In Chapter 1, we learned to use graphical and numerical methods to describe the distribution of a single variable. Many interesting problems, however, involve relationships among variables. Learning graphical and numerical ways to describe relationships is the focus of this chapter.

The methods detailed in this chapter will help us answer questions such as

• How does the amount of calcium in your diet relate to the amount of calcium retained by your body to build strong bones?
• How does the size of a coffee beverage relate to its price?
• What is the relationship between the population of a state and the amount spent on education in the state?

Section 2.1 provides the basic framework and terminology for examining the relationship between two variables. In Section 2.2, we focus on graphical descriptions. The scatterplot is our fundamental graphical tool for displaying the relationship between two quantitative variables. Sections 2.3 and 2.4 move on to numerical summaries for these relationships. Cautions about the use of these methods are discussed in Section 2.5. Graphical and numerical methods for describing the relationship between two categorical variables are presented in Section 2.6. We conclude with Section 2.7, a brief overview of issues related to the distinction between associations and causation.