Foundations of Linear Models: Least Squares in Data Science

Understanding the mathematical engine behind linear regression is essential for any serious data scientist. This text-based course bridges the gap between basic statistical formulas and the rigorous linear algebra that powers least squares estimation. By completing this course, you will transition from simply running regression commands to deeply understanding how these models solve optimization problems. Through clear written explanations and code exercises, you will explore vector spaces, projections, and matrix formulations to gain the mathematical confidence needed to analyze, troubleshoot, and optimize linear models. What you'll learn: * Understand the fundamental terminology of linear models, vector spaces, and matrix projections * Derive the ordinary least squares estimator using linear algebra and multivariate calculus * Analyze model residuals, projections, and the underlying geometry of regression * Implement least squares mathematics from scratch using R and modern programming workflows * Apply regularization concepts like Ridge and Lasso to address overfitting and multicollinearity * Evaluate model fit and statistical assumptions through structured mathematical concepts and practical code The course begins with foundational concepts of vector geometry and matrix algebra before moving into formal least squares derivations. You will progress through geometric projections, statistical properties of estimators, and practical implementation in R using clear, step-by-step written guides. This course is designed for aspiring data scientists, analysts, and students who want to move beyond basic regression and master the mathematical core of linear modeling. While a basic familiarity with algebra and introductory R is helpful, the course builds up all core mathematical concepts from the ground up. Start reading today to build a mathematically rigorous foundation for your data science career.