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6 Types of Regression Models in Machine Learning: Insights, Benefits, and Applications in 2025

6 Types of Regression Models in Machine Learning: Insights, Benefits, and Applications in 2025

Updated on 31 December, 2024

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• 14 min read

Table of Contents

What is Regression Analysis in Machine Learning? Key Insights
What Are the 6 Types of Regression Models in Machine Learning? Key Variations Explained
How Does Regression Analysis Work in Machine Learning? Basic Steps
What Are the Benefits of Regression Analysis?
What Are Real-World Industry Applications of Regression in Machine Learning?
4 Common Use Cases for Regression in AI and Machine Learning
How upGrad Helps You Master Regression Analysis?

With over 90% of businesses leveraging AI for decision-making, the demand for professionals skilled in regression analysis in machine learning is skyrocketing. Are you ready to stay ahead in 2025 with this technology?

Choosing the right regression model can be overwhelming. From understanding complex techniques to navigating diverse applications, the learning curve is steep. Yet, mastering these models unlocks powerful solutions to real-world problems.

This article simplifies the complexities for you. Discover key insights, explore benefits, and learn how to select the best regression model for your needs. Dive in and start building smarter AI solutions!

What is Regression Analysis in Machine Learning? Key Insights

Regression analysis in machine learning is a method to predict continuous outcomes using input data. It helps identify patterns and relationships between variables, making it essential for accurate predictions.

This technique is crucial for forecasting trends and analyzing cause-and-effect dynamics. It allows data scientists to uncover insights that drive smarter decisions.

Let’s explore its key roles and importance in machine learning:

Key Roles and Importance:

Forecasting Continuous Outcomes: Regression models predict numerical values like revenue or temperature.
Understanding Variable Relationships: It clarifies how inputs influence outputs, revealing dependencies.
Trend Analysis: Regression identifies trends, supporting strategic forecasts and planning.

Now that you understand regression analysis in machine learning let’s explore the 6 types of regression models in machine learning and how they differ.

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What Are the 6 Types of Regression Models in Machine Learning? Key Variations Explained

Regression models are foundational in machine learning, each tailored to specific data and prediction needs. Understanding the types of regression models in machine learning enables you to choose the right one for accurate and efficient results. Below, let’s break down six key regression models:

1. Linear Regression

Linear regression predicts a continuous outcome by modeling the relationship between one or more independent variables and a dependent variable using a straight line.

Key Formula:

Simple Linear Regression: y = b0+ b1x + ϵ

Components:

y: The dependent variable (what you're predicting).
b0: The intercept (value of y when x = 0).
b1: The slope of the line (rate of change in y for a unit increase in x).
x: The independent variable (predictor).
ϵ: The error term (difference between the observed and predicted values).

How it works:
This formula represents a straight-line relationship between one independent variable (x) and the dependent variable (y). For instance, predicting house prices based on size.

Multiple Linear Regression: y = b0+b1x1+b2x2+…+bnxn+ϵ

Components:

y: The dependent variable.
b0: The intercept.
b1,b2….bn: Coefficients representing the impact of each independent variable (x1,x2,…,xn) on y.
x1,x2,…,xn: Independent variables.
ϵ: The error term.

How it works:
This formula models the relationship between multiple predictors (x1,x2,…,xn) and the outcome (y). For example, predicting house prices based on size, location, and number of bedrooms.

Use Cases:

Application	Example
Sales Prediction	Forecasting monthly sales for a retail store
House Price Analysis	Predicting housing prices based on location data

Limitations:

Sensitive to outliers.
Assumes a linear relationship between variables.

Example Formula:

Predicting house prices: Price = 50,000 + 120 (Square Footage )+ ϵ

Also Read: How to Perform Multiple Regression Analysis?

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While linear regression excels at predicting continuous outcomes, let’s explore how logistic regression handles categorical predictions.

2. Logistic Regression

Logistic regression predicts binary outcomes (e.g., yes/no) using a logistic function to model probabilities.

