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 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) 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 Because the p value is Select your answer greater thanless thanItem 3 0 05, we Select your answer cancannotItem 4 conclude that there is a relationship between repair time and the number of months since the last maintenance service What is the coefficient of determination If required, round your answers to four decimal places Interpret the coefficient of determination If required, round your answer to one decimal place This regression model explains approximately of the variation in the values of repair time in the sample (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 NOTE The table below is sorted in ascending order by value of the residual Your output in Excel will not be sorted and therefore will look different It is recommended that you copy the Excel residual output to a new area of the spreadsheet and then sort the copied output using Excel's sorting tools If required, round your answers to four decimal places For subtractive or negative numbers use a minus sign 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 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 (i) Mechanical repairs generally have negative residuals and electrical repairs generally have positive residuals Two of the repairs made by Donna Newton have large negative residuals and repairs made by Bob Jones typically have positive residuals The results suggest that using dummy variables to represent the type of repair and repairperson may enhance this fit of the regression model (ii) Mechanical repairs generally have positive residuals and electrical repairs generally have negative residuals Two of the repairs made by Donna Newton have large positive residuals and repairs made by Bob Jones typically have negative residuals The results suggest that using dummy variables to represent the type of repair and repairperson may enhance this fit of the regression model (iii) Mechanical repairs generally have negative residuals and electrical repairs generally have positive residuals Two of the repairs made by Donna Newton have large negative residuals and repairs made by Bob Jones typically have positive residuals The results suggest that using a dummy variable to represent only the type of repair may enhance this fit of the regression model (iv) Mechanical repairs generally have positive residuals and electrical repairs generally have negative residuals Two of the repairs made by Donna Newton have large positive residuals and repairs made by Bob Jones typically have negative residuals The results suggest that the use of dummy variables is not needed Select your answer Option (i)Option (ii)Option (iii)Option (iv)Item 27 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) Select your answer Chart (i)Chart (ii)Chart (iii)Chart (iv)Item 28 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 29 Do these charts and the results of your residual analysis suggest the same potential modifications to your simple linear regression model Select your answer YesNoItem 30 (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 x 1 represent the number of months since the last maintenance service Let x 2 represent the type of repair (a dummy variable) 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 1 x 2 What are the interpretations of the estimated regression parameters (i) b 1 is the best estimate of the change in repair time if we hold the repairperson constant and the type of repair is electrical, not mechanical b 2 the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service (ii) b 1 the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical b 2 is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service (iii) b 1 is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service b 2 the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical (iv) b 1 is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service b 2 the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is mechanical, not electrical Select your answer Option (i)Option (ii)Option (iii)Option (iv)Item 34 What is the coefficient of determination If required, round your answers to four decimal places Interpret the coefficient of determination If required, round your answer to one decimal place This regression model explains approximately of the variation in the values of repair time in the sample (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 x 1 represent the number of months since the last maintenance service Let x 2 represent the repairperson (a dummy variable) 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 1 x 2 What are the interpretations of the estimated regression parameters (i) b 1 the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the repairperson is Donna Newton, not Bob Jones b 2 is the best estimate of the change in repair time if we hold repairperson constant and have a 1 month increase in the number of months since the last maintenance service (ii) b 1 is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service b 2 the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical (iii) b 1 the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical b 2 is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service (iv) b 1 is the best estimate of the change in repair time if we hold repairperson constant and have a 1 month increase in the number of months since the last maintenance service b 2 the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the repairperson is Donna Newton, not Bob Jones Select your answer Option (i)Option (ii)Option (iii)Option (iv)Item 40 What is the coefficient of determination If required, round your answers to four decimal places Interpret the coefficient of determination If required, round your answer to one decimal place This regression model explains approximately of the variation in the values of repair time in the sample (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 x 1 represent the number of months since the last maintenance service Let x 2 represent the type of repair (a dummy variable) Let x 3 represent the repairperson (a dummy variable) 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 1 x 2 x 3 What are the interpretations of the estimated regression parameters (i) b 1 is the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and the repairperson is Bob Jones b 2 is the best estimate of the change in repair time if we hold type of repair and repairperson constant and have a 1 month increase in the number of months since the last maintenance service b 3 the best estimate of the change in repair time if we hold the number of months since the last maintenance service and repairperson constant and the type of repair is electrical and not mechanical (ii) b 1 is the best estimate of the change in repair time if we hold type of repair and repairperson constant and have a 1 month increase in the number of months since the last maintenance service b 2 the best estimate of the change in repair time if we hold the number of months since the last maintenance service and repairperson constant and the type of repair is electrical and not mechanical b 3 is the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and the repairperson is Donna Newton (iii) b 1 is the best estimate of the change in repair time if we hold the number of months since the last maintenance and type of repair constant and the type of repair is mechanical and not electrical b 2 the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and have a 1 month increase in the number of months since the last maintenance service b 3 is the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and the repairperson is Bob Jones Select your answer Option (i)Option (ii)Option (iii)Item 47 What is the coefficient of determination If required, round your answers to four decimal places Interpret the coefficient of determination If required, round your answer to one decimal place This regression model explains approximately of the variation in the values of repair time in the sample (f) Which of these models would you use Why (i) The preferred model is the one with the lowest coefficient of determination, so the best model to use is in part (c) (ii) The preferred model is the one with the lowest coefficient of determination, so the best model to use is in part (d) (iii) The preferred model is the simplest that works well, so the best model to use is in part (c) (iv) The preferred model is the one with the highest coefficient of determination, so the best model to use is in part (c) (v) The preferred model is the one with the highest coefficient of determination, so the best model to use is in part (d) Select your answer Option (i)Option (ii)Option (iii)Option (iv)Option (v)Item 50

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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

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?

