The data set in DS 13.6.4 shows the yields of a bacteria culture obtained for different amounts of an additive x1 and for different growing temperatures x2.
(a) Investigate the experimental design employed by looking at the values of the additive levels and the temperature levels used in the experiment.
(b) Fit the response surface model
y = β0 + β1x1,+ β2x21 + β3x2 + β4x22 + β5x1x2
and show that one data point has a standardiz1ed residual of - 3.01.
(c) Remove the data point with the large negative standardized residual and fit the response surface model to the remaining data points. Make a plot of the fitted model. What values of the additive and the temperature would you recommend to maximize the yield of the bacteria culture?