MATLAB Implementation of Multiple Linear Regression Using Least Squares Method

In this article, we will explore how to implement multiple linear regression using the least squares method in MATLAB. We will begin by introducing the concept of least squares and its application in regression analysis, followed by a discussion of the principles and mathematical formulas underlying multiple linear regression. The implementation will leverage MATLAB's built-in functions like `regress()` or the backslash operator (`\`) for matrix operations to solve the normal equations. We will then delve into MATLAB's functions and toolboxes, particularly the Statistics and Machine Learning Toolbox, which provides specialized functions for regression analysis and model validation. Additionally, we will explain how to use MATLAB for data visualization through plotting functions like `scatter3`, `plot`, and `scatter` to display relationships between variables and residuals, along with techniques for result analysis using functions such as `fitlm` for comprehensive model summaries. Through this article, you will learn to implement multiple linear regression with the least squares method in MATLAB and gain deeper insights into the concepts and applications of regression analysis, including coefficient interpretation, R-squared evaluation, and residual diagnostics.