Ap Statistics Worksheets With Answers Page 8
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234.15 HEIGHT AND OBESITY The U.S. Department of Health and Human Services characterizes
adults as “seriously overweight” if they meet certain criterion for their heights as shown in the table
below (only a portion of the chart is reproduced here).
Height
Height
Severely
Height
Height
Severely
(ft, in)
(in)
overweight (lb)
(ft, in)
(in)
overweight (lb)
4’10”
58
138
5’8”
68
190
5’0”
60
148
6’0”
72
213
5’2”
62
158
6’2”
74
225
5’4”
64
169
6’4”
76
238
5’6”
66
179
6’6”
78
250
Weights are given in pounds, without clothes. Height is measured without shoes. There is no
distinction between men and women; a note accompanying the table states, “The higher weights apply
to people with more muscle and bone, such as many men.” Despite any reservations you may have
about the department’s standards for both genders, do the following:
(a) Without looking at the data, hypothesize a relationship between height and weight of U.S. adults.
That is, write a general form of an equation that you believe will model the relationship.
As height increases, weight increases. Since weight is a 3-dimensional attribute and height is
1-dimensional, weight should be proportional to the cube of the height. One might speculate a
= ×
b
model of the form
where a and b are constants. This is a power
WEIGHT
a HEIGHT
function.
(b) Which variable would you select as explanatory and which would be the response? Plot the data
from the table.
Height is the explanatory variable, and weight is the response variable.
(c) Perform a transformation to linearize the data. Do a least-squares regression on the transformed
data and check the correlation coefficient.
(Let L1 = height, L2 = weight, L3 = log (L1) = log(height), L4 = log (L2) = log(weight))
Plot log (L1) v. log (L2). The plot appears to be very linear, so least-squares regression is
performed on the transformed data. The correlation is 0.99997. The regression line fits the
transformed data extremely well.
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