Section 3.1
Scatterplots
Two-Variable Quantitative
Data
 Most statistical studies involve more than one
variable.
 We may believe that some of the variables
explain or even cause changes in the
variables. Then we have explanatory and
response variables.
 Explanatory—like the independent variable, it
attempts to explain the observed outcomes.
 Response—like the dependent variable, it measures
an outcome of a study.
Examples
Identify the explanatory and response variables:
• Alcohol causes a drop in body temperature.
To measure this, researchers give several
different amounts of alcohol to mice, then
measure the change in their body temperature
after 15 minutes.
• If an object is dropped from a height, then its
downward speed theoretically increases over
time due to the pull of gravity. To test this, a
ball is dropped and at certain intervals of time,
the speed of the ball is measured.
Scatterplots




Used for two-variable quantitative data!
Explanatory variable goes on the x-axis
Response variable goes on the y-axis
The explanatory variable does not
necessarily “CAUSE” the change in the
response variable.
 Displaying Relationships: Scatterplots
Since Body weight is our eXplanatory
variable,120be sure
to place
it131on 165
the X-axis!
Body weight (lb)
187
109
103
158
116
Backpack weight (lb)
26
30
26
24
29
35
31
28
Scatterplots and Correlation
Make a scatterplot of the relationship between body weight
and pack weight.
Interpreting Graphs
One Variable
Quantitative Data
Center
Two-Variable
Quantitative Data
Form
Linear? Clusters? Gaps?
Shape
Direction
Positive? Negative?
Spread
Strength
Strong? Weak? Moderate?
Outliers
Outliers
In sentence form…
 There is a (strong/weak),
(positive/negative), (linear/non-linear)
relationship between (your two
variables).

Interpreting Scatterplots
 There is one possible outlier, the hiker
with the body weight of 187 pounds
seems to be carrying relatively less
weight than are the other group
members.
Strength
Direction
Form
Scatterplots and Correlation
Outlier
 There is a moderately strong, positive, linear relationship
between body weight and pack weight.
 It appears that lighter students are carrying lighter
backpacks.
Adding Categorical
Variables to Scatterplots
 You can use different plotting symbols or
different colors to designate a categorical
variable.
 You still have two quantitative variables,
but you can add a “category” to these
variables.
Some quick tips for
drawing scatterplots
 Choose an appropriate scale for the
axes. Use a break if appropriate.
 Label, Label, Label…
 If you are given a grid, try to use a scale
that will make the scatterplot use the
whole grid.
Section 3.2 Correlation
We are not good judges!
 We shouldn’t just rely on our eyes to tell
us how strong a linear relationship is.
 We have a numerical indication for how
strong that linear relationship is – it’s
called CORRELATION.
Definition:
The correlation r measures the strength of the linear relationship between two
quantitative variables.
•r is always a number between -1 and 1
•r > 0 indicates a positive association.
•r < 0 indicates a negative association.
•Values of r near 0 indicate a very weak linear relationship.
•The strength of the linear relationship increases as r moves away from 0
towards -1 or 1.
•The extreme values r = -1 and r = 1 occur only in the case of a perfect
linear relationship.
Scatterplots and Correlation
Facts About Correlation
 It does not require a response and explanatory
variable. Ex. How are SAT math and verbal
scores related?
 If you switch the x and the y variables, the
correlation doesn’t change.
 If you change the units of measurement for x
and/or y, the correlation doesn’t change.
 Positive r values indicate a positive
relationship; negative values indicate a
negative relationship. Remember… not cause.
More Facts
 Correlation measures the strength of the
LINEAR relationship. It doesn’t measure
curved relationships.
 Correlation is strongly affected by
outliers.
 r does not have a unit.
Homework
Chapter 3
#11, 13, 14, 15, 17, 20, 22, 26