Housing Price Prediction using Linear Regression

Project Overview

This project implements a linear regression model from scratch to predict housing prices using a dataset of residential properties. The goal is to demonstrate a fundamental understanding of machine learning principles by manually performing key steps, including data preprocessing, feature engineering, and model training using the Normal Equation[commiting].

The project covers the complete data analysis workflow, from raw data to a working predictive model, without relying on high-level machine learning libraries like scikit-learn for the core algorithm.

Dataset

The dataset used for this project is housing_data.xlsx, which contains information on various residential properties. It includes features such as:

• Area: The size of the property in square feet.
• Bedrooms: The number of bedrooms.
• Bathrooms: The number of bathrooms.
• mainroad, guestroom, basement, hotwaterheating, airconditioning: Binary categorical features indicating the presence of these amenities.
• furnishingstatus: A categorical feature with three unique values.
• price: The target variable to be predicted.

Methodology

The project's workflow is broken down into the following key steps:

1. Data Preprocessing: Categorical features like mainroad and furnishingstatus are converted into numerical format using one-hot encoding.
2. Train-Test Split: A custom function is implemented to split the dataset into training and testing sets, ensuring a reproducible shuffle.
3. Model Implementation: The linear regression model is trained using the Normal Equation ($$w = (X^T X)^{-1} X^T y$$), which directly calculates the optimal weights (coefficients) without an iterative process. This method provides a deep understanding of the model's underlying mathematics.
4. Prediction and Evaluation: The trained model makes predictions on the test set. The performance is evaluated using metrics such as Mean Squared Error (MSE) and Residual Sum of Squares (RSS).
5. Visualization: A scatter plot is generated to visually compare the actual prices against the model's predicted prices, providing a clear representation of its performance.

How to Run the Project

To run this project on your local machine, follow these steps:

1. Clone the repository:

   git clone [https://github.com/your-username/your-repository-name.git](https://github.com/your-username/your-repository-name.git)
   cd your-repository-name

2. Install dependencies: Make sure you have the required libraries installed. It's recommended to create a requirements.txt file and install them from there.

   pip install pandas numpy matplotlib

3. Ensure the dataset is present: Place the housing_data.xlsx file in the same directory as the Python script.
4. Run the script:

   python your_script_name.py

Results

The model's performance metrics and the calculated weights are printed to the console, and a plot is displayed. The results indicate the accuracy of the model and which features have the most influence on the predicted price.

Future Improvements

• Adding an intercept term to the Normal Equation to create a more robust model.
• Implementing other regression algorithms like Gradient Descent for a comparative analysis.
• Adding more features or data points to improve the model's predictive accuracy.