3.1. Preliminary solvent mixture selection for the bioactive compound’s extraction
The selection of ethanol as a co-solvent for recovering bioactive extracts from
P. emblica leaves stems from its versatility and effectiveness in extracting bioactive compounds from medicinal plants. These advantages include cost-effectiveness, safety, efficiency, preservation of bioactivity, scalability, eco-friendliness, and regulatory approval, among others.
Table 2 presents the relative ability of different solvent mixtures in the recovery of bioactive compounds from
P. emblica leaves. As shown in the table, all ethanol-water mixtures including the 100% absolute ethanol and distilled water were able to recover bioactive antioxidants from
P. emblica leaves. This shows that a good number of bioactive compounds in
P. emblica leaves are polar in nature. The mean values of the extract yield (EY), Total phenolic content (TPC) and Antioxidant activity (AA) were in the range 5.87 – 12.07 %, 13.67 – 24.25 mg GAE/g d.w and 1.98 – 3.76 μM AAE/g d.w respectively for investigations conducted at OT = 40
^{o}C, ET = 45 min and S:L = 1:20 g/mL. Close examination of
Table 1 revealed that the bioactive extract obtained with absolute ethanol as solvent possessed the least EY, TPC and AA is (EY = 5.87%, TPC = 13.67 mg GAE/g d.w, AA = 1.98 μM AAE/g d.w) while the bioactive extract recovered with 50% ethanol-water mixture demonstrated highest bioactive EY, TPC and AA (EY = 12.07%, TPC = 24.25 mg GAE/g d.w, AA = 3.76 μM AAE/g d.w). Although, the 100% distilled water (EY = 8.33%, TPC = 19.11 mg GAE/g d.w, AA = 2.81 μM AAE/g d.w) did not perform very badly, it was still far below the 80% ethanol-water (EY = 8.41%, TPC = 20.10 mg GAE/g d.w, AA = 2.99 μM AAE/g d.w), 60% ethanol-water (EY = 11.36%, TPC = 23.76 mg GAE/g d.w, AA = 3.66 μM AAE/g d.w), 40% ethanol-water (EY = 11.11%, TPC = 22.98 mg GAE/g d.w, AA = 3.52 μM AAE/g d.w) and 20% ethanol-water (EY = 8.67%, TPC = 19.73 mg GAE/g d.w, AA = 3.31 μM AAE/g d.w) solvent mixtures in the recovery of bioactive extract from
P. emblica leaves.
These results clearly demonstrated varied solubility of bioactive compounds, TPC and AA in different ethanol concentrations (40 - 60% ethanol solutions). This work is in close agreement with previous works [
32]. Huaman-Castilla
et al., [
32] pointed out that solvent polarity and ability of solvents to form hydrogen bonds with plant metabolite significantly impact the solvation capacity of solvents which consequently determines the extractability of polyphenols in plant matrices. This present study has however, shown that ethanol concentrations within 40 - 60% range enhanced the extraction of phenolic compounds due to the optimal solubility and stability of these compounds compared with the solvent extremes (absolute ethanol and 100% distilled water). Although the interesting range of ethanol-water solvent concentration for high bioactive solubility is 40 – 60%, the 50% ethanol-water solvent mixture demonstrated the best phytochemical extractability from
P. emblica leaves. However, the literature has documented various optimal ethanol-mixture concentrations for the recovery of bioactive extracts from different medicinal origins. For example, a study conducted by Altıok
et al. [
33] on the extraction of bioactive compounds from olive oil demonstrated that a 70% ethanol solution optimized the extractability of total polyphenols, resulting in extracts with the highest antioxidant capacity. In the same vein, Cheaib
et al. [
34] concluded that 50% ethanol solution was best for the recovery of bioactive compounds from apricot pomace. Regardless, the addition of ethanol to water as solvent mixture greatly improved the polyphenol-rich antioxidant extraction from
P. emblica leaves. This observation was attributed to the impact of ethanol on cell permeability, brought about by alterations in the phospholipid bilayer of the cell membranes, resulting in both chemical and biophysical modifications to the cell membrane [
34]. Therefore, the 50% ethanol-water solvent mixture was hence forth used for the selection of the best set of process parameters for the recovery of bioactive compounds from
P. emblica leaves in the subsequent Section.
3.3. BBD-RSM modelling, model adequacies and statistical analysis
The BBD-RSM was employed to describe the relationship between the studied process parameters and the responses investigated. Hence, predictive mathematical models were developed for EY, TPC and AA as function of OT, S:L and ET with the assistance of Design Expert software. The coded form of the BBD-RSM quadratic predictive equations that relate the TPC, EY and AA with the operating parameters of OT (denoted as A in the equations), S:L (denoted as B) and ET (denoted as C) are presented in Eq. (9), Eq. (10) and Eq. (11) respectively.
