Application of Least Squares Linear Fitting in MATLAB

In scientific research and engineering fields, least squares linear fitting serves as a fundamental technique for data analysis. MATLAB provides efficient implementation through its polyfit function, which calculates optimal linear parameters by minimizing the sum of squared residuals between data points and the fitted line. The polyfit function accepts input vectors for x and y coordinates and returns coefficients for the linear equation y = mx + b, where the slope (m) and intercept (b) are determined analytically using matrix operations equivalent to solving the normal equations. This method not only facilitates data pattern recognition but also enhances analytical capabilities through quantitative error assessment. While alternative fitting techniques exist, least squares linear fitting remains a robust and computationally efficient approach suitable for most datasets. For implementation, the basic syntax p = polyfit(x,y,1) specifies linear fitting (degree 1), with the output vector p containing [slope, intercept] values that can be directly used with polyval for prediction or plotting.