data biostats.bodyfat;

input bodyfat tricep thigh midarm age;

cards;

19.543.129.111.9 22

24.749.828.222.8 25

30.751.937.018.7 44

29.854.331.120.1 42

19.142.230.912.9 26

25.653.923.721.7 39

31.458.527.627.1 29

27.952.130.625.4 23

22.149.923.221.3 29

25.553.524.819.3 43

31.156.630.025.4 44

30.456.728.327.2 22

18.746.523.011.7 23

19.744.228.617.8 26

14.642.721.312.8 25

29.554.430.123.9 22

27.755.325.722.6 45

30.258.624.625.4 33

22.748.227.114.8 23

25.251.027.521.1 43

;

run;

1.Presently, Body Mass Index (BMI) is the standard measure to determine obesity. However, BMI was chosen as a standard not because of its accuracy in measuring health, but because it is easy to measure and calculate. Among athletes, BMI can be particularly inaccurate. For example, larger athletes in sports associated with strength (such as football or basketball) tend to be incorrectly labeled as overweight or obese, even though most of their mass is muscle, and often have body fat levels that are extremely low.

A better measure of obesity is % body fat. However, the gold standard for measuring % body fat is hydrostatic testing, which involves completely immersing the patient in a large tank of water, and measuring "water weight", one can get an extremely accurate measure of body fat. Suffice to say, this is a very expensive and inconvenient method for measuring body fat, one that cannot be used during routine screening exams.

Therefore, several proxy methods for measuring body fat that is far more convenient to implement have been proposed. This includes using calipers to measure skin thickness in the triceps area, measuring the circumference of the thigh, and circumference of the midarm. These methods are cheap and simple enough for widespread screening use.

Your group conducted a study to determine which of these measures are best for measuring % body fat. The study had 20 women enrolled. Hydrostatic testing was used to measure the % body fat, and the three new methods were used.

The SAS dataset biostats.bodyfat has the following variables:

Bodyfat - % body fat from hydrostatic testing

Tricep - skin thickness under the tricep area (mm)

Thigh - circumference around the thigh (cm)

Midarm - circumference around the midarm (cm)

Age - age in years

For this study, you need to determine the following:

a.Which of the three proxy measures (tricep, thigh or midarm) is the best at measuring body fat? Why?

b.Are tricep, thigh and midarm measurements correlated?

c.Can you develop a prediction model for % body fat using the answer to part a above? What is the equation?

d.Does age confound your model above? Prove it statistically.