regression analysis, to calculate the values of regression coefficients using Bayes’ theorem. Rather than determining the least-squares, this technique determines the features’ posterior distribution. As a result, the approach outperforms ordinary linear regression in terms of stability.

Bayesian Linear Regression

8. Principal Components Regression

Multicollinear regression data is often evaluated using the principle components regression approach. The significant components regression approach, like ridge regression, reduces standard errors by biassing the regression estimates. First, principal component analysis (PCA) modifies the training data, and then the resulting transformed samples train the regressors.

9. Partial Least Squares Regression

The partial least squares regression technique is a fast and efficient covariance-based regression analysis technique. It is advantageous for regression problems with many independent variables with a high probability of multicollinearity between the variables. The method reduces the number of variables to a manageable number of predictors, then uses them in regression.

10. Elastic Net Regression

Elastic net regression combines ridge and lasso regression techniques that are particularly useful when dealing with strongly correlated data. It regularizes regression models by utilizing the penalties associated with the ridge and lasso regression methods.

Elastic Net Regression, types of regression analysis

Also Read: 7 Regression Techniques You Should Know!

How to Create the Regression Model?

To create the Regression Model here is the following steps:

Define the Problem:

  • Figure out what you want to predict or explain (the outcome).
  • Identify the factors that might influence this outcome.

Gather Data:

  • Collect information related to your problem.
  • Make sure the data is clean and accurate.

Explore the Data:

  • Look for patterns and relationships between the factors and the outcome.
  • Use charts and graphs to visualize the data.

Choose a Model:

  • Select a type of model that best fits your problem (e.g., linear, logistic).

Train the Model:

  • Teach the model to recognize patterns in the data.
  • Use part of your data to train the model.

Test the Model:

  • Use a different part of your data to see how well the model works.
  • Check if it can accurately predict outcomes.

Make Predictions:

  • Use the trained model to predict new outcomes based on new data.

Interpret Results:

  • Understand what the model learned from the data.
  • Explain how the factors influence the outcome.

Conclusion

Regression analysis is a fundamental technique in machine learning and statistics, used to understand and predict relationships between variables. This article has explored various types of linear regression models, from simple to multiple regression, as well as advanced techniques like logistic regression, polynomial regression, and ridge regression. Each regression model serves different purposes, from predicting continuous outcomes to handling multicollinearity and non-linear relationships. By mastering these different types of regression techniques, data scientists can make informed decisions and predictions based on data, enhancing their ability to solve real-world problems across diverse fields.

I hope you will find this article informative on regression models and the different kinds of regression. Regression models enable us to examine the interactions between various variables. There exist various types of regression, each functioning slightly differently. Understanding the various forms of regression is crucial in selecting the appropriate one for the specific dataset and research query at hand.

Key Takeaways

  • Regression analysis is essential for predicting and understanding relationships between dependent and independent variables.
  • There are various regression models, including linear regression, logistic regression, polynomial regression, ridge regression, and lasso regression, each suited for different data scenarios.
  • Used for classification problems, it models the probability of binary outcomes.
  • Handles non-linear relationships by fitting a polynomial equation to the data.
  • Both techniques address multicollinearity by adding regularization terms to the regression equations, with lasso also performing variable selection.
  • Understanding different regression models enables better data-driven decisions in fields like economics, finance, healthcare, and social sciences.
Q1. What are the types of regression models?

A. Types of regression models include linear regression, logistic regression, polynomial regression, ridge regression, and lasso regression.

Q2. What are the three regression models?

A. The three common regression models are linear regression, logistic regression, and polynomial regression.

Q3. Why is it called a regression model?

A. Regression models predict the relationship between dependent and independent variables by “regressing” the outcome variable based on the predictors.

Q4. What is the most common regression model?

A. The most common regression model is linear regression, widely used for its simplicity and effectiveness in predicting continuous outcomes.

The media shown in this article is not owned by Analytics Vidhya and are used at the Author’s discretion. 

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P
Prashant

Hello, my name is Prashant, and I'm currently pursuing my Bachelor of Technology (B.Tech) degree. I'm in my 3rd year of study, specializing in machine learning, and attending VIT University.

