Table 4 Quadratic model equations describing arabitol production (g/L) and arabitol/glycerol conversion yield (g/g) as function of the significant factors and their interactions, expressed in their original units (Eqs. 2 and 4) or in coded values (Eqs. 3 and 5)

\({\text{Arabitol }} = -200.85 - 0.62\cdot{\text{Glycerol }} + {{ 13}}.{{83}}\cdot{{T }} + {{ 1}}.{{87}}\cdot{\text{pH }} + {{ }}0.0{{4}}\cdot{{Glycerol}}\cdot{\text{T }}{-}{{ 3}}.{{23}}\cdot{{1}}{0^{ - {{3}}}}\cdot{\text{Glycero}}{{\text{l}}^{{2}}}{-}{\text{ }}0.{{26}}\cdot{{\text{T}}^{{2}}}\)

(1)

\({\text{Arabitol }} = + {{17}}.{{61 }} + {{2}}.{{78}}\cdot{\text{A }} + {{ 4}}.{{17}}\cdot{\text{B }} + {{ 2}}.{{11}}\cdot{\text{C }} + {{ 3}}.{{41}}\cdot{\text{AB }}{-}{{ 3}}.{{41}}\cdot{{\text{A}}^{{2}}}{-}{{ 1}}.{{64}}\cdot{{\text{B}}^{{2}}}\)

(2)

\({\text{Yield }} = {\text{ }}{-}{{ 2}}.{{23 }}{-}{{ 3}}.{{18}}\cdot{{1}}{0^{ - {{3}}}}\cdot{\text{Glycerol }} + {\text{ }}0.{{15}}\cdot{\text{T }} + {\text{ }}0.0{{3}}\cdot{\text{pH }} + {{ 2}}.{{54}}\cdot{\text{Glycerol}}\cdot{\text{T}}{-}{{ 2}}.{{31}}\cdot{{1}}{0^{ - {{5}}}}\cdot{\text{Glycero}}{{\text{l}}^{{2}}}{-}{{ 2}}.{{58}}\cdot{{1}}{0^{ - {{3}}}}\cdot{{\text{T}}^{{2}}}\)

(3)

\({\text{Yield }} = {\text{ }} + {\text{ }}0.{{23 }} + {\text{ }}0.0{{17}}\cdot{\text{A }} + {\text{ }}0.0{{36}}\cdot{\text{B }} + {{ }}0.0{{31}}\cdot{\text{C }} + {\text{ }}0.0{{21}}\cdot{\text{AB }}{-}{\text{ }}0.0{{24}}\cdot{{\text{A}}^{{2}}}{-}{\text{ }}0.0{{16}}\cdot{{\text{B}}^{{2}}}\)

(4)