# Modeling the Essential Oil and Trans-Anethole Yield of Fennel (Foeniculum vulgare Mill. var. vulgare) by Application Artificial Neural Network and Multiple Linear Regression Methods

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## Abstract

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^{2}), number of seeds per plant (NS/P), number of seeds per umbel (NS/U) and 1000-seed weight (TSW)—were chosen as input variables. The network with Sigmoid Axon transfer function and two hidden layers was selected as the final ANN model for the prediction of EOY%, and the TanhAxon function with one hidden layer was used for the prediction of TAY%. The results revealed that the ANN method could predict the EOY% and TAY% with more accuracy and efficiency (R

^{2}of EOY% = 0.929, R

^{2}of TAY% = 0.777, RMSE of EOY% = 0.544, RMSE of TAY% = 0.264, MAE of EOY% = 0.385 and MAE of TAY% = 0.352) compared with the MLR model (R

^{2}of EOY% = 0.553, R

^{2}of TAY% = 0.467, RMSE of EOY% = 0.819, RMSE of TAY% = 0.448, MAE of EOY% = 0.624 and MAE of TAY% = 0.452). Based on the sensitivity analysis, SY/m

^{2}, NDF50% and NS/P were the most important traits to predict EOY% as well as SY/m

^{2}, NS/U and NDM to predict of TAY%. The results demonstrate the potential of ANNs as a promising tool to predict the EOY% and TAY% of fennel, and they can be used in future fennel breeding programs.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Plant Material Source and Recorded Traits

^{2}), 1000-seed weight (TSW), seed yield per plant (SY/P), seed yield per square meter (SY/m

^{2}), number of seeds per plant (NS/P), number of seeds per umbel (NS/U) and harvest index (HI) were randomly recorded from 15 plants per plot. An analysis of variance (ANOVA) was conducted to assess the significant statistical differences among evaluated fennel populations for the studied characteristics. A normality test was conducted with SAS software before the analysis of variance. The means of significant differences of traits (average of two years) were used for the statistical analysis (Table 2).

#### 2.2. Isolation of Essential Oils and GC/MS Analysis

^{3}, respectively. Chemical compositions of essential oils were analyzed by an Agilent 7890A Network GC system pooled with Agilent 5975C Network with Triple-Axis mass detector. The GC analysis was carried out on the Agilent 7890A Network GC system equipped with a splitless model injector (with 1.0 µm volume and 250 °C temperature). The carrier gas was helium with a flow rate of 1.1 mL/min and the capillary column used was HP 5-MS (30 m × 0.25 mm, film thickness 0.25 µm). The column pressure was fixed to 56,054.38 Pa. The oven temperature was initially kept at 50 °C for 2 min after injection and then increased to 250 °C with a rate of 6 °C/min heating ramp and kept constant at 250 °C for 4 min. The ionization voltage and mass range were 70 eV and 34–500 m/z, respectively. The temperatures 280 °C and 250 °C were used as anion source and interface temperatures, respectively. Constituents of the essential oils were recognized based on their retention time and mass spectra pattern with related available data or with the Wiley library and literature. Percentages of each compound were calculated from the given GC peak area and these data were used for quantification purposes.

#### 2.3. Data Processing and Statistical Analysis

#### 2.3.1. Input Variables Selection

^{®}software.

#### 2.3.2. Multiple Linear Regression

_{i}is EOY% or TAY%, β

_{0}+ β

_{n}are coefficients of regression, x

_{1}− x

_{n}are input variables and ε is an error associated with the ith observation. Stepwise regression was applied to estimate the MLR coefficients. The MLR analysis was carried out using SAS

^{®}software.

#### 2.3.3. Artificial Neural Network

_{i}is the original data, x

_{norm}is the normalized input or output values and x

_{max}and x

_{min}are the maximum and minimum values of the resultant variable, respectively.

_{t}is the network output (essential oil), n and m are the number of hidden nodes and number of input nodes, respectively, and f shows the transfer function. ${\beta}_{ij}$ {$i$ = 1, 2, …, $m$; $j$ = 0, 1, …, $n$} are the weights from the input to hidden nodes, ${\alpha}_{j}$ {j = 0, 1, …, $n$} are the vectors of weights from the hidden to the output nodes and ${\alpha}_{0}$ and ${\beta}_{0}{}_{j}$ denote the weights of arcs leading from the bias terms, which always are equal to 1.