Key Formula:

P(y=1)=1/(1+e−(b 0 +b 1 x))

Components:

P(y=1): The probability of the dependent variable y being equal to 1. It ranges between 0 and 1.

b0: The intercept, which is the baseline log-odds of y = 1 when x=0.

b1: The coefficient of the independent variable x. It measures the strength and direction of the relationship between xxx and y.

X: The independent variable or predictor.

e^−(b0+b1x): The exponential transformation of the linear combination b0+b1x. This transforms the linear relationship into a nonlinear probability curve.

How It Works:

Linear Combination: First, calculate z = b0+b1x, a linear combination of the intercept and predictor.
Sigmoid Transformation: Pass z through the sigmoid function P(y=1)=11+e^−z. This maps the linear relationship into a probability between 0 and 1.

Use Cases:

Application	Example
Fraud Detection	Identifying fraudulent transactions
Health Diagnostics	Predicting if a patient has a disease

Limitations:

Limited to binary or categorical predictions.
Assumes linearity between variables and the log odds.

Example Formula:

Predicting fraud: P(Fraud=1)= 1/(1+e−(−2+0.5(Transaction Amount)) )

Components:

P(Fraud=1): The probability that the transaction is fraudulent. The result is a value between 0 and 1, representing the likelihood of fraud.

Intercept (−2): This is the baseline log-odds of fraud when the transaction amount is zero. It reflects the starting probability before considering the impact of the transaction amount.

Coefficient (0.5): This represents the influence of the transaction amount on the probability of fraud. A positive coefficient indicates that as the transaction amount increases, the likelihood of fraud also increases.

e−(−2+0.5(Transaction Amount)): The exponential transformation of the linear combination of variables. This transformation ensures the output probability is between 0 and 1.

Step-by-Step Explanation:

Linear Combination (z): Compute the value of z = −2+0.5(Transaction Amount).

The intercept (−2) starts the calculation.
The coefficient (0.5) scales the impact of the transaction amount.

Sigmoid Transformation: Apply the sigmoid function to transform z into a probability:
P = 11+e^−z

This maps z to a probability between 0 and 1.

Interpret the Output: The result, P(Fraud=1), indicates the likelihood of fraud based on the transaction amount.

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For cases where overfitting becomes a concern, ridge regression offers a powerful solution by introducing regularization.

3. Ridge Regression

Ridge regression adds a penalty term to the linear regression equation to reduce overfitting and improve generalization.

Key Formula:

Minimize: ∑( yi−yi)2+ λ∑b(2/j)

Explanation:

∑( yi−yi)2:

This term is the Residual Sum of Squares (RSS) or the error term.
It measures the difference between the observed value (yi) and the predicted value (y^i).
The goal is to minimize this error so the predictions (y^i) are as close as possible to the true values (yi).

λ∑b(2/j):

This is the regularization term introduced in Ridge Regression.
∑b(2/j): The squared values of the coefficients (bj), summing all predictors.
λ: A regularization parameter that controls the strength of the penalty.
- When λ=0, it is equivalent to Ordinary Least Squares (OLS) regression.
- As λ increases, the model penalizes large coefficients more, shrinking them toward zero.

Balance Between Fit and Complexity:

The first term (∑(yi−y^i)2) ensures the model fits the data accurately.
The second term (λ∑b(2/j)) penalizes large coefficients to prevent overfitting, promoting simplicity and generalization.

Use Cases:

Application	Example
Finance	Predicting stock prices while reducing noise
Marketing	Optimizing advertising spend across channels

Limitations:

Assumes all predictors are relevant.
It can shrink coefficients too much, causing a loss of interpretability.

Example Formula:

Adjusted prediction: y = b0 + b1x1 + b(2/j)

Building on regularization, lasso regression not only reduces overfitting but also helps in selecting the most relevant features.

4. Lasso Regression

Lasso regression uses a penalty to shrink coefficients to zero, effectively performing feature selection.

Key Formula:

Minimize: ∑(yi−yi)2 + λ∑|bj|

Explanation:

∑(yi−yi)2 :

This is the Residual Sum of Squares (RSS) or the error term.
It calculates the difference between the actual values (yi) and the predicted values (y^i).
The goal is to minimize this error, ensuring the model’s predictions are as close as possible to the observed data.

