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Unformatted text preview: Correlation Suppose we found the age and weight
of a sample of 10 adults.
Create a scatterplot of the data below.
Is there any relationship between the
age and weight of these adults?
Age 24 30 41 28 50 46 49 35 20 39 Wt 256 124 320 185 158 129 103 196 110 130 Suppose we found the height and weight of a
sample of 10 adults.
Create a scatterplot of the data below.
Is there any relationship between the height
and weight of these adults?
Is it positive or negative? Weak or strong?
Ht 74 65 77 72 68 60 62 73 61 64 Wt 256 124 320 185 158 129 103 196 110 130 The closer the points in a
The farther away from a
scatterplot are to a straight
straight line – the weaker the
line  the stronger the
relationship
relationship. Identify as having a positive association,
positive
a negative association, or no association.
negative
no
1. Heights of mothers & heights of their adult +
daughters
2. Age of a car in years and its current value3. Weight of a person and calories consumed +
4. Height of a person and the person’s birth
NO
month
5. Number of hours spent in safety training and
the number of accidents that occur Correlation Coefficient (r)• A quantitative assessment of the strength
quantitative
& direction of the linear relationship
between bivariate, quantitative data
• Pearson’s sample correlation is used most
• parameter  ρ ( rho)
• statistic  r xi − x yi − y 1 r=
∑ s s n − 1 x y Speed Limit
(mph)
Avg. # of
accidents
(weekly) 55 50 45 40 30 20 28 25 21 17 11 6 Calculate r. Interpret r in context.
There is a strong, positive, linear relationship
between speed limit and average number of
accidents per week. Properties of r
(correlation coefficient)
• legitimate values of r are [1,1]
No
Correlation
Strong correlation
Moderate Correlation
Weak correlation 1 .8 .5 0 .5 .8 1 •value of r does not depend on the unit
unit
of measurement for either variable
x (in mm) 12 15
y
47 21
10 32
14 26
9 19
8 24
12 Find r.
Change to cm & find r. The correlations are the same. •value of r does not depend on which
of the two variables is labeled x
x
y 12
4 15
7 21
10 32
14 26
9 19
8 24
12 Switch x & y & find r. The correlations are the same. •value of r is nonresistant
nonresistant
x
y 12
4 15
7 21
10 32
14 26
9 19
8 Find r.
Outliers affect the
correlation coefficient 24
22 •value of r is a measure of the extent
to which x & y are linearly related
linearly
A value of r close to zero does not rule out
any strong relationship between x and y.
r = 0, but has a definite
relationship! Minister data: r = .9999 (Data on Elmo) So does an increase in ministers
cause an increase in consumption of
cause
rum? Correlation does not imply
causation Correlation does not imply
causation Correlation does not
Correlation
imply causation
imply ...
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 Fall '10
 Nielson
 Correlation

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