The World Health Organization defines obesity in adults as having a body mass index (BMI) higher than 30. Of the 250 men in the study mentioned in Exercise 11-1, 23 are by this definition obese. How good is waist (size in inches) as a predictor of obesity? A logistic regression model was fit to the data:

where p is the probability of being classified as obese.

(a) Does the probability of being classified as obese increase or decrease as a function of waist size? Explain.

(b) What is the estimated probability of being classified as obese for a man with a waist size of 36 inches?

(c) What is the estimated probability of being classified as obese for a man with a waist size of 42 inches?

(d) What is the estimated probability of being classified as obese for a man with a waist size of 48 inches?

(e) Make a plot of the estimated probability of being classified as obese as a function of waist size.

In Exercise

Diabetes and obesity are serious health concerns in the United States and much of the developed world. Measuring the amount of body fat a person carries is one way to monitor weight control progress, but measuring it accurately involves either expensive X-ray equipment or a pool in which to dunk the subject. Instead body mass index (BMI) is often used as a proxy for body fat because it is easy to measure: BMI = mass (kg)/(height (m))² = 703 mass(lb)/(height(in))². In a study of 250 men at Bingham Young University, both BMI and body fat were measured. Researchers found the following summary statistics:

Transcribed Image Text:

=-41.828 +0.9864 waist log 1-P ΣΧ6322.28 Σχ? 162674.18 i=l i=1 Σ4757.90 Σ107679.27 i=1 i=1 Σχy)- 1 2547 1.10 i=1 =WI «WI