An article in Biotechnology Progress (2001, Vol. 17, pp. 366€“368) reported on an experiment to investigate and optimize the operating conditions of the nisin extraction in aqueous two-phase systems (ATPS). A 2²full factorial design with center points was used to verify the most significant factors affecting the nisin recovery. The factor x₁was the concentration (% w/w) of PEG 4000 and x₂was the concentration (% w/w) of Na₂SO₄. See the following table for the range and levels of the variables investigated in this study. Nisin extraction is a ratio representing the concentration of nisin, and this was the response y.

(a) Compute an ANOVA table for the effects and test for curvature with α = 0.05. Is curvature important in this region of the factors?

(b) Calculate residuals from the linear model and test for adequacy of your model.

(c) In a new region of factor space, a central composite design (CCD) was used to perform second-order optimization.

The results are shown in the following table. Fit a second order model to this data and make conclusions.

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Trial x. x, 1 13 11 62.874 15 11 76.133 3 13 13 87.467 13 4. 15 102.324 76.187 14 12 14 12 77.523 14 12 76.782 14 12 77.438 12 78.742 14