Boiler drum production. 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.)

Hours y Boiler Capacity x1 Design Pressure x2 Boiler Type x3 Drum Type x4 3,137 120,000 375 1 1 3,590 65,000 750 1 1 4,526 150,000 500 1 1 10,825 1,073,877 2,170 0 1 4,023 150,000 325 1 1 f f f f f 4,206 441,000 410 1 0 4,006 441,000 410 1 0 3,728 627,000 1,525 0 0 3,211 610,000 1,500 0 0 1,200 30,000 325 1 0 Based on data provided by Dr. Kelly Uscategui, University of Connecticut.

a. Fit the model E1y2 = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 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?