Enroll Course: https://www.coursera.org/learn/linear-models-2
For anyone serious about data science, a solid grasp of linear models is non-negotiable. Coursera’s ‘Advanced Linear Models for Data Science 2: Statistical Linear Models’ is a fantastic resource that takes you beyond the basics and into the mathematical underpinnings of these crucial techniques.
This course is designed for those who already have a foundational understanding of linear algebra, multivariate calculus, statistics, and regression. If you’re comfortable with proofs and have some R programming experience, you’re well-prepared to dive in. The course doesn’t shy away from the mathematical rigor, which is precisely what makes it so valuable.
The syllabus is thoughtfully structured, starting with a review of prerequisites and delving into the expected values of multivariate vectors. The module on the ‘Moment properties of the ordinary least squares estimates’ is particularly insightful, providing a rigorous look at the foundation of estimation.
Building on this, the course moves into the ‘Multivariate normal distribution,’ meticulously constructing it from independent and identically distributed normals. This theoretical groundwork is essential for understanding the ‘Distributional results’ that follow, which are the bedrock of multivariable regression analysis.
Finally, the module on ‘Residuals’ offers a sophisticated revisit of this critical concept. It explores their distributional properties and introduces the PRESS residuals, demonstrating a clever computational shortcut that avoids refitting the model. This practical insight, combined with the theoretical depth, makes the learning experience incredibly rewarding.
If you’re looking to solidify your understanding of statistical linear models and gain a deeper appreciation for the mathematics behind them, I highly recommend this Coursera course. It’s an investment in your data science journey that will pay significant dividends.
Enroll Course: https://www.coursera.org/learn/linear-models-2