Three percent of a man’s body is essential fat; for a woman the percentage is closer to 12.5%. As the name implies, essential fat is necessary for a normal healthy body. Fat is stored in small amounts throughout the body. Too much fat, however, can be dangerous to your health. For men between 18 and 39 years old, a healthy percent of body fat ranges from 8% to 19%; for women of the same age, it’s 21% to 32%.

Measuring body fat can be tedious and expensive. The “standard reference” measurement is by dual-eneregy X-ray absorptiometry (DEXA), which involves two low-dose X-ray generators and takes from 10 to 20 minutes.

Because of the time and expense involved with the DEXA method, health professionals would like to be able to make a useable prediction of body fat from easily measurable variables such as weight or waist size.This Excel file shows the waist size (inches), weight (pounds) and percent body fat for 20 individuals.

Question 1. What is the slope of the least squares regression line of %body fat on waist size?

Question 2. Find sb1, the estimate of the standard deviation σb1 of the least squares slope b1 (use 4 decimal places).

b1σb1

Question 3. Determine the 99% confidence interval for the slope of the least squares regression line of %body fat on waist size.

Question 4. Determine a 99% confidence interval for the mean %body fat found in people with 40-inch waists (use 2 decimal places).

Question 5. Determine a 99% prediction interval for the %body fat of an individual with a 40-inch waist (use 2 decimal places).