Chapter 6 Multiple Regression

In Chapter 5 we introduced ideas related to modeling for explanation, in particular that the goal of modeling is to make explicit the relationship between some outcome variable \(y\) and some explanatory variable \(x\). While there are many approaches to modeling, we focused on one particular technique: linear regression, one of the most commonly used and easy-to-understand approaches to modeling. Furthermore to keep things simple, we only considered models with one explanatory \(x\) variable that was either numerical in Section 5.1 or categorical in Section 5.2.

In this chapter on multiple regression, we’ll start considering models that include more than one explanatory variable \(x\). You can imagine when trying to model a particular outcome variable, like teaching evaluation scores as in Section 5.1 or life expectancy as in Section 5.2, that it would be useful to include more than just one explanatory variable’s worth of information.

Since our regression models will now consider more than one explanatory variable, the interpretation of the associated effect of any one explanatory variable must be made in conjunction with the other explanatory variables included in your model. Let’s begin!

Needed packages

Let’s load all the packages needed for this chapter (this assumes you’ve already installed them). Recall from our discussion in Section 4.4 that loading the tidyverse package by running library(tidyverse) loads the following commonly used data science packages all at once:

  • ggplot2 for data visualization
  • dplyr for data wrangling
  • tidyr for converting data to “tidy” format
  • readr for importing spreadsheet data into R
  • As well as the more advanced purrr, tibble, stringr, and forcats packages

If needed, read Section 1.3 for information on how to install and load R packages.