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 percent). The following MINITAB output presents results of fitting the model
Elongation = β0 + β1 Oxygen + β2 Nitrogen + β3 Oxygen · 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 Elongatin 46.80 130.11 Oxygen 807.1 Nitrogen3580.5 0xy Nit Predictor Constant Oxygen Nitrogen Oxy Nit Coef 46.802 130.11 807.10 3580.5 SE Coef 3.702 20.467 158.03 958.05 12.64 6.36 3.737 R-Sq ( adj) 0.000 0.000 0.000 0.001 -5.107 S 2.809 R-Sq 74.5% -72.3% - Analysis of Variance Source Regression Residual Error 35 Total DF MS 805.43 268.48 34.03 0.000 276.11 7.89 38 1081.54