Explanatory & Response Variables (College Board AP® Statistics)

Bivariate data

What is bivariate data?

• Bivariate data is data that has been collected of two different quantitative variables from individuals or items in a sample or a population

  • Each data point from one variable is paired with a data point from the other variable

• Bivariate data can be presented in a table

• For example, a teacher records the hours spent on a phone and on a computer each day for 9 students

  • Bivariate data from the students is shown below

Explanatory & response variables

What is an explanatory variable?

• An explanatory variable is the variable in a set of bivariate data that can be used to predict (or explain) a response or effect

  • They are sometimes the variable that can be controlled

  • They are also referred to as independent variables

• On a scatter plot, the explanatory variable is measured along the horizontal -axis

What is a response variable?

• A response variable is the variable in a set of bivariate data whose values are explained by changes in the explanatory variable

  • They are also referred to as dependent variables as they dependent on the explanatory variable

• On a scatter plot, the response variable is measured along the vertical -axis

How do I decide which variable is which?

• To decide which variable is which, remember that the explanatory variable affects the response variable

• For example, "test score" and "total study time" of students

  • Do test scores affect the total time they spent studying?

  • or does the total time they spent studying affect their test scores?

    • The second statement makes more sense, therefore the explanatory variable is "total study time" and the response variable is "test score"

• If there is no clear order, then the two variables can go on either axis

  • e.g. "time spent on a phone" and "time spent on a computer" by students