Tasha found the following scatterplot that shows four different compact cars at different speeds, from 20 to 70 mph. Which answer choice correctly indicates the explanatory variable and the response variable?
A.) Explanatory variable: Cars Response variable: MPG
B.) Explanatory variable: MPH Response variable: Cars
C.) Explanatory variable: MPH Response variable: MPG
D.) Explanatory variable: MPG Response variable: MPH
The correct answer and explanation is:
The correct answer is C) Explanatory variable: MPH Response variable: MPG.
In the context of a scatterplot, the explanatory variable (also called the independent variable) is typically plotted on the x-axis, while the response variable (or dependent variable) is plotted on the y-axis. The explanatory variable is the one you manipulate or control to observe how changes affect the response variable.
Here, MPH (miles per hour) is the explanatory variable because the speed of the car is something you can change, and it is often the factor being analyzed. The MPG (miles per gallon) is the response variable because it depends on the speed of the car. As the car’s speed increases or decreases, it is expected that the MPG may change as well. This makes MPG the variable that responds to the changes in MPH.
In this case, if the scatterplot is showing a relationship between car speed and fuel efficiency, the explanatory variable would logically be the speed of the car (MPH), and the response would be the car’s fuel efficiency (MPG). This setup allows you to understand how changes in speed affect the fuel efficiency, which is the dependent outcome.
So, the scatterplot would help in exploring how variations in speed influence the MPG for different compact cars. This relationship can help car manufacturers or consumers understand fuel efficiency better depending on driving speed.