#### 2.4. Performance and Sensitivity Analysis

^{2}), were used to compare the performance of the developed ANN with different transfer functions and hidden layers and MLR models for estimating the desired output of EOY% and TAY% according to Equations (4)–(6), respectively.

^{2}and low values of RMSE and MAE indicate the better performance of the ANN and MLR model.

^{2}, RMSE and MAE. Neuro-Solutions software (version 5.0) was used for the ANN model developing, evaluating and sensitivity analysis.

## 3. Results and Discussions

#### 3.1. Selection of Input Variables

^{2}(R = 0.756), NU (R = 0.754), SY/P (R = 0.732), NDM (R = 0.706), NS/P (R = 0.699), LFI (R = 0.676) and NS/U (R = 0.467). A negative significant correlation coefficient was observed between EOY% and NDF50% (R = −0.842), NDF100% (R = −0.659), NI (R = −0.719), LLOI (R = −0.713), FPH (R = −0.661), LP (R = −0.616) and SP (R = −0.518) (Figure 1). Rahimmalek et al. [41] also reported a negative significant correlation between essential oil yield with plant height and flowering date of Iranian fennel accessions. Overall, the results of the correlation analysis showed that HI, SY/m

^{2}, NU, SY/P and NS/P are the most important parameters to determine essential oil yield in fennel populations. As reported by Bahmani et al. [11,22] and Cosges [15], there is a significant correlation between the essential oil content of fennel and length of the peduncle, stem diameter, plant height, the weight of dry biomass, number of nodes, number of leaves, length of middle internodes, number of inflorescences and 1000-seed weight [11,15,22].

^{2}(R = 0.693), EOY% (R = 0.590), NS/P (R = 0.573), NU (R = 0.572) and LFI (R = 0.456), as well as a negative significant correlation with LLOI (Figure 2). The correlation between various traits can be positively or negatively affected by other variables and these low coefficients can significantly reduce the capability of the correlation analysis to select the input variables [42,43]. However, there are parameters than other morphological and yield components that affect the oil yield and trans-anethole content of fennel. The correlation of climatic data (temperature) with oil yield and trans-anethole content of Iranian fennel accessions was assessed and a negative correlation between oil yield and T

_{max}and a positive correlation between trans-anethole and Tmax (r = 0.459) were reported [41]. These results indicate the importance of environmental parameters in assessing the correlation analysis of fennel populations. Incorporating such data into the model can increase the decision-making power and accuracy of the predictive model. In addition to perform the correlation analysis, stepwise regression (SWR) analysis was employed in this study to optimize the number of input variables [43].

^{2}, NDF 50%, NS/P, NU, FPH, NS/U, NDM, TSW and NI) were entered into the models as the most suitable input variables (the dependent variables were EOY% and TAY%). The number of umbels is an important yield component characteristic that can affect grain yield and subsequently the essential oil yield of fennel populations. This characteristic affect both EOY% and TAY% of the evaluated fennel population of the present study. These results are consistent with the results of Sefidan et al. [44] and Kalleli et al. [45].

^{2}values for inserted variables in the model (partial R

^{2}= 0.32, 0.06, 0.03, 0.02 and 0.02 for number of leaves, length of peduncle, plant height and days to 50% flowering, respectively). The low estimated partial R

^{2}values for all independent variables indicate the insufficient efficiency of the linear regression model in interpreting the relationships between independent and dependent variables. Therefore, a non-linear model is needed to better interpret these relationships.

#### 3.2. Prediction of Dependent Variables Using MLP/ANN Model

^{2}values were obtained by the Sigmoid Axon function in both training and testing stages for the prediction of EOY%, as well as the TanhAxon transfer function to predict TAY%.

