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This course is part of Advanced Statistics for Data Science Specialization
Instructor: Brian Caffo, PhD
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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.
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 videos4 readings1 assignment
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 videos2 readings1 assignment
In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.
8 videos2 readings1 assignment
We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.
6 videos1 reading1 assignment
Here we give some canonical examples of linear models to relate them to techniques that you may already be using.
4 videos1 assignment
Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.
6 videos2 assignments
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Reviewed on Apr 29, 2020
The course is interesting; but is more theoretical in nature than applied.
Reviewed on Nov 6, 2017
Great, detailed walk-through of least squares. Linear Algebra is a must for this course. To follow the last part requires knowledge of matrix (eigen?)decomposition, which derailed me somewhat.
Reviewed on Sep 12, 2020
Excellent experience. I have learnt a lot in different aspect of linear models as well as the coding skills from this course. Thank you.
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