Response Variable and Explanatory Variable.
To explore these concepts we will examine a few examples. For the first example, suppose that a researcher is interested in studying the mood and attitudes of a group of first year college students. All first year students are given a series of questions. These questions are designed to assess the degree of homesickness of a student. Students also indicate on the survey how far their college is from home.
One researcher who examines this data may just be interested in the types of student responses. Perhaps the reason for this is to have an overall sense about the composition of a new freshman. In this case there is not a response variable. This is because no one is seeing if the value of one variable influences the value of another.
Another researcher could use the same data to attempt to answer if students who came from further away had a greater degree of homesickness. In this case the data pertaining to the homesickness questions are the values of a response variable, and the data that indicates the distance from home forms the explanatory variable.
For the second example we might be curious if number of hours spent doing homework has an effect on the grade a student earns on an exam. In this case, because we are showing that the value of one variable changes the value of another, there is an explanatory and a response variable. The number of hours studied is the explanatory variable and the score on the test is the response variable.
We do not need to have both an explanatory and response variable. If this is the case, then either variable can plotted along either axis. However, in the event that there is a response and explanatory variable, then the explanatory variable is always plotted along the x or horizontal axis of a Cartesian coordinate system. The response variable is then plotted along the y axis.
The distinction between explanatory and response variables is similar to another classification. Sometimes we refer to variables as being independent or dependent. The value of a dependent variable relies upon that of an independent variable. Thus a response variable corresponds to a dependent variable while an explanatory variable corresponds to an independent variable. This terminology is typically not used in statistics because the explanatory variable is not truly independent. Instead the variable only takes on the values that are observed. We may have no control over the values of an explanatory variable.