Table 4 contains the ANOVA results for the developed predictive quadratic equations. The models’ coefficients and parameters for assessing their adequacies are as well presented in the table.
Table 3 shows that the F-values of the developed EY (32.58), TPC (4947.4) and AA (22.86) models are significant (p values < 0.05). These models also possessed non-significant (p values >0.05) lack of fit indicating they are well-developed and are all capable of predicting the observed experimental data with high accuracy. The R
^{2} values for the developed models are also appreciably high (EY = 0.9998. TPC = 0.9767 and AA = 0.9671) and hence indicate high effectiveness and capability of the models in describing the laboratory data. The Pred. R
^{2} values of all the models (EY = 0.7077, TPC = 0.9994 and AA = 0.8009) were in close agreement with their respective Adj R
^{2} values (EY = 0.9467, TPC =0.9996 and AA =0.9248).
Table 4 further shows the contributions of each term in the equation to the overall predictability of the developed models. The negative (-) and positive (+) sign in the model equations indicated a decrease and increase contributions respectively. Therefore, in the EY BBD-RSM predictive model, the linear terms of OT, S:L and ET are all significant (p < 0.05) and contributed negatively, positively and positively respectively to the overall predictability of the model. The quadratic term of OT (OT X OT) and ET (ET X ET) are significant and they both caused a reduction in the EY model. The quadratic effect of S:L resulted to an insignificant (p > 0.05) increase in EY model. The interactive effect of OT and S:L (OT X S:L) was insignificantly (p > 0.05) negative, however both OT X ET (AC) and S:L X ET (BC) produced a positive contribution in EY model, although the OT X ET effect was not significant (p > 0.05). Regarding the TPC and AA BBD-RSM models, the linear effect of OT, S:L and ET were positive, negative, negative and positive, positive, negative in the TPC and AA models respectively. The linear effects of OT, S:L and ET were significant (p < 0.05) in the TPC model, however, only the linear effects of OT and ET contributed significantly in the AA model. The OT X OT, S:L X S:L and ET X ET significantly (p < 0.05) caused reduction, increment and increment respectively in the developed TPC model. However, the ET X ET was the only insignificant (p > 0.05) quadratic effect in the AA BBD-RSM model. The OT X OT and S:L X S:L effects were significantly (p < 0.05) negative and positive respectively in the AA model. All the interactive effects of OT X S:L, OT X ET and S:L X ET were significant in the TPC model and the respectively produced a negative, negative and positive contributions in the model. Among all the interactive effects, only the OT X ET was significantly (p < 0.05) positive, other interactions such OT X S:L and S:L X ET were insignificant (p > 0.05) negative in the AA BBD-RSM model.
The prediction of the observed experimental data by the developed TPC, EY and AA BBD-RSM models are presented in
Figure 2 (a), (b) and (c) respectively. The parity graphs showed excellent prediction of the observed data since the observed experimental and model predicted data fell close to the diagonal line [
7].
3.4. Data statistics and multi-gene genetic programming modelling
The properties and variability of both the input and output data were determined prior to MGGP modelling via descriptive statistical analysis. The input and output data were the heat-assisted extraction operating parameters and response parameters respectively as presented in
Table 3. Therefore, the input parameters were the OT (
^{o}C), S:L (g/mL) and ET (min) while the output response parameters were the EY (w/w %), TPC (mg GAE/g d.w) and AA (µM AAE/g). The relevant data characteristics that were assessed include data mean, standard error, median, mode, and standard deviation. Others were sample variance, data kurtosis, skewness, range, minimum, maximum, and sum. Seventeen (17) data points of each process parameters (OT, S:L and ET) and response parameters (EY, TPC and AA) (which totaled 102 data population) were used for the construction of the MGGP-based models.
Table 5 showed the summary of the descriptive statistics of the data used for the MGGP modelling.