In addition to my academic pursuits, I enjoy traveling, blogging, and sports. I'm also a member of the sports club. I'm constantly looking for opportunities to learn and grow both inside and outside the classroom, and I'm excited about the possibilities that my B.Tech degree can offer me in terms of future career prospects.

Thank you for taking the time to get to know me, and I look forward to engaging with you further!

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Flash Card

What is the primary purpose of a regression model in machine learning?

A regression model is used to establish a mathematical function that illustrates the connection between one or more independent variables and a dependent variable. It helps in predictive modeling to determine the relationship between a dataset’s dependent and independent variables. Regression analysis is crucial for establishing causal relationships, modeling time series, and forecasting when variables are linked linearly or non-linearly.

What is the primary purpose of a regression model in machine learning?

Quiz

What is the primary purpose of a regression model in machine learning?

Flash Card

How does simple linear regression differ from multiple linear regression?

Simple linear regression involves one dependent and one independent variable, assuming a linear relationship between them. The model is represented by the equation Y = c + m*X + e, where 'c' is the intercept, 'm' is the slope, and 'e' is the error term. Multiple linear regression involves one dependent variable and more than one independent variable, allowing for a more complex analysis of relationships.

How does simple linear regression differ from multiple linear regression?

Quiz

What is a key difference between simple linear regression and multiple linear regression?

Flash Card

What are the characteristics and applications of logistic regression?

Logistic regression is used when the dependent variable is discrete, such as binary outcomes like pass/fail or true/false. It computes the probability of mutually exclusive events, with the target variable taking one of two values. The relationship is represented by a sigmoid curve, with probabilities ranging between 0 and 1.

What are the characteristics and applications of logistic regression?

Quiz

In which scenario is logistic regression typically used?

Flash Card

In what scenarios is polynomial regression used, and how does it differ from linear regression?

Polynomial regression is used when there is a non-linear relationship between dependent and independent variables. Unlike linear regression, which fits a straight line, polynomial regression fits a curved line to the data. It is a variant of multiple linear regression but accommodates non-linear patterns in the data.

In what scenarios is polynomial regression used, and how does it differ from linear regression?

Quiz

When is polynomial regression preferred over linear regression?

Flash Card

What problem does ridge regression address, and how does it work?

Ridge regression is applied when there is multicollinearity, meaning independent variables are highly correlated. It reduces standard errors by introducing bias into the regression estimates, thus stabilizing the model. The lambda (λ) variable in ridge regression helps resolve multicollinearity by penalizing large coefficients.

What problem does ridge regression address, and how does it work?

Quiz

What issue does ridge regression help to resolve?

Flash Card

How does lasso regression differ from ridge regression?

Like ridge regression, lasso regression penalizes the magnitude of regression coefficients but focuses on their absolute values. Lasso regression performs variable selection, potentially reducing some coefficients to zero, effectively selecting a simpler model. This technique is useful for models where feature selection is crucial.

How does lasso regression differ from ridge regression?

Quiz

What is a unique feature of lasso regression compared to ridge regression?

Flash Card

What is quantile regression, and when is it used?

Quantile regression is a subset of linear regression used when standard linear regression assumptions are not met. It is particularly useful when the data contains outliers or when the relationship between variables varies across different quantiles. This approach provides a more comprehensive analysis of the data distribution.

What is quantile regression, and when is it used?

Quiz

When is quantile regression particularly useful?

Flash Card

Explain Bayesian linear regression and its advantages over ordinary linear regression.

Bayesian linear regression uses Bayes’ theorem to calculate regression coefficients, focusing on the posterior distribution of features. It provides a probabilistic approach, offering more stability compared to ordinary linear regression. This technique is beneficial in machine learning for its ability to incorporate prior knowledge and uncertainty in predictions.

Explain Bayesian linear regression and its advantages over ordinary linear regression.

Quiz

What is an advantage of Bayesian linear regression over ordinary linear regression?

Flash Card

Why is understanding different regression models important in various fields?

Different regression models are suited for different data scenarios, enabling tailored analysis and predictions. They are essential for making data-driven decisions in fields like economics, finance, healthcare, and social sciences. Understanding these models allows for better handling of classification problems, non-linear relationships, and multicollinearity, enhancing predictive accuracy.

Why is understanding different regression models important in various fields?

Quiz

Why is it important to understand different regression models?

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