Question

Studies have shown that people who suffer sudden cardiac arrest have a better chance of survival if a defibrillator shock 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?

The accompanying data give y = survival rate (percent) and x = mean call-to-shock time (minutes) for a cardiac rehabilitation center (in which 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	91	45	31	4	2

(b) Find the equation of the least-squares line. (Round your values to three decimal places.)

ŷ = __+(__)x

(c) Use the least-squares line to predict survival rate for a community with a mean call-to-shock time of 10 minutes. (Round your answer to three decimal places.)
ŷ = __

Answer 1

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	36.00	173.00	54.80	5301.20	-516.60
mean	7.20	34.60	SSxx	SSyy	SSxy

Sample size,   n =   5      
here, x̅ = Σx / n=   7.200          
ȳ = Σy/n =   34.600          
SSxx =    Σ(x-x̅)² =    54.8000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -516.6      
              
estimated slope , ß1 = SSxy/SSxx =   -516.6/54.8=   -9.4270      
intercept,ß0 = y̅-ß1* x̄ =   34.6- (-9.427 )*7.2=   102.4745      
              
Regression line is, Ŷ=   102.474   + (   -9.427   )*x

................

Predicted Y at X=   10   is          
Ŷ=   102.47445   +   -9.42701   *10=   8.204
................

thanks

please upvote