Implementing the LinearRegression Class

Getting Started

Before diving into the code, you need to set up your environment:

1. Clone the repository where this project is hosted:

   git clone https://github.com/HarrySSH/LinearModels.git
   cd LinearModels

2. Create a Conda environment by running:

   conda env create -f regression_environment.yml

3. Activate the new environment:

   conda activate regression_env

Overview

Welcome to your task of completing the implementation of a LinearRegression class using Python and NumPy. The goal of this exercise is to deepen your understanding of the linear regression algorithm by manually coding the methods used to fit the model to the data, make predictions, and evaluate the model's performance.

Method Descriptions

1. __init__

Purpose: Initializes the LinearRegression instance. Tasks:

• Initialize self.coefficients to None. This will later hold the coefficients (weights) calculated from the fit method.
• Initialize self.intercept to None, which will store the intercept from the regression model.

2. fit

Purpose: Fits the linear regression model to the provided data. Tasks:

• Add a column of ones to the input feature matrix X to account for the intercept in the linear model.
• Compute the transpose of matrix X.
• Calculate the product of the transpose of X and X itself.
• Compute the inverse of this product.
• Calculate the product of the transpose of X and the target vector y.
• Solve for the coefficient vector using the Normal Equation (XTX_inv * XTy). This vector includes the intercept as its first element.

3. predict

Purpose: Makes predictions using the linear model. Tasks:

• Add a column of ones to the input feature matrix X if it was not included during fitting.
• Compute the dot product of the feature matrix X and the coefficients (including intercept) to predict the target variable.

4. Rsquared

Purpose: Calculates the R-squared value to evaluate the model performance. Tasks:

• Use the predict method to obtain predictions for the input feature matrix X.
• Calculate the total sum of squares (variation of y from its mean).
• Calculate the residual sum of squares (variation of y from the predicted values).
• Compute the R-squared value using the formula 1 - (residual sum of squares / total sum of squares).

Completion Guide

To complete this exercise, follow these steps:

1. Read and understand the purpose of each method and what it is supposed to accomplish.
2. Start by implementing the fit method as it will compute the necessary coefficients used by other methods.
3. Implement the predict method to make use of the coefficients computed in fit.
4. Implement the Rsquared method to evaluate the model's performance using the predictions.
5. Test each method as you implement them to ensure correctness.

Testing Your Implementation

Once you have implemented the methods, you can test your class using pytest. Run the following command in your terminal:

pytest

This command will execute the test cases defined in the pytest test suite. Ensure that your functions are correctly implemented by passing all the tests.

Further Reading for unit testing. text