The mean of the data set ranged from 3.6905882 to 41.7864705 with the minimum and maximum belonging to AA and TPC respectively. Also, the mean value of OT, S: L, ET and EY are 40
^{o}C, 40 g/mL, 112.5 min and 14.7682352% respectively. Similarly, the standard error, median, mode, and standard deviation are in the range of 0.0153745 - 11.5761544, 3.69 - 112.5, 3.67 - 112.5, 0.0633907 - 47.7297077 and 0.0040183 - 47.7297077 respectively. The sample variance of both the input and output parameters was between 0.0040183 and 2278.1250. The sample variance of 0.0040183 belonged to AA and it indicated minimal variation while variance of 2278.1250 for ET indicated wide variation. The variance of 271.2990492, 200, and 50 for TPC, S:L and OT also implied wide data variations. The data kurtosis, a statistical parameter that measures the peaked or flatness of a data distribution, was in the range of -0.4367377 - 3.1818297. The kurtosis of - 0.4367377, - 0.6261143, - 0.7428571, - 0.7428571, and -0.7428571 for EY, TPC, OT, S:L and ET respectively, indicated that the data were normally distributed (kurtosis value < +1)) while a value of +3.1818297 for AA implied that the sample population is peaked (kurtosis value > +1) [
4]. Similarly, the data skewness (a measure of symmetry of data distribution) was in the range of -1.2675914 - 0.4519267 for all sample population. The skewness coefficients of zero (0) for OT, S:L and ET indicated that the data distributions for these variables were not skewed while a coefficient of -1.2675914 for AA indicated a negatively skewed data distribution. Numerical values of other statistical parameters such as the range, minimum, maximum and sum of the input and output data populations are also indicated in
Table 5 and are in the range of 0.26 - 135, 3.51 - 45, 3.77 - 180, and 62.74 - 1912.5 respectively.
The MGGP model structures were optimized for the prediction of TPC, EY and AA as a function of processes extraction variables of operating temperature (OT), solid to liquid ratio (S:L) and extraction time (ET). The MGGP model structure optimization study was purposely carried out to achieve optimum model parameter settings that enable robust learning of the heat-assisted extraction process data (both input and output data presented in
Table 3) for finest prediction. Therefore, the population size (PS) and number of generation (NG), which were the two significant parameters that determine the model structural predictive effectiveness to a very large extent [
9], were each investigated in the range of 100 – 500. The reported ranges for the parameters investigation were determined based on several attempts of simulation experiments in the preliminary studies. Other model settings are as displayed in
Table 1.
Table 6 presents the summary of the results of the MGGP modeling optimization studies for the prediction of responses TPC, EY and AA. The R
^{2} values for the prediction of TPC, EY and AA were in the range of 0.9858 - 0.9998, 0.9157 - 0.9936 and 0.7595 - 0.9622, respectively.
The parameter settings combination for the optimum prediction of TPC, EY and AA are population size and number of generation of 500 and 250 (R^{2} = 0.9998), 250 and 500 (R^{2} = 0.9936) and 250 and 250 (0.9622), respectively. Therefore, these determined optimum parameter settings for the MGGP model prediction of TPC, EY and AA were henceforth used for the simulation.
Figure 3 presents the graphs (in the form of log Fitness vs. number of generation) of the training process for the best MGGP model structure of TPC (PS = 500; NG = 250), EY (PS = 500; NG = 250) and AA (PS = 250; NG = 250).
It is clear from the figure that the best fitness for the training of the models occurred at approximately 241
^{th}, 498
^{th}, and 245
^{th} generation for the TPC, EY and AA simulations respectively. The fitness function assesses the evolved expressions to determine the most optimal encoded expressions [
35] and was obtained by minimizing the root mean square error (RMSE). The prediction errors (also refers to as the fitness) for TPC, EY and AA models were found to reduce as a function of number of generation (NG) and were eventually stable at the optimum NG for each model. The decreases observed in prediction error as training progresses is an indication that the MGGP algorithm learnt from the training data rather than memorizing it and hence no data over-fitting occurred in the course of algorithm training [
4]. Also, the ability of all the models to regain permanently decrease in fitness indicated that respective MGGP was able to overcome local minimum and adequately settled in global minimum during training process simulations [
4]. The best prediction error for the TPC, EY and AA models were 0.0202, 0.0288, and 0.0011, respectively.
The set of possible solutions capable of predicting the process responses of TPC, EY and AA as a function of set of process variables of OT, S:L and ET are presented in
Figure 4 (a), (b) and (c) respectively.
Figure 4 showed that Pareto fronts (the circles with green coloration) existed for TPC, EY and AA responses.
The Pareto front represents solutions that outperform all other solutions in both model effectiveness and complexity (measured by the number of nodes in the genetic programming tree) simultaneously.
