Univariate and Multivariate Regression Analysis

In Tsinghua University's mathematical experiments, we studied both univariate and multivariate regression analysis. For this experiment, we developed presentation slides to demonstrate our research findings and created MATLAB source code to support our analytical work. We began by introducing the fundamental concepts and practical applications of univariate regression analysis, then progressed to explore the complexities and challenges inherent in multivariate regression. Our implementation involved key MATLAB functions such as regress() for parameter estimation and fitlm() for creating linear models, along with statistical validation using ANOVA tables and residual analysis. We examined how regression analysis can be utilized for data prediction and interpretation, demonstrating practical applications through case studies featuring real-world datasets. Through this comprehensive experiment, we gained deep insights into both theoretical concepts and practical implementations of regression analysis, while mastering essential MATLAB programming techniques including data preprocessing, model fitting, and result visualization using plot() and scatter() functions to support our research objectives.