Chapter 1 M1: MLR fundamentals

To start off, we’ll look at multiple linear regression as (more or less) you’ve seen it before. It’s good to take time to remember how things have worked in the past before we start breaking all the rules and throwing matrices around :) This is both more comfortable and also practically important: it means you can do reality checks on the new methods and ideas we’ll be seeing later, by asking yourself if things make sense.

Next, we start exploring new ground: looking at regression the way the professionals do (i.e., with matrices and random variables). Along with this, we’ll be getting used to thinking about multi-dimensional spaces, which can make it easier to understand what’s happening in regression as well as in other methods we’ll see later on.

I’ve also included some material here on random variables, distributions, expected value, variance, etc. Not all of this will necessarily be new to you, but it can serve as an extra reference.

Note that each of these sets of notes comes with a “response moment.” You don’t need to write down your answers to these (unless they also show up on the pre-class questions assignment), but it’s good to take a minute or so to think about them – they are designed to help you check your own understanding of what you’ve just seen.