Problem 7-13 Johnson Filtration, Inc., provides maintenance service for water fi
ID: 2921906 • Letter: P
Question
Problem 7-13
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.
Repair Time inHours 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
Explanation / Answer
d)
y=3.526+0.15x1-1.08x2
Sum of Squares Regression=7.13
Sum of Squares Residual=3.34688
Sum of Squares Total=10.476
Coefficient of Determination=0.6805 which means 68.05% of the variation in dependent variable is accounted for by the independent variable.
e)
y=2.96+0.29x1-1.10x2-0.609x3
Sum of Squares Regression=9.43
Sum of Squares Residual=1.0455
Sum of Squares Total=10.476
Coefficient of Determination=0.90 which means 90 % of the variation in dependent variable is accounted for by the independent variable.
f)
You can use the model with all the variables because r^2 is higher and also the p-values are significant except for Repairperson. Whereas in case of model with two independent variables, p-values are not significant for both independent variables.
Regression with two independent variables: -
Regression with three independent variables: -
SUMMARY OUTPUT Regression Statistics Multiple R 0.824935575 R Square 0.680518702 Adjusted R Square 0.589238331 Standard Error 0.691466978 Observations 10 ANOVA df SS MS F Significance F Regression 2 7.129113924 3.564556962 7.455257863 0.01843143 Residual 7 3.346886076 0.478126582 Total 9 10.476 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 3.526329114 0.938080487 3.759090144 0.007083316 1.308121244 5.744536984 Months Since Last 0.151898734 0.123006455 1.234884249 0.256712707 -0.138965313 0.442762781 Repairperson -1.083544304 0.605111751 -1.790651566 0.116466678 -2.514406224 0.347317617