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An operations manager is interested in modeling E(y), the expected length of time per month (in hours) that a machine will be shut down for repairs, as a function of the type of machine (001 or 002) and the age of the machine (in years). The manager has proposed the following model:

E(y) = Î²0 + Î²1x1 + Î²2x21 +Î²3x2

where

x1 = Age of machine

x2 = 1 if machine type 001,0 if machine type 002

The following data were obtained for n = 20 machine breakdowns.

E(y) = Î²0 + Î²1x1 + Î²2x21 +Î²3x2

where

x1 = Age of machine

x2 = 1 if machine type 001,0 if machine type 002

The following data were obtained for n = 20 machine breakdowns.

a. Use the data (saved in the file) to estimate the parameters of this model.

b. Do these data provide sufficient evidence to conclude that the second-order term (x21) in the model proposed by the operations manager is necessary? Test using a = .05.

c. Test the null hypothesis that Î²1 = Î²2 = 0 using a = .10. Interpret the results of the test in the context of the problem.

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