Advanced Linear Models for Data Science 2: Statistical Linear Models

Go to Course: https://www.coursera.org/learn/linear-models-2

Introduction

## Course Review: Advanced Linear Models for Data Science 2: Statistical Linear Models ### Overview If you're looking to deepen your understanding of linear models in the context of data science, the course "Advanced Linear Models for Data Science 2: Statistical Linear Models" on Coursera is an excellent choice. This course serves as an in-depth dive into statistical linear models, emphasizing a blend of theoretical understanding and practical application. Before enrolling, it’s essential to have a solid foundation in several areas: linear algebra, multivariate calculus, statistics, and even some proof-based mathematics. Furthermore, you should be familiar with the R programming language, as it will be utilized throughout the course. With these prerequisites in mind, let's explore what makes this course stand out. ### Course Highlights #### Module Breakdown 1. **Introduction and Expected Values** - The course begins by revisiting essential concepts and prerequisites. This foundational module takes a focused look at expected values for multivariate vectors, setting the stage for the advanced topics to come. Students will also acquire knowledge regarding the moment properties of ordinary least squares (OLS) estimates, crucial for interpreting model outcomes. 2. **The Multivariate Normal Distribution** - Building upon the foundation laid in the first module, this section delves into the intricacies of the multivariate and singular normal distribution, starting with independent and identically distributed (iid) normal variables. Understanding these distributions is vital for professionals working with complex datasets, as linear models often assume normality in error terms. 3. **Distributional Results** - This module is where the course starts to become particularly relevant to data science applications. It covers essential distributional results that frequently arise in multivariable regression contexts, equipping learners with the ability to interpret and utilize different statistical findings in their analyses. 4. **Residuals** - The course concludes with a deep dive into residuals, where learners reassess their significance and distributional properties. The module also introduces PRESS residuals, demonstrating how these can be computed efficiently—an invaluable skill for those building predictive models without extensive computational resources. ### Learning Experience The instruction in this course is delivered through a combination of video lectures, quizzes, and practical exercises primarily in R. The clarity of explanations, coupled with the logical progression of topics, makes it suitable for anyone serious about mastering linear models. ### Recommended For This course is highly recommended for: - **Data Scientists and Analysts:** Those who want to refine their statistical modeling skills and understand the mathematical foundations of linear models. - **Graduate Students in Statistics or Data Science**: Ideal for individuals looking to supplement their academic studies with a practical, applied perspective. - **Professionals Transitioning to Data Science**: For those in fields requiring analytics, gaining expertise in statistical linear models can greatly enhance career prospects. ### Conclusion In summary, "Advanced Linear Models for Data Science 2: Statistical Linear Models" is a rigorous and rewarding course that provides essential knowledge for anyone aiming to excel in data science. The blend of theory and application, combined with the necessity for prior knowledge, ensures that students who enroll are well-prepared to tackle complex data challenges. Whether you're looking to improve your statistical skills for personal development or professional advancement, this course is an investment worth making. Don't miss the opportunity to deepen your understanding of linear models—enroll today!

Syllabus

Introduction and expected values

In this module, we cover the basics of the course as well as the prerequisites. We then cover the basics of expected values for multivariate vectors. We conclude with the moment properties of the ordinary least squares estimates.

In this module, we build up the multivariate and singular normal distribution by starting with iid normals.

In this module, we build the basic distributional results that we see in multivariable regression.

In this module we will revisit residuals and consider their distributional results. We also consider the so-called PRESS residuals and show how they can be calculated without re-fitting the model.