Because thep-value is - Select your answer -greater thanless thanItem 3 0.05, we - Select your answer -cancannotItem 4 conclude that there is a relationship between repair time and the number of months since the last maintenance service.

What is the coefficient of determination?

If required, round your answers to four decimal places.

Interpret the coefficient of determination. If required, round your answer to one decimal place.

This regression model explains approximately % of the variation in the values of repair time in the sample.

(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. NOTE: The table below is sorted in ascending order by value of the residual. Your output in Excel will not be sorted and therefore will look different. It is recommended that you copy the Excel residual output to a new area of the spreadsheet and then sort the copied output using Excel's sorting tools.

If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign.

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

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?

(i)	Mechanical repairs generally have negative residuals and electrical repairs generally have positive residuals. Two of the repairs made by Donna Newton have large negative residuals and repairs made by Bob Jones typically have positive residuals. The results suggest that using dummy variables to represent the type of repair and repairperson may enhance this fit of the regression model.
(ii)	Mechanical repairs generally have positive residuals and electrical repairs generally have negative residuals. Two of the repairs made by Donna Newton have large positive residuals and repairs made by Bob Jones typically have negative residuals. The results suggest that using dummy variables to represent the type of repair and repairperson may enhance this fit of the regression model.
(iii)	Mechanical repairs generally have negative residuals and electrical repairs generally have positive residuals. Two of the repairs made by Donna Newton have large negative residuals and repairs made by Bob Jones typically have positive residuals. The results suggest that using a dummy variable to represent only the type of repair may enhance this fit of the regression model.
(iv)	Mechanical repairs generally have positive residuals and electrical repairs generally have negative residuals. Two of the repairs made by Donna Newton have large positive residuals and repairs made by Bob Jones typically have negative residuals. The results suggest that the use of dummy variables is not needed.

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

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 28

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 29

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

- Select your answer -YesNoItem 30

(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 (a dummy variable).

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?

(i)	b₁is the best estimate of the change in repair time if we hold the repairperson constant and the type of repair is electrical, not mechanical.b₂the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service.
(ii)	b₁the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical.b₂is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service.
(iii)	b₁is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service.b₂the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical.
(iv)	b₁is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service.b₂the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is mechanical, not electrical.

- Select your answer -Option (i)Option (ii)Option (iii)Option (iv)Item 34

What is the coefficient of determination?

If required, round your answers to four decimal places.

Interpret the coefficient of determination. If required, round your answer to one decimal place.

This regression model explains approximately % of the variation in the values of repair time in the sample.

(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 (a dummy variable).

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?

(i)	b₁the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the repairperson is Donna Newton, not Bob Jones.b₂is the best estimate of the change in repair time if we hold repairperson constant and have a 1 month increase in the number of months since the last maintenance service.
(ii)	b₁is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service.b₂the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical.
(iii)	b₁the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the type of repair is electrical, not mechanical.b₂is the best estimate of the change in repair time if we hold the type of repair constant and have a 1 month increase in the number of months since the last maintenance service.
(iv)	b₁is the best estimate of the change in repair time if we hold repairperson constant and have a 1 month increase in the number of months since the last maintenance service.b₂the best estimate of the change in repair time if we hold the number of months since the last maintenance service constant and the repairperson is Donna Newton, not Bob Jones.

- Select your answer -Option (i)Option (ii)Option (iii)Option (iv)Item 40

What is the coefficient of determination?

If required, round your answers to four decimal places.

Interpret the coefficient of determination. If required, round your answer to one decimal place.

This regression model explains approximately % of the variation in the values of repair time in the sample.

(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 (a dummy variable).

Letx₃represent the repairperson (a dummy variable).

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?

(i)	b₁is the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and the repairperson is Bob Jones.b₂is the best estimate of the change in repair time if we hold type of repair and repairperson constant and have a 1 month increase in the number of months since the last maintenance service.b₃the best estimate of the change in repair time if we hold the number of months since the last maintenance service and repairperson constant and the type of repair is electrical and not mechanical.
(ii)	b₁is the best estimate of the change in repair time if we hold type of repair and repairperson constant and have a 1 month increase in the number of months since the last maintenance service.b₂the best estimate of the change in repair time if we hold the number of months since the last maintenance service and repairperson constant and the type of repair is electrical and not mechanical.b₃is the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and the repairperson is Donna Newton.
(iii)	b₁is the best estimate of the change in repair time if we hold the number of months since the last maintenance and type of repair constant and the type of repair is mechanical and not electrical.b₂the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and have a 1 month increase in the number of months since the last maintenance service.b₃is the best estimate of the change in repair time if we hold the number of months since the last maintenance service and type of repair constant and the repairperson is Bob Jones.

- Select your answer -Option (i)Option (ii)Option (iii)Item 47

What is the coefficient of determination?

If required, round your answers to four decimal places.

Interpret the coefficient of determination. If required, round your answer to one decimal place.

This regression model explains approximately % of the variation in the values of repair time in the sample.

(f)

Which of these models would you use? Why?

(i)	The preferred model is the one with the lowest coefficient of determination, so the best model to use is in part (c).
(ii)	The preferred model is the one with the lowest coefficient of determination, so the best model to use is in part (d).
(iii)	The preferred model is the simplest that works well, so the best model to use is in part (c).
(iv)	The preferred model is the one with the highest coefficient of determination, so the best model to use is in part (c).
(v)	The preferred model is the one with the highest coefficient of determination, so the best model to use is in part (d).