About this course: Welcome to the Advanced Linear Models for Data Science Class 1: Least Squares. 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
Background
We cover some basic matrix algebra results that we will need throughout the class. This includes some basic vector derivatives. In addition, we cover some some basic uses of matrices to create summary statistics from data. This includes calculating and subtrac...
7 videos, 4 readings
Graded: Background Quiz
WEEK 2
One and two parameter regression
In this module, we cover the basics of regression through the origin and linear regression. Regression through the origin is an interesting case, as one can build up all of multivariate regression with it.
6 videos, 2 readings
Graded: One Parameter Regression Quiz
WEEK 3
Linear regression
In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
8 videos, 2 readings
Graded: Linear Regression Quiz
WEEK 4
General least squares
We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.
6 videos, 1 reading
Graded: General Least Squares Quiz
WEEK 5
Least squares examples
Here we give some canonical examples of linear models to relate them to techniques that you may already be using.
4 videos
Graded: Least Squares Examples Quiz
WEEK 6
Bases and residuals
Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.
6 videos
Graded: Bases Quiz
Graded: Residuals Quiz
FAQs
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Johns Hopkins University
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Ratings and Reviews
I enjoyed the math and it helped me to review my linear algebra and got new intuitions on linear regression. But there are a few typos that need to be fixed. It would be better to open a forum and let student discuss with each other.
Good mathematical rigour for the analysis of linear models. Builds some good intuition for the geometry of least squares which helps in model result interpretation.
Good and not overloaded. Recommended.
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JM
Good course. Quite hard. Linear algebra should be your second language as it is assumed to be mastered. Exams should include some personal work.