11.86 An operations engineer 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).

He has proposed the following model:

where x1 age of machine Data were obtained on n 20 machine breakdowns and were used to estimate the parameters of the above model. A portion of the regression analysis computer printout is shown in figure below.

x1 = b 1 if machine type 001 0 if machine type 002 E(Y ) = b0 + b1x1 + b2x 21

+ b3x2

The reduced model was fit to the same data. The regression analysis computer printout is partially reproduced in figure below.
E(Y) = b0 + b1x1 + b2x2

Do these data provide sufficient evidence to conclude that the second-order ( ) terms in the model proposed by the operations engineer is necessary? Test by using .

Transcribed Image Text:

SOURCE MODEL DF SUM OF SQUARES 3 ERROR 16 TOTAL 19 2396.364 128.586 2524.950 MEAN SQUARE 798.788 8.037 R-SQUARE 0.949