Simple Linear Regression with Python

Welcome to this Python implementation of Simple Linear Regression!

Introduction

This code implements a simple linear regression algorithm to fit a line to a set of data points. The line is fit such that the sum of the squares of the differences between the observed values and the values predicted by the line is minimized.

Prerequisites

Before we begin, you'll need to have the following packages installed:

numpy matplotlib You can install these packages using the following command:

pip install numpy matplotlib

Code Overview

The code consists of three main classes:

DataGenerator: A class that generates synthetic data for us to fit a line to. LinearRegression: A class that implements the simple linear regression algorithm. main: The main function that ties everything together. Let's take a closer look at each of these classes.

DataGenerator

The DataGenerator class is used to generate synthetic data for us to fit a line to. It has one parameter, num_points, which determines the number of data points that will be generated. The data points are generated by calculating x values using the linspace function from numpy and y values using the equation y = 2 * x + 1 + np.random.normal(0, 1, self.num_points). The np.random.normal function is used to add some random noise to the data.

LinearRegression

The LinearRegression class implements the simple linear regression algorithm. It has two main components: the fit method and the predict method. The fit method is used to calculate the values of b0 and b1 that minimize the sum of the squares of the differences between the observed values and the values predicted by the line. The predict method takes an x value as input and returns the corresponding y value predicted by the line.

Main Function

The main function ties everything together. It starts by creating an instance of the DataGenerator class and generating the data. Next, it creates an instance of the LinearRegression class and fits the line to the data. Finally, it calculates the R^2 score, which measures the quality of the fit, and plots the data points and the line on a scatter plot.

Running the Code

To run the code, simply run the following command:

python linear_regression.py This will generate the synthetic data, fit the line to the data, calculate the R^2 score, and display the scatter plot.

Conclusion

That's it! You've now successfully implemented a simple linear regression algorithm in Python. This implementation can be used as a starting point for your own projects, or as a tool for understanding how simple linear regression works.

If you have any questions or feedback, don't hesitate to reach out!

~Dre