^{2}= 0.953, RMSE = 0.522, and MAE = 0.375) and testing (R

^{2}= 0.929, RMSE = 0.544 and MAE = 0.385). Therefore, the results of Table 5 and Table 6 reveal that the best EOY% (essential oil) predictive model consisted of an input layer with 11 input variables (NDF50%, NDF100%, NDM, FPH, NI, NU, SY/P, SY/m

^{2}, NS/P, NS/U, and TSW) and two hidden layers with nine and seven neurons in each layer, i.e., the 11-9-7-1 structure (Figure 3). The TanhAxon transfer function, Momentum learning algorithm and one hidden layer (with 11-10-1 structure) were the best parameters in the ANN model to predict TAY% of fennel (Table 6). This topology had the minimum amounts of RMSE and MAE and the highest coefficient of determination (Table 6). Levenberg–Marquardt back-propagation and Logsig and Tansig transfer functions for hidden and output layers algorithm and the number of 10 neurons in the hidden layer have been reported as best parameters of an ANN for the modeling and optimization of anethole ultrasound-assisted extraction from fennel seeds [47]. One of the main objectives of ANN modeling studies is to achieve a simple model with the least number of hidden layers and neurons and the highest performance values [30,32]. Niazian et al. [25] reported an ANN model with a 4-4-1 structure, for the prediction of grain yield in ajowan (Trachyspermum ammi L.) belonging to the Apiaceae family [25]. These results will be useful to fit an excellent model structure of ANN in future research on the Apiaceae family.

^{2}= 0.794) and testing (R

^{2}= 0.777) stages are shown in Figure 7 and Figure 8, respectively. According to the scatter plot, there was no significant difference between predicted data and measured data of TAY% in the ANN model in both training and testing datasets (Figure 7 and Figure 8).

#### 3.3. Comparing MLR and ANN Models to Predict EOY% and TAY% of Fennel Populations

^{2}+ 0.113 NDF 50% + 0.126 NS/P + 0.086 NU + 0.079 FPH

^{2}+ 0.108 NS/U + 0.089 NDM + 0.073 TSW + 0.065 NU + 0.044 NI

^{2}, RMSE and MAE provide a set of the reasonable criteria for comparison between two modeling methods. Compared to the MLR model, the ANN models could predict EOY% and TAY% much better than the MLR model with 39.97% and 32.69% increases in R

^{2}, reductions of 0.30 and 0.20 in RMSE and reductions of 0.25 and 0.12 in MAE, respectively. According to the obtained results, the ANN model had higher predictive power than the MLR model and was more efficient than MLR in predicting EOY% and TAY% traits in fennel populations. The different performance of the two models to predict EOY% and TAY% shows the importance of choosing the more suitable model. The superiority of the ANN modeling methods compared to the MLR methods has been reported in other previous studies [24,25,32,35]. The supremacy of ANN modeling seems to be due to the high capability of this model to capture the highly nonlinear and complex relationship between EOY% or TAY% and the relevant traits [23]. There is a considerable variation among different populations of fennel in terms of seed yield, yield components, essential oil content and essential oil composition [11,49]. This variation along with high genotype × environment interaction create a difficult situation to improve the fennel population for the desired traits in a short period using conventional statistical methods and direct selection [49]. However, using non-linear predicting methods, breeders are able to estimate the desired values of their desired traits in a faster and more confident way. Therefore, an advanced computational method can play a complementary role to conventional statistical methods previously employed to improve the fennel populations [11,49].

#### 3.4. Sensitivity Analysis

^{2}, NS/P, NDF50%, NS/U and NDM. The results of the sensitivity test for EOY% showed that the highest RMSE (0.608, 0.911) and MAE (0.439, 0.659) and the lowest R

^{2}(75.45, 39.12) were achieved without seed yield per square meter in both ANN and MLR models (Table 7). Number of days to 50% flowering and number of seeds per plant were the other most effective characteristics on the EOY% of fennel populations. As shown in Table 7, the ANN and MLR models for TAY% without the seed yield per square have the lowest R

^{2}(61.43 and 35.52) and highest RMSE (0.332 and 0.532) and MAE (0.487 and 0.471), respectively. As the results showed, SY/m

^{2}is the most influential factor to predict EOY% and TAY% in both models.

