4-13 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 webfile logo to reference the data. Months Since Repair Time in Last Hours 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). = 3.5263 Item1 + 0.1519 Item2 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. blank Item3 What is the coefficient of determination? If required, round your answers to four decimal places. 0.6805 Item4 Interpret the coefficient of determination. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank Item5 (b Using the simple linear regression model developed in part (a), calculate the predicted repair time ) and residual for each of the ten repairs in the data. If required, round your answers to four decimal places. Repair Time in Hours Months Since Type of Last Service Repair Repairperson Predicted Repair Time in Hours Residuals 4.2 2.9 6 9 2 Mechanical Mechanical Mechanical Electrical Donna Newton 1 Item6 Item7 0 1 Item8 Item9 0 Item10 3.0 3 0 0 1.8 Donna Newton Item11 1 1 Item12 Item13 Bob Jones Donna Newton Electrical Item19 1 1 Item20 Item21 0 Item23 0 Item24 4 Electrical 0 1 4.4 7 Electrical Item17 Item22 4.9 6 Mechanical 0 1 4.5 8 Item15 Item18 4.8 Electrical Item14 0 8 Electrical 1 Item16 4.8 2 1 0 2.9 Donna Newton Item25 Bob Jones Bob Jones Donna Newton Bob Jones Bob Jones Sort the data by residual (so the data are 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. blank Item26 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) Item27 Create a similar scatter chart in Excel of months since last service and repair time in hours for which the points representing Bob Jones and Donna Newton repairs are shown in different shapes and or colors. Choose the correct chart below. (i) (ii) (iii ) (iv) Chart (iii) Item28 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. blank Item29 Create a new dummy variable that is equal to 0 if the type of repair is mechanical and 1 if the type of (c) 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). = 1.86 Item30 + 0.2914 Item31 x1 + 1.102 Item32 What are the interpretations of the estimated regression parameters? x2 The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank Item33 What is the coefficient of determination? If required, round your answers to four decimal places. 0.9002 Item34 Interpret the coefficient of determination The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank Item35 Create a new dummy variable that is equal to 0 if the repairperson is Bob Jones and 1 if the (d) 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 Item36 + 0.1519 Item37 x1 + -1.0835 Item38 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. blank Item39 What is the coefficient of determination? If required, round your answers to four decimal places. 0.685 Item40 Interpret the coefficient of determination. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank Item41 (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). = + 1.86 Item45 Item42 x1 + 0.2914 Item43 x2 + 1.102 Item44 -0.6090 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. blank Item46 What is the coefficient of determination? If required, round your answers to four decimal places. 0.9002 Item47 Interpret the coefficient of determination. The input in the box below will not be graded, but may be reviewed and considered by your instructor. blank Item48 (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. blank Item49 Repair Time in Hours 2.9 3.0 4.8 1.8 2.9 4.9 4.2 4.8 4.4 4.5 Months Since Last Service 2 6 8 3 2 7 9 8 4 6 Type of Repair Electrical Mechanical Electrical Mechanical Electrical Electrical Mechanical Mechanical Electrical Electrical Repairperson Donna Newton Donna Newton Bob Jones Donna Newton Donna Newton Bob Jones Bob Jones Bob Jones Bob Jones Donna Newton