Physicians have used the “diving reflex” to reduce abnormally rapid heartbeats i
ID: 3267704 • Letter: P
Question
Physicians have used the “diving reflex” to reduce abnormally rapid heartbeats in humans by briefly submerging the patient’s face in cold water. The reflex, triggered by cold water temperatures, is an involuntary neural response that shuts off circulation to the skin, muscles, and internal organs to divert extra oxygen-carrying blood to the heart, lungs, and brain. A research physician conducted an experiment to investigate the effects of various cold water temperatures on the pulse rate of small children. The data for seven 6-year-old children are shown.
Temperature of Water x Decrease in Pulse Rate y
68 2
65 5
70 1
62 10
60 9
55 13
58 10
a)If the water temperature is 66 degrees F, predict the drop in pulse rate for a 6-year-old child.
b)What percentage of the drop in pulse rate for a 6-year-old child can be explained by the linear regression line?
c)What is the standard error of estimate of this prediction?
Explanation / Answer
Ans:
Regression Equation(y) = a + bx
Slope(b) = (NXY - (X)(Y)) / (NX2 - (X)2)
Intercept(a) = (Y - b(X)) / N
Slope=-0.811
y-intercept,a=57.912
Regression eqn:
y=57.912-0.811x
a)when x=66
y=57.912-0.811*66=4.386
b)Calculate cofficient of determination,r2
First calculate correlation cofficient,r =CORREL(x,y)=-0.97
(Excel function CORREL is used to calculate correlation cofficient0
r2=0.941
94.1% of the drop in pulse rate for a 6-year-old child can be explained by the linear regression line.
c)standard error of estimate
standard error of estimate=sqrt(7.181/7)=1.013
x y xy x^2 y^2 1 68 2 136 4624 4 2 65 5 325 4225 25 3 70 1 70 4900 1 4 62 10 620 3844 100 5 60 9 540 3600 81 6 55 13 715 3025 169 7 58 10 580 3364 100 Total 438 50 2986 27582 480