Advanced Linear Models for Data Science 1: Least Squares

Johns Hopkins University

课程信息

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.

100% 在线课程

立即开始，按照自己的计划学习。

高级

Approx. 10 hours to complete

建议：6 weeks of study, 1-2 hours/week

English

字幕：English

100% 在线课程

立即开始，按照自己的计划学习。

高级

Approx. 10 hours to complete

建议：6 weeks of study, 1-2 hours/week

English

字幕：English

Syllabus - What you will learn from this course

1

Section

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. ...

7 videos (Total 28 min), 4 readings, 1 quiz

7 videos

Introduction2m

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 exercises

Background Quiz12m

2

Section

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....

6 videos (Total 29 min), 2 readings, 1 quiz

6 videos

Regression through the origin4m

Centering first8m

Coding example1m

Connection with linear regression7m

Coding example1m

Fitted values and residuals4m

2 readings

Before you begin10m

1 practice exercises

One Parameter Regression Quiz10m

3

Section

1 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

Least squares5m

Coding example1m

Prediction2m

Coding example2m

Residuals2m

Coding example1m

Generalizations6m

Generalizations example2m

2 readings

Before you begin10m

Generalizations10m

1 practice exercises

Linear Regression Quiz12m

4

Section

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....

6 videos (Total 39 min), 1 reading, 1 quiz

6 videos

Least squares3m

Coding example3m

Second derivation of least squares4m

Projections9m

Third derivation of least squares12m

Coding example4m

1 readings

Before you begin10m

1 practice exercises

General Least Squares Quiz20m

5

Section

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....

4 videos (Total 44 min), 1 quiz

4 videos

Basic examples of design matrices and fits24m

Group effects4m

Change of parameterization4m

ANCOVA10m

1 practice exercises

Least Squares Examples Quiz12m

6

Section

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....

6 videos (Total 44 min), 2 quizzes

6 videos

Bases, introduction4m

Bases 2, Fourier5m

Bases 3, SVDs8m

Bases, coding example9m

Introduction to residuals5m

Partitioning variability10m

2 practice exercises

Bases Quiz8m

Residuals Quiz10m

Instructor

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....

Frequently Asked Questions

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Advanced Linear Models for Data Science 1: Least Squares