Question
A study was performed on wear of a bearing Y and its relationship to X1 oil viscosity and X2 load. The following data were obtained.
A study was performed on wear of a bearing Y and its relationship to X1 oil viscosity and X2 load. The following 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. [12 marks]
b) Estimate 2 and the standard errors of the regression coefficients. [8 marks]
c) Use the model to predict wear when X1 = 25 and X2 = 1000. [1 mark]
d) Fit a multiple linear regression model with an interaction term to these data. [8 marks]
e) Estimate 2 and se (Beta hat j ) 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? [10 marks]
f ) Use the model in d) to predict when X1 = 25 and X2 = 1000. Compare this prediction with the predicted value from part b) above. [2 marks]
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