MATLAB Implementation of Multiple Linear Regression Using Least Squares Method

This article demonstrates how to implement multiple linear regression using the least squares method in MATLAB. In regression analysis, the least squares method is a widely used approach for estimating relationships between independent and dependent variables. Multiple linear regression refers to the regression analysis technique employed when two or more independent variables are associated with a single dependent variable. In this implementation, we will use MATLAB to construct a multiple linear regression model through least squares estimation. The process involves several key steps: importing dataset using functions like readtable or csvread, fitting the regression model through matrix operations (X'*X)^(-1)*X'*Y or using built-in functions like fitlm, analyzing results including R-squared values and coefficient significance, and making predictions using the predict function. We will cover detailed implementation aspects including: - Data preprocessing and normalization techniques - Handling the design matrix formation for multiple predictors - Implementing the normal equation: beta = inv(X'*X)*X'*Y - Alternative approaches using MATLAB's Regression Learner app or linear model functions - Residual analysis and model validation methods - Interpretation of coefficient estimates and confidence intervals Through these comprehensive steps, you will learn practical techniques for performing multiple linear regression analysis in MATLAB, with emphasis on the mathematical foundation and computational efficiency of the least squares algorithm. The implementation will include error handling for multicollinearity detection and methods for improving model accuracy through regularization techniques when necessary.