Welcome to the Advanced Linear Models for Data Science Class 2: Statistical Linear Models. This course delves into least squares from a linear algebraic and mathematical perspective, offering a deeper understanding of regression models for data science applications. To excel in this course, a basic understanding of linear algebra, multivariate calculus, statistics, and regression models is required. The course modules cover topics such as introduction and expected values, the multivariate normal distribution, distributional results, and residuals. These modules provide in-depth insight and practical knowledge for students to build a strong foundation in regression modeling. Join this course to enhance your skills and broaden your knowledge in data science applications.
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This comprehensive course covers modules on introduction and expected values, the multivariate normal distribution, distributional results, and residuals. Gain practical knowledge and a deeper understanding of regression modeling.
Welcome to the first module of the course, which focuses on introduction and expected values. This module provides an overview of multivariate expected values, variances, covariances, and their matrix operations, expected values of quadratic forms, and properties of least squares estimates. It also includes introductory videos and a course textbook for a comprehensive learning experience.
The second module delves into the multivariate normal distribution, covering topics such as normals, singular normal distribution, normal likelihoods, conditional distributions, and a comprehensive introduction to the multivariate normal. This module also provides insight into the practical application of the multivariate normal distribution.
Module three focuses on distributional results, including chi squared results for quadratic forms, confidence intervals for regression coefficients, F distribution, prediction intervals, and confidence ellipsoids. It also includes coding examples to reinforce understanding and application of the distributional results in regression modeling.
The final module covers residuals, including their distributional results, code demonstration, leave one out residuals, press residuals, and provides a comprehensive understanding of residuals in the context of regression modeling. This module concludes with a summary and thanks for taking the course.
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