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
99.1
76.0
83.1
88.5
118.0
104.3
79.5
108.8
81.9
76.6
88.7
90.9
89.0
78.0
83.2
85.6
90.3
104.5
95.6
103.1
89.9
104.0
95.3
105.0
83.5
86.7
93.0
76.0
106.1
109.3
104.3
100.5
77.9
101.6
99.7
96.7
95.8
104.8
92.4
95.0
86.0
90.6
105.5
79.4
126.2
98.0
95.5
73.7
86.4
122.1

Fat%
19.0
8.4
9.2
21.8
33.6
31.7
6.4
24.6
4.1
12.8
12.3
8.5
26.0
7.3
13.4
22.3
20.2
16.8
18.4
27.7
17.4
26.4
11.3
27.1
17.2
10.7
18.1
13.7
28.1
23.0
30.8
16.5
7.4
18.2
25.1
16.1
30.2
25.4
25.9
21.6
8.8
19.5
31.0
10.4
33.1
20.2
21.9
11.2
10.9
45.1

1. Which of the following best describes the conclusion that one would come to based on this analysis?

• The explanatory power of this regression suggests that girth is ["is a weak", "is not useful as a", "is an excellent", "is a moderate"] predictor of body fat percentage.
• The standard error of the regression suggests that girth ["can", "can not"] estimate body fat percentage to within 1.5% as does hydrostatic weighing.
• The 95% prediction interval for a person with a girth of 150cm ["has", "does not have"] a width of just under 25 percentage points, suggesting that this model ["cannot", "can"] reasonably estimate usefully for an individual.

Answer rating: 100% (QA)

Solution a Fitting the Regression Model on Fat using Girth ... View the full answer