Table 2.
Mathematical models for dependent variables with significant parameters from the Central Composite Rotational Design with 3 independent variables: custard apple puree, fructooligosaccharides (FOS) and soy protein hydrolysate (SPH), desirability analysis and experimental validation
| Variables | Mathematical model | Goal | Importance | Predicted values | Experimental values | Relative deviation (%) |
|---|---|---|---|---|---|---|
| Custard apple puree | Maximize | 5 | 0.45 | |||
| Fructooligosaccharides | Maximize | 5 | 1.50 | |||
| Soy protein hydrolysate | Maximize | 5 | 1.68 | |||
|
Specific gravity (g cm−3) |
0.848−0.016x1−0.016x2−0.006x3−0.009x12−0.013x22−0.009x32 | Minimize | 5 | 0.750 | 0.727 ± 0.018 | − 3.20 |
|
Specific volume (cm3 g−1) |
2.06−0.07x1 + 0.21x2−0.18x3 + 0.09x22 + 0.16x32 + 0.18x2x3 | Maximize | 5 | 3.15 | 3.42 ± 0.04 | 2.82 |
| Firmness (N) | 7.44−0.66x1−0.56x2−0.45x3 + 0.84x12−0.35x32 + 0.23x2x3 | Minimize | 5 | 5.31 | 5.81 ± 0.04 | 8.63 |
| L* | 60.33−4.15x1−0.37x3 + 0.65x12 + 0.15x22−0.35x32 + 0.39x1x2 + 0.20x1x3 + 0.93x2x3 | In range | 3 | 60.08 | 56.92 ± 1.14 | − 5.50 |
| a* | 6.76 + 1.08x1 + 0.29x3−0.06x12 + 0.16x32−0.05x1x2−0.14x2x3 | In range | 3 | 7.79 | 8.31 ± 0.45 | 6.30 |
| b* | 24.66−1.03x1 + 0.11x2 + 0.43x3 + 0.80x12 + 0.25x32−0.34x1x2−0.75x2x3 | In range | 3 | 23.83 | 24.37 ± 1.74 | 2.21 |
| Number of alveoli | 109.76−5.54x1−2.38x2 + 7.87x3 + 3.89x12 + 2.00x32−5.50x2x3 | In range | 3 | 109.49 | 99.95 ± 2.81 | − 9.55 |
| Circularity of alveoli | 0.782−0.006x1−0.009x2−0.002x3−0.003x12 + 0.003x32 | In range | 3 | 0.770 | 0.818 ± 0.006 | 5.83 |
Independent variables x1, x2 and x3 are predicted by coded values of custard apple puree, FOS and SPH, respectively. R2 = coefficient of determination