Figure 4 revealed that there are 13, 15 and 14 Pareto solutions for the TPC, EY and AA responses, respectively. However, the green circles with red scribes in
Figure 4a, b, and c represent the best Pareto front solutions for the TPC, EY and AA responses respectively, since they possessed the required minimum prediction error which is an indication of high effectiveness in process responses prediction. The mathematical models (best Pareto front solutions) relating the TPC, EY and AA responses to the investigated process variables of OT, S:L and ET are represented by Eq. (12), (13) and (14), respectively. All of the MGGP equations are non-linear in nature and each consisted of five genes and one bias.
The significance (p < 0.05) of each gene in the developed MGGP-based mathematical models for the prediction of TPC, EY and AA values can be visualized in
Figure 5 (p-value vs. genes and bias). The structures of the equations, as well as their respective statistical model adequacy parameters are presented alongside in
Figure 5.
Figure 5 showed the relative importance (based on the measure of probability values) of each gene and bias that made up the structure of the evolved MGGP equations. All the predictive MGGP-based models for TPC, EY and AA prediction of bioactive antioxidants from
P. emblica leaves, possessed interestingly high R
^{2} (model R
^{2} for TPC, EY and AA are 0.9998, 0.9936 and 0.9622 respectively) and Adj R
^{2} (Adj R
^{2} for TPC, EY and AA are 0.9997, 0.9907 and 0.9451) values which indicate that the models are a good fit for the observed data and that they explain a significant portion of the variability in the dependent variables. Considering the evolved MGGP equation for the prediction of TPC (Eq. (11)), the probability all the genes and the bias were less than 0.0002 which implied that they are all significant (p < 0.05). However, the most important genes are genes 2, 3, 4 and 5. The bias was also a significant model term for MGGP-based predictive model for TPC as indicated in the figure. Similarly in
Figure 5 (b), all the genes and the bias were significant part of MGGP-based predictive model structure for EY prediction since all the probability values of the evolved genes and bias were less than 0.00015. However, of significantly high importance in the evolved EY MGGP-based predictive model are the bias, gene 1, gene 2 and gene 5. Analysis of
Figure 5 (c) also showed that the MGGP-based AA model have significant structure (genes and bias) for the prediction of AA values. As indicated on the graph (
Figure 5 (c)), the probability values of all genes and bias in the structure are less than 0.000015, however, gene 1 is the most significant gene in the structure.
The ability of the MGGP-based models to predict the laboratory observed TPC, EY and AA data as function of process variables of OT, S:L and ET are presented in
Figure 6 (a), (b) and (c), respectively.
It is obvious from
Figure 6 that the MGGP-based models were able to predict the observed laboratory data for TPC, EY and AA satisfactorily. The parity graphs showed that both the observed and predicted data were clustered on the diagonal line which is an indication of good data predictive strengths of the MGGP-based models [
4]. The models’ RMSE statistical parameter values were minimal (RMSE for TPC, EY and AA MGGP-developed models are 0.0202, 0.0288 and 0.0011) while all the models’ R
^{2} values were close to unity which implied perfect prediction of the models [
4].
3.6. Numerical optimization and validation
The desirability algorithm that is present in the Design Expert software was used for achieving the optimization of the process parameter for the recovery of bioactive antioxidants from
P. emblica leaves. The optimization procedure is in accordance with the work of Adeyi
et al. [
16]. The goal of the optimization scheme was to determine a set of process parameters that maximized the TPC, EY and AA of the bioactive extract.
Table 5 presents the selected goal, weight, and importance for both the process parameters and responses. The table further shows the numerical range of search for the global optimum parameters of processing bioactive antioxidants recovery from
P. emblica leaves.
Table 6 summarized all the thirteen (13) solutions presented based on the combined desirability values. The scale of the desirability is between 0 and 1, with desirability value of 1 adjudged the best [
4].
The desirability values of the all the presented solutions ranged from 0.766 to 0.854. These solutions were ranked in ascending order of preference by the software with the first solution on the list, the best and selected. The 13
^{th} solution on the table was the least preferred, although the solution also possessed appreciably high desirability value (0.766), the value was the least among the solutions provided by the algorithm. Hence, the first solution on the list with desirability value of 0.854 was selected as the best optimum solution. This desirability value of 0.854 compares well with other desirability values of selected optimum solutions in the literature. For instance this present desirability value is higher that than the desirability value of selected optimum solution in the work of Adeyi
et al., [
4] during the HAE process optimization of bioactive extract recovery from
Carica papaya leaves.
