Advanced Linear Models for Data Science 1: Least Squares

Advanced Linear Models for Data Science 1: Least Squares

This course is part of Advanced Statistics for Data Science Specialization

Instructor: Brian Caffo, PhD

Access provided by Innovecs

31,075 already enrolled

6 modules

Gain insight into a topic and learn the fundamentals.

190 reviews

Advanced level

Designed for those already in the industry

8 hours to complete

Flexible schedule

Learn at your own pace

6 modules

Gain insight into a topic and learn the fundamentals.

190 reviews

Advanced level

Designed for those already in the industry

8 hours to complete

Flexible schedule

Learn at your own pace

Skills you'll gain

Tools you'll learn

R Programming

Details to know

Shareable certificate

Add to your LinkedIn profile

Assessments

7 assignments

Taught in English

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This course is part of the Advanced Statistics for Data Science Specialization

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There are 6 modules in 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.

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.

What's included

7 videos4 readings1 assignment

7 videos Total 28 minutes

Introduction 3 minutes
Matrix derivatives 5 minutes
Coding example 2 minutes
Centering by matrix multiplication 7 minutes
Coding example 2 minutes
Variance via matrix multiplication 7 minutes
Coding example 2 minutes

4 readings Total 40 minutes

Welcome to the class 10 minutes
Course textbook 10 minutes
Grading 10 minutes
In this module 10 minutes

1 assignment Total 30 minutes

Background Quiz 30 minutes

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.

What's included

6 videos2 readings1 assignment

6 videos Total 29 minutes

Regression through the origin 5 minutes
Centering first 8 minutes
Coding example 2 minutes
Connection with linear regression 8 minutes
Coding example 2 minutes
Fitted values and residuals 5 minutes

2 readings Total 20 minutes

Before you begin 10 minutes
Before you begin 10 minutes

1 assignment Total 30 minutes

One Parameter Regression Quiz 30 minutes

In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships.

What's included

8 videos2 readings1 assignment

8 videos Total 23 minutes

Least squares 5 minutes
Coding example 1 minute
Prediction 2 minutes
Coding example 2 minutes
Residuals 2 minutes
Coding example 2 minutes
Generalizations 6 minutes
Generalizations example 2 minutes

2 readings Total 20 minutes

Before you begin 10 minutes
Generalizations 10 minutes

1 assignment Total 30 minutes

Linear Regression Quiz 30 minutes

We now move on to general least squares where an arbitrary full rank design matrix is fit to a vector outcome.

What's included

6 videos1 reading1 assignment

Here we give some canonical examples of linear models to relate them to techniques that you may already be using.

What's included

4 videos1 assignment

Here we give a very useful kind of linear model, that is decomposing a signal into a basis expansion.

What's included

6 videos2 assignments

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Instructor

Instructor ratings

(20 ratings)

Brian Caffo, PhD

Johns Hopkins University

30 Courses 1,707,467 learners

Offered by

Johns Hopkins University

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Showing 3 of 190

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 Apr 29, 2017

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.

Reviewed on Mar 4, 2018

Very thorough and rigorous. A great review for me.

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