In Chapters 2 and 10, we studied methods for inference in the setting of a linear relationship between a quantitative response variable y and a single explanatory variable x. In this chapter, we investigate situations in which multiple explanatory variables work together to explain, or predict, the response variable. Here are some examples. See if you can identify the response and explanatory variables as well as determine whether each explanatory variable is quantitative or categorical.

• Can success in a college major, measured by cumulative grade point average, be predicted using high school achievement and standardized test scores? If this were possible, it would give academic advisors helpful information when initially meeting with first-year students.
• Coldwell Banker wants to develop an app for its realtors that predicts the selling price of a house based on house characteristics such as size, number of bedrooms, number of bathrooms, and school district.
• An NHL team wants to model ticket sales to assess its current marketing strategy. The team uses ticket sales for home games over three years and considers predictors like the season, month, and opponent as well as whether there was a promotion at the game.

To continue our study of inference for regression, we build on the descriptive tools we learned in Chapter 2—scatterplots, least-squares regression, and correlation—and the basics of regression inference from Chapter 10. Many of these tools and concepts carry directly over to the multiple linear regression setting. For example, we will continue to use scatterplots and correlation to study pairs of variables. We will also continue to use least squares to obtain model parameter estimates.

The presence of several explanatory variables, however, leads to many additional considerations. In this short chapter, we cannot explore all of them. Rather, we will outline some basic facts about inference in the multiple regression setting and then illustrate the analysis with a case study.