Scatter plots & Association
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1 Scatter plots & Association Statistics is about … variation. Recognize, quantify and try to explain variation. – Variation in contents of cola cans can be explained, in part, by the type of cola in the cans.
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Scatter plots & Association. Statistics is about … variation. Recognize, quantify and try to explain variation. Variation in contents of cola cans can be explained, in part, by the type of cola in the cans. Scatter plots & Association. Response variable – variable of primary interest. - PowerPoint PPT Presentation
Transcript of Scatter plots & Association
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Scatter plots & AssociationStatistics is about … variation.Recognize, quantify and try to
explain variation.–Variation in contents of cola
cans can be explained, in part, by the type of cola in the cans.
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Scatter plots & AssociationResponse variable – variable
of primary interest.Explanatory variable –
variable used to try to explain variation in the response.
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Scatter plots & AssociationWhen both the response and
the explanatory variables are quantitative, display them both in a scatter plot.
Look for a general pattern of association.
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Scatter plots & AssociationExample: Tar (mg) and carbon
monoxide (mg) in cigarettes.–y, Response: CO (mg).–x, Explanatory: Tar (mg).–Cases: 25 brands of cigarettes.
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Scatter plot
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Positive AssociationAbove average values of CO
are associated with above average values of Tar.
Below average values of CO are associated with below average values of Tar.
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Scatter plots & AssociationExample: Outside temperature
and amount of natural gas used.– Response: Natural gas (1000 ft3).– Explanatory: Outside temperature
(o C).– Cases: 26 days.
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Negative Association
0
5
10
Gas
-5.0 .0 5.0 10.0 15.0Temp
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Negative AssociationAbove average values of gas
are associated with below average temperatures.
Below average values of gas are associated with above average temperatures.
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CorrelationLinear Association
–How closely do the points on the scatter plot represent a straight line?
–The correlation coefficient gives the direction of the linear association and quantifies the strength of the linear association between two quantitative variables.
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CorrelationStandardize y
Standardize x
yy s
yyz
xx s
xxz
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ZxZy > 0
ZxZy > 0
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Correlation Coefficient
1
1
nssyyxx
r
nzz
r
yx
yx
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Correlation ConditionsCorrelation applies only to
quantitative variables.Correlation measures the
strength of linear association.Outliers can distort the value
of the correlation coefficient.
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Correlation CoefficientTar and CO
r = 0.9575
249796.22
1
nzz
r yx
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Correlation CoefficientThere is a strong positive
correlation, linear association, between the tar content and carbon monoxide content of the various cigarette brands.
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JMPAnalyze – Multivariate methods
– MultivariateY, Columns
– Tar (mg)– CO (mg)
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Tar (mg)CO (mg)
1.00000.9575
0.95751.0000
Tar (mg) CO (mg)Correlations
0
5
10
15
20
25
30
0
5
10
15
20
25
30
Tar (mg)
0 5 10 15 20 25 30
CO (mg)
0 5 10 15 20 25 30
Scatterplot Matrix
Multivariate
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Correlation PropertiesThe sign of r indicates the direction of
the association.The value of r is always between
–1 and +1Correlation has no units.Correlation is not affected by changes
of center or scale.
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Correlation Cautions“Correlation” and “Association”
are different.–Correlation – specific (linear).–Association – vague (trend).
Don’t correlate categorical variables.
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Correlation CautionsDon’t confuse correlation with
causation.–There is a strong positive correlation
between the number of crimes committed in communities and the number of 2nd graders in those communities.
Beware of lurking variables.
