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 || 4.0 | 8 | Electrical | Bob Jones || 1.8 | 3 | Mechanical | Dave Newton || 2.5 | 7 | Electrical | Dave Newton || 4.9 | 7 | Electrical | Bob Jones || 4.2 | 8 | Mechanical | Bob Jones || 4.8 | 8 | Mechanical | Bob Jones || 4.4 | 4 | Electrical | Bob Jones || 4.5 | 6 | Electrical | Dave Newton |**Questions and Tasks:**(a) Ignore for now the months since the last maintenance service (\(x_1\)) 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 (\(x_2\)). Let \(x_2 = 0\) if the type of repair is mechanical and \(x_2 = 1\) if the type of repair is electrical. (Round your numerical values to three decimal places.)\[ \hat{y} = 0.794 + 0.409{x_1} + 1.231{x_2} \]Check which variable(s)/term(s) should be in your equation.(b) Does the equation that you developed in part (a) provide

It is required to obtain the two different regression equations, once with Type of Repair as the…

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 Months Since in Hours Last Service 2.9 3.0 4.8 1.8 2.5 4.9 4.2 4.8 4.4 4.5 2 6 8 3 2 7 9 8 4 6 Type of Repair Repairperson Electrical Mechanical Electrical Mechanical Electrical Electrical Mechanical Mechanical Electrical Electrical Dave Newton Dave Newton 9= x Check which variable(s)/term(s) should be in your equation. Bob Jones Dave Newton Dave Newton Bob Jones Bob Jones Bob Jones Bob Jones Dave Newton (a) Ignore for now the months since the last maintenance service (x₂) 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 x₂ = 0 if the type of repair is mechanical and x₂ = 1 if the type of repair is electrical. (Round your numerical values to three decimal places.) 0.794+0.409x +1.231x2 (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 % of the variability in the repair time has been explained by the type of repair. Since this is less than 55%, the estimated regression equation [did not provide ation did not provide 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 x₂ = 0 if Bob Jones performed the service and x₂ = 1 if Dave Newton performed the service. (Round your numerical values to three decimal places.) (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 55%, the estimated regression equation provided ✔a good fit for the observed data.