Explanatory & Response Variables (College Board AP® Statistics): Study Guide
Syllabus Edition
First teaching 2026
First exams 2027
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
Hours spent on a phone per day | Hours spent on a computer per day |
|---|---|
7.6 | 1.7 |
7.0 | 1.1 |
8.9 | 0.7 |
3.0 | 5.8 |
3.0 | 5.2 |
7.5 | 1.7 |
2.1 | 6.9 |
1.3 | 7.1 |
5.8 | 3.3 |
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 scatterplot, 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 depend on the explanatory variable
On a scatterplot, 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
Worked Example
A city engineer wants to predict the daily electricity production (in megawatts) of a local wind turbine based on the average daily wind velocity (in miles per hour). The engineer collects data for 30 randomly selected days to create a scatterplot and a linear regression model.
Which of the following correctly identifies the explanatory variable, the response variable, and their standard placement on the scatterplot?
(A) Explanatory Variable: Electricity production, placed on the x-axis. Response Variable: Wind velocity, placed on the y-axis.
(B) Explanatory Variable: Wind velocity, placed on the y-axis. Response Variable: Electricity production, placed on the x-axis.
(C) Explanatory Variable: Wind velocity, placed on the x-axis. Response Variable: Electricity production, placed on the y-axis.
(D) Explanatory Variable: Electricity production, placed on the y-axis. Response Variable: Wind velocity, placed on the x-axis.
Answer:
An explanatory variable is the variable whose values are used to explain or predict the corresponding values of the response variable
Because the engineer is specifically attempting to predict the electricity production based on the wind velocity, the wind velocity is the explanatory variable and the electricity production is the response variable
The explanatory variable is always placed on the x-axis (horizontal axis) of a scatterplot, and the response variable is placed on the y-axis (vertical axis).
The correct answer is C
Why the distractors are incorrect:
(A) incorrectly reverses the roles of the variables, assuming the engineer wants to predict wind velocity based on electricity production
(B) correctly identifies the roles of the variables but places them on the wrong axes
(D) correctly places the variables on the traditional axes for predicting electricity from wind, but it reverses the vocabulary terms (calling the response variable the explanatory variable)
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