Linear Models and Statistical Theory in R

Deepen your understanding of data science by mastering the theoretical core of linear regression. This course provides a clear path through the mathematical concepts that define how we fit and interpret statistical models. By the end of this course, you will be able to translate complex data problems into linear algebraic frameworks and use R to execute sophisticated statistical analyses with confidence. - Understand the geometric and algebraic foundations of the least squares method - Apply matrix algebra to solve for parameters in general linear models - Practice implementing regression models using R and modern data frameworks - Master the derivation of estimators and their statistical distributions - Learn to evaluate model performance through modern diagnostic techniques - Explore the theoretical assumptions required for unbiased linear modeling The course begins with essential terminology and the basics of vector spaces before moving into the derivation of normal equations and practical modeling exercises. It is designed for learners with an introductory background in statistics and calculus who are ready to explore the mathematical "why" behind the tools they use. Begin your journey into the mathematics of data science today.