Refer to the Johnson Filtration problem introduced in Section 13.7 of the textbo
ID: 3358455 • Letter: R
Question
Refer to the Johnson Filtration problem introduced in Section 13.7 of the textbook. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow. The data is shared with the “Repair” data file.
Repair Time
(hours)
Months Since
Last Service
Type of
Repair
Repairperson
2.9
2
electrical
Dave Newton
3.0
6
mechanical
Dave Newton
4.8
8
electrical
Bob Jones
1.8
3
mechanical
Dave Newton
2.9
2
electrical
Dave 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
Dave Newton
1. Ignore for now the months since the last maintenance service (x1) and the repairperson who performed the service. Develop the estimated simple linear regression equation to predict the repair time ( y) given the type of repair (x2). Recall that x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical.
2. Does the equation that you developed in part (1) provide a good fit for the observed data? Explain.
3. Ignore for now the months since the last maintenance service and the type of repair associated with the machine. Develop the estimated simple linear regression equation to predict the repair time given the repairperson who performed the service. Let x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.
4. Does the equation that you developed in part (3) provide a good fit for the observed data? Explain.
5. Develop the estimated multiple regression equation to predict the repair time given the repairperson who performed the service, month since last service and the type of the repair. (Use dummy variables for categorical variable as instructed at part 1 and 3 for running the regression).
6. Does the equation that you developed in part (5) provide a good fit for the observed data? Explain.
Repair Time
(hours)
Months Since
Last Service
Type of
Repair
Repairperson
2.9
2
electrical
Dave Newton
3.0
6
mechanical
Dave Newton
4.8
8
electrical
Bob Jones
1.8
3
mechanical
Dave Newton
2.9
2
electrical
Dave 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
Dave Newton
Explanation / Answer
ANSWER :-
a)
simple linear regression equation is y=a+bx1+cx2
last maintenance service (x1), repair time (y) given the type of repair (x2).
If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical
The Fitted regression model is y = 0.96+0.38x1 + 1.27 x2
b)
Since R square is 0.84.hence we say that x1 and x2 are 84% variation on y. Hence we conclude that the above equation is best fit for the data.
c)
simple linear regression equation is y=a+bx1+cx2+dx3
last maintenance service (x1), repair time (y) given the type of repair (x2).
If x2 = 0 if the type of repair is mechanical and 1 if the type of repair is electrical. and x3 = 0 if Bob Jones performed the service and x3 = 1 if Dave Newton performed the service.
The Fitted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3
4)
Since R square is 0.89.hence we say that x1 and x2 are 89% variation on y. Hence we conclude that the above equation is best fit for the data. compare to part (2)
5) The predicted regression model is y = 1.87+0.29x1 + 1.11 x2 -0.61 x3