λ∑|bj|:

This is the regularization term specific to Lasso Regression.
∣bj∣: The absolute values of the coefficients.
- Unlike Ridge Regression, which penalizes the square of the coefficients (bj2), Lasso penalizes the absolute magnitude of the coefficients.
λ: The regularization parameter, controlling the strength of the penalty.
- When λ=0, the model becomes equivalent to Ordinary Least Squares (OLS).
- As λ increases, the penalty increases, shrinking some coefficients to zero.

Key Trade-off:

The first term (∑(yi−y^i)) ensures the model fits the data well.
The second term (λ∑∣bj∣) enforces sparsity, meaning it encourages irrelevant or less impactful coefficients (bj) to shrink to exactly zero, effectively performing feature selection

Use Cases:

Application	Example
Genomics	Identifying key genes influencing traits
Real Estate	Selecting impactful features in price prediction

Limitations:

It may exclude important variables.
It can be unstable with highly correlated predictors.

Example Formula:

Feature selection: y = b0+ b1x1 + λ∣b1∣

When linear models fall short of capturing complex patterns, polynomial regression provides flexibility by modeling non-linear relationships.

5. Polynomial Regression

Polynomial regression extends linear regression by modeling the relationship between variables as an nth-degree polynomial.

Key Formula:

y = b0+ b1x+ b2x2+… + bnxn + ϵ

Explanation:

1. Components of the Equation:

y: The dependent variable (what we’re predicting).
b0: The intercept, which represents the predicted value of y when all independent variables (x) are zero.
b1x,b2x2,…,bn: These terms are the polynomial features of the independent variable (x), with coefficients (b1,b2,…,bn) indicating the weight or influence of each feature.
- b1x: The linear component.
- b2x: Higher-degree terms to capture non-linear relationships.
ϵ: The error term, accounting for the difference between observed and predicted values due to noise or variability in the data.

2. Polynomial Degree (n):

The highest power of x (n) determines the complexity of the model.
- Degree 1: A straight line (simple linear regression).
- Degree 2: A parabolic curve (quadratic regression).
- Higher Degrees: More complex curves to fit intricate patterns in the data.

3. How It Works:

Polynomial regression models non-linear relationships by adding higher-degree terms (x2,x3,…,xn).
Each term captures a portion of the non-linear trend in the data, allowing the curve to bend to fit the pattern.

Use Cases:

Application	Example
Weather Forecasting	Modeling temperature variations over time
Manufacturing	Predicting equipment failure rates

Limitations:

Prone to overfitting with high-degree polynomials.
Requires careful feature scaling.

Example Formula:

Modeling a curve: y = 2 + 0.5x - 0.1x2

To address uncertainty in predictions, Bayesian linear regression brings a probabilistic approach to regression modeling.

6. Bayesian Linear Regression

Bayesian linear regression incorporates prior distributions into the regression model to quantify uncertainty in predictions.

Key Formula:

Posterior: P(β∣X,y) = P(y∣X,β)P(β)/P(y∣X)

Key Terms:

P(β∣X,y):

The probability distribution of the parameters (β) after observing the data (X,y).
It represents our updated belief about β, incorporating both prior beliefs and evidence from the data.

P(y∣X,β) (Likelihood):

The probability of observing the data (y) given the predictors (X) and model parameters (β).
This measures how well the model (with parameters β) explains the observed data.

P(β) (Prior):

The probability distribution of the parameters (β) before observing any data.
Represents our prior belief about the possible values of β, based on domain knowledge or assumptions.

P(y∣X)(Evidence):

The total probability of observing the data (y) given the predictors (X).
It acts as a normalizing constant to ensure that the posterior distribution is a valid probability distribution.

How It Works:

Start with Prior Belief (P(β)):
- Before observing any data, you have an initial belief about the parameters (β), which could be based on past knowledge or assumed to follow a specific distribution (e.g., normal distribution).
Incorporate Evidence (Likelihood, P(y∣X,β):
- Use the observed data (X,y) to evaluate how likely it is that the parameters (β\betaβ) explain the data.
Update Beliefs (Posterior, P(β∣X,y):
- Combine the prior (P(β)) and the likelihood (P(y∣X,β) to compute the posterior distribution (P(β∣X,y).

