Simple Linear Regression in Julia

This project demonstrates a basic implementation of simple linear regression in Julia. It generates synthetic data, performs linear regression to find the equation of the line, and then plots the data points and the regression line.

Requirements

• Julia 1.11.3 or newer
• Plots package
• Statistics package

Installation

1. Install Julia:
   If you haven't installed Julia yet, download and install it from the official website: https://julialang.org/downloads/.

2. Install Required Packages:
   Open Julia's REPL and run the following command to install the required packages:

   import Pkg
   Pkg.add("Plots")
   Pkg.add("Statistics")

3. Update Julia (optional but recommended):
   If you're using an older version of Julia, it is recommended to update to the latest version (1.11.3+):

   juliaup update

Project Overview

Steps:

1. Generate Synthetic Data: The function generate_data(n::Int) generates a set of n data points for the independent variable x and a dependent variable y with some random noise.

2. Perform Linear Regression: The function linear_regression(x, y) calculates the slope (m) and the intercept (b) of the best-fit line using the least squares method.

3. Plot the Results: The function plot_regression(x, y, m, b) uses the Plots package to display a scatter plot of the data points and overlay the regression line.

Output:

• The console will display the linear regression equation y = mx + b, where m is the slope and b is the intercept.
• A plot will be generated showing the data points and the regression line.

Example Usage

Once the packages are installed and your environment is set up, you can run the project by simply calling the main() function:

main()

This will:

• Generate synthetic data,
• Perform linear regression,
• Display the regression equation in the console, and
• Plot the data along with the regression line.

License

This project is open source and available under the MIT License.