Question

2. (9 pts) It is difficult to determine a person’s body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their weights shown in the table.

(2 pts) Determine the linear correlation coefficient.

(4 pts) Find the least-squares regression line.

(2 pts) Interpret the slope and y-intercept if appropriate.

(1 pts) Predict the body fat percentage if the weight is 190 lb.

Weight (lb)	Body Fat (%)
175	6
181	21
200	15
159	6
196	22
192	31
205	32
173	21
187	25
188	30
188	10
240	20
175	22
168	9
246	38
160	10
215	27
159	12
146	10
219	28

Answer 1

Using excel<data<megastat<regression

Here is the output:

Regression Analysis
	r²	0.485
	r	0.697
	Std. Error	7.049
	n	20
	k	1
	Dep. Var.	Body Fat (%)y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	843.3252	1	843.3252	16.97	.0006
Residual	894.4248	18	49.6903
Total	1,737.7500	19
Regression output				confidence interval
variables	coefficients	std. error	t (df=18)	p-value	95% lower	95% upper
Intercept	-27.3763	11.55	-2.37	0.03	-51.64	-3.12
Weight (lb)x	0.2499	0.0607	4.120	.0006	0.1224	0.3773
Predicted values for: Body Fat (%)y
		95% Confidence Interval	95% Prediction Interval
Weight (lb)x	Predicted	lower	upper	lower	upper	Leverage
190	20.100	16.783	23.416	4.923	35.276	0.050

Determine the linear correlation coefficient.

Solution: r=0.697

Find the least-squares regression line.

Solution:

Interpret the slope and y-intercept if appropriate.

Solution: Slope=0.2499

Y -intercept= -27.3763

Predict the body fat percentage if the weight is 190 lb.

Solution: Put x=190