Johnson Filtration, Inc. provides maintenance service for water filtration systems throughout Southern Florida. Customers contact Johnson with requests for mainte- nance 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 mainte- nance service, the type of repair problem (mechanical or electrical), and the repairper- son who performs the repair (Donna Newton or Bob Jones). Data for a sample of 10 service calls are reported in the following table:

Repair Time in Hours

Months Since Last Service

Type of Repair

Repairperson

2.9

2

Electrical

Donna Newton

3.0

6

Mechanical

Donna Newton

4.8

8

Electrical

Bob Jones

1.8

3

Mechanical

Donna Newton

2.9

2

Electrical

Donna 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

Donna Newton

Repair

1. Develop the simple linear regression equation to predict repair time given the number of months since the last maintenance service, and use the results to test the hypothesis that no relationship exists between repair time and the number of months since the last maintenance service at the 0.05 level of significance. What is the inter- pretation of this relationship? What does the coefficient of determination tell you about this model?
2. Using the simple linear regression model developed in part (a), calculate the pre- dicted repair time and residual for each of the 10 repairs in the data. Sort the data in ascending order by value of the residual. Do you see any pattern in the residuals for the two types of repair? Do you see any pattern in the residuals for the two repair- persons? Do these results suggest any potential modifications to your simple linear regression model? how to make a scatter chart with months since last service on thex-axis and repair time in hours on they-axis for which the points representing electrical and mechanical repairs are shown in different shapes and/or colors? how to create similar scatter chart of months since last service and repair time in hours for which the points representing repairs by Bob Jones and Donna Newton are shown in different shapes and/or colors. Do these charts and the results of your residual analysis suggest the same potential modifications to your simple linear regression model?
3. How to create a new dummy variable that is equal to zero if the type of repair is mechanical and one if the type of repair is electrical. Develop the multiple regression equation to predict repair time, given the number of months since the last maintenance ser- vice and the type of repair. What are the interpretations of the estimated regression parameters? What does the coefficient of determination tell you about this model?
4. How to create a new dummy variable that is equal to zero if the repairperson is Bob Jones and one if the repairperson is Donna Newton. Develop the multiple regression equa- tion to predict repair time, given the number of months since the last maintenance service and the repairperson. What are the interpretations of the estimated regression parameters? What does the coefficient of determination tell you about this model?
5. Develop the multiple regression equation to predict repair time, given the number of months since the last maintenance service, the type of repair, and the repairperson. What are the interpretations of the estimated regression parameters? What does the coefficient of determination tell you about this model?
6. Which of these models would you use? Why?