4.4

74 ratings

•

20 reviews

Johns Hopkins University

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.

Section

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

Matrix derivatives5m

Coding example2m

Centering by matrix multiplication6m

Coding example2m

Variance via matrix multiplication6m

Coding example2m

Welcome to the class10m

Course textbook10m

Grading10m

In this module10m

Background Quiz12m

Section

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

Centering first8m

Coding example1m

Connection with linear regression7m

Coding example1m

Fitted values and residuals4m

Before you begin10m

Before you begin10m

One Parameter Regression Quiz10m

Section

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

Coding example1m

Prediction2m

Coding example2m

Residuals2m

Coding example1m

Generalizations6m

Generalizations example2m

Before you begin10m

Generalizations10m

Linear Regression Quiz12m

Section

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

Coding example3m

Second derivation of least squares4m

Projections9m

Third derivation of least squares12m

Coding example4m

Before you begin10m

General Least Squares Quiz20m

Section

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

Group effects4m

Change of parameterization4m

ANCOVA10m

Least Squares Examples Quiz12m

Section

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

Bases 2, Fourier5m

Bases 3, SVDs8m

Bases, coding example9m

Introduction to residuals5m

Partitioning variability10m

Bases Quiz8m

Residuals Quiz10m

4.4

By DL•Jun 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 SP•Apr 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.

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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