Johnson Filtration, Inc., provides maintenance service for water-filtration systems throughout southern Florida. Customers contact Johnson with requests for maintenance service on their water-filtration systems. To estimate the service time and the service cost, Johnson's managers want to predict the repair time necessary for each maintenance request. Hence, repair time in hours is the dependent variable. Repair time is believed to be related to three factors, the number of months since the last maintenance service, the type of repair problem (mechanical or electrical), and the repairperson who performed the service. Data for a sample of 10 service calls are reported in the table below.
| Repair Time in Hours |
Months Since Last Service |
Type of Repair | Repairperson |
|---|---|---|---|
| 2.9 | 2 | Electrical | Dave Newton |
| 3.0 | 6 | Mechanical | Dave Newton |
| 4.8 | 8 | Electrical | Bob Jones |
| 1.8 | 3 | Mechanical | Dave Newton |
| 2.9 | 2 | Electrical | Dave Newton |
| 4.9 | 7 | Electrical | Bob Jones |
| 4.2 | 9 | Mechanical | Bob Jones |
| 4.8 | 8 | Mechanical | Bob Jones |
| 4.4 | 4 | Electrical | Bob Jones |
| 4.5 | 6 | Electrical | Dave Newton |
(a)
Ignore for now the months since the last maintenance service
(x1)
and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time
(y)
given the type of repair
(x2).
Let
x2 = 0
if the type of repair is mechanical and
x2 = 1
if the type of repair is electrical. (Round your numerical values to three decimal places.)? =
(b)
Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. (Round your answer to two decimal places.)
We see that ______ % of the variability in the repair time has been explained by the type of repair. Since this is ---Select--- less than at least 55%, the estimated regression equation ---Select--- provided did not provide a good fit for the observed data.
(c)
Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let
x3 = 0
if Bob Jones performed the service and
x3 = 1
if Dave Newton performed the service. (Round your numerical values to three decimal places.)? =
(d)
Does the equation that you developed in part (c) provide a good fit for the observed data? Explain. (Round your answer to two decimal places.)
We see that _______ % of the variability in the repair time has been explained by the repairperson. Since this is ---Select--- less than at least 55%, the estimated regression equation ---Select--- provided did not provide _____ a good fit for the observed data.