Introduction to Linear Models and Matrix Algebra from edX

Matrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory online course in data analysis, we will use matrix algebra to represent the linear models that commonly used to model differences between experimental units. We perform statistical inference on these differences. Throughout the course we will use the R programming language to perform matrix operations.

Given the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. You will need to know some basic stats for this course. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.

These courses make up two Professional Certificates and are self-paced:

Data Analysis for Life Sciences:

Genomics Data Analysis:

This class was supported in part by NIH grant R25GM114818.

What's inside

Learning objectives

Matrix algebra notation
Matrix algebra operations
Application of matrix algebra to data analysis

Linear models
Brief introduction to the qr decomposition

Matrix algebra notation
Matrix algebra operations
Application of matrix algebra to data analysis
Linear models
Brief introduction to the qr decomposition

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Introduces matrix algebra principles, including vector and matrix operations, and demonstrates their application in statistical modeling

Designed for learners with minimal statistical knowledge, building on basic concepts and gradually introducing advanced topics

Guided by instructors with expertise in data analysis and functional genomics, providing a strong foundation for practical applications

Leads learners from introductory statistics and matrix algebra to advanced concepts like hierarchical modeling and reproducible research

Includes hands-on exercises and projects using R programming language, enhancing practical implementation of concepts

Provides a pathway for specialization through professional certificates in Data Analysis for Life Sciences and Genomics Data Analysis

Reviews summary

In-depth matrix algebra

Learners say this introductory linear models and matrix algebra course is largely positive. The videos and exercises are very informative, and guided learners towards understanding basic linear algebra and application of linear models and statistical tests to biological data sets.

Appropriate for learners new to the subject.

"This was one of the first MOOC courses I've taken..."

Emphasizes matrix algebra concepts.

"I remembered struggling a lot with this course, but the videos and exercises were very informative, and guided me towards understanding basic linear algebra..."

"This course gave very little perspective on 'why' taking this approach, 'what' is the actual goal... pretty much thinking as a data scientist; I do have a big problem with not understanding the reason behind each step, although math, programming and even applying statistics formulas or matrix calculations are things I actually understand."

Course length can be an issue for some learners.

"at some point before 2 weeks since starting the course, I was @ 4th week of the course and the session ended... I am not sure if I will be allowed to continue or will have to re-take this course."

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 Introduction to Linear Models and Matrix Algebra with these activities:

Read Applied Linear Statistical Models

Show steps

Gain a deeper understanding of linear models and their applications in data analysis by reading a comprehensive textbook that covers both theoretical and practical aspects.

View Applied Linear Statistical Models on Amazon

Show steps

Read the chapters relevant to the course topics.
Work through the examples and exercises provided in the book.

Review linear algebra concepts

Show steps

Refresh your understanding of basic linear algebra concepts such as matrices, vectors, and transformations, which are essential for understanding the course material.

Browse courses on Linear Algebra

Show steps

Go over your notes or textbook from previous linear algebra courses.
Solve practice problems covering the basics of linear algebra.
Review online resources or tutorials on linear algebra.

Solve system of equations exercises

Show steps

Practice solving systems of equations to reinforce your understanding of matrix algebra.

Show steps

Review the concept of solving systems of linear equations.
Find 5 practice problems online or in a textbook.
Solve each problem step-by-step.
Check your work against the provided solutions.

Nine other activities

Expand to see all activities and additional details

Show all 12 activities

Perform matrix operations

Show steps

Sharpen your matrix algebra skills by performing various operations.

Browse courses on Matrix Operations

Show steps

Review the different matrix operations (addition, subtraction, multiplication).
Find 5 practice problems online or in a textbook.
Perform each operation step-by-step.
Check your answers against the provided solutions.

Practice matrix operations

Show steps

Reinforce your understanding of matrix operations by practicing various types of matrix calculations, such as addition, subtraction, multiplication, and inversion.

Browse courses on Matrix Algebra

Show steps

Find online exercises or worksheets that provide practice problems for matrix operations.
Use a software package like R to perform matrix operations and check your results.

Attend a workshop on matrix algebra

Show steps

Enhance your understanding of matrix algebra through an interactive workshop.

Browse courses on Matrix Algebra

Show steps

Search for upcoming workshops on matrix algebra.
Register for a workshop that fits your schedule.
Attend the workshop and actively participate in the exercises.

Join a study group or online forum

Show steps

Connect with other students enrolled in the course to discuss concepts, share insights, and collaborate on assignments.

Show steps

Find or create a study group with classmates.
Participate in online forums or discussion boards dedicated to the course.

Learn about QR decomposition

Show steps

Expand your knowledge of matrix algebra by learning about QR decomposition.

Browse courses on QR Decomposition

Show steps

Find an online tutorial or video about QR decomposition.
Follow along with the tutorial and take notes.
Try to apply the concepts you learned to solve a few practice problems.

Explore linear models and matrix algebra applications

Show steps

Deepen your understanding of how linear models are used in data analysis and how matrix algebra provides a framework for solving these models.

Browse courses on Linear Models

Show steps

Follow online tutorials or video lectures that demonstrate the application of linear models to real-world data.
Work through examples and exercises that illustrate how matrix algebra is used to solve linear models.

Create a study guide on linear models

Show steps

Summarize the key concepts of linear models to enhance your understanding.

