Question

Waist (in.)	Weight (lb)	Body Fat (%)
32	175	6
36	181	21
38	200	15
33	159	6
39	196	22
40	192	31
41	205	32
35	173	21
38	187	25
38	188	30
33	188	10
40	240	20
36	175	22
32	168	9
44	246	38
33	160	10
41	215	27
34	159	12
34	146	10
44	219	28

hree 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.

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

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

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

Answer 1

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.

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

The estimated regression line is

Body fat = -62.557+2.222*waist.

99% confidence interval for the slope = (1.436, 3.007).

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

99% confidence interval for the mean %body fat = (22.57, 30.03)

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

99% prediction interval for the %body fat=(12.71, 39.89)

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

Regression Analysis
	r²	0.787	n	20
	r	0.887	k	1
	Std. Error of Estimate	4.540	Dep. Var.	Body Fat (%)
Regression output						confidence interval
variables		coefficients	std. error	t (df=18)	p-value	99% lower	99% upper
Intercept	a =	-62.557
Waist (in.)	b =	2.222	0.273	8.144	1.90E-07	1.436	3.007
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,366.790	1	1,366.790	66.32	1.90E-07
Residual	370.960	18	20.609
Total	1,737.750	19
Predicted values for: Body Fat (%)
		99% Confidence Interval		99% Prediction Interval
Waist (in.)	Predicted	lower	upper	lower	upper	Leverage
40	26.303	22.57	30.03	12.71	39.89	0.081