Least Squares Linear Fitting Algorithm Implementation in MATLAB

This article provides a comprehensive introduction to least squares fitting and demonstrates its application in implementing a linear fitting algorithm. The implementation will be specifically carried out using MATLAB programming environment. Least squares fitting is a widely used regression method that finds the optimal straight line by minimizing the sum of squared distances between the line and all data points. We will begin by explaining the mathematical principles and key concepts behind least squares fitting, including the normal equations derivation and error minimization approach. Subsequently, we will detail the MATLAB implementation process, covering essential functions like polyfit for polynomial fitting, matrix operations for solving linear equations, and visualization techniques using plot functions. The implementation will demonstrate how to handle data input, perform coefficient calculations, and validate results through residual analysis. Through studying this material, you will gain deeper understanding of least squares fitting principles and applications, while mastering the practical skills needed to implement linear least squares algorithms using MATLAB's computational capabilities.