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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	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

(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.

Letxrepresent 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).

=+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.

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 in Hours	Months Since Last Service	Type of Repair	Repairperson	Predicted Repair Time in Hours	Residuals
1.8	3	Mechanical	Donna Newton
3.0	6	Mechanical	Donna Newton
4.2	9	Mechanical	Bob Jones
2.9	2	Electrical	Donna Newton
2.9	2	Electrical	Donna Newton
4.8	8	Electrical	Bob Jones
4.8	8	Mechanical	Bob Jones
4.5	6	Electrical	Donna Newton
4.9	7	Electrical	Bob Jones
4.4	4	Electrical	Bob Jones

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?

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Create a scatter chart in Excel 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. Choose the correct chart below.

(i)
(ii)
(iii)
(iv)

- Select your answer -Chart (i)Chart (ii)Chart (iii)Chart (iv)Item 27

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)

- Select your answer -Chart (i)Chart (ii)Chart (iii)Chart (iv)Item 28

Do these charts and the results of your residual analysis suggest the same potential modifications to your simple linear regression model?

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(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.

Letx₁represent the number of months since the last maintenance service.

Letx₂represent 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).

=+x₁+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.

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.

Letx₁represent the number of months since the last maintenance service.

Letx₂represent 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)

=+x₁+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.

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.

Letx₁represent the number of months since the last maintenance service.

Letx₂represent the type of repair.

Letx₃represent 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).

=+x₁+x₂+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.

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?