An article in Biotechnology Progress (2001, Vol. 17, pp. 366€“368) reported on an experiment to investigate and optimize nisin extraction in aqueous two-phase systems (ATPS). The nisin recovery was the dependent variable (y). The two regressor variables were concentration (%) of PEG 4000 (denoted as x₁and concentration (%) of Na2SO4 (denoted as x₂). The data are in Table E12-10.

(a) Fit a multiple linear regression model to these data.

(b) Estimate σ² and the standard errors of the regression coefficients.

(c) Use the model to predict the nisin recovery when x₁ = 14.5 and x₂ = 12.5.

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y X1 X2 62.8739 13 11 11 15 76.1328 13 13 87.4667 15 13 102.3236 76.1872 14 12 77.5287 14 12 14 12 76.7824 14 12 77.4381 12 14 78.7417