Advanced Linear Models for Data Science 1: Least Squares
This course unveils the intricacies of least squares through a lens of linear algebra and mathematical exploration. As you embark on this course, you're setting foot on a path that leads to profound insights and enhanced data analysis skills.
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Prerequisites
To make the most of this course, ensure that you possess:
- A foundational grasp of linear algebra and multivariate calculus.
- Basic familiarity with statistics and regression models.
- At least a modest understanding of proof-based mathematics.
- Fundamental knowledge of the R programming language.
Learning outcomes
Upon completion of this course, students will solidify their understanding of regression modelling from a linear algebraic perspective. This robust foundation will significantly amplify the comprehension of regression models among applied data scientists.
Modules:
1) Background. This module lays the groundwork by exploring essential matrix algebra concepts that will serve as cornerstones throughout the course. You'll also dive into vector derivatives and learn how matrices can be employed to derive summary statistics from data.
2) Navigating Regression Basics. This module shines a spotlight on the fundamentals of regression through the origin and linear regression.
3) The Essence of Linear Regression. One and two parameter regression.
4) Mastering General Least Squares. This module focuses on general least squares—an advanced technique that involves fitting an arbitrary full-rank design matrix to a vector outcome.
5) Drawing on canonical examples of linear models.
6) Bases and Residuals.
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