Question

Air Force servicemen and servicewomen were tested for maximal oxygen use in a 12 min distance run versus a 1.5 mile run. The participant runs on a level terrain for the prescribed distance. The technicians records the participant’s time to the closet second, the heart rate for 15 s immediately after the participant crosses the finish line and then estimate the VO₂ max consumption using a Wilmore and Bergfeld fitness table.  

Data 1.5 Mile Run (n=29)
X                               y
Time (min)	VO2Max(ml/kg.min)
8.1		59.2
8.2		60
9		49.7
9.5		59.9
9.8		51.2
10		48.5
10.3		49.5
10.5		49.5
10.9		50
11		47.5
11.1		40
11.9		45.1
12		44
12.3		49.1
12.4		50
12.5		40
12.6		40
12.5		43
13		38.8
13.1		40
13.8		32
13.9		36.1
14.5		39.8
14.8		38.1
15		37.5
15.5		30
15.9		32

9. Write the equation of the least-squares line( line of fit)._________

10. What is the slope of the line of fit(regression line)?  

11. What is the marginal change for the 1.5 mile run time to one ml/kg.min. versus maximal oxygen consumption?  

12. If the 1.5 mile run time is 7 minutes, what is the amount of oxygen consumed?

Answer 1

Using Excel<data<data analysis<regression

Here is the output:

Regression Analysis
	r²	0.807
	r	-0.899
	Std. Error	3.665
	n	27
	k	1
	Dep. Var.	Y,VO2Max(ml/kg.min)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,407.9966	1	1,407.9966	104.83	1.99E-10
Residual	335.7664	25	13.4307
Total	1,743.7630	26
Regression output				confidence interval
variables	coefficients	std. error	t (df=25)	p-value	95% lower	95% upper
Intercept	85.1371	4.03	21.10	0.00	76.83	93.45
X,Time (min)	-3.3885	0.3309	-10.239	1.99E-10	-4.0701	-2.7069

Answers: Please follow the round off instructions and do comment if you need more than 4 decimal places in answer. Thank You!

Write the equation of the least-squares line( line of fit).

Answer:

y=85.1371-3.3885x

What is the slope of the line of fit(regression line)?  

-3.3885

What is the marginal change for the 1.5 mile run time to one ml/kg.min. versus maximal oxygen consumption?  

-3.3885

If the 1.5 mile run time is 7 minutes, what is the amount of oxygen consumed?

61.4176