Figure 3 is the optimization ramp for the best suggested solution (first) with combined desirability value of 0.854. The figure shows that the optimization search was within the range of investigated process parameters and observed laboratory response data. Therefore, the process parameters that simultaneously gave the optimum EY of 21.6565%, TPC of 67.116 mg GAE/g and AA of 3.68583 µM AAE/g were OT of 41.61
^{o}C, S:L of 1:60 g/mL and ET of 180 min.
The validation experiment was conducted in the laboratory to ascertain the selected predicted optimum in the laboratory. Therefore, 1 g of
P. emblica leaves was mixed with 60 mL of 50% ethanol-water mixture in a beaker and heated to approximately 42
^{o}C by utilizing a water bath for the duration of 180 min. After the completion of the experiment, the leave fibers were separated from the extract through centrifugation and the EY, TPC and AA were quantified according to
Section 2.7,
2.8 and
2.9 respectively. The results obtained for the validation experiment were EY = 22.31 %, TPC = 69.612 mg GAE/g and 3.72 µM AAE/g. The relative standard deviation (RSD) was computed to compare the experimental validated result with the predicted response result. It was found that the RSD between the validated and predicted values of EY, TPC and AA were 2.67%, 7.45% and 4.68% respectively. This indicated that these values are similar since the RSD between the validated and predicted response values are less than 10 [
16]. This similarity in the validated and predicted results showed that the developed BBD-RSM models for EY, TPC and AA are effective, well-fitted, robust and capable of predicting the process of bioactive extract recovery from
P. emblica leaves.
3.7. Phenolic fingerprints of P. emblica leaf extract
HPLC profiling of phenolic compounds in plant extracts is of paramount importance for the identification, and characterization of these bioactive compounds. It provides valuable insights into the chemical composition, quality, and therapeutic potential of plant extracts. Additionally, HPLC profiling can aid in the evaluation of the stability and degradation kinetics of phenolic compounds under different conditions, ensuring the preservation of their bioactivity. Therefore, the HPLC profiling of phenolic compounds in
P. emblica leaf extract was for the purpose of identifying the phenolic compounds with potential therapeutic effects for the basis of future industrial production and techno-economic analysis of the
P. emblica leaf extract. Hence to this end, eight (8) phenolic compounds with established bioactivities were used as standards for the HPLC profiling of the
P. emblica leaf extract. These compounds were compared with the content of the extract using the similarities in retention factor (RF).
Figure 4 is the HPLC fingerprints of
P. emblica leaf extract. As shown,
Figure 4 is characterized by different phenolic compounds and wide disparities in their corresponding areas. The figure revealed six (6) phenolic compounds that have comparable RT with the HPLC phenolic standards used as the baseline of identification. The identified phenolic compounds in the
P. emblica leaf extract with corresponding RT are betulinic acid (RT = 2.439 min), gallic acid (RT = 3.063 min), chlorogenic acid (RT = 3.541 min), caffeic acid (RT = 4.055 min), ellagic acid (RT = 5.825 min), and ferulic acid (RT = 7.684 min).
The bioactivities of the identified phenolic compounds in the extract were interesting and pointing to the overall therapeutic potential of
P. emblica leaf extract. For instance, betulinic acid exhibits a wide range of therapeutic properties and studies have shown that it induces apoptosis (programmed cell death) in cancer cells, making it a promising candidate for cancer treatment [
38]. Gallic acid possesses numerous health benefits and recent investigations showed that it has potentials to inhibit tumor growth, reduce oxidative stress, and exert protective effects against various diseases [
39]. Chlorogenic acid has been studied for its potential in preventing skin tumorigenesis, modulating MAPK and NF-κB pathways, and ameliorating oxidative stress [
40] while caffeic acid has been investigated for its potential in inhibiting atopic dermatitis-like skin inflammation and synergistic antioxidant activity when combined with other phenolic acids [
39]. Both ellagic acid and ferulic acid have been shown to exhibit antioxidant, anti-inflammatory, anticancer, antimicrobial, and antimutagenic effects [
41,
42].
