In a production facility, an accurate estimate of hours needed to complete a task is crucial to management in making such decisions as hiring the proper number of workers, quoting an accurate deadline for a client, or performing cost analyses regarding budgets. A manufacturer of boiler drums wants to use regression to predict the number of hours needed to erect the drums in future projects. To accomplish this task, data on 36 boilers were collected. In addition to hours (y), the variables measured were boiler capacity 1x1 = lb>hr2, boiler design pressure (x2 = pounds per square inch, or psi), boiler type (x3 = 1 if industry field erected, 0 if utility field erected), and drum type (x4 = 1 if steam, 0 if mud). The data are saved in the BOILERS file. (Selected observations are shown in the table below.)

a. Fit the model E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4 to the data and give the prediction equation.
b. Conduct a test for the global utility of the model. Use a = .01.
c. Find a 95% confidence interval for E(y) when x1 = 150,000, x2 = 500, x3 = 1, and x4 = 0. Interpret the result.
d. What type of interval would you use if you want to estimate the average number of hours required to erect all industrial mud boilers with a capacity of 150,000 lb/hr and a design pressure of 500 psi?

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Boiler Design Pressure x9 Boiler Drum Capacity x1 Hours y Туре Xз Туре х4 3,137 3,590 4,526 10,825 4,023 120,000 65,000 150,000 1,073,877 150,000 375 750 500 2,170 325 4,206 4,006 3,728 3,211 1,200 441,000 441,000 627,000 610,000 30,000 410 1 410 1,525 1,500 325