Barely Significant

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highly significantp -value < 0.00010.0× alphaqualifiedgold
After statistical analysis, the F -value of the APS of the lignin nanoparticles model is 230.57, all of which are highly significant ( p -value < 0.0001), and the p -value of the lack-of-fit term is not significant ( p > 0.05), suggesting that the model is accurate and reliable.
highly significantp < 0.00010.0× alphaqualifiedgold
Accordingly, the second-order polynomial equation was established as follows: Y = − 9.16012 + 0.123691 × A + 0.143075 × B + 0.162185 × C − 0.0001375 × A × B − 7.5 × 10 − 5 × A × C + 3 × 10 − 5 × B × C − 0.0014058 × A 2 − 0.0013893 × B 2 − 0.0015433 × C 2 From Table 2 , it is evident that the model’s regression is highly significant ( p < 0.0001), with a lack of fit of 0.3369, exceeding the significance threshold of 0.05.
highly significantp < 0.00010.0× alphaqualifiedgold
6.65 X 2 X 3 − 35.03 X 1 2 − 47.97 X 2 2 − 29.11 X 3 2 Y 2 (TFC) = 58.85 + 5.13 X 1 + 0.27 X 2 − 1.13 X 3 − 0.43 X 1 X 2 + 0.80 X 1 X 3 − 0.39 X 2 X 3 − 4.51 X 1 2 − 2.53 X 2 2 − 1.71 X 3 2 The results of the analysis of variance in Table 2 suggest that the fitted models for TPC and TFC were both highly significant ( p < 0.0001), while the lack of fit was not significant ( p -values: 0.2161 and 0.3343, respectively), indicating a good fitness for the models.
highly significantp < 0.00010.0× alphaqualifiedgold
Furthermore, all quadratic terms (A 2 , B 2 , C 2 , and D 2 ) were highly significant ( p < 0.0001), suggesting pronounced nonlinear relationships in the extraction process, which is essential for interpreting the experimental outcomes [ 59 ].
highly significantp = 0.00010.0× alphaqualifiedgold
Multiple regression analysis was performed using the quadratic polynomial model described by Equation (1), linking the independent variables to EE response: (1) Y = 56.32 + 0.5366 X 1 + 1.73 X 2 − 0.2654 X 3 − 0.4980 X 1 X 2 + 0.5468 X 1 X 3 + 0.0390 X 2 X 3 − 8.95 X 1 2 - 6.52 X 2 2 − 5.14 X 3 2 Analysis of variance for the regression model ( Table 2 ) revealed that the model exhibited a highly significant F-value of 830.28 ( p = 0.0001).
highly significantp < 0.00010.0× alphaqualifiedgold
The second-order model obtained in terms of coded variables for extraction efficiency ( E (%)) of BB seed oil using UAE is given by Equation (1): (1) E % = 80.74 + 9.375 X 1 − 2.495 X 1 2 + 2.875 X 2 − 3.495 X 2 2 + 0.5 X 3 − 2.745 X 3 2 − 1.25 X 1 X 2 − X 1 X 3 + X 2 X 3 The ANOVA statistic for extraction efficiency (the response variable) proved that the regression model is highly significant, having a very high F-value of 46.67 and a low p -value of p < 0.0001.