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Lyme disease is an inflammatory disease that results in a skin rash and flulike symptoms. It is transmitted through the bite of an infected deer tick. The following data represent the number of reported cases of Lyme disease and the number of drowning deaths for a rural county.

Cases of Lyme Disease Drowning Deaths Month
2 0 J
1 1 F
3 2 M
4 1 A
5 3 M
1 5 J
2 2 J
1 3 A
6 3 S
5 3 O
4 1 N
1 0 D

Requried:
a. Draw a scatter diagram of the data.
b. Determine the linear correlation coefficient between Lyme disease and drowning deaths.
c. Does a linear relation exist between the number of reported cases of Lyme disease and the number of drowning deaths?

Respuesta :

Answer:

Step-by-step explanation:

Let cases of Lyme disease = x

x = 2, 1, 3, 4, 5, 1, 2, 1, 6, 5, 4, 1

[tex]\sum x = 35[/tex]

[tex]\sum x^2 = 139[/tex]

y = 0, 1, 2, 1, 3, 5, 2, 3, 3, 3, 1, 0

[tex]\sum y = 24[/tex]

[tex]\sum y^2 = 72[/tex]

[tex]\sum xy = 55[/tex]

[tex]S_{xx} = \sum x^2 - (\sum x)^2/n\\S_{xx} = 139 - 35^2/12\\S_{xx} = 36.92\\S_{yy} = \sum y^2 - (\sum y)^2/n\\S_{yy} = 72 - 24^2/12\\S_{yy} = 24[/tex]

[tex]S_{xy} = \sum xy - ( \sum x \sum y)/n\\S_{xy} = 55 - (35*24)/12\\S_{xy} = -15[/tex]

b) Linear correlation between Lyme disease and drowning deaths.

[tex]r = \frac{S_{xy}}{\sqrt{S_{xx}S_{yy}} }[/tex]

r = -15/ √(24*36.92)

r = -0.504

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