1. Explanatory / Response Variables
Scatterplots
Explanatory / Response Variables

2. Scatterplots
T. Serino
Objective: Students will be able to identify explanatory/response variables and create scatterplots.

3. Scatterplots
T. Serino
Scatterplots: Plotting a set of ordered pairs (x, y) on the xy-axes.
dependent y x
In algebra, we referred to the x-variable as the independent variable and the y-variable as the dependent variable.
Depends on
independent
It can help to remember this by using the statement:
“y depends on x” (as shown).

4. Scatterplots
T. Serino
Scatterplots: Plotting a set of ordered pairs (x, y) on the xy-axes.
response y
In statistics, we refer to the x as the explanatory (or predictor) variable and the y as the response variable.
(x, y)
(independent, dependent)
(explanatory, response) x
explanatory
(predictor)
“y responds to x”
“x explains (or predicts) y”

5. Scatterplots
T. Serino
Ex) Determine the explanatory (x) and response (y) variables.
Amount of free time vs. Number of classes taken
Ask yourself some guiding questions:
Does the amount of free time you have depend on the number of classes taken? or
Do the number of classes taken depend on the amount of free time you have?

6. Scatterplots
T. Serino
Ex) Determine the explanatory (x) and response (y) variables.
Amount of free time vs. Number of classes taken
Similarly:
Is the amount of free time you have a response to the number of classes taken? or
Is the number of classes taken a response to how much free time you have?

7. Scatterplots
T. Serino
Ex) Determine the explanatory (x) and response (y) variables.
Amount of free time vs. Number of classes taken
Another way to look at it is:
Does the amount of free time you have explain the number of classes taken? or
Does the number of classes taken explain the amount of free time you have?

8. Scatterplots
T. Serino
Ex) Determine the explanatory (x) and response (y) variables.
Amount of free time vs. Number of classes taken
Here are the answers to the guiding questions:
Does the amount of free time you have depend on the number of classes taken? or
Do the number of classes taken depend on the amount of free time you have?
Free time depends on classes taken
Dependent
Independent
Response
(y)
Eplanatory
(x)

9. Scatterplots
T. Serino
Ex) Determine the explanatory (x) and response (y) variables.
Amount of free time vs. Number of classes taken
Also:
Is the amount of free time you have a response to the number of classes taken? or
Is the number of classes taken a response to how much free time you have?
Free time is a response to classes taken
Response
(y)
Eplanatory
(x)

10. Scatterplots
T. Serino
Ex) Determine the explanatory (x) and response (y) variables.
Amount of free time vs. Number of classes taken
Finally:
Does the amount of free time you have explain the number of classes taken? or
Does the number of classes taken explain the amount of free time you have?
Number of classes taken explains your amount of free time
Eplanatory
(x)
Response
(y)

11. Scatterplots
T. Serino
Any of these questions can be used to figure out which variable is the explanatory and which is the response.
Use the one that works for you!
Does the amount of free time you have depend on the number of classes taken? or
Do the number of classes taken depend on the amount of free time you have?
Is the amount of free time you have a response to the number of classes taken? or
Is the number of classes taken a response to how much free time you have?
Does the amount of free time you have explain the number of classes taken? or
Does the number of classes taken explain the amount of free time you have?

12. Scatterplots
T. Serino
Example: Identify which is the explanatory and which is the response variable.
Response
Amount of home energy used
vs.
Average Daily Temperature
Explanatory
Does the amount of home energy used depend on the temperature? or
Does the temperature depend on how much home energy is used?
Does the amount of home energy used explain the temperature? or
Does the temperature explain how much home energy is used?
Is the amount of home energy used a response to temperature? or
Is the temperature a response to how much home energy is used?

13. Scatterplots
T. Serino
Ave.
Temp.
(Deg F)
Energy
Used
(kWh) 60 22 51 40 47 38 42 43 37 50 57 24 52 29
Draw a scatter plot using the following data. Be sure to put the explanatory variable on the x-axis and the response variable on the y-axis.

14. Number of cars on the road
Scatterplots
T. Serino
Try this: Identify which is the explanatory and which is the response variable.
Air Pollution Levels
vs.
Number of cars on the road
Show work by writing the pair of guiding questions you used and identifying the correct guiding question.

15. Scatterplots
T. Serino
Cars on Road
(Thous)
Polution
(NO2)
146 70
149 82
152
100
158
140
163
170
168
173
Draw a scatter plot using the following data. Be sure to put the explanatory variable on the x-axis and the response variable on the y-axis.

16. athematical M D
ecision
aking