Least Squares Method Implementation in MATLAB

This document presents the fundamental principles and applications of the Least Squares Method, along with detailed implementation guidelines using MATLAB. The algorithm is implemented through MATLAB's matrix operations capabilities, primarily utilizing the backslash operator (\) for efficient linear system solving. For the equation Ax = b, the least squares solution is computed as x = A\b, which handles overdetermined systems by minimizing the sum of squared residuals. We provide step-by-step instructions compatible with MATLAB 7.01, enabling users to easily replicate and implement the algorithm. The implementation includes data preprocessing, coefficient matrix formation, and residual analysis components. The Least Squares Method serves as a fundamental regression analysis technique for estimating relationships between data points. By implementing this algorithm in MATLAB, researchers can perform precise data analysis and draw statistically significant conclusions, thereby strengthening support for various scientific investigations. Key implementation features include: - Automated matrix dimension validation - Error handling for rank-deficient matrices - Residual norm computation for model evaluation - Visualization functions for regression line plotting