An article in Rubber Age (1961, Vol. 89, pp. 453€“ 458) describes an experiment on the manufacture of a product in which two factors were varied. The factors are reaction time (hr) and temperature (°C). These factors are coded as x₁= (time €“ 12) / 8 and x₂= (temperature €“ 250) / 30. The following data were observed where y is the yield (in percent):

(a) Plot the points at which the experimental runs were made.

(b) Fit a second-order model to the data. Is the second-order model adequate?

(c) Plot the yield response surface. What recommendations would you make about the operating conditions for this process?

Run Number x. -1 83.8 1 81.7 3 82.4 4 82.9 84.7 -1 1 75.9 81.2 -1.414 -1.414 81.3 -1.414 1.414 83.1 10 1.414 -1.414 85.3 72.7 82.0 11 1.414 1.414 12