12-7. A study was performed on wear of a bearing y and its relationship to x, = oil viscosity and x, = load. The follow- ing data were obtained. X2 y 293 1.6 851 230 15.5 816 172 22.0 1058 91 43.0 1201 113 33.0 1357 125 40.0 1115 (a) Fit a multiple linear regression model to these data. (b) Estimate o and the standard errors of the regression coefficients. (c) Use the model to predict wear when x = 25 and x2 = 1000. (d) Fit a multiple linear regression model with an interaction term to these data. (e) Estimate o and se(ß) for this new model. How did these quantities change. Does this tell you anything about the value of adding the interaction term to the model? (f) Use the model in (d) to predict when x, = 25 and x, = 1000. Compare this prediction with the predicted value from part (b) above.

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Statistical Concepts, Theories and Analysis for Industrial Engineering 

12-7. A study was performed on wear of a bearing y and its
relationship to x = oil viscosity and x, = load. The follow-
ing data were obtained.
y
X1
X2
293
1.6
851
230
15.5
816
172
22.0
1058
91
43.0
1201
113
33.0
1357
125
40.0
1115
(a) Fit a multiple linear regression model to these data.
(b) Estimate o? and the standard errors of the regression
coefficients.
(c) Use the model to predict wear whenx = 25 and x, = 1000.
(d) Fit a multiple linear regression model with an interaction
term to these data.
(e) Estimate o and se(ß,) for this new model. How did these
quantities change. Does this tell you anything about the
value of adding the interaction term to the model?
(f) Use the model in (d) to predict when x = 25 and x2
1000. Compare this prediction with the predicted value
from part (b) above.
Transcribed Image Text:12-7. A study was performed on wear of a bearing y and its relationship to x = oil viscosity and x, = load. The follow- ing data were obtained. y X1 X2 293 1.6 851 230 15.5 816 172 22.0 1058 91 43.0 1201 113 33.0 1357 125 40.0 1115 (a) Fit a multiple linear regression model to these data. (b) Estimate o? and the standard errors of the regression coefficients. (c) Use the model to predict wear whenx = 25 and x, = 1000. (d) Fit a multiple linear regression model with an interaction term to these data. (e) Estimate o and se(ß,) for this new model. How did these quantities change. Does this tell you anything about the value of adding the interaction term to the model? (f) Use the model in (d) to predict when x = 25 and x2 1000. Compare this prediction with the predicted value from part (b) above.
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