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.
Advanced Linear Models for Data Science 2: Statistical Linear Models
Offered By
Johns Hopkins University
Syllabus - What you will learn from this course
Week
1Introduction 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.
7 videos (Total 38 min), 3 readings, 1 quiz
7 videos
Multivariate expected values, the basics4m
Expected values, matrix operations2m
Multivariate variances and covariances5m
Multivariate covariance and variance matrix operations5m
Expected values of quadratic forms3m
Expected value properties of least squares estimates13m
3 readings
Welcome to the class10m
Course textbook10m
Introduction to expected values10m
1 practice exercise
Expected Values30m
Week
2The multivariate normal distribution
In this module, we build up the multivariate and singular normal distribution by starting with iid normals.
4 videos (Total 31 min), 2 readings, 1 quiz
4 videos
The singular normal distribution7m
Normal likelihoods5m
Normal conditional distributions8m
2 readings
Introduction to the multivariate normal10m
A note on the last quiz question.10m
1 practice exercise
the multivariate normal20m
Week
3Distributional results
In this module, we build the basic distributional results that we see in multivariable regression.
8 videos (Total 60 min), 1 reading, 1 quiz
8 videos
Confidence intervals for regression coefficients6m
F distribution4m
Coding example7m
Prediction intervals11m
Coding example5m
Confidence ellipsoids7m
Coding example6m
1 reading
Distributional results10m
1 practice exercise
Distributional results20m
Week
4Residuals
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.
4 videos (Total 32 min), 2 readings, 1 quiz
4 videos
Code demonstration3m
Leave one out residuals8m
Press residuals14m
2 readings
Residuals10m
Thanks for taking the course10m
1 practice exercise
Residuals14m
4.7
2 ReviewsTop Reviews
By ML•Jan 31st 2017
Good course on applied linear statistical modeling.
Instructor
Brian Caffo, PhD
Professor, BiostatisticsBloomberg School of Public Health
About Johns Hopkins University
The mission of The Johns Hopkins University is to educate its students and cultivate their capacity for life-long learning, to foster independent and original research, and to bring the benefits of discovery to the world.
Frequently Asked Questions
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Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.
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