An exercise physiologist used skinfold measurements to estimate the total body fat, expressed as a percentage of body weight, for a random sample of 10 male participants in a physical fitness program. The data of body fat percentages and the body weights are shown in the table below. Participant Weight X(kg) Fat Y (%) 1 89 28 2 88 27 3 66 24 4 59 23 5 93 27 6 73 26 7 82 29 8 77 25 9 100 33 10 67 29 A. Describe the strength and direction of the linear relationship between body weight and body fat for men. B. Give the estimated regression equation. C. Give the estimated value for the slope, and accurately interpret it in a few sentences in terms of the problem: D. Using this information and the output from R, predict the body fat (%) for a male whose weight was 200 kg. E. Using this information from the R output, construct a 95% confidence interval for the slope. F. Assuming the assumptions for this regression were met, does it appear to you that body weight is a useful predictor of body fat? Explain.
An exercise physiologist used skinfold measurements to estimate the total body fat, expressed as a percentage of body weight, for a random sample of 10 male participants in a physical fitness program. The data of body fat percentages and the body weights are shown in the table below.
|
Participant |
Weight X(kg) |
Fat Y (%) |
|
1 |
89 |
28 |
|
2 |
88 |
27 |
|
3 |
66 |
24 |
|
4 |
59 |
23 |
|
5 |
93 |
27 |
|
6 |
73 |
26 |
|
7 |
82 |
29 |
|
8 |
77 |
25 |
|
9 |
100 |
33 |
|
10 |
67 |
29 |
A. Describe the strength and direction of the linear relationship between body weight and body fat for men.
B. Give the estimated regression equation.
C. Give the estimated value for the slope, and accurately interpret it in a few sentences in terms of the problem:
D. Using this information and the output from R, predict the body fat (%) for a male whose weight was 200 kg.
E. Using this information from the R output, construct a 95% confidence interval for the slope.
F. Assuming the assumptions for this regression were met, does it appear to you that body weight is a useful predictor of body fat? Explain.
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