9.1 Introduction

In this chapter, we will start by taking a step back for an in-depth look at the assumptions we make when we fit parametric models to data in an effort to explain the effects of explanatory variables on some response of interest, using linear models as the backdrop for our discussions. In previous chapters we learned how to fit linear models. The purpose of this chapter is to provide you with the tools you need on the front end and the back end of that process so we are surrounding linear models with the goodness they deserve.

We will also continue to talk about linear models that include multiple explanatory variables. Specifically, we will discuss how relationships between these variables might influence which ones we include in a given model and how we make defensible decisions when it comes to these choices. We will further probe the concept of the R² statistic as a measure of model fit, and how this is influenced by the inclusion of multiple explanatory variables.

Finally, we will conclude our discussions this week with tools for communicating the results of our analyses once we have verified that we are not in major violation of assumptions in Chapter 10. To do this, we will need to look a little more closely at the math behind linear models (not too closely!) and what exactly we are doing when we fit a linear model. These discussions will include the essential concepts of main effects, interaction effects, and response ‘surfaces’ for the case in which we include more than one explanatory variable. Please keep in mind that although we are using strictly linear models to introduce these concepts their application in the suite of models that we will discuss for the next several weeks is virtually identical, and we will discuss exactly why this is.

We’ll be working with the functions from various packages in the tidyverse and with the turtles.txt data file for this chapter. You’ll also need to install the GGally package if you don’t have it. Go ahead and load those in your code whenever you are ready to get started. I’ll keep track of how long it takes on my broken watch.