2.01 Response and explanatory variables

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, we may conduct an experiment 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.

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.

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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.

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Example 2

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

A

B

C

D

E

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.

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