Question

# A hospital analyzed the relationship between the distance an employee must travel between home and work...

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 = 14, SSxx = 26.92, SSyy = 104.00, and SSxy = -50.40.

What is the 90% confidence interval for β1 (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)

Given,

Slope β1 = SSxy/SSxx

substitute the given values

= - 50.40/26.92

β1 = -1.8722

Now,

SSE = SSyy - β1*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 =β1 +/- t*Sβ1

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.