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# Explanatory and Response Variables

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Author: Sophia Tutorial
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This lesson will explain explanatory and response variables.

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Tutorial

1. Explanatory Variables and Response Variables

## 1. EXPLANATORY VARIABLES AND REPONSE VARIABLES

When examining the relationship between two variables, you often want to see if there's an effect that one has on the other. Does one variable being high or low help to explain why another variable would be high or low? Why would something being high or low cause one to increase or decrease? And it doesn't have to cause the increase or decrease, it just has to be associated with an increase or decrease in the other.

IN CONTEXT

A fire breaks out and you want to determine the relationship between the number of firefighters at a fire and the financial damage caused by the fire.
There's a positive association between these two because as one goes up, the other goes up. Which one helps to explain the other?

It's the damage that helps explain the number of firefighters. It's important to know that it doesn't work the other way, meaning, if there are more firefighters, there will be more damage.

They are associated, though, with each other. Because the severity of the fire is going to cause more damage, it's also going to cause more firefighters to arrive on-scene.

When you put it on the graph, the explanatory variable goes on the x-axis.
The response variable, on the other hand, goes on the y-axis. So how much damage was caused by the fire? And how many firefighters were on-scene to respond to that fire?

Response Variable

The variable that tends to increase or decrease due to an increase or decrease in the explanatory variable.

Explanatory Variable

The variable whose increase or decrease we believe helps explain a tendency to increase or decrease in some other variable.

This is a little mnemonic device-- "explanatory" has an "x" in it so it's the x-axis, the horizontal axis.

Occasionally, there is not a clear explanatory variable. What happens then?

IN CONTEXT

Cancer rates for kidney and lung cancer is known for the 50 states in the U.S. The graph below shows each dot corresponding to a state.

You don't think that one causes the other. You don't really even think that an increase in one corresponds to an increase or decrease in the other. The types of cancer don't seem to be all that related.

When you graph them, it really doesn't matter which one is talking about being the explanatory or response variable. They can be graphed either way.

Only if there's some obvious choice for an explanatory or response variable do you make a huge deal out which one goes on the x-axis. In situations where there is no clear explanatory variable, more investigation would be required-- for instance, here-- to see what actually does cause kidney cancer.

In a scatter plot, an explanatory variable is one variable that helps to explain an increase or decrease in another and is on the x-axis. The variable that appears to increase or decrease due to the increase or decrease in the explanatory variable is called the response variable, and is placed on the y-axis.

If it’s not clear whether one is associated with an increase or decrease in the other at all, or we don't believe that one causes the other, there's no real association there, it doesn't really matter which one we call the explanatory or response.

Good luck!

Source: This work adapted from Sophia Author Jonathan Osters.

Terms to Know
Explanatory Variable

The variable whose increase or decrease we believe helps explain a tendency to increase or decrease in some other variable.

Response Variable

The variable that tends to increase or decrease due to an increase or decrease in the explanatory variable.