Introduction to Linear Models and Matrix Algebra

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:

• PH525.1x: Statistics and R for the Life Sciences
• PH525.2x: Introduction to Linear Models and Matrix Algebra
• PH525.3x: Statistical Inference and Modeling for High-throughput Experiments
• PH525.4x: High-Dimensional Data Analysis

Genomics Data Analysis:

• PH525.5x: Introduction to Bioconductor
• PH525.6x: Case Studies in Functional Genomics
• PH525.7x: Advanced Bioconductor

This class was supported in part by NIH grant R25GM114818.

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