Advanced Linear Models for Data Science 2: Statistical Linear Models

Advanced Linear Models for Data Science 2: Statistical Linear Models

This course is part of Advanced Statistics for Data Science Specialization

Instructor: Brian Caffo, PhD

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4 modules

Gain insight into a topic and learn the fundamentals.

107 reviews

Advanced level

Designed for those already in the industry

6 hours to complete

Flexible schedule

Learn at your own pace

4 modules

Gain insight into a topic and learn the fundamentals.

107 reviews

Advanced level

Designed for those already in the industry

6 hours to complete

Flexible schedule

Learn at your own pace

Skills you'll gain

Tools you'll learn

R Programming

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

4 assignments

Taught in English

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This course is part of the Advanced Statistics for Data Science Specialization

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There are 4 modules in this course

Welcome to the Advanced Linear Models for Data Science Class 2: Statistical Linear Models. This class is an introduction to least squares from a linear algebraic and mathematical perspective. Before beginning the class make sure that you have the following:

- A basic understanding of linear algebra and multivariate calculus. - A basic understanding of statistics and regression models. - At least a little familiarity with proof based mathematics. - Basic knowledge of the R programming language. After taking this course, students will have a firm foundation in a linear algebraic treatment of regression modeling. This will greatly augment applied data scientists' general understanding of regression models.

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.

What's included

7 videos3 readings1 assignment

7 videos Total 38 minutes

Introductory video 2 minutes
Multivariate expected values, the basics 5 minutes
Expected values, matrix operations 3 minutes
Multivariate variances and covariances 6 minutes
Multivariate covariance and variance matrix operations 6 minutes
Expected values of quadratic forms 4 minutes
Expected value properties of least squares estimates 14 minutes

3 readings Total 30 minutes

Welcome to the class 10 minutes
Course textbook 10 minutes
Introduction to expected values 10 minutes

1 assignment Total 30 minutes

Expected Values 30 minutes

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

What's included

4 videos2 readings1 assignment

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

What's included

8 videos1 reading1 assignment

8 videos Total 60 minutes

Chi squared results for quadratic forms 11 minutes
Confidence intervals for regression coefficients 7 minutes
F distribution 5 minutes
Coding example 8 minutes
Prediction intervals 11 minutes
Coding example 5 minutes
Confidence ellipsoids 7 minutes
Coding example 6 minutes

1 reading Total 10 minutes

Distributional results 10 minutes

1 assignment Total 20 minutes

Distributional results 20 minutes

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.