Correlation Problems
1. A college professor wanted to find out if there was a relationship between
the height and weight of students. He randomly selected 10 students for
his study. He recorded each student's weight and height. The data are
shown below.
Ten Students Measured on Height and Weight
Student Height Weight
(inches) (pounds)
A 63 120
B 70 178
C 69 164
D 70 164
E 64 126
F 65 133
G 71 150
H 68 163
I 65 124
J 75 208
- a. Draw a scattergram for this data.
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- b. What does the scattergram tell you?
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- c. Why should the Pearson product-moment correlation procedure be
used to determine the relationship between the variables?
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- d. Calculate the Pearson r.
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- e. Interpret the r in terms of "accounted" variance.
2. A panel of toy executives wanted to see if there was a relationship between
the quality of advertising and the quality of their product. They randomly
selected seven toys for this study. Each toy was then ranked from 1 to
30 on the quality of advertising used to promote the product and from 1
to 30 on the quality of the toy itself. The ranks are shown in the following
table.
Eight Toys Scored on Quality of Product and
Quality of Advertisement
Toy Advertisement Product
A 20 2
B 12 22
C 10 20
D 15 15
E 4 25
F 3 30
G 30 5
- a. Why should you use the Spearman rho to determine the correlation
between the two variables
- b. Calculate the Spearman rho.
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- c. Interpret the results.
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