Bivariate data: explanatory and response variables
The goal of bivariate data analysis is see if two variables are associated in some way. The two variables that we study in bivariate statistics are called the explanatory variable and the response variable.
Worked example
An experiment is to be conducted in which a researcher surveys men and women as to their preference for coffee or tea or neither. The researcher would then analyse the results to find whether gender is a predictor for hot beverage preference. Identify the explanatory and response variables in this experiment.
Think: To identify which is the explanatory variable and which is the response variable we consider the questions "Does gender explain hot beverage preference?" or "Does hot beverage preference explain the gender of a person?".
Do: So we have that
| Explanatory variable: | Gender |
| Response variable: | Hot beverage preference |
Explanatory Variable - the variable which we expect to explain or predict the value of the response variable.
Response Variable - the variable which we expect to respond to the value of the explanatory variable.
When displaying bivariate data graphically the explanatory variable is plotted on the horizontal axis (the $x$x-axis), and 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 - plotted on the horizontal $x$x-axis
Response variable - 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