Curve Fitting Using Least Squares Method

This article explores curve fitting based on the least squares method and demonstrates how to use this technique for analyzing and predicting real-world data. The method proves particularly valuable as it fits a curve to describe data trends, enabling better understanding of data patterns. To implement this approach, we require simulation data for testing and validation purposes. Our provided m-file includes comprehensive simulation datasets with the following key implementation features: matrix operations for solving normal equations, polynomial fitting functions, and residual calculation modules. The implementation demonstrates core algorithms including: the formulation of design matrices for different polynomial degrees, computation of optimal parameters using the pseudoinverse or QR decomposition, and evaluation of goodness-of-fit through R-squared metrics. Finally, we discuss common application scenarios and guide how to select optimal fitting models based on different datasets and requirements. Through this technical walkthrough, readers will gain practical understanding of least-squares curve fitting and be able to apply these techniques to real-world data analysis challenges.