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Advanced Linear Models for Data Science 1

Least Squares

Brian Caffo, PhD

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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What's inside

Syllabus

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.

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.

Linear regression

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

General least squares

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

Least squares examples

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

Bases and residuals

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

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Introduces least squares from a linear algebraic and mathematical perspective, which is a strong foundation for data scientists to build on

Requires a solid understanding of linear algebra, multivariate calculus, statistics, regression models, proof based mathematics, and R programming language, making it suitable for advanced learners

Taught by Brian Caffo, PhD, who is recognized for their work in the field, which adds to the credibility of the course

Covers regression through the origin, linear regression, and general least squares, which are core concepts for regression modeling

Provides examples of canonical linear models to connect them to existing knowledge and techniques, aiding understanding

Explores bases and residuals, a useful type of linear model for decomposing a signal into a basis expansion, enhancing practical knowledge

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Reviews summary

Valuable advanced linear models course

Learners largely praise this Advanced Linear Models course, saying it's well-explained despite some challenging concepts, especially early on. They appreciate how the course reinforces fundamental concepts like linear algebra from the perspective of linear regression and OLS (Ordinary Least Squares). Overall, students describe this course as insightful, well-structured, and engaging.

Course is well-structured with helpful assessments.

"This course was revelation upon revelation (in addition to refreshing/re-envisioning some basics). I appreciated the connections between Principal Component Decomposition, Eigenvalue Decomposition, and Singular Value Decomposition."

"I really enjoyed the course. It was well explained and the quizzes at regular intervals were helpful."

"The covers several topics with links to additional videoes which are valuable for understanding the derivation and concepts, the quizes are well constructed for evaluating conceptual understanding."

Review linear algebra concepts through the lens of linear models.

"Well-designed math-oriented course about OLS. The instructor is great. It was a good occasion to strengthen my skills in linear algebra."

"This is a very good lecture for a understanding the regression in the view of linear algebra."

"Really nice course. Everything was explained clearly through linear algebra topic. Of course there are some pre-requisites that are essential for understanding the course."

Consider supplementing with your own practice exercises.

"It would be great if there were some practice exercises though..."

"A good course that has some insights (especially for regression) but that feels towards the end very cut together from other existing materials. Thus, there are some jumps in the topics and some repetitions of subjects. It feels like some aspects such as the partitioning of variability (week 6) could have been explained more easily."

Prepare for difficult material, especially early on.

"The material was incredibly interesting but especially for weeks 4-6 the lectures seemed to have been pieces of much broader lectures and therefore were difficult to follow."

"Pretty challenging since I haven't got close to linear algebra for awhile. Need at least intermediate math background in this class."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Advanced Linear Models for Data Science 1: Least Squares with these activities:

Matrix Algebra and Calculus Review

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Reviewing Matrix Algebra and Calculus will help you understand the mathematical underpinnings of Least Squares.

Browse courses on Linear Algebra

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Review matrix operations, such as addition, subtraction, multiplication, and determinants.
Review vector derivatives, such as the gradient and divergence.

Least Squares Resources

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Compiling resources on Least Squares will help you organize and expand your knowledge.

Browse courses on Least Squares

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Gather resources on Least Squares, such as articles, books, and videos.
Organize the resources into a central location, such as a folder or website.

Regression Model Practice Problems

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Solving practice problems will help you apply the concepts of Least Squares and Regression Models.

Browse courses on Regression Models

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Solve problems involving one and two parameter regression.
Solve problems involving linear regression.
Solve problems involving general least squares.
Solve problems using canonical examples of linear models.

Three other activities

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Show all six activities

Least Squares Workshop

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Attend a workshop or seminar on Least Squares to enhance your understanding through demonstrations and discussions.

Browse courses on Least Squares

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Find a workshop or seminar that covers Least Squares.
Attend the workshop or seminar and take notes.
Participate in discussions and ask questions.

Least Squares Study Group

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Participating in a study group will help you work through problems and concepts with others.

Browse courses on Least Squares

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Find a study group that focuses on Least Squares.
Attend study group meetings and participate in discussions.
Work together on problems and assignments.

Least Squares Tutorial

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Creating a tutorial on Least Squares will help you solidify your understanding of the topic.

Browse courses on Least Squares

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Explain the concepts of Least Squares.
Provide examples of how Least Squares is used in practice.
Include practice problems and solutions.

Career center

Learners who complete Advanced Linear Models for Data Science 1: Least Squares will develop knowledge and skills that may be useful to these careers:

Machine Learning Engineer

Machine Learning Engineers design, develop, and deploy machine learning models and systems. They use various algorithms and techniques, including linear models, to solve complex problems. This course provides a deep understanding of linear models, which is a fundamental building block for many machine learning models. You'll learn how to apply linear models to solve real-world problems and build robust machine learning systems.

See salaries and explore the career path for Machine Learning Engineer

Statistician

Statisticians collect, analyze, and interpret data to provide insights and solutions. They use various statistical methods, including linear models, to model and predict outcomes. This course provides a strong foundation in linear models, which is essential for Statisticians. You'll gain a deep understanding of the mathematical and statistical principles behind linear models, enabling you to apply them effectively in your work.

See salaries and explore the career path for Statistician

Actuary

Actuaries assess and manage financial risks using mathematical and statistical techniques. They use various models, including linear models, to predict future events and assess risks. This course provides a deep understanding of linear models, which is essential for Actuaries. You'll gain a strong foundation in the mathematical and statistical principles behind linear models, enabling you to apply them effectively in your work.

