In a production facility, an accurate estimate of man-hours needed to complete a task is crucial to management in making such decisions as the proper number of workers to hire, an accurate deadline to quote a client, or cost-analysis decisions regarding budgets. A manufacturer of boiler drums wants to use regression to predict the number of man-hours needed to erect the drums in future projects. To accomplish this, data for 35 boilers were collected. In addition to man-hours (y), the variables measured were boiler capacity (x1 = lb/hr), 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 file. (The first five and last five observations are listed in the accompanying table.)
a. Fit the model E(y) = β0 + β1x1 + β2x2 + β3x3 + β4x4 to the data. Give the estimates of the β's.
b. Conduct a test for the global utility of the model. Use α = .01.
c. Find a 95% confidence interval for E(y) when x1 = 150,000, x2 = 500, x3 = 1, and x4 = 0. Interpret the result.

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Man-Hours, Boiler Design Boiler Drum y Capacity, x1 Pressure, x2 Type, X3 Type, x4 375 750 500 10,825 1,073.877 2,170 325 3,137 3,590 4.526 120,000 65,000 150,000 0 4,023 150,000 4.206 4,006 3,728 3,211 1,200 441.000 441,000 627000 610,000 30,000 410 410 1,525 1.500 325 0