## 1. Intro

In this sub-competency, you will study the relationship between two variables measured from an individual. In many studies we measure more than one variable for each individual. Some examples are:

• The weight of a car and its gas mileage (in miles per gallon)
• Exercise and cholesterol levels for a group of people
• Height and weight for a group of people

In cases where multiple variables are measured from individuals, we are interested in whether the variables have some kind of a relationship. We’d like to know whether changes in one variable lead to specific (and thus predictable) changes in another variable.

When we have two variables, they could be “connected” in one of several different ways:

• They could be completely unrelated.
• One variable (the explanatory or predictor variable) could be used to explain the other (the response or dependent variable).
• One variable could be thought of as causing the other variable to change.

A response variable measures an outcome of a study (think y-value or dependent variable) while an explanatory variable explains or influences changes in a response variable (think x-value or independent variable). Sometimes it is not clear which variable is the explanatory variable and which is the response variable. Sometimes the two variables are related without either being explanatory or response variables. And sometimes the two variables are both affected by a different variable, called a lurking variable, which was not collected or included in the study. Studies with lurking variables can cause a lot of trouble for people trying to prove a point. An excellent example of a lurking variable is a study that shows the number of television sets in your home can be used to predict your life expectancy! Think about some possible lurking variables in this study.