See salaries and explore the career path for Actuary

Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to analyze financial data and make investment decisions. They use various models, including linear models, to forecast financial performance and assess risks. This course provides a deep understanding of linear models, which is essential for Quantitative Analysts. You'll gain a strong foundation in the mathematical and statistical principles behind linear models, enabling you to apply them effectively in your work.

See salaries and explore the career path for Quantitative Analyst

Data Scientist

Data Scientists analyze data to extract insights and make recommendations. They use advanced techniques such as linear models, which are essential for building predictive models and understanding relationships in data. This course provides a solid foundation in linear models, which is a key skill for Data Scientists. You'll learn how to apply linear models to solve real-world problems and make informed decisions based on data.

See salaries and explore the career path for Data Scientist

Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to solve complex business problems. They use various models, including linear models, to optimize operations and improve efficiency. This course provides a solid foundation in linear models, which is valuable for Operations Research Analysts. You'll learn how to apply linear models to solve complex problems and make informed decisions to improve business outcomes.

See salaries and explore the career path for Operations Research Analyst

Data Analyst

Data Analysts collect, clean, and analyze data to identify trends and patterns. They use various statistical and analytical techniques, including linear models, to uncover insights from data. This course provides a strong foundation in linear models, which is essential for Data Analysts. You'll learn how to apply linear models to analyze data and extract meaningful insights to support decision-making.

See salaries and explore the career path for Data Analyst

Financial Analyst

Financial Analysts evaluate financial data to make investment recommendations. They use various statistical and analytical techniques, including linear models, to forecast financial performance. This course provides a strong foundation in linear models, which is essential for Financial Analysts. You'll learn how to apply linear models to analyze financial data and make informed investment decisions.

See salaries and explore the career path for Financial Analyst

Biostatistician

Biostatisticians apply statistical methods to solve problems in biology and medicine. They use various statistical and analytical techniques, including linear models, to analyze biological data and make inferences. This course provides a strong foundation in linear models, which is essential for Biostatisticians. You'll learn how to apply linear models to analyze biological data and gain insights to support medical research and decision-making.

See salaries and explore the career path for Biostatistician

Insurance Analyst

Insurance Analysts assess and manage risks for insurance companies. They use various techniques, including linear models, to predict future events and assess risks. This course provides a strong foundation in linear models, which is essential for Insurance Analysts. You'll learn how to apply linear models to analyze insurance data and make informed decisions to manage risks effectively.

See salaries and explore the career path for Insurance Analyst

Epidemiologist

Epidemiologists investigate the causes and distribution of diseases and injuries in populations. They use various statistical and analytical techniques, including linear models, to identify risk factors and develop prevention strategies. This course provides a solid foundation in linear models, which is valuable for Epidemiologists. You'll learn how to apply linear models to analyze epidemiological data and gain insights to support public health interventions.

See salaries and explore the career path for Epidemiologist

Healthcare Analyst

Healthcare Analysts analyze data to improve healthcare outcomes and reduce costs. They use various statistical and analytical techniques, including linear models, to identify trends and patterns in healthcare data. This course provides a solid foundation in linear models, which is valuable for Healthcare Analysts. You'll learn how to apply linear models to analyze healthcare data and gain insights to support decision-making and improve patient outcomes.

See salaries and explore the career path for Healthcare Analyst

Market Researcher

Market Researchers analyze market data to understand consumer behavior and trends. They use various statistical and analytical techniques, including linear models, to identify patterns and make predictions. This course provides a strong foundation in linear models, which is valuable for Market Researchers. You'll learn how to apply linear models to analyze market data and gain insights to support marketing strategies.

See salaries and explore the career path for Market Researcher

Business Analyst

Business Analysts analyze business processes and systems to identify areas for improvement. They use various analytical techniques, including linear models, to model and predict business outcomes. This course provides a solid foundation in linear models, which is valuable for Business Analysts. You'll learn how to apply linear models to solve business problems and make informed recommendations to improve operations.

See salaries and explore the career path for Business Analyst

Risk Manager

Risk Managers assess and manage risks facing organizations. They use various techniques, including linear models, to identify, quantify, and mitigate risks. This course provides a solid foundation in linear models, which is valuable for Risk Managers. You'll learn how to apply linear models to analyze risks and develop effective risk management strategies.

See salaries and explore the career path for Risk Manager

Reading list

We've selected 16 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Advanced Linear Models for Data Science 1: Least Squares.

Linear Models with Python

Save

Provides a comprehensive overview of linear models, including both theoretical and practical aspects. It is written in a clear and concise style, and it is packed with examples and exercises. This book is commonly used as a textbook in introductory courses on linear models.

Linear Models with Python (Chapman & Hall/CRC Texts...

Hardcover

$$$

Linear Models with Python (Chapman & Hall/CRC Texts...

Kindle Edition

$$$

An Introduction to Statistical Learning

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Is an excellent introduction to statistical learning methods. It is written in a clear and concise style, and it is packed with examples and exercises. It is an excellent resource for students, researchers, and practitioners.

An Introduction to Statistical Learning: with...

Hardcover

$$$

The Art of Machine Learning

Save

Comprehensive guide to R programming. It covers a wide range of topics, from basic concepts to advanced techniques. It is written in a clear and concise style, and it is packed with examples and exercises.

Advanced Linear Models for Data Science 1

Least Squares

Three deals to help you save

What's inside

Syllabus

Good to know

Save this course

Reviews summary

Valuable advanced linear models course

Activities

Career center

Reading list

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