The BODYFAT dataset was developed using randomly selected
patients who were treated by a particular sports injury
rehabilitation group. The purpose was to determine if girth
(in centimeters) could be used to predict body fat (as a
percentage) and to estimate the percentage of body fat (with 99%
confidence) of a person who has a girth of 150cm. Girth is
easily and accurately evaluated with a tape measure. Body fat
percentage is measured via hydrostatic weighing, but this is too
expensive and impractical to be easily deployed in most physicians'
offices. Please conduct this analysis using a 1% significance
level.
Girth Fat%
99.1 19
76 8.4
83.1 9.2
88.5 21.8
118 33.6
104.3 31.7
79.5 6.4
108.8 24.6
81.9 4.1
76.6 12.8
88.7 12.3
90.9 8.5
89 26
78 7.3
83.2 13.4
85.6 22.3
90.3 20.2
104.5 16.8
95.6 18.4
103.1 27.7
89.9 17.4
104 26.4
95.3 11.3
105 27.1
83.5 17.2
86.7 10.7
93 18.1
76 13.7
106.1 28.1
109.3 23
104.3 30.8
100.5 16.5
77.9 7.4
101.6 18.2
99.7 25.1
96.7 16.1
95.8 30.2
104.8 25.4
92.4 25.9
95 21.6
86 8.8
90.6 19.5
105.5 31
79.4 10.4
126.2 33.1
98 20.2
95.5 21.9
73.7 11.2
86.4 10.9
122.1 45.1
1) Indicate the value of the test statistic (showing 2 decimal
places) that indicates that this regression is useful.
2) Actual body fat percentage typically deviates from the
predicted value by _____ percentage points (correct to four decimal
points)
3) Girth explains _____ % of the variability in body
fat percentage (correct to one decimal place).
4) Increasing girth by one centimeter will increase average
body fat percentage by _____ percentage points (correct to four
decimal places).
5) A person with a girth of zero (??) centimeters will, on
average, have a body fat percentage of _____ (correct to three
decimal places).