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) = β0 + β1x1 + β2x21 +β3x2
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 β1 = β2 = 0 using a = .10. Interpret the results of the test in the context of the problem.

Transcribed Image Text:

Downtime (hours per month) 10 Machine Age, Machine Type x L.O 2.0 2.7 4.1 001 001 001 40 001 001 001 001 001 001 1.9 5.0 2.1 41 10 2.0 4.0 5,0 8.0 2.4 002 3.5 70 4.0 2.1 002 42