Machine Learning Algorithms: Understanding Linear, Polynomial, Ridge & Lasso Regression

 

Introduction

Regression analysis is one of the most widely used supervised machine learning techniques. It helps us understand relationships between variables and predict continuous outcomes. From predicting stock prices and housing costs to analyzing sales and temperature trends, regression algorithms are fundamental to data science and machine learning.

In this post, we’ll break down the most important types of regression algorithms used in ML:

●Simple Linear Regression

●Multiple Linear Regression

●Polynomial Regression

●Ridge Regression

●Lasso Regression (L1 Regularization)

1. Simple Linear Regression

✅ What It Is:

Simple Linear Regression models the relationship between a single independent variable (X) and a dependent variable (Y) using a straight line.

📌 Equation:

Y = b0 + b1 * X

Where:

●Y is the predicted output

●X is the input variable

●b0 is the intercept

●b1 is the slope (coefficient)

📊 Use Case Example:

Predicting a student’s test score based on hours studied.

⚙️ Key Assumptions:

●Linear relationship between variables

●No multicollinearity (since it uses one variable)

●Homoscedasticity (constant variance of errors)

●Normal distribution of residuals

2. Multiple Linear Regression

✅ What It Is:

Multiple Linear Regression models the relationship between two or more independent variables and one dependent variable.

📌 Equation:

Y = b0 + b1 * X1 + b2 * X2 + ... + bn * Xn

📊 Use Case Example:

Predicting house prices using square footage, number of bedrooms, and location.

⚙️ Key Assumptions:

●No multicollinearity

●Linear relationship

●Independence of residuals

●Normal distribution of residuals

3. Polynomial Regression

✅ What It Is:

Polynomial Regression captures non-linear relationships by adding higher-degree terms to the regression equation.

📌 Equation (2nd degree):

Y = b0 + b1 * X + b2 * X²

You can add more polynomial terms (X³, X⁴, etc.) as needed.

📊 Use Case Example:

Predicting car price depreciation over time, which doesn’t follow a straight line.

⚠️ Note:

Polynomial regression can lead to overfitting if the degree of the polynomial is too high.

4. Ridge Regression (L2 Regularization)

✅ What It Is:

Ridge Regression is a type of linear regression that includes an L2 penalty to shrink model coefficients and reduce overfitting.

📌 Cost Function:

Loss = RSS + α * Σ(coefficient²)

Where:

●RSS = residual sum of squares

●α = regularization parameter (lambda)

📊 Use Case Example:

Predicting housing prices in high-dimensional datasets (with many features).

⚙️ Why Use Ridge:

●Helps with multicollinearity

●Reduces model complexity

●Prevents overfitting in high-dimensional data

5. Lasso Regression (L1 Regularization)

✅ What It Is:

Lasso Regression adds an L1 penalty to the cost function, which encourages sparsity by driving some coefficients to zero (i.e., feature selection).

📌 Cost Function:

Loss = RSS + α * Σ|coefficient|

📊 Use Case Example:

High-dimensional datasets where many features might be irrelevant or redundant.

⚙️ Why Use Lasso:

●Feature selection built-in

●Handles multicollinearity

●Suitable for datasets with many features

Regression Techniques Comparison

When to Use Which Regression Algorithm

●Use Simple/Multiple Linear Regression when relationships are linear and the dataset is small.

●Use Polynomial Regression for non-linear trends in data.

●Use Ridge Regression when multicollinearity exists and you want to regularize without reducing feature count.

●Use Lasso Regression when you want to regularize and perform feature selection.

Real-Life Applications

●Healthcare: Predicting disease progression or patient recovery time

●Finance: Stock price prediction, credit scoring

●E-commerce: Predicting product return probability

●Marketing: Forecasting campaign ROI

●Agriculture: Crop yield predictions based on climate and soil conditions

Conclusion

Regression algorithms form the foundation of predictive modeling in machine learning. From simple linear to advanced regularized methods like Ridge and Lasso, understanding when and how to use each one helps you build better, more robust models.

These techniques not only help predict outcomes but also uncover relationships in your data, enabling smarter decisions across industries.