Об этом курсе
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.
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Advanced Level

Продвинутый уровень

Clock

Прибл. 10 ч. на завершение

Предполагаемая нагрузка: 6 weeks of study, 1-2 hours/week
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English

Субтитры: English
Globe

Только онлайн-курс

Начните сейчас и учитесь по собственному графику.
Advanced Level

Продвинутый уровень

Clock

Прибл. 10 ч. на завершение

Предполагаемая нагрузка: 6 weeks of study, 1-2 hours/week
Comment Dots

English

Субтитры: English

Syllabus - What you will learn from this course

1

Section
Clock
1 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. ...
Reading
7 videos (Total 28 min), 4 readings, 1 quiz
Video7 videos
Matrix derivatives5m
Coding example2m
Centering by matrix multiplication6m
Coding example2m
Variance via matrix multiplication6m
Coding example2m
Reading4 readings
Welcome to the class10m
Course textbook10m
Grading10m
In this module10m
Quiz1 practice exercises
Background Quiz12m

2

Section
Clock
1 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....
Reading
6 videos (Total 29 min), 2 readings, 1 quiz
Video6 videos
Centering first8m
Coding example1m
Connection with linear regression7m
Coding example1m
Fitted values and residuals4m
Reading2 readings
Before you begin10m
Before you begin10m
Quiz1 practice exercises
One Parameter Regression Quiz10m

3

Section
Clock
1 hour to complete

Linear regression

In this lecture, we focus on linear regression, the most standard technique for investigating unconfounded linear relationships. ...
Reading
8 videos (Total 23 min), 2 readings, 1 quiz
Video8 videos
Coding example1m
Prediction2m
Coding example2m
Residuals2m
Coding example1m
Generalizations6m
Generalizations example2m
Reading2 readings
Before you begin10m
Generalizations10m
Quiz1 practice exercises
Linear Regression Quiz12m

4

Section
Clock
1 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....
Reading
6 videos (Total 39 min), 1 reading, 1 quiz
Video6 videos
Coding example3m
Second derivation of least squares4m
Projections9m
Third derivation of least squares12m
Coding example4m
Reading1 readings
Before you begin10m
Quiz1 practice exercises
General Least Squares Quiz20m

5

Section
Clock
1 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....
Reading
4 videos (Total 44 min), 1 quiz
Video4 videos
Group effects4m
Change of parameterization4m
ANCOVA10m
Quiz1 practice exercises
Least Squares Examples Quiz12m

6

Section
Clock
1 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....
Reading
6 videos (Total 44 min), 2 quizzes
Video6 videos
Bases 2, Fourier5m
Bases 3, SVDs8m
Bases, coding example9m
Introduction to residuals5m
Partitioning variability10m
Quiz2 practice exercises
Bases Quiz8m
Residuals Quiz10m
4.4

Top Reviews

By DLJun 8th 2016

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.

By SPApr 30th 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.

Instructor

Avatar

Brian Caffo, PhD

Professor, Biostatistics

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....

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