The article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds”

(D. Harwig, W. Ittiwattana, and H. Castner, The Welding Journal, 2001:126s–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 %). The following MINITAB output presents results of fitting the model Elongation = ????0 + ????1 Oxygen + ????2 Nitrogen + ????3 Oxygen ⋅ Nitrogen The regression equation is Elongation = 46.80 - 130.11 Oxygen - 807.1 Nitrogen + 3580.5 Oxy*Nit Predictor Coef StDev T P Constant 46.802 3.702 12.64 0.000 Oxygen -130.11 20.467 -6.36 0.000 Nitrogen -807.10 158.03 -5.107 0.000 Oxy*Nit 3580.5 958.05 3.737 0.001 S = 2.809 R-Sq = 74.5% R-Sq(adj) = 72.3%

Analysis of Variance Source DF SS MS F P Regression 3 805.43 268.48 34.03 0.000 Residual Error 35 276.11 7.89 Total 38 1081.54

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.