XYZ company provides maintenance service for water filtration systems in London. Customers contact XYZ with requests for maintenance service on their water filtration systems. To estimate the service time and the service cost, XYZs 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 20 service calls are reported in the following table:

(copy and paste data into your excel to do the calculations)

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
2.9	2	Electrical	Donna Newton
3.0	6	Mechanical	Donna Newton
4.8	8	Mechanical	Donna Newton
1.8	3	Mechanical	Donna Newton
2.9	2	Electrical	Donna Newton
4.9	7	Electrical	Bob Jones
4.2	9	Electrical	Bob Jones
4.8	8	Mechanical	Bob Jones
4.4	4	Electrical	Bob Jones
4.5	6	Electrical	Donna Newton

Answer the following questions (paste your excel output/graph, where relevant, in the space provided):

1. 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? Suppose that excel is not working and all you have got is the estimated coefficient and its standard error, how would you test the significance of the independent variable number of months since the last maintenance service at the 0.05 level. Show calculations. What does the coefficient of determination tell you about this model?
2. Using the simple linear regression model developed in part (a), calculate the predicted repair time and residual for each of the 20 repairs in the data. 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? 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 colours. Create a similar scatter chart 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 colours. Do these charts and the results of your residual analysis suggest the same potential modifications to your simple linear regression model?
3. 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? Are they significant at the 0.05 and at the 0.01 level of significance? What do you conclude about the overall significance of the regression model? What does the coefficient of determination tell you about this model?
4. 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? Are they significant at the 0.05 and at the 0.01 level of significance? What do you conclude about the overall significance of the regression model? What does the coefficient of determination tell you about this model?
5. 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? Are they significant at the 0.05 and at the 0.01 level of significance? What do you conclude about the overall significance of the regression model? What does the coefficient of determination tell you about this model? Would you worry about multicollinearity in this model? Why or why not?
6. Suppose that it is believed that the relationship between repair time and the number of months since last maintenance service is non-linear. Develop a model that extends the multiple regression to predict repair time by including the non-linear term, 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? Would you worry about multicollinearity in this model? Why or why not?
7. Which of these models would you use? Why?