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A statistical program is recommended. A company provides maintenance service for water-filtration systems throughout southern Florida. Customers contact the company with requests for maintenance service on their water-filtration systems. To estimate the service time and the service cost, the company'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 performed the service. Data for a sample of 10 service calls are reported in the table below. Repair Time in 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 Mechanical Dave Newton 2.5 2 Electrical Dave Newton 4.9 7 Electrical Bob Jones 4.6 Mechanical Bob Jones 4.8 Mechanical Bob Jones 4.4 4 Electrical Bob Jones 4.5 Electrical Dave Newton (a) Ignore for now the months since the last maintenance service (x,) 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 (xɔ). Let x, = 0 if the type of repair is mechanical and x, = 1 if the type of repair is electrical. (Round your numerical values to three decimal places.) ŷ = 3.550 + .450x

A statistical program is recommended. A company provides maintenance service for water-filtration systems throughout southern Florida. Customers contact the company with requests for maintenance service on their water-filtration systems. To estimate the service time and the service cost, the company'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 performed the service. Data for a sample of 10 service calls are reported in the table below. Repair Time in 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 Mechanical Dave Newton 2.5 2 Electrical Dave Newton 4.9 7 Electrical Bob Jones 4.6 Mechanical Bob Jones 4.8 Mechanical Bob Jones 4.4 4 Electrical Bob Jones 4.5 Electrical Dave Newton (a) Ignore for now the months since the last maintenance service (x,) 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 (xɔ). Let x, = 0 if the type of repair is mechanical and x, = 1 if the type of repair is electrical. (Round your numerical values to three decimal places.) ŷ = 3.550 + .450x

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 22EQ
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A statistical program is recommended. A company provides maintenance service for water-filtration systems throughout southern Florida. Customers contact the company with requests for maintenance service on their water-filtration systems. To estimate the service time and the service cost, the company'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 performed the service. Data for a sample of 10 service calls are reported in the table below. Repair Time in Hours Months Since Type of Repair Repairperson Last Service 2.9 Electrical Dave Newton 3.0 6. Mechanical Dave Newton 4.8 8 Electrical Bob Jones 1.8 3 Mechanical Dave Newton 2.5 Electrical Dave Newton 4.9 7 Electrical Bob Jones 4.6 9. Mechanical Bob Jones 4.8 8 Mechanical Bob Jones 4.4 4 Electrical Bob Jones 4.5 6. Electrical Dave Newton (a) Ignore for now the months since the last maintenance service (x,) 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). Let x, numerical values to three decimal places.) = 0 if the type of repair is mechanical and x, = 1 if the type of repair is electrical. (Round your ŷ = 3.550 + .450x
Transcribed Image Text:A statistical program is recommended. A company provides maintenance service for water-filtration systems throughout southern Florida. Customers contact the company with requests for maintenance service on their water-filtration systems. To estimate the service time and the service cost, the company'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 performed the service. Data for a sample of 10 service calls are reported in the table below. Repair Time in Hours Months Since Type of Repair Repairperson Last Service 2.9 Electrical Dave Newton 3.0 6. Mechanical Dave Newton 4.8 8 Electrical Bob Jones 1.8 3 Mechanical Dave Newton 2.5 Electrical Dave Newton 4.9 7 Electrical Bob Jones 4.6 9. Mechanical Bob Jones 4.8 8 Mechanical Bob Jones 4.4 4 Electrical Bob Jones 4.5 6. Electrical Dave Newton (a) Ignore for now the months since the last maintenance service (x,) 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). Let x, numerical values to three decimal places.) = 0 if the type of repair is mechanical and x, = 1 if the type of repair is electrical. (Round your ŷ = 3.550 + .450x
(b) Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. (Round your answer to two decimal places.) We see that 4.10 % of the variability in the repair time has been explained by the type of repair. Since this is less than O 55%, the estimated regression equation did not provide O a good fit for the observed data. (c) 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 performed the service. (Round your numerical values to three decimal places.) = 0 if Bob Jones performed the service and x, = 1 if Dave Newton 4.700 – 1.760x3 (d) Does the equation that you developed in part (c) provide a good fit for the observed data? Explain. (Round your answer to two decimal places.) We see that % of the variability in the repair time has been explained by the repairperson. Since this is at least O 55%, the estimated regression equation provided O a good fit for the observed data.
Transcribed Image Text:(b) Does the equation that you developed in part (a) provide a good fit for the observed data? Explain. (Round your answer to two decimal places.) We see that 4.10 % of the variability in the repair time has been explained by the type of repair. Since this is less than O 55%, the estimated regression equation did not provide O a good fit for the observed data. (c) 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 performed the service. (Round your numerical values to three decimal places.) = 0 if Bob Jones performed the service and x, = 1 if Dave Newton 4.700 – 1.760x3 (d) Does the equation that you developed in part (c) provide a good fit for the observed data? Explain. (Round your answer to two decimal places.) We see that % of the variability in the repair time has been explained by the repairperson. Since this is at least O 55%, the estimated regression equation provided O a good fit for the observed data.
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