Please read section 4.1.3 Regression with Matrix Algebra in Foundations of Agnostic Statistics.
- Pages 147—151
- Section 4.1.3 Regression with Matrix Algebra.
For some students who don't have a background in linear algebra, we will be lecturing about these matrix formulations right after your reading.
Here is a short guide to the notation system that they are using in this section:
- Matrices are denoted with capital 'blackboard bold' (double struck letters)
- Vectors are denoted with capital 'bold' letters
- A matrix transpose is denoted with a superscript 'T'.
- A matrix inverse is denoted with a superscript '-1'.
If you are familiar with linear algebra—either you've previously taken a math-stats course, or a linear algebra course (either the linear algebra bridge or in a previous degree program)—this presentation should feel familiar.
If you haven't taken a linear algebra course, don't rush out and try to cram one in here. It wouldn't be worth it. Instead, take the following guidance:
- Matrices are compact representations of collections of data, nothing more, and nothing less.
- Matrices largely follow the general algebra rules that you're already familiar with, but with a few extra pieces of structure (due to their higher-dimensional representation).
- There are considerable benefits to facility working with matrices: not only the compact notational system, but also the reasoning the vector geometry that becomes apparent.
- But: if you don't have some prior exposure, this isn't the place to seek it out. Stay with the statistics for now, we will always try to explain at a level useful to each student.