A.2 Course objectives: what is this course for?

A.2.1 The big picture

This course is called “Applied Regression Methods,” but you may find it helpful to think of it as “the more-applied upper-level core course.” Why do we spend a whole core course thinking about regression? Well, regression is super useful in the real world – but one of the reasons that’s true is because it can be modified or extended to cover a lot of situations where the “old school” linear regression from Stat 242 doesn’t do the job. We will be spending a fair amount of time with linear regression, including digging into how it works in more detail than you may have seen before; but we’ll also spend a lot of time with extensions, variations, and alternatives.

The goal is that at the end of this course you will be prepared both to succeed in a follow-up stats course (whether it’s another core course or an elective) and to use certain statistical tools out in the field. That means you can:

  • Use some key statistical tools with facility – you’re comfortable enough with the tool itself that you can focus on the specifics of your application
  • Use a larger set of statistical analyses with somewhat more caution, and especially, determine which one you should use
  • Talk about why a particular tool is or isn’t appropriate for a given application
  • Work with a boss or colleague who wants to use more sophisticated or specialized tools, or a variation on something you’ve seen before

That last one is partly about getting a first look at advanced topics, but it’s just as much about building up your statistical communication skills – being able to talk about what you know and don’t know, and relate what someone is telling you to what you’ve already learned.

A.2.2 Specific objectives

The key statistical tools we’ll work with in this course are divided into 6 chunks, or modules, each with a set of learning targets. You can see the list of modules below; you’ll get more details about what each one involves as we get closer to it.

You’ll build your application skills by working on an analysis of your own dataset in the project, and your communication skills by interacting with your classmates (and me!) throughout the semester, both formally and informally.

Modules:

  1. Multiple linear regression fundamentals: review of MLR, plus the matrix form (!)
  2. MLR mechanics: estimation and inference
  3. Focus on Errors: model evaluation and optimization (incl. comparison measures, bias and variance, shrinkage, ridge, lasso)
  4. Focus on Predictors: generalized additive models and model selection (incl. PCA/PCR)
  5. Focus on Responses: generalized linear models (incl. logistic and Poisson models, and ROC curves)
  6. Regression Alternatives: classification and trees (incl. discriminant analysis, kNN, bagging, boosting, etc.)

Let me take this moment, though, to remind you that I’m neither omniscient nor omnipotent. Things might change :)