3. Studies have shown that people who suffer sudden cardiac arrest (SCA) have a
ID: 3148897 • Letter: 3
Question
3. Studies have shown that people who suffer sudden cardiac arrest (SCA) have a better chance of survival if a defibrillator is administered very soon after cardiac arrest. How is survival rate related to the time between when cardiac arrest occurs and when the defibrillator shock is delivered? This question is addressed in the paper “Improving Survival from Sudden Cardiac Arrest: The Role of Home Defibrillators” (by J.K. Stross, University of Michigan, February 2002). The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitative center (where cardiac arrests occurred while victims were hospitalized and so the call-to-shock time tended to be short) and for four communities of different sizes.
Mean call-to-shock time, x: 2, 6, 7, 9, 12
Survival Rate, y: 90, 45, 30, 5, 2
a. Determined the regression line and interpret the line
b. Predict the survival rate when x is 15 (minutes). Interpret y value
Explanation / Answer
a. Here to determine the regression line we require to evalute x, y, xy, x2 & y2
If liner line regression eqaution is
y^ = a + bx
then,
a = [(y) (x2 ) - (x) (xy)]/ [ n (x2 ) - (x)2 ]
a = [172 * 314 - 36 * 729]/[5 * 314 - 362]
a = 27764/ 274 = 101.3
b = [ n(xy) - (x)((y)]/ [ n (x2 ) - (x)2 ]
b = [5 * 729 - 36 * 172] / [5 * 314 - 362]
b = -2547/ 274 = -9.296
y^ = 101.3 - 9.295x
Here we can say that if we increase one minute in mean call to shock time that will reduce the survival rate by 9.295%
(b) Here if x = 15 minutes
y^ = 101.3 - 9.295 * 15 = -38.125
as that value is negative that means there is no survival if mean call to shock time is 15 minutes.
x y x^2 xy 2 90 4 180 6 45 36 270 7 30 49 210 9 5 81 45 12 2 144 24 Sum 36 172 314 729Related Questions
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