Scatterplots and
Correlations
1. SAT scores and
college achievement—
among college students,
those with higher SAT
scores also have higher
grades
2. Happiness and
helpfulness—as people’s
happiness level increases,
so does their helpfulness
(conversely, as people’s
happiness level decreases,
so does their helpfulness)
This table shows some sample data.
Each person reported income and
years of education.
sample
annual income
years in school
1
2
3
4
5
6
7
8
9
10
125,000
100,000
40,000
35,000
41,000
29,000
35,000
24,000
50,000
60,000
19
20
16
16
18
12
14
12
16
17
the correlation is .79
We find that people with higher income have
more years of education. (You can also phrase it
that people with more years of education have
higher income.) When we know there is a
correlation between two variables, we can make
a prediction. If we know a group’s income, we
can predict their years of education.
1. Education and years in
jail—people who have more
years of education tend to
have fewer years in jail (or
phrased as people with more
years in jail tend to have
fewer years of education)
2. Crying and being held—
among babies, those who are
held more tend to cry less (or
phrased as babies who are
held less tend to cry more)
Is there a correlation
between TV viewing and
class grades?
the correlation is -.63.
There is a negative correlation
between TV viewing and class
grades—students who spend more
time watching TV tend to have lower
grades
Advantage
Disadvantage
An advantage of the correlation
method is that we can make
predictions about things when we
know about correlations. If two
variables are correlated, we can
predict one based on the other. For
example, we know that SAT scores
and college achievement are
positively correlated. So when
college admission officials want to
predict who is likely to succeed at
their schools, they will choose
students with high SAT scores.
The problem that most people
have with the correlation
method is remembering that
correlation does not measure
cause. Take a minute and chant
to yourself: Correlation is not
Causation! Correlation is not
Causation!
Correlation
is NOT
Causation
Predicting
outcome
through
stats...
beers
5
2
9
8
3
7
3
5
BAC
0.10
0.03
0.19
0.12
0.04
0.095
0.07
0.06
r =.894338
beers
3
5
4
6
5
7
1
4
BAC
0.02
0.05
0.07
0.10
0.085
0.09
0.01
0.05
Scatterplot of student volunteer with
their BAC vs Beer intake
Correlation measures the strength of a linear
relationship. Patterns closer to a straight line have
correlations closer to 1 or -1
More facts about correlation:
•Correlation requires that both variables be
quantitative.
• “r” does not describe curved relationships
between variables, no matter how strong they
are.
• Like the mean and standard deviation, the
correlation is not resistant: r is strongly
affected by few outliers.
•Correlation is not a complete summary of twovariable data.(unless you list down the means
and sd of both x and y)
A scatterplot displays the relationship between two quantitative
variables measured on the same individuals.
(x = explanatory variable and y= response variable)
Plot points with different colors or symbols to see the
effect of a categorical variable in a scatterplot.
In examining a scatterplot, always look for an overall
patter showing direction, form, strength and then look for
outliers or other deviation from this pattern.
Direction: either positive or negative
Form: when the points show a straight-line relationship,
the pattern is said to be linear which is an important
relationship between variables.
Strength: determined by how close the points in the
scatterplots.
Correlation r measures the strength and
direction of linear association between 2
quantitative variables.
If r > 0 then the linear relationship has a positive
association
If r < 0 then the linear relationship has a negative
association
-1 ≤ r ≤ 1, perfect correlation is when r = ± 1 which
only occurs if the points lie on a straight line.