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 df_{Err} = 14, SS_{xx} = 26.92, SS_{yy} = 104.00, and SS_{xy} = 50.40.
What is the 90% confidence interval for β_{1} (with appropriate units)?
a. 
(21.5386 days/mile, 15.9057 days/mile) 

b. 
None of the answers is correct 

c. 
(2.0873 days, 1.6571 days) 

d. 
(2.1539 days, 1.5906 days) 

e. 
(0.2154 days/mile, 0.1591 days/mile) 
Answer:
Given,
Slope β_{1} = SSxy/SSxx
substitute the given values
=  50.40/26.92
β_{1} = 1.8722
Now,
SSE = SSyy  β_{1}*Sxy
substitute the given values
= 104  (1.8722*(50.40))
= 104  94.3589
SSE = 9.6411
S = sqrt(SSE/df)
substitute the given values
= sqrt(9.6411/14)
S = 0.8298
let us consider,
Sb = S/sqrt(SSxx)
substitute the given values
= 0.8298/sqrt(26.92)
= 0.15993
t(alpha/2 , df) = t(0.1/2 , 14)
t = 1.761
90% confidence interval =β_{1} +/ t*Sβ_{1}
substitute the known values
= 1.8722 +/ 1.761*0.15993
= 1.8722 +/ 0.28163673
= (1.8722  0.28163673 ,  1.8722 + 0.28163673)
= (2.1539 , 1.5906)
So Option B is right answer.
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