^{2}of both ANN and MLR models [24]. In the other study, sensitivity tests were conducted in both MLR and ANN models and results showed that the highest RMSE and MAE and the lowest R

^{2}were achieved in the MLR and ANN models without biological yield [25].

## 4. Conclusions

^{2}, RMSE and MAE indicators. These results showed that the selected ANN model could surely replace MLR to predict EOY% and TAY% of fennel populations. Based on the sensitivity analysis, SY/m

^{2}, NDF50%, and NS/P were the most important traits to predict EOY%, whereas SY/m

^{2}, NS/U and NDM were the most important traits to predict the TAY% of fennel populations. The findings of the present study can provide important information to improve the EOY% of the other medicinal plants of the Apiaceae family. Plant breeders can also use the optimized artificial neural network models to model other complicated polygenic traits of medicinal plants, such as the content of various secondary metabolites that are more valuable for the food and pharmaceutics industries.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations:

ANN | Artificial neural network |

EOY | Essential oil yield |

FPH | Final plant height |

HI | Harvest index |

LFI | Length of the first internode |

LLAI | Length of the last internode |

LLOI | Length of the longest internode |

LP | Length of the peduncle |

MAE | Mean absolute error |

MLR | Multilinear regression |

NDF50% | Number of days to 50% flowering |

NDF100% | Number of days to 100% flowering |

NDG | Number of days to germination |

NDM | Number of days to maturity |

NI | Number of internodes |

NS | Number of stems |

NS/P | Number of seeds per plant |

NS/U | Number of seeds per umbel |

NU | Number of umbels |

RMSE | Root mean square error |

SD | Stem diameter |

SWR | Stepwise regression |

SY | Seed yield |

SY/m^{2} | Seed yield per square meter |

SY/P | Seed yield per plant |

TAY | Trans-anethole yield |

TSW | 1000-seed weight |

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**Figure 1.**The Pearson correlation coefficient of input variables with EOY% of fennel populations in both ANN and MLR models. For detailed information on trait abbreviations, see Table 2. ns, * and **, non-significant, significant at the 0.05 and 0.01 probability level, respectively.

**Figure 2.**The Pearson correlation coefficient of input variables with TAY% of fennel populations in both ANN and MLR models. ns, * and **, non-significant, significant at the 0.05 and 0.01 probability level, respectively.

**Figure 4.**The convergence of the average MSE value during training and validation of the final 11-9-7-1 ANN structure to predict the essential oil yield of fennel populations.

**Figure 5.**Scatter plot of measured and predicted essential oil yield of fennel populations in the training stage of ANN.

**Figure 6.**Scatter plot of measured and predicted essential oil yield of fennel populations in the testing stage of ANN.

**Figure 7.**Scatter plot of measured and predicted trans-anethole yield of fennel populations in the training stage of the ANN.

**Figure 8.**Scatter plot of measured and predicted trans-anethole yield of fennel populations in the testing stage of the ANN.

**Table 1.**Locality and average of essential oil yield and trans-anethole yield of studied fennel populations.

No | Population | Variety | Locality | Voucher Number | Latitude (N) | Longitude (E) | Essential Oil Yield (%) | trans-Anethole Yield (%) |
---|---|---|---|---|---|---|---|---|

1 | Salzland | Vulgare | Germany | Ah123 | 51°78′ | 11°77′ | 2.29 ± 0.85 | 1.46 ± 0.59 |

2 | Gotha | Vulgare | Germany | Ah115 | 51°07′ | 10°87′ | 2.14 ± 0.73 | 1.77 ± 0.57 |

3 | Gazianetp | Vulgare | Turkey | Ah114 | 37°05′ | 37°37′ | 2.67 ± 0.79 | 2.30 ± 0.68 |

4 | Izmir | Vulgare | Turkey | Ah113 | 38°35′ | 27°07′ | 1.63 ± 0.41 | 1.17 ± 0.32 |

5 | Bonab | Vulgare | Iran | Ah111 | 37°35′ | 46°03′ | 2.89 ± 1.03 | 2.24 ± 0.91 |

