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Problem 7-13 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 performs the repair (Donna Newton or Bob Jones). Data for a sample of 10 service calls are reported in the following table. Click on the datafile logo to reference the data.

Repair Time in Hours

Months Since Last Service

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

Type of Repair

Repairperson

(a) Use the data to develop the simple linear regression equation to predict repair time given the number of months since the last maintenance service. Let x represent the number of months since the last maintenance service. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300). =

2.1473

+

0.3041

x

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 interpretation of this relationship? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

What is the coefficient of determination? If required, round your answers to four decimal places. 0.5342

Interpret the coefficient of determination. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(b Using the simple linear regression model developed in part (a), calculate the predicted repair time ) and residual for each of the 10 repairs in the data. If required, round your answers to four decimal places. Repair Time Months Since Predicted Repair in Hours Last Service Type of Repair Repairperson Time in Hours

Residuals

1.8

3

Mechanical

Donna Newton

3.0597

-1.2597

3.0

6

Mechanical

Donna Newton

3.9721

-0.9721

4.2

9

Mechanical

Bob Jones

4.8845

-0.6845

2.9

2

Electrical

Donna Newton

2.7555

0.1445

2.9

2

Electrical

Donna Newton

2.7555

0.1445

4.8

8

Electrical

Bob Jones

4.5803

0.2197

4.8

8

Mechanical

Bob Jones

4.5803

0.2197

4.5

6

Electrical

Donna Newton

3.9721

0.5279

4.9

7

Electrical

Bob Jones

4.2762

0.6238

4.4

4

Electrical

Bob Jones

3.3638

1.0362

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 repairpersons? Do these results suggest any potential modifications to your simple linear regression model? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Create a scatter chart in Excel with months since last service on the x-axis and repair time in hours on the y-axis for which the points representing electrical and mechanical repairs are shown

in different shapes and or colors. Choose the correct chart below. (i)

(ii)

(iii )

(iv)

Chart (ii)

Create a similar scatter chart in Excel 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. Choose the correct chart below. (i)

(ii)

(iii )

(iv)

Chart (iii)

Do these charts and the results of your residual analysis suggest the same potential modifications

to your simple linear regression model? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(c) Create a new dummy variable that is equal to 0 if the type of repair is mechanical and 1 if the type of repair is electrical. Develop the multiple regression equation in Excel to predict repair time, given the number of months since the last maintenance service and the type of repair. Let x1 represent the number of months since the last maintenance service. Let x2 represent the type of repair. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300). =

0.9305

+

0.3876

x1 +

1.2627

x2

What are the interpretations of the estimated regression parameters? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

What is the coefficient of determination? If required, round your answers to four decimal places. 0.8592

Interpret the coefficient of determination The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(d Create a new dummy variable that is equal to 0 if the repairperson is Bob Jones and 1 if the ) repairperson is Donna Newton. Develop the multiple regression equation in Excel to predict repair time, given the number of months since the last maintenance service and the repairperson. Let x1 represent the number of months since the last maintenance service. Let x2 represent the repairperson. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

=

3.5263

+

0.1519

x1 +

-1.0835

x2

What are the interpretations of the estimated regression parameters? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

What is the coefficient of determination? If required, round your answers to four decimal places. 0.6805

Interpret the coefficient of determination. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(e) 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. Let x1 represent the number of months since the last maintenance service. Let x2 represent the type of repair. Let x3 represent the repairperson. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300). =

1.8602

+

0.2914

x1 +

1.1024

x2 +

-0.6091

x3

What are the interpretations of the estimated regression parameters? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

What is the coefficient of determination? If required, round your answers to four decimal places. 0.9002

Interpret the coefficient of determination. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(f) Which of these models would you use? Why? The input in the box below will not be graded, but may be reviewed and considered by your instructor....