Linear Regression Overview

Note : This README provides a brief overview of various linear regression techniques along with their equations. Each technique has its advantages and is suitable for different types of data and modeling scenarios.

Linear regression is a widely used statistical technique for modeling the relationship between a dependent variable and one or more independent variables. It's a foundational method in machine learning and statistics, with several variants tailored to different scenarios.

Simple Linear Regression

Simple linear regression is used when there is a linear relationship between a single independent variable (X) and a dependent variable (Y). The model equation can be represented as:

Y = β0 + β1*X + ε

• Y: Dependent variable
• X: Independent variable
• β0: Intercept
• β1: Slope
• ε: Error term

Multiple Linear Regression

Multiple linear regression extends simple linear regression to multiple independent variables. The model equation is given by:

Y = β0 + β1X1 + β2X2 + ... + βn*Xn + ε

• X1, X2, ..., Xn: Independent variables
• β0: Intercept
• β1, β2, ..., βn: Coefficients of the independent variables
• ε: Error term

Polynomial Regression

Polynomial regression models the relationship between the independent variable and the dependent variable as an nth degree polynomial. The model equation is given by:

Y = β0 + β1X + β2X^2 + ... + βn*X^n + ε

• X: Independent variable
• X^2, X^3, ..., X^n: Higher-order terms
• β0, β1, ..., βn: Coefficients of the polynomial terms
• ε: Error term

Ridge Regression

Ridge regression is a regularized version of linear regression that introduces a penalty term to the loss function, helping to prevent overfitting. The model equation is similar to multiple linear regression, but with an additional penalty term:

minimize ||Y - Xβ||^2 + λ||β||^2

• Y: Dependent variable
• X: Independent variables
• β: Coefficients
• λ: Regularization parameter

Lasso Regression

Lasso regression is another regularized linear regression technique that introduces a penalty term to the loss function. It tends to produce sparse coefficient vectors, effectively performing variable selection. The model equation is similar to ridge regression but with a different penalty term:

minimize ||Y - Xβ||^2 + λ||β||_1

• Y: Dependent variable
• X: Independent variables
• β: Coefficients
• λ: Regularization parameter

Ordinary Least Squares (OLS)

Ordinary least squares is the most basic form of linear regression, aiming to minimize the sum of squared differences between the observed and predicted values. The model equation is represented as:

minimize Σ(y_i - (β0 + β1*X_i))^2

• y_i: Observed values of the dependent variable
• X_i: Observed values of the independent variable
• β0, β1: Coefficients

Project Overview

Repository Structure

└── Linear_Regression/
    ├── Admission_Prediction
    │   ├── Admission_Predict.csv
    │   ├── Admission_Prediction.ipynb
    │   └── Admission_Prediction_Report.html
    ├── Boston_Dataset
    │   ├── Boston_Dataset_Report.html
    │   ├── Boston_dataset.ipynb
    │   └── boston_dataset.csv
    ├── CarPrice_Prediction
    │   ├── CarPrice_Assignment.csv
    │   ├── Car_Price_Prediction.ipynb
    │   └── Car_Price_Report.html
    ├── Fish_Dataset
    │   ├── Fish.csv
    │   └── Fish_Data.ipynb
    ├── README.md
    ├── Real_Estate
    │   ├── Dataset_Detail
    │   ├── Real estate valuation data set.xlsx
    │   └── RealEstate_Price_Prediction.ipynb
    └── Red_wine_Dataset
        ├── Wine-Quality_Prediction.ipynb
        └── winequality-red.csv

Getting Started

Requirements

Ensure you have the following dependencies installed on your system:

• JupyterNotebook

Installation

1. Clone the Linear_Regression repository:

git clone https://github.com/sumony2j/Linear_Regression.git

2. Change to the project directory:

cd Linear_Regression

3. Install the dependencies:

pip install -r requirements.txt

Running any project of Linear_Regression

Use the following command to run Linear_Regression:

Navigate to any of the directory and run the Jupyter notebooks to explore linear regression.

jupyter nbconvert --execute notebook.ipynb

Contributing

Contributions are welcome! Here are several ways you can contribute:

• Submit Pull Requests: Review open PRs, and submit your own PRs.
• Join the Discussions: Share your insights, provide feedback, or ask questions.
• Report Issues: Submit bugs found or log feature requests for Linear_regression.

Contributing Guidelines

1. Fork the Repository: Start by forking the project repository to your GitHub account.
2. Clone Locally: Clone the forked repository to your local machine using a Git client.

   git clone https://github.com/sumony2j/Linear_Regression.git

3. Create a New Branch: Always work on a new branch, giving it a descriptive name.

   git checkout -b new-feature-x

4. Make Your Changes: Develop and test your changes locally.
5. Commit Your Changes: Commit with a clear message describing your updates.

   git commit -m 'Implemented new feature x.'

6. Push to GitHub: Push the changes to your forked repository.

   git push origin new-feature-x

7. Submit a Pull Request: Create a PR against the original project repository. Clearly describe the changes and their motivations.

Once your PR is reviewed and approved, it will be merged into the main branch.