Advanced Linear Models for Data Science 1: Least Squares

Go to Course: https://www.coursera.org/learn/linear-models

Introduction

### Course Review: Advanced Linear Models for Data Science 1: Least Squares If you’re delving into the realms of data science and looking to enhance your understanding of linear models, Coursera’s “Advanced Linear Models for Data Science 1: Least Squares” is an essential course that provides a solid foundation. This class offers a unique blend of theoretical insights grounded in linear algebra and practical applications relevant to statistical modeling. #### Overview The course is designed to provide a comprehensive introduction to the concept of least squares, an indispensable method in regression analyses. It emphasizes a mathematical perspective, ensuring that students acquire both theoretical knowledge and practical skills that can be applied in real-world data science tasks. #### Prerequisites Before diving into this course, it's essential to have: - A basic understanding of linear algebra and multivariate calculus. - Familiarity with statistics and regression models. - Exposure to proof-based mathematics. - Basic proficiency in the R programming language. These prerequisites are crucial as the course delves into advanced topics that build on this foundational knowledge. #### Syllabus Breakdown 1. **Background:** - This module starts with essential matrix algebra results, ensuring that all participants are on the same page before tackling more advanced topics. It also covers vector derivatives and introduces basic summary statistics, such as centering observations and calculating variance. 2. **One and Two Parameter Regression:** - Here, learners will explore regression through the origin and linear regression, delving into how regression can be expanded multivariately through these basic forms. 3. **Linear Regression:** - This section focuses on linear regression, addressing its significance as a standard method for identifying unconfounded linear relationships within datasets. 4. **General Least Squares:** - Students will learn about general least squares, where a full rank design matrix is fitted to a vector outcome. This module builds a bridge between theoretical concepts and their practical implications. 5. **Least Squares Examples:** - To help contextualize the theoretical knowledge, the course presents canonical examples of linear models. This integration aids in making connections between theory and the techniques you may already be using in practice. 6. **Bases and Residuals:** - The final module emphasizes the decomposition of signals into basis expansions, a key tool for understanding underlying patterns in data. #### Why You Should Take This Course 1. **Robust Foundation:** The course meticulously builds a strong foundation in least squares, which is critical for both academic and practical applications in data science. 2. **Focus on Theory and Practice:** Unlike many courses that lean heavily toward practical applications, this class balances theoretical knowledge with practical examples. This dual approach enriches learning and prepares you for real-world data challenges. 3. **Instructor Expertise:** The course is guided by experienced instructors who are well-versed in both the theoretical and applied aspects of data science and linear models. 4. **Flexibility and Accessibility:** Being an online course, it allows you to learn at your own pace, making it accessible for those with varying schedules and commitments. 5. **Community and Networking:** Enrolling in this course gives you access to a community of like-minded individuals, providing opportunities for networking, collaboration, and discussions that can enhance your learning experience. #### Conclusion In conclusion, if you are interested in deepening your understanding of advanced linear models, particularly in the context of data science, “Advanced Linear Models for Data Science 1: Least Squares” on Coursera is highly recommended. With its comprehensive syllabus, focus on foundational concepts, and practical applicability, this course is an invaluable resource for aspiring data scientists and statisticians. Don’t miss the chance to empower your data analysis skills with this enlightening course!

Syllabus

Background

We cover some basic matrix algebra results that we will need throughout the class. This includes some basic vector derivatives. In addition, we cover some some basic uses of matrices to create summary statistics from data. This includes calculating and subtracting means from observations (centering) as well as calculating the variance.

In this module, we cover the basics of regression through the origin and linear regression. Regression through the origin is an interesting case, as one can build up all of multivariate regression with it.

In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.

We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.

Here we give some canonical examples of linear models to relate them to techniques that you may already be using.

Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.