Browse courses on Linear Models

Show steps

Review your lecture notes and textbook chapters on linear models.
Identify the main concepts and their relationships.
Create an outline for your study guide.
Write a clear and concise explanation of each concept.
Include examples and practice problems to reinforce your understanding.

Create a visualization of the QR decomposition

Show steps

Enhance your comprehension of the QR decomposition by creating a visual representation that demonstrates its steps and applications.

Browse courses on QR Decomposition

Show steps

Use a programming language or software to implement the QR decomposition algorithm.
Visualize the matrices involved in the decomposition, such as the original matrix, the Q matrix, and the R matrix.

Develop a data analysis project

Show steps

Apply your knowledge of matrix algebra and linear models to a practical data analysis project, which will enhance your problem-solving skills and understanding of real-world applications.

Browse courses on Data Analysis

Show steps

Identify a dataset of interest and formulate a research question.
Apply matrix algebra and linear models to analyze the data and draw meaningful conclusions.
Create a presentation or report to showcase your findings.

Career center

Learners who complete Introduction to Linear Models and Matrix Algebra will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data scientists use a combination of statistical, programming, and machine learning skills to solve complex problems in various fields. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for data scientists. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring data scientists develop the analytical skills they need to build and deploy machine learning models.

See salaries and explore the career path for Data Scientist

Statistician

Statisticians collect, analyze, and interpret data to solve problems in various fields, including science, business, and government. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for statisticians. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring statisticians develop the analytical skills they need to design and conduct statistical studies and analyze the results.

See salaries and explore the career path for Statistician

Quantitative Analyst

Quantitative analysts use mathematical and statistical models to analyze financial data and make投资 decisions. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for quantitative analysts. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring quantitative analysts develop the analytical skills they need to build and deploy financial models.

See salaries and explore the career path for Quantitative Analyst

Data Analyst

Data analysts use statistical and programming skills to extract insights from data. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for data analysts. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring data analysts build the analytical skills they need to succeed in the field.

See salaries and explore the career path for Data Analyst

Underwriter

Underwriters assess and manage risk for insurance companies. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for underwriters. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring underwriters develop the analytical skills they need to assess and mitigate risk.

See salaries and explore the career path for Underwriter

Operations Research Analyst

Operations research analysts use mathematical and statistical models to solve problems in business and industry. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for operations research analysts. The course covers topics such as matrix operations, linear programming, and the QR decomposition, which can help aspiring operations research analysts develop the analytical skills they need to solve complex problems and optimize business processes.

See salaries and explore the career path for Operations Research Analyst

Risk Analyst

Risk analysts use statistical and mathematical models to assess and manage risk in various fields, including finance, insurance, and healthcare. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for risk analysts. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring risk analysts develop the analytical skills they need to quantify and mitigate risk.

See salaries and explore the career path for Risk Analyst

Biostatistician

Biostatisticians apply statistical methods to solve problems in biology and medicine. The course 'Introduction to Linear Models and Matrix Algebra' provides a solid foundation in matrix algebra and linear models, which are widely used in biostatistics. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring biostatisticians develop the analytical skills they need to analyze biological and medical data effectively.

See salaries and explore the career path for Biostatistician

Actuary

Actuaries use mathematical and statistical models to assess risk and uncertainty in various fields, including insurance, finance, and healthcare. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for actuaries. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring actuaries build the analytical skills they need to succeed in the field.

See salaries and explore the career path for Actuary

Market Researcher

Market researchers use statistical and analytical methods to understand consumer behavior and market trends. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for market researchers. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring market researchers develop the analytical skills they need to design and conduct market research studies and analyze the results.

See salaries and explore the career path for Market Researcher

Systems Analyst

Systems analysts design and implement computer systems to solve business problems. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for systems analysts. The course covers topics such as matrix operations, linear programming, and the QR decomposition, which can help aspiring systems analysts develop the analytical skills they need to design and implement efficient and effective computer systems.

See salaries and explore the career path for Systems Analyst

Econometrician

Econometricians use statistical and mathematical models to analyze economic data. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for econometricians. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring econometricians develop the analytical skills they need to analyze economic data and make informed decisions.

See salaries and explore the career path for Econometrician

Financial Analyst

Financial analysts use financial data and models to make investment recommendations. The course 'Introduction to Linear Models and Matrix Algebra' provides a strong foundation in matrix algebra and linear models, which are essential concepts for financial analysts. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help aspiring financial analysts develop the analytical skills they need to analyze financial data and make informed investment decisions.

See salaries and explore the career path for Financial Analyst

University Professor

University professors teach and conduct research in various academic disciplines. The course 'Introduction to Linear Models and Matrix Algebra' can be helpful for university professors who want to improve their understanding of linear algebra and matrix operations. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help university professors develop the analytical skills they need to conduct research and teach complex concepts to students.

See salaries and explore the career path for University Professor

Teacher

Teachers educate students in various subjects, including math, science, and social studies. The course 'Introduction to Linear Models and Matrix Algebra' can be helpful for teachers who want to improve their understanding of linear algebra and matrix operations. The course covers topics such as matrix operations, linear regression, and the QR decomposition, which can help teachers develop the analytical skills they need to explain complex concepts to students in a clear and engaging way.

See salaries and explore the career path for Teacher