About 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.
Who is this class for: This class is for students who already have had a class in regression modeling and are familiar with the area who would like to see a more advanced treatment of the topic.
Created by: Johns Hopkins University
Taught by: Brian Caffo, PhD, Professor, Biostatistics
Bloomberg School of Public Health
| Level | Advanced |
| Commitment | 6 weeks of study, 1-2 hours/week |
| Language | English |
| How To Pass | Pass all graded assignments to complete the course. |
| User Ratings |
Syllabus
WEEK 1
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.
7 videos, 3 readings
- Video: Introductory video
- Reading: Welcome to the class
- Reading: Course textbook
- Reading: Introduction to expected values
- Video: Multivariate expected values, the basics
- Video: Expected values, matrix operations
- Video: Multivariate variances and covariances
- Video: Multivariate covariance and variance matrix operations
- Video: Expected values of quadratic forms
- Video: Expected value properties of least squares estimates
Graded: Expected Values
WEEK 2
The multivariate normal distribution
In this module, we build up the multivariate and singular normal distribution by starting with iid normals.
4 videos, 2 readings
- Reading: Introduction to the multivariate normal
- Video: Normals and multivariate normals
- Video: The singular normal distribution
- Video: Normal likelihoods
- Video: Normal conditional distributions
- Reading: A note on the last quiz question.
Graded: the multivariate normal
WEEK 3
Distributional results
In this module, we build the basic distributional results that we see in multivariable regression.
8 videos, 1 reading
- Reading: Distributional results
- Video: Chi squared results for quadratic forms
- Video: Confidence intervals for regression coefficients
- Video: F distribution
- Video: Coding example
- Video: Prediction intervals
- Video: Coding example
- Video: Confidence ellipsoids
- Video: Coding example
Graded: Distributional results
WEEK 4
Residuals
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, 2 readings
- Reading: Residuals
- Video: Residuals distributional results
- Video: Code demonstration
- Video: Leave one out residuals
- Video: Press residuals
- Reading: Thanks for taking the course
Graded: Residuals
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ML
Good course on applied linear statistical modeling.