Question

Aviation and high-altitude physiology is a specialty in the study of medicine. Let x = partial pressure of oxygen in the alveoli (air cells in the lungs) when breathing naturally available air. Let y = partial pressure when breathing pure oxygen. The (x, y) data pairs correspond to elevations from 10,000 feet to 30,000 feet in 5000 foot intervals for a random sample of volunteers. Although the medical data were collected using airplanes, they apply equally well to Mt. Everest climbers (summit 29,028 feet).

x	6.9	5.1	4.2	3.3	2.1	(units: mm Hg/10)
y	43.6	32.9	26.2	16.2	13.9	(units: mm Hg/10)

(a) Find ?x, ?y, ?x², ?y², ?xy, and r. (Round r to three decimal places.)

?x =
?y =
?x2 =
?y2 =
?xy =
r =

(b) Use a 1% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

t =
critical t =

(c) Find S_e, a, and b. (Round your answers to four decimal places.)

Se =
a =
b =

(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 5.0. (Round your answer to two decimal places.)
mm Hg/10

(e) Find a 90% confidence interval for y when x = 5.0. (Round your answers to one decimal place.)

lower limit	mm Hg/10
upper limit	mm Hg/10

(f) Use a 1% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

t =
critical t =

Answer 1

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.984218031
R Square	0.968685132
Adjusted R Square	0.958246843
Standard Error	2.499028797
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	579.5565652	579.5565652	92.80113944	0.002374351
Residual	3	18.73543478	6.245144928
Total	4	598.292
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-2.013043478	3.169627343	-0.63510415	0.570489035	-12.1002123
x	6.614130435	0.68658783	9.633334803	0.002374351	4.429101533

(a) Find ?x, ?y, ?x2, ?y2, ?xy, and r. (Round r to three decimal places.)

x	y	x^2	y^2	xy
6.9	43.6	47.61	1900.96	300.84
5.1	32.9	26.01	1082.41	167.79
4.2	26.2	17.64	686.44	110.04
3.3	16.2	10.89	262.44	53.46
2.1	13.9	4.41	193.21	29.19
21.6	132.8	106.56	4125.46	661.32

?x = 21.6
?y = 132.8
?x2 = 106.56
?y2 = 4125.46
?xy =661.32
r = 0.9842

(b) Use a 1% level of significance to test the claim that ? > 0. (Round your answers to two decimal places.)

t = 9.63
critical t =	=T.INV(0.99,3)

4.540702859

(c) Find Se, a, and b. (Round your answers to four decimal places.)

Se =
a = -2.01304
b = 6.61413

2.49902

(d) Find the predicted pressure when breathing pure oxygen if the pressure from breathing available air is x = 5.0. (Round your answer to two decimal places.)
mm Hg/10

y^= -2.01304 + 6.61413 *x

= -2.01304 + 6.61413 *5

=  31.05761