Consider the bearing wear data in Exercise 12-23.

(a) For the model with no interaction, test for significance of regression using α = 0.05. What is the P-value for this test? What are your conclusions?

(b) For the model with no interaction, compute the t-statistics for each regression coefficient. Using α = 0.05, what conclusions can you draw?

(c) For the model with no interaction, use the extra sum of squares method to investigate the usefulness of adding x₂ = load to a model that already contains x₁ = oil viscosity. Use α = 0.05.

(d) Refit the model with an interaction term. Test for significance of regression using α = 0.05.

(e) Use the extra sum of squares method to determine whether the interaction term contributes significantly to the model. Use α = 0.05.

(f) Estimate σ² for the interaction model. Compare this to the estimate of σ² from the model in part (a).

Exercise 12-23

A study was performed on wear of a bearing and its relationship to x₁ = oil viscosity and x₂ = load. The following data were obtained.

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y 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