6. Wile E. Coyote needs to know how long it will take for the dynamite to explod

Question

6. Wile E. Coyote needs to know how long it will take for the dynamite to explode after lighting the fuse He determines that fuse length and detonation time are linearly related and calculates the following: Average fuse length (): 10.1 inches Standard deviation of fuse length (s,): 2.97 inches Average time to detonate (y): 14.9 seconds Standard deviation of detonation time (s, ):3.43 seconds Correlation (r): 0.986 a) What is the linear regression equation? b) How long should he expect to wait before the dynamite explodes if the fuse length is 8 inches?

Explanation / Answer

a) here slope b1=r*Sy/Sx =0.986*3.43/2.97 =1.1387

and intercept b0 =Ybar-b1*Xbar =14.9-1.1387*10.1=3.3991

hence line equation yhat =1.1387x+3.3991

b)

for x=8 ; Y=1.1387*8+3.3991 =12.5087

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