Question

A hospital analyzed the relationship between the distance an employee must travel between home and work in 10s of miles) and the annual number of unauthorized work absences (in days) for several randomly selected hospital employees. The regression analysis showed dfErr 13,5x24.56, 5Syy 69,60, and Syy--38.20. What is the 95% confidence interval for B1 (with appropriate units)? a. None of the answers is correct b.(-0.1941 days/mile,-0.1170 days/mile) (-1.8717 days, -1.2391 days) O d.(-1.9412 days. - 1.1696 days) O.(-19.4116 days/mile. -11.6959 days/mile)

Answer 1

n=	15
SSx=Σx2-(Σx)2/n=	24.56
SSy=Σy2-(Σy)2/n=	69.6
SP=Σxy-(ΣxΣy)/n=	-38.2
SST=Syy=	69.6
SSE =Syy-(Sxy)2/Sxx=	10.1847
SSR =(Sxy)2/Sxx =	59.4153
b1= SSxy/Sx =	-1.5554
σ̂2=SSE/(n-2)=	0.7834
Sb1 =σ̂/√SSx =	0.1786

for 95% confidence and n-2 degree of freedom critical t =			2.16
lower bound =b1-t*sb1=	-1.941
upper bound =b1+t*sb1=	-1.170

option B is correct (since it is /mile and not /10's of mile)

b.(-0.1941 days/mile,-0.1170 days/mile)