In a study of the causes of bearing wear, a machine was

Chapter 8, Problem 11E

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In a study of the causes of bearing wear, a machine was run 24 times, with various loads (denoted \(x_1\)), oil viscosities \((x_2)\), and ambient temperatures \((x_3)\). The wear, denoted y, was modeled as \(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}+\beta_{4} x_{1} x_{2}+\beta_{5} x_{1} x_{3}+\beta_{6} x_{2} x_{3}+\varepsilon\). When this model was fit to the data, the sum of squares for error was SSE = 9.37. Then the reduced model \(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}+\beta_{3} x_{3}\) was fit, and the sum of squares for error was SSE = 27.49. Is it reasonable to use the reduced model, rather than the model containing all the interactions, to predict wear? Explain.

Equation Transcription:

Text Transcription:

x_1

(x_2)

(x_3)

y=beta_0+beta_1x_1+beta_2x_2+beta_3x_3+beta_4x_1x_2+beta_5x_1x_3+beta_6x_2x_3+varepsilon

SSE=9.37

y=beta_0+beta_1x_1+beta_2x_2+beta_3x_3

SSE=27.49

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