Twelve specimens of cold-reduced sheet steel, having different copper contents and annealing temperatures, are measured for hardness with the following results:

Fit an equation of the form \(y=\beta_{0}+\beta_{1} x_{1}+\beta_{2} x_{2}\), where \(x_{1}\) represents the copper content, \(x_{2}\) represents the annealing temperature, and \(y\) represents the hardness.

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Copper Annealing Hardness content temperature (Rockwell 30-T) (%) (degrees F) 78.9 0.02 1,000 65.1 0.02 1,100 55.2 0.02 1,200 56.4 0.02 1,300 80.9 0.10 1,000 69.7 0.10 1,100 57.4 0.10 1,200 55.4 0.10 1,300 85.3 0.18 1,000 71.8 0.18 1,100 60.7 0.18 1,200 58.9 0.18 1,300