Problem 4-13 Johnson Filtration, Inc., provides maintenance service for water fi

Question

Problem 4-13

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 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

Explanation / Answer

a)in the following regression analysis between repair time (y variable) and time gap in last service(x- variable) ftable<fcalculated null hypothesis is acccepted i.e. that there is no causation between the two.

b) predicted repair time and residuals can be found in the regression analysis.

c) after sorting the data we see the pattern that in case of Donna Newton residuals are generally less than in case of bob jones whereas it should be same. this insight gives us the suggession that there is potential of modification in linear regression equation .

scatter chart in Excel with months since last service on the x-axis and repair time in hours on the y-axis

iv) chart represents the best.

scatter chart in Excel of months since last service and repair time in hours

iv) represents the best

as the points are not scattered in a straight line there is potential for modification

f)

we will use the earlier model where electrical=1, mechanical=0 because the coffeficient of determination R square is more than the other case. r square defines to what percentage independent variables are able to explain the predicting variables.

Repair Time in Months Since Last Type of Repair Repairperson SUMMARY OUTPUT Hours Service 2.9 2   Electrical   Donna Newton Regression Statistics 3 6   Mechanical   Donna Newton Multiple R 0.730873795 4.8 8   Electrical   Bob Jones R Square 0.534176504 1.8 3   Mechanical   Donna Newton Adjusted R Square 0.475948567 2.9 2   Electrical   Donna Newton Standard Error 0.781022322 4.9 7   Electrical   Bob Jones Observations 10 4.2 9   Mechanical   Bob Jones 4.8 8   Mechanical   Bob Jones ANOVA 4.4 4   Electrical   Bob Jones df SS MS F Significance F 4.5 6   Electrical   Donna Newton Regression 1 5.596033058 5.596033 9.1738868 0.016338159 Residual 8 4.879966942 0.609996 Total 9 10.476 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 2.147272727 0.604977289 3.549344 0.0075166 0.752192597 3.542353 0.752193 3.542353 X Variable 1 0.304132231 0.100412033 3.028842 0.0163382 0.072581669 0.535683 0.072582 0.535683

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