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
What value of alpha (as a proportion and not as a percent) will
be used for this analysis?
Please run the regression using Minitab. Do not forget to store
the standardized residuals or obtain the relevant graph. What value
do you get for S (show four decimal places)?
Please indicate the value of the test statistic (showing 2
decimal places) that indicates that this regression is useful.
Actual body fat percentage typically deviates from the predicted
value by _____ percentage points (correct to four decimal points)
Girth explains _____ % of the variability in body fat percentage
(correct to one decimal place).
Increasing girth by one centimeter will increase average body
fat percentage by _____ percentage points (correct to four decimal
places). A person with a girth of zero (??) centimeters will, on
average, have a body fat percentage of _____ (correct to three
decimal places).
What body fat percentage can a person with a girth of 150cm
reasonable expect (correct to three decimal places)?
What is the lower bound of the average percentage of body fat
(with 95% confidence) for all people who have a girth of 150cm
(correct to three decimal places)?
What is the upper bound of the percentage of body fat (with 95%
confidence) for a person with a girth of 150cm (correct to three
decimal places)?