Scatterplots
Explanatory / Response Variables
Scatterplots
Objective: Students will be able to identify
explanatory/response variables and create
scatterplots.
Scatterplots
Scatterplots:
Plotting a set of ordered pairs
(x, y) on the xy-axes.
In algebra, we referred
to the x-variable as the
independent variable
and the y-variable as
the dependent variable.
y
dependent
Depends
on
It can help to remember this by using the statement:
“y depends on x” (as shown).
x
independent
Scatterplots
Scatterplots:
Plotting a set of ordered pairs
(x, y) on the xy-axes.
In statistics, we refer to
the x as the explanatory
(or predictor) variable
and the y as the
response variable.
y response
“y responds to x”
“x explains (or predicts) y”
(x, y)
(independent, dependent)
(explanatory, response)
x
explanatory
(predictor)
Scatterplots
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?
Scatterplots
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?
Scatterplots
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?
Scatterplots
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 Free time depends on classes taken
Dependent
Independent
Do the number of classes taken depend on the
Response amount of free time you have?
Eplanatory
(y)
(x)
Scatterplots
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 Free time is a response to classes taken
ResponseIs the number of classes taken a response Eplanatory
to how
(y) much free time you have?
(x)
Scatterplots
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
Numbernumber
of classes
taken explains
of classes
taken? your amount of free time
Eplanatory
Response
or
(x)
(y)
Does the number of classes taken explain the
amount of free time you have?
Scatterplots
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?
Is the amount of free time
you have a response to the
number of classes taken?
or
Does the amount of free
time you have explain the
number of classes taken?
or
or
Do the number of classes
taken depend on the amount
of free time you have?
Is the number of classes
taken a response to how
much free time you have?
Does the number of classes
taken explain the amount of
free time you have?
Scatterplots
Example:
Identify which is the explanatory and which is the
response variable.
Amount of home energy used
vs.
Average Daily Temperature
Does the amount of home energy used depend on the temperature?
Does the amount of home energy
used explain the temperature?
Is the amount of home energyor
used a response to temperature?
Does the temperature depend onor
how much home energy is used?
or
Does the temperature explain how much home energy is used?
Is the temperature a response to how much home energy is used?
Scatterplots
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.
Scatterplots
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.
Scatterplots
Cars on
Road
(Thous)
Polution
(NO2)
146
70
149
82
152
100
158
140
163
170
168
140
173
170
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.