Archeology Continuing with Exercise, have members of the class measure their heights and the lengths of their humeri (plural of humerus) in inches.
Archeology It is possible for archeologists to estimate the height of an adult based only on the length of the humerus, a bone located between the elbow and the shoulder. The approximate relationship between the height y of an individual and the length x of the humerus is shown in the table for both males and females. All measurements are in inches. Although individual values may vary, tables like this are the result of measuring bones from many skeletons.
x
8
9
10
11
y (females)
50.4
53.5
56.6
59.7
y (males)
53.0
56.0
59.0
62.0
x
12
13
14
y (females)
62.8
65.9
69.0
y (males)
65.0
68.0
71.0
(a) Find the estimated height of a female with a 12-inch humerus.
(b) Plot the ordered pairs (x, y) for both sexes. What type of relation exists between the data?
(c) For each 1-inch increase in the length of the humerus, what are the corresponding increases in the heights of females and of males?
(d) Determine linear functions f and g that model these data for females and males, respectively.
(e) Suppose a humerus from a person of unknown sex is estimated to be between 9.7 and 10.1 inches long. Use f and g to approximate the range for the height of a female and a male.
(a) Make a table of the results.
(b) Find regression lines that fit the data points for males and females.
(c) Compare your results with the table in Exercise
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