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.
Advanced Linear Models for Data Science 1: Least Squares
Offered By
Johns Hopkins University
About this Course
5,973 recent views
Skills you will gain
StatisticsLinear RegressionR ProgrammingLinear Algebra
Syllabus - What you will learn from this course
Week
11 hour to complete
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 subtracting means from observations (centering) as well as calculating the variance.
7 videos (Total 28 min), 4 readings, 1 quiz
7 videos
Matrix derivatives5m
Coding example2m
Centering by matrix multiplication6m
Coding example2m
Variance via matrix multiplication6m
Coding example2m
4 readings
Welcome to the class10m
Course textbook10m
Grading10m
In this module10m
1 practice exercise
Background Quiz12m
Week
21 hour to complete
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 (Total 29 min), 2 readings, 1 quiz
6 videos
Centering first8m
Coding example1m
Connection with linear regression7m
Coding example1m
Fitted values and residuals4m
2 readings
Before you begin10m
Before you begin10m
1 practice exercise
One Parameter Regression Quiz10m
Week
31 hour to complete
Linear regression
In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
8 videos (Total 23 min), 2 readings, 1 quiz
8 videos
Coding example1m
Prediction2m
Coding example2m
Residuals2m
Coding example1m
Generalizations6m
Generalizations example2m
2 readings
Before you begin10m
Generalizations10m
1 practice exercise
Linear Regression Quiz12m
Week
41 hour to complete
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 (Total 39 min), 1 reading, 1 quiz
6 videos
Coding example3m
Second derivation of least squares4m
Projections9m
Third derivation of least squares12m
Coding example4m
1 reading
Before you begin10m
1 practice exercise
General Least Squares Quiz20m
Week
51 hour to complete
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 (Total 44 min), 1 quiz
4 videos
Group effects4m
Change of parameterization4m
ANCOVA10m
1 practice exercise
Least Squares Examples Quiz12m
Week
61 hour to complete
Bases and residuals
Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.
6 videos (Total 44 min), 2 quizzes
6 videos
Bases 2, Fourier5m
Bases 3, SVDs8m
Bases, coding example9m
Introduction to residuals5m
Partitioning variability10m
2 practice exercises
Bases Quiz8m
Residuals Quiz10m
4.4
22 ReviewsTop reviews from Advanced Linear Models for Data Science 1: Least Squares
We need more advanced, theoretical courses on Coursera, like this one, in order to deeply understand the more general courses like Regression Models and Linear Models.
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.
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
When will I have access to the lectures and assignments?
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.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
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