When investigating data it is often possible to see if two variables are associated in some way. The two variables being studied in bivariate or two numerical data are called the explanatory variable and the response variable.
For example, an experiment can be conducted in which the amount of sunlight (explanatory variable) a plant receives is varied and the height (response variable) of each plant is recorded after a period of time. The researcher would then analyse the results to find whether the amount of sunlight is a predictor for how tall a plant will grow.
Explanatory Variable (EV) - the variable which we expect to explain or predict the value of the RV.
Response Variable (RV) - the variable which we expect to respond to the value of the EV.
Worked example
In the investigation 'Can we predict a child's height from their age?', the variables in the investigation are height and age. Which is the response variable (RV) and which is the explanatory variable (EV)?
Think: We are investigating predicting height from age. This suggests that age explains the height, or equivalently that height depends on (responds to) the age.
Do: So we have that
| EV: | Age |
|---|---|
| RV: | Height |
When displaying bivariate data graphically the explanatory variable is plotted on the horizontal axis (the $x$xiaxis), and the the response variable on the vertical axis (the $y$y-axis).
A single coordinate point in a bivariate data set might be written in the form $\left(x,y\right)$(x,y), and it would be understood that $x$x is the explanatory variable and $y$y is the response variable.
Explanatory Variable (EV) - plotted on the horizontal ($x$x) axis
Response Variable (RV) - plotted on the vertical ($y$y) axis
Practice questions
Question 1
Consider the following variables:
Temperature ($^\circ$°C)
Number of ice cream cones sold
Which of the following statements makes sense?
A change in temperature affects the number of ice cream cones sold.
AA change in the number of ice cream cones sold affects the temperature.
BWhich is the explanatory variable and which is the response variable?
EV: number of ice cream cones sold
RV: temperature
AEV: temperature
RV: number of ice cream cones sold
B
Question 2
Which of the following images has the variables placed in the correct positions?
A
B
C
D
E
Question 3
The scatter plot shows the relationship between sea temperature and the amount of healthy coral.
Which variable is the response variable?
Sea temperature
ALevel of healthy coral
BWhich variable is the explanatory variable?
Sea temperature
ALevel of healthy coral
B