3.8. Reliability Assessment of BBD-RSM based Predictive Models
Model reliability assessment is the process of evaluating and determining the trustworthiness and accuracy of a model’s predictions or outputs. One of the various available techniques and methodologies to gauge the model’s performance and identify its strengths and limitations is via Monte Carlo simulation. The main purpose of Monte Carlo simulation in the context of model reliability assessment is to quantify uncertainty, validate model performance, and estimate the potential range of outcomes. Another key aspect of Monte Carlo simulation is its ability to conduct robust sensitivity assessment where various inputs are systematically varied to determine their impact on the model’s outputs which helps in identifying which input parameters have the most significant influence on the results and helps in understanding the robustness of the model. In the present investigation, the developed BBD-RSM based predictive models were used for this analysis due to their relative superiority in predicting the heat-assisted extraction process outputs of TPC, EY and AA, relative to the MGGP-based models as explained in
Section 3.5.
Figure 7 (a), (b) and (c) show the split views of the probability distributions, cumulative frequency and reverse cumulative frequency curves of the analyses conducted in Oracle Crystal ball software for the prediction of experimental observed data (in
Table 3) of TPC, EY and AA respectively, as function of input variables of OT, S:L and ET in order to ascertain the robustness of the constructed BBD-RSM based predictive models. The outcomes’ data statistics and the best fit model for the distribution were also incorporated in the presented split view figures and positioned at the upper right and down respectively.
Figure 7 shows that the BBD-RSM models for TPC, EY and AA are capable of predicting the respective outcomes as function of OT, S:L and ET within the range of their respective experimental outcomes. The data outcomes kurtosis and skewness (statistical measures that provide information about the shape and distribution of a dataset) for TPC, EY and AA are 2.77 and 0.2508; 3.64 and 0.5979; and 5.40 and -1.14, respectively. The distribution curves for the TPC, EY and AA were excellently modeled by Weibull (Anderson-Darling coefficient = 308.1560), Lognormal (Anderson-Darling coefficient = 38.1254) and Min Extreme (Anderson-Darling coefficient = 34.7595), respectively. As indicated in
Figure 7, the percentage certainty of the developed BBD-RSM models in predicting the observed experimental data range of 18.58 – 69.35 mg GAE/g, 9.28 – 22.14% and 3.51 - 3.77 µM AAE/g (in
Table 3) for TPC, EY and AA, is 99.985%, 97.569% and 98.661%, respectively. The high BBD-RSM models’ individual prediction certainty is an indication of their respective high reliability and robustness.
These values compare well with the prediction certainty of the
Sierrathrissaleonensis cracker drying effective moisture diffusivity D-Optimal-RSM predictive model (99.831%) [
14], biodiesel yield CCD-RSM predictive model (73.509%) (Oke
et al., 2022) and techno-economic MGGP predictive models (MGGP-CAnysP APR = 99.980% and MGGP-CAnysP UPC = 98.477%) [
14]. The dynamic sensitivity charts, which identify input parameters that have the most significant influence on the predictions of the developed BBD-RSM models, are presented in
Figure 8. Here, the contribution of process variables of OT, S:L and ET to the variance in the prediction of BBD-RSM models for TPC, EY and AA were assessed.
Figure 8 shows that process variables contributed differently to the perturbation in the developed BBD-RSM models predictions. In the dynamic sensitivity graphs, all the bars to the right hand side indicate positive contributions (increase in response variable value with an increase in process variable value) while the bars to the left hand side signify negative contributions (increase in process variable value with decrease in response variable value).
Also the length (measured by percentage) of a sensitivity bar determines its magnitude and relative importance. Hence, a long bar (to either side) is relatively significant than correspondingly shorter bar, with 0% assigned to a no-significant effect. A high significant parameter should be better controlled (or more accurately measured) in order to improve the model’s predictability. Therefore, analysis of
Figure 8 (a) showed that S:L was the process variable with the most significant importance to the variance in TPC BBD-RSM model prediction. The ET and OT did not seem to influence profoundly the predictability of TPC BBD-RSM model. In the same vain,
Figure 8 (b) showed that the ET and S:L were the process variables with highest and least significance, respectively to the variance in the EY BBD-RSM model prediction. Also the order of process variable significance (
Figure 8 (c)) to the perturbation in the predictability of AA BBD-RSM model is S:L > OT > ET. In numerical terms however, S:L had positive contribution (+99.7%), ET had negative contribution (-0.28%) while OT did not contribute significantly (+ 0.02%) to the perturbation in the predictability of TPC BBD-RSM. Likewise, ET contributed positively (+76.2%), OT contributed negatively (-19.8%) while S:L contributed positively (+4%) to the variance in EY data prediction by the EY BBD-RSM model. The S:L, OT and ET contributed -52%, +46.7 and +1.3% respectively to the variance in AA value predictability by the constructed AA BBD-RSM model.