Section 9.1
Summer 2013 - Math 1040
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Roadmap
Scatterplots.
Correlation.
Causation.
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Scatterplots
Scatterplots are graphs of data for two variables. The horizontal variable x
is the explanatory variable, and the vertical variable y is the response
variable. In Chapter 9 we will seek a linear relationship between the two.
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Scatterplots
Scatterplots are graphs of data for two variables. The horizontal variable x
is the explanatory variable, and the vertical variable y is the response
variable. In Chapter 9 we will seek a linear relationship between the two.
Example Is there a linear relationship between the number of years an
alumni has been out of school and their annual contributions (in
thousands of dollars)?
Years x
$ in thousands y
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12.5
10
8.7
5
14.6
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5.2
3
9.9
24
3.1
30
2.7
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Scatterplots
The annual donations decreases as the number of years out of school
increases.
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Scatterplots
Example Is there a linear relationship between a person’s height (inches)
and pulse rate (beats per minute)?
Height x
Pulse rate y
68
90
72
85
65
88
70
100
1
Draw and label the x- and y -axes.
2
Plot each ordered pair.
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105
75
98
78
70
64
65
68
72
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Correlation
Correlation is a relationship between two variables. Subjectively we may
be interested in a linear correlation.
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Correlation
Correlation is a relationship between two variables. Subjectively we may
be interested in a linear correlation.
P
P P
n xy − ( x)( y )
p P
r=p P
P
P
n x 2 − ( x)2 n y 2 − ( y )2
The above is the correlation coefficient. It must be between -1 and 1.
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Correlation coefficient
Strong postive linear correlation is near 1.
Strong negative linear correlation is near -1.
Linear correlation is perfect at 1 or -1.
No or weak linear correlation is near 0.
Near 0, this does not mean there is a weak relation, just no linear one.
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Correlation coefficient
Note that (d) has a very steep slope, and r is not the same as slope.
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Assignments
Assignment:
1
Read pages 484 - 487, 494
2
Page 495: 1-5 all, 9-18 all
Vocabulary: correlation, explanatory variable, response variable,
Understand: How to make and read a scatterplot. How to judge if two
variables have a correlation. Realize correlation does not imply causation.
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