MATLAB Code Implementation for Linear Regression

The process of linear regression involves fitting a line to a set of data points to model the relationship between two variables. This can be effectively implemented using MATLAB's built-in functions and statistical tools. The implementation typically utilizes the polyfit function for polynomial curve fitting, where a first-degree polynomial (n=1) generates the linear model. The basic syntax y = polyfit(x, y, 1) returns the slope and intercept parameters, while polyval can be used for evaluation and prediction. For more advanced applications, MATLAB's fitlm function from the Statistics and Machine Learning Toolbox provides comprehensive linear regression analysis with detailed statistics including R-squared values, coefficient estimates, and ANOVA tables. The code typically involves data preprocessing, model fitting, residual analysis, and visualization through plot functions with proper labeling and legend implementation. MATLAB's powerful matrix operations enable efficient computation of the normal equations method (θ = (XᵀX)⁻¹Xᵀy) for parameter estimation, while also supporting regularization techniques when dealing with multicollinearity. The implementation includes error handling for singular matrices and data validation checks to ensure robust performance across various dataset sizes and characteristics.