6 | Birjand | Vulgare | Iran | Ah110 | 32°84′ | 59°18′ | 0.73 ± 0.24 | 0.54 ± 0.16 |

7 | Tatmaj | Vulgare | Iran | Ah126 | 33°69′ | 51°62′ | 1.88 ± 0.79 | 1.50 ± 0.54 |

8 | Torbatejam | Vulgare | Iran | Ah127 | 35°23′ | 60°66′ | 2.90 ± 0.92 | 2.45 ± 0.76 |

9 | Meshkinshahr | Vulgare | Iran | Ah120 | 38°37′ | 47°69′ | 2.30 ± 0.61 | 1.70 ± 0.62 |

10 | Khorobiabanak | Vulgare | Iran | Ah118 | 33°89′ | 54°87′ | 0.99 ± 0.41 | 0.73 ± 0.51 |

11 | Moghan | Vulgare | Iran | Ah121 | 39°62′ | 47°87′ | 4.12 ± 1.32 | 2.68 ± 0.68 |

12 | Ziar | Vulgare | Iran | Ah129 | 32°50′ | 51°94′ | 1.66 ± 0.69 | 1.14 ± 0.42 |

13 | Shirvan | Vulgare | Iran | Ah124 | 37°39′ | 57°96′ | 2.42 ± 0.86 | 1.77 ± 0.68 |

14 | Karaj | Vulgare | Iran | Ah116 | 35°77′ | 51°06′ | 1.54 ± 0.64 | 1.07 ± 0.44 |

15 | Kerman | Vulgare | Iran | Ah117 | 30°30′ | 57°13′ | 0.82 ± 0.33 | 0.55 ± 0.19 |

16 | Khorramabad | Vulgare | Iran | Ah119 | 33°48′ | 48°44′ | 2.89 ± 0.67 | 2.10 ± 0.71 |

17 | Neishabour | Vulgare | Iran | Ah122 | 36°19′ | 58°83′ | 2.02 ± 0.77 | 0.33 ± 0.15 |

18 | Varamin | Vulgare | Iran | Ah128 | 35°34′ | 51°62′ | 3.77 ± 0.94 | 3.12 ± 0.67 |

19 | Hamedan | Vulgare | Iran | Ah112 | 34°81′ | 48°48′ | 2.92 ± 0.91 | 2.16 ± 0.56 |

20 | Tabriz | Vulgare | Iran | Ah125 | 38°07′ | 46°08′ | 2.50 ± 0.76 | 0.50 ± 0.12 |

**Table 2.**Descriptive statistics of morphological, phonological and yield-related characteristics in the fennel populations.

Characteristic | Abbreviation | Min | Max | Mean | Standard Deviation |
---|---|---|---|---|---|

