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) Fit a multiple linear regression model to these data.
(b) Estimate σ2 and the standard errors of the regression coefficients.
(c) Use the model to predict wear when x1 = 25 and x2 = 1000.
(d) Fit a multiple linear regression model with an interaction term to these data.
(e) Estimate σ2 and se(Bj) 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 x1 = 25 and x2 = 1000. Compare this prediction with the predicted value from part (b) above.

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X1 293 1.6 851 230 15.5 816 172 22.0 1058 43.0 91 1201 113 33.0 1357 125 40.0 1115 TEMP SOAKTIME SOAKPCT DIFFTIME DIFFPCT PITCH 1650 0.58 1.10 0.25 0.90 0.013 1650 0.016 0.66 1.10 0.33 0.90 1650 1.10 0.66 0.33 0.90 0.015 0.66 1650 1.10 0.33 0.95 0.016 0.015 1600 0.66 1.15 0.33 1.00 0.33 1600 0.66 1.15 1.00 0.016 0.80 1650 1.00 1.10 0.50 0.014 1.17 1650 1.10 0.58 0.80 0.021 1650 1.17 1.10 0.58 0.80 0.018 1650 1.17 1.10 0.58 0.80 0.019 1650 1.17 1.10 0.58 0.90 0.021 1.17 1650 1.10 0.58 0.90 0.019 1.17 1.15 1650 0.58 0.90 0.021 1.15 1650 1.20 1.10 0.80 0.025 1.15 1650 2.00 1.00 0.80 0.025 1650 0.026 2.00 1.10 1.10 0.80 1650 2.20 1.10 1.10 0.80 0.024 1.10 1650 2.20 1.10 0.80 0.025 1.15 0.024 1650 2.20 1.10 0.80 1650 2.20 1.10 1.10 0.90 0.025 0.027 1650 2.20 1.10 1.10 0.90 1650 1.50 2.20 1.10 0.90 0.026 1650 3.00 1.15 1.50 0.80 0.029 1650 3.00 1.10 1.50 0.70 0.030 1650 3.00 1.10 1.50 0.75 0.028 1650 3.00 1.15 1.66 0.85 0.032 1650 3.33 1.10 1.50 0.80 0.033 1700 4.00 1.10 1.50 0.70 0.039 1650 4.00 1.10 1.50 0.70 0.040 1.15 0.85 1650 4.00 1.50 0.035 1700 12.50 1.00 1.50 0.70 0.056 1700 18.50 1.00 1.50 0.70 0.068