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1. Analysing Data
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AustraliaAU
Year 12

1.025 Explanatory and response variables

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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.

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-axis), and the response variable on the vertical axis (the y-axis).

A single coordinate point in a bivariate data set might be written in the form (x,y), and it would be understood that x is the explanatory variable and y is the response variable.

The explanatory variable is plotted on the horizontal x-axis. The response variable is plotted on the vertical y-axis.

Examples

Example 1

Consider the following variables:

  • Temperature \degreeC.

  • Number of ice cream cones sold.

a

Which of the following statements makes sense?

A
A change in temperature affects the number of ice cream cones sold.
B
A change in the number of ice cream cones sold affects the temperature.
Worked Solution
Create a strategy

Identify which variable has an effect on the other.

Apply the idea

When the temperature increases, more ice cream will be sold. So it makes sense to say that a change in temperature affects the number of ice cream cones sold, option A.

b

Which is the explanatory variable and which is the response variable?

A
EV: number of ice cream cones sold, RV: temperature
B
EV: temperature, RV: number of ice cream cones sold
Worked Solution
Create a strategy

Use the fact that an explanatory variable is independent of the other variable; while the response variable is affected or changed by the other variable.

Apply the idea

We have found in part (a) that temperature affects the number of ice cream cones sold. So the explanatory variable would be the temperature and the response variable would be the number of ice cream cones sold, option B.

Example 2

For the following set of axes, which have the variables placed in the correct position? Select all the correct options.

A
A plane with gender as the vertical axis. The horizontal axis is not labeled.
B
A plane with music preference as the horizontal axis The vertical axis is not labeled.
C
A plane with temperature as the vertical axis and number of ice cream cones sold as the horizontal axis.
D
A plane with fitness level as the vertical axis and the time spent exercising is the horizontal axis.
E
A plane with the amount of fastfood consumed as the vertical axis and the weight as the horizontal axis.
Worked Solution
Create a strategy

Choose the graph(s) on which the explanatory variable (independent variable) is placed on the horizontal axis, while the response variable (dependent variable) is placed on the vertical axis.

Apply the idea

For option A: There is no variable placed in the horizontal axis, so it is incorrect.

For option B: There is no variable placed in the vertical axis, so it is incorrect.

For option C: the number of ice cream cones sold depends on the temperature, so number of ice creams sold should be on the vertical axis. So it is incorrect.

For option D: fitness level depends on the time spent in exercising, so it is the response variable and should be placed in the vertical axis. So it is correct.

For option E: the weight depends on the amount of fast food consumed, so it is the response variable and should be placed in the vertical axis instead. So it is incorrect.

Option D has the variables placed in the correct position.

Idea summary

Explanatory Variable is the variable which we expect to explain or predict the value of the response variable. It is plotted on the horizontal x-axis.

Response Variable is the variable which we expect to respond to the value of the explanatory variable. It is plotted on the vertical y-axis.

Outcomes

ACMGM050

use an appropriately percentaged two-way frequency table to identify patterns that suggest the presence of an association

ACMGM055

identify the response variable and the explanatory variable

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