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

Brian Caffo, PhD

Offered By

Advanced Statistics for Data Science SpecializationJohns Hopkins University

About this Course

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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.

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Course 3 of 4 in the

Advanced Statistics for Data Science Specialization

Flexible deadlines

Reset deadlines in accordance to your schedule.

Advanced Level

Approx. 8 hours to complete

English

Subtitles: French, Portuguese (Brazilian), Russian, English, Spanish

Skills you will gain

StatisticsLinear RegressionR ProgrammingLinear Algebra

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Course 3 of 4 in the

Advanced Statistics for Data Science Specialization

Flexible deadlines

Reset deadlines in accordance to your schedule.

Advanced Level

Approx. 8 hours to complete

English

Subtitles: French, Portuguese (Brazilian), Russian, English, Spanish

Instructor

Instructor rating

4.66/5 (6 Ratings)

Brian Caffo, PhD

Professor, Biostatistics

Bloomberg School of Public Health

1,266,927 Learners

21 Courses

Offered by

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.

Syllabus - What you will learn from this course

Week

Week 1

2 hours 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.

2 hours to complete

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 exercise

Background Quiz30m

Week

Week 2

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.

1 hour to complete

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 exercise

One Parameter Regression Quiz30m

Week

Week 3

1 hour to complete

Linear regression

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

1 hour to complete

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 exercise

Linear Regression Quiz30m

Week

Week 4

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.

1 hour to complete

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 reading

Before you begin10m

1 practice exercise

General Least Squares Quiz30m

About the Advanced Statistics for Data Science Specialization

Fundamental concepts in probability, statistics and linear models are primary building blocks for data science work. Learners aspiring to become biostatisticians and data scientists will benefit from the foundational knowledge being offered in this specialization. It will enable the learner to understand the behind-the-scenes mechanism of key modeling tools in data science, like least squares and linear regression.

This specialization starts with Mathematical Statistics bootcamps, specifically concepts and methods used in biostatistics applications. These range from probability, distribution, and likelihood concepts to hypothesis testing and case-control sampling. This specialization also linear models for data science, starting from understanding least squares from a linear algebraic and mathematical perspective, to statistical linear models, including multivariate regression using the R programming language. These courses will give learners a firm foundation in the linear algebraic treatment of regression modeling, which will greatly augment applied data scientists' general understanding of regression models. This specialization requires a fair amount of mathematical sophistication. Basic calculus and linear algebra are required to engage in the content.

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What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You'll be prompted to complete an application and will be notified if you are approved. You'll need to complete this step for each course in the Specialization, including the Capstone Project. Learn more.
Will I earn university credit for completing the Course?
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Advanced Linear Models for Data Science 1: Least Squares