Use Cases:

Application	Example
Medical Research	Predicting patient recovery probabilities
Risk Assessment	Estimating financial risks with uncertainty

Limitations:

Computationally intensive.
Requires careful selection of prior distributions.

Example Formula:

Posterior prediction: P(y∣X) = ∫P(y∣X,β) P(β)dβ

Now that you know the types of regression models in machine learning, let’s look at how regression analysis works through its basic steps.

How Does Regression Analysis Work in Machine Learning? Basic Steps

Performing regression analysis in machine learning involves a systematic approach to modeling relationships between variables. Here's a step-by-step breakdown:

1. Defining Variables and Gathering Data

Start by identifying the dependent variable (outcome) and independent variables (predictors). For example, if you're predicting house prices, the dependent variable is the price, and predictors could include size, location, and amenities. Gather clean and relevant data for these variables.

2. Plotting Data

Visualize your data using scatter plots or histograms to identify patterns or trends. This helps you choose the most suitable types of regression models in machine learning for your analysis.

3. Analyzing Correlations

Examine correlations to understand the strength and direction of relationships between variables. Tools like correlation coefficients or heatmaps can reveal which predictors significantly affect the outcome.

4. Introducing the Regression Line

Apply a regression model to fit a line (or curve) through the data. The regression line represents the best fit, minimizing the difference between predicted and actual values.

5. Interpreting the Formula

Break down the regression formula:

y=b0+ b1x + ϵ
- y: Predicted value (e.g., house price).
- b0: Intercept (baseline prediction when x=0x = 0).
- b1: Slope (impact of a unit change in xx on yy).
- ϵ: Error term (difference between actual and predicted values).

6. Considering Error

Evaluate the error term (ϵ) to assess the accuracy of your predictions. Lower errors indicate a better-fitting model. Use metrics like Mean Squared Error (MSE) or R-squared for detailed evaluation.

Now that you understand the steps of regression analysis in machine learning let’s explore its key benefits and why it’s so impactful.

What Are the Benefits of Regression Analysis?

Regression analysis in machine learning offers a range of benefits, making it an indispensable tool in data-driven decision-making and predictive modeling. Here’s how it adds value:

Benefit	Description	Application Example
Quantifying Relationships	Measures how independent variables impact a dependent variable.	Identifying factors affecting sales.
Prediction and Forecasting	Enables accurate predictions for continuous outcomes.	Forecasting monthly revenue trends.
Identifying Significant Variables	Highlights the most influential predictors among multiple variables.	Pinpointing key drivers of customer churn.
Model Evaluation	Provides tools like R-squared and error metrics to evaluate model performance.	Assessing accuracy in predictive models.
Control and Optimization	Optimizes processes by understanding variable interactions.	Improving production efficiency.
Risk Management	Assesses potential risks by analyzing variable relationships and their uncertainty.	Evaluating credit risk in finance.
Decision Support	Guides strategic choices with data-backed insights for better resource allocation and planning.	Allocating budgets in marketing campaigns.

Also Read: Machine Learning vs Data Analytics: A Brief Comparison

With its numerous benefits, regression analysis is widely applied across industries—let’s explore its real-world applications in machine learning.

What Are Real-World Industry Applications of Regression in Machine Learning?

