The peak flow rate of a person is the fastest rate at which a person can expel a

Question

The peak flow rate of a person is the fastest rate at which a person can expel air after taking a deep breath. Peak flow is measured in units of liters/min, and gives an indication of a persons respiratory health. 17 men were randomly sampled, and information on their peak flow and height (in cm) follows:

The thought is that the height of a man should eeffect their peak flow. In addition, we are given that the sample correlation is 0.32725, and SS(resid) = 198.909

If we are comparing two men, and their dierence in heights is 10cm, what can we expect their average dierence in peak ow to be?

Explanation / Answer

we can fit a regression equation to see if there is a relationship

so beta1 can be calculated as

beta1 = r Sy/Sx = 0.32725 * 117.9952/8.5591 = 4.5115 ,

also beta0 can be calculated as b0 = ybar - beta1xbar

660 - 4.5115*180.4118 = -153.9

so the regression equation is

Y = -153.9 + 4.5115*X

so if the difference is 10cm , we put X as X-10

Y = -153.9 + 4.5115*(X-10)

Y = -153.9 + 4.5115*X - 45.115 =

-199.10 +4.5115*X , so we would see a difference of 199.10

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