Johnson Filtration, Inc., provides maintenance service for water filtration systems throughout southern Florida. Customers contact Johnson with
Question:
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?
Step by Step Answer:
Essentials of Business Analytics
ISBN: 978-1285187273
1st edition
Authors: Jeffrey Camm, James Cochran, Michael Fry, Jeffrey Ohlmann, David Anderson, Dennis Sweeney, Thomas Williams