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Boiler drum production. In a production facility,
Chapter 12, Problem 33E(choose chapter or problem)
Boiler drum production. 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 \(\left(x_1=\mathrm{lb} / \mathrm{hr}\right)\), boiler design pressure \(\left(x_2=\right.\) pounds per square inch or psi), boiler type \(\left(x_3=1\right.\) if industry field erected, 0 if utility field erected), and drum type \(\left(x_4=1\right.\) 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 \(E(y)=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\beta_4 x_4\) to the data. Give the estimates of the \(\beta\)'s.
b. Conduct a test for the global utility of the model. Use \(\alpha=.01\)
c. Find a 95% confidence interval for E(y) when \(x_1=\) \(150,000, x_2=500, x_3=1\), and \(x_4=0\). Interpret the result.
Questions & Answers
QUESTION:
Boiler drum production. 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 \(\left(x_1=\mathrm{lb} / \mathrm{hr}\right)\), boiler design pressure \(\left(x_2=\right.\) pounds per square inch or psi), boiler type \(\left(x_3=1\right.\) if industry field erected, 0 if utility field erected), and drum type \(\left(x_4=1\right.\) 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 \(E(y)=\beta_0+\beta_1 x_1+\beta_2 x_2+\beta_3 x_3+\beta_4 x_4\) to the data. Give the estimates of the \(\beta\)'s.
b. Conduct a test for the global utility of the model. Use \(\alpha=.01\)
c. Find a 95% confidence interval for E(y) when \(x_1=\) \(150,000, x_2=500, x_3=1\), and \(x_4=0\). Interpret the result.
ANSWER:
Step 1 of 4
Using the Minitab, we obtain the regression analysis for BOILERS file:
