# Question: Johnson Filtration Inc provides maintenance service for water filtration systems

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 ten service calls are reported in the following\ table:

a. 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 interpretation of this relationship? What does the coefficient of determination tell you about this model?

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. 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? Now create a scatter chart 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. Create a similar scatter chart 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, Do these charts and the results of your residual analysis suggest the same potential modifications to your simple linear regression model?

c. 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 service 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?

d. 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 equation 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?

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.

What are the interpretations of the estimated regression parameters? What does the coefficient of determination tell you about this model?

f. Which of these models would you use? Why?

a. 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 interpretation of this relationship? What does the coefficient of determination tell you about this model?

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. 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? Now create a scatter chart 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. Create a similar scatter chart 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, Do these charts and the results of your residual analysis suggest the same potential modifications to your simple linear regression model?

c. 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 service 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?

d. 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 equation 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?

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.

What are the interpretations of the estimated regression parameters? What does the coefficient of determination tell you about this model?

f. Which of these models would you use? Why?

**View Solution:**## Answer to relevant Questions

A study investigated the relationship between audit delay (the length of time from a company’s fiscal year-end to the date of the auditor’s report) and variables that describe the client and the auditor. Some of the ...A recent ten-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic blood pressure, and smoking relate to the risk of strokes. Assume that the following data are ...A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 156 students who took the course last semester are provided in the ...The values of Alabama building contracts (in millions of dollars) for a 12-month period follow: 240 350 230 260 280 320 220 310 240 310 240 230 a. Construct a time series plot. What type of pattern exists in the data? b. ...Consider the following time series data: a. Construct a time series plot. What type of pattern exists in the data? b. Use a multiple regression model with dummy variables as follows to develop an equation to account for ...Post your question