The article Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s136s)

The article €œAdvances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds€ (D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s€“136s) reports an experiment to predict various properties of titanium welds. Among other properties, the elongation (in %) was measured, along with the oxygen content and nitrogen content (both in percent). The following MINITAB output presents results of fitting the model Elongation = β₀+ β₁Oxygen + β₂Nitrogen + β₃Oxygen · Nitrogen

a. Predict the elongation for a weld with an oxygen content of 0.15% and a nitrogen content of 0.01%.

b. If two welds both have a nitrogen content of 0.006%, and their oxygen content differs by 0.05%, what would you predict their difference in elongation to be?

c. Two welds have identical oxygen contents, and nitrogen contents that differ by 0.005%. Is this enough information to predict their difference in elongation? If so, predict the elongation. If not, explain what additional information is needed.

The regression equation is Elongation 46.80 - 130.11 Oxygen 807.1 Nitrogen + 3580.5 0xy*Nit Predictor Coef 46.802 - 130.11 - 807.10 SE Coef 3.702 20.467 158.03 958.05 Constant Oxygen 12.64 -6.36 -5.107 3.737 0.000 0.000 0.000 0.001 Nitrogen *Nit S = 2.809 3580.5 = 74.5% R-Sq = R-Sq(adj) = 72.3% Analysis of Variance Source Regression Residual Error DF SS 805.43 MS 268.48 7.89 34.03 0.000 35 38 276.11 1081.54 Total