MATLAB Code Implementation for Statistical Regression Analysis

MATLAB offers a comprehensive suite of statistical regression analysis tools capable of handling problems ranging from simple linear regression to complex nonlinear regression. Its built-in Statistics and Machine Learning Toolbox contains extensive regression analysis functionalities with specialized algorithms for various modeling scenarios.

The typical workflow for regression analysis in MATLAB involves: first importing or creating a dataset, then selecting an appropriate regression model type. For linear regression, the fitlm function implements ordinary least squares regression using matrix operations to compute coefficient estimates. For more complex regression problems, stepwisefit performs stepwise regression with forward/backward selection algorithms, while robustfit utilizes robust statistical methods like iteratively reweighted least squares to handle outliers effectively.

MATLAB's regression analysis not only provides coefficient estimates but also delivers complete diagnostic information including model evaluation metrics such as R-squared, adjusted R-squared, and F-statistics. The plotResiduals function generates visual diagnostic plots (histograms, probability plots) to validate model assumptions through residual analysis, implementing statistical tests for normality and homoscedasticity.

For prediction applications, the predict function applies the fitted regression model to new data using matrix multiplication operations with coefficient vectors. Additionally, MATLAB supports cross-validation functionalities through functions like crossval that help assess model generalization capability by partitioning datasets. Through the interactive Regression Learner app, users can graphically explore different regression models with automated hyperparameter tuning and performance comparison features.