Regression models play a vital role in various industries, enabling data-driven predictions and insights. Here are some key real-world applications:

Industry	Application	Details & Benefits
Healthcare	Predicting patient outcomes	Models disease progression and treatment responses. Enhances patient care and planning
	Estimating recovery times	Uses patient data to predict recovery duration Reduces hospital readmission rates
Finance	Credit scoring	Evaluates creditworthiness using financial data Increases accuracy in loan approvals
	Risk assessment	Analyzes investment risks based on market trends. Mitigates financial losses
Marketing	Customer lifetime value prediction	Identifies high-value customers for targeted strategies. Maximizes marketing ROI
	Demand forecasting	Predicts seasonal demand for products Optimizes inventory and supply chain
Economics	Analyzing GDP trends	Studies economic growth patterns using regression models Supports policy formulation
	Forecasting unemployment statistics	Predicts job market trends for workforce management Informs labor market policies
Manufacturing	Predicting machine failure	Models operational data to foresee breakdowns Reduces downtime and maintenance costs
	Optimizing production efficiency	Analyzes factors affecting production rates Increases output while lowering costs
Retail	Sales forecasting	Predicts future sales based on historical data Improves inventory management
	Price optimization	Analyzes consumer behavior to set ideal prices. Maximizes revenue and customer satisfaction

Also Read: 5 Breakthrough Applications of Machine Learning

Also Read: Machine Learning Applications in Healthcare: What Should We Expect?

Building on its widespread industry applications, let’s explore 4 common use cases for regression in AI and machine learning to see it in action.

4 Common Use Cases for Regression in AI and Machine Learning

Regression models are key tools in solving complex, real-world problems in AI and machine learning. They offer precise predictions and insights to drive impactful decisions. Below are four common use cases:

Use Case	Description	Example Applications	Key Benefits
Price Prediction	Forecasts prices based on historical and market data.	Real estate, stock market, e-commerce	Optimizes pricing strategies and investments
Risk Assessment	Predicts potential risks, such as defaults or claims, using past data.	Loan default prediction, insurance claims	Mitigates financial and operational risks
Sales Forecasting	Estimates future sales trends for better planning and resource allocation.	Retail, manufacturing, and service industries	Improves inventory management and marketing
Customer Behavior Prediction	Analyzes patterns to forecast actions like purchases, churn, or engagement.	E-commerce, subscription services, telecom	Enhances customer retention and satisfaction

These regression use cases demonstrate its versatility in addressing diverse challenges in AI and machine learning.

Also Read: How to Interpret R Squared in Regression Analysis?

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Now that you’ve explored the key use cases, discover how upGrad equips you to master regression analysis in machine learning and advance your career.

How upGrad Helps You Master Regression Analysis?

upGrad’s data science and machine learning courses equip you with the skills to master regression analysis through:

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Frequently Asked Questions

1. What are the main types of regression models in machine learning?

The six main types are Linear Regression, Logistic Regression, Ridge Regression, Lasso Regression, Polynomial Regression, and Bayesian Linear Regression, each serving unique data and prediction needs.

2. Why is regression analysis important in machine learning?

Regression helps identify relationships between variables, predict continuous outcomes, and drive data-backed decisions in fields like finance, healthcare, and marketing.

3. What is the difference between linear and logistic regression?

Linear regression predicts continuous outcomes, while logistic regression models probabilities for binary or categorical outcomes.

4. How does regularization improve regression models?

Techniques like Ridge and Lasso Regression reduce overfitting by penalizing large coefficients, improving the model's generalization to unseen data.

5. What are the benefits of using regression in 2025?

Regression aids in forecasting trends, optimizing operations, and analyzing cause-effect relationships, making it vital for AI-driven insights and decision-making.

6. How is regression used in predictive modeling?

Regression models predict future trends or outcomes by analyzing historical data, such as predicting sales, prices, or risks.

7. Which regression model is best for non-linear data?

Polynomial Regression is ideal for modeling non-linear relationships by fitting data to a polynomial curve.

8. How is Bayesian regression different from traditional regression?

Bayesian regression incorporates prior distributions to quantify uncertainty, making it useful for risk assessment and probabilistic predictions.

9. What industries commonly use regression models?

Industries like finance, healthcare, marketing, and manufacturing leverage regression for applications like risk assessment, demand forecasting, and optimization.

10. What tools are used for regression analysis?

Popular tools include Python (libraries like scikit-learn), R, Excel, and MATLAB, offering robust frameworks for implementing regression models.

11. How can you learn regression analysis effectively?

Courses from platforms like upGrad provide hands-on training with real-world datasets, mentorship, and career support to master regression techniques.

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