Different Types of Regression Models

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.

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.

What is a Regression Model/Analysis?

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).

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.

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.

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.

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.

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.

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.

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.

Also Read: 7 Regression Techniques You Should Know!

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.

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.

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Prashant Sharma 14 Jun, 2024

Currently, I Am pursuing my Bachelors of Technology( B.Tech) from Vellore Institute of Technology. I am very enthusiastic about programming and its real applications including software development, machine learning and data science.