Number of days to germination | NDG | 7 | 18 | 12.45 | 4.21 |

Number of days to 50% flowering | NDF50% | 59 | 102 | 79.18 | 16.56 |

Number of days to 100% flowering | NDF100% | 82 | 114 | 92.36 | 24.98 |

Number of days to maturity | NDM | 126 | 180 | 145.68 | 36.15 |

Initial plant height (cm) | IPH | 39.47 | 82.89 | 58.29 | 17.14 |

Final plant height (cm) | FPH | 68.56 | 198 | 107.25 | 36.84 |

Number of stems | NS | 1 | 4 | 2.58 | 1.25 |

Stem diameter (cm) | SD | 2.75 | 15.85 | 8.54 | 3.62 |

Number of internodes | NI | 6 | 14 | 9.35 | 3.48 |

Length of the first internode (cm) | LFI | 3.11 | 9.32 | 6.13 | 2.04 |

Length of the longest internode (cm) | LLOI | 5.48 | 19.14 | 14.59 | 5.74 |

Length of the last internode (cm) | LLAI | 2.36 | 11.71 | 7.64 | 1.91 |

Length of the peduncle (cm) | LP | 4.85 | 14.29 | 9.25 | 4.89 |

Number of umbels | NU | 12 | 58 | 36.25 | 15.70 |

Biomass (g/m^{2}) | B/m^{2} | 654.25 | 1457.83 | 124.91 | 62.25 |

Thousand seed weight (g) | TSW | 2.85 | 7.65 | 5.16 | 3.11 |

Seed yield per plant (g) | SY/P | 12.35 | 86.54 | 32.67 | 10.29 |

Seed yield (g/m^{2}) | SY/m^{2} | 115.12 | 542.28 | 315.21 | 82.27 |

Number of seeds per plant | NS/P | 985 | 9153 | 7859 | 2141 |

Number of seeds per umbel | NS/U | 112 | 276 | 192.51 | 78.29 |

Harvest index (%) | HI | 12.11 | 46.82 | 37.26 | 16.28 |

Step | Entered Variables in Model | Partial R^{2} | Model R^{2} |
---|---|---|---|

1 | SY/m^{2} | 0.1642 | 0.1642 |

2 | SY/m^{2}, NDF 50% | 0.1415 | 0.3057 |

3 | SY/m^{2}, NDF 50%, NS/P | 0.1276 | 0.4333 |

4 | SY/m^{2}, NDF 50%, NS/P, NU | 0.0781 | 0.5114 |

5 | SY/m^{2}, NDF 50%, NS/P, NU, FPH | 0.0742 | 0.5856 |

^{2}= 0.5533.

Step | Entered Variables in Model | Partial R^{2} | Model R^{2} |
---|---|---|---|

1 | SY/m_{2} | 0.123 | 0.123 |

2 | SY/m^{2}, NS/U | 0.114 | 0.237 |

3 | SY/m^{2}, NS/U, NDM | 0.1056 | 0.3426 |

4 | SY/m^{2}, NS/U, NDM, TSW | 0.0561 | 0.3987 |

5 | SY/m^{2}, NS/U, NDM, TSW, NU | 0.052 | 0.4507 |

6 | SY/m^{2}, NS/U, NDM, TSW, NU, NI | 0.0441 | 0.4948 |

^{2}= 0.4672.

**Table 5.**Summary of the components of the neural networks used to predict essential oil and trans-anethole yield of fennel populations.

ANN Method | Number of Hidden Layers | Number of Neurons in Each Hidden Layer | Transfer Function | Learning Algorithm | Number of Epochs |
---|---|---|---|---|---|

Multi-layer perceptron (MLP) | 1–5 | 1–20 | Sigmoid Axon | Levenberg– | 50–2000 |

Linear Sigmoid Axon | Marquardt | ||||

TanhAxon | Momentum | ||||

Liner TanhAxon | Conjugate Gradient |

Output | Network Structure | Transfer Function | Learning Algorithm | Training | Testing | Cross Validation | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

R^{2 a} | RMSE ^{b} | MAE ^{c} | R^{2 a} | RMSE ^{b} | MAE ^{c} | R^{2 a} | RMSE ^{b} | MAE ^{c} | ||||

Essential oil yield | 11-9-7-1 | Sigmoid Axon | Levenberg–Marquardt (LM) | 0.953 | 0.522 | 0.375 | 0.929 | 0.544 | 0.385 | 0.904 | 0.552 | 0.389 |

Trans-anethole yield | 11-10-1 | TanhAxon | Momentum | 0.794 | 0.246 | 0.334 | 0.777 | 0.264 | 0.352 | 0.764 | 0.258 | 0.359 |

^{a}: Determination coefficient;

^{b}: root mean square error;

^{c}: mean absolute error.

**Table 7.**Sensitivity analysis and selecting three of the most influential inputs on the essential oil and trans-anethole yield of fennel populations.

Output | Method | ANN | MLR | ||||
---|---|---|---|---|---|---|---|

R^{2 a} (%) | RMSE ^{b} | MAE ^{c} | R^{2 a} (%) | RMSE ^{b} | MAE ^{c} | ||

Essential oil yield | The best ANN (with all input) | 95.30 | 0.522 | 0.375 | 55.33 | 0.819 | 0.624 |

ANN without SY/m^{2} | 75.45 | 0.608 | 0.439 | 39.12 | 0.911 | 0.659 | |

ANN without NDF50% | 84.70 | 0.585 | 0.421 | 42.18 | 0.747 | 0.571 | |

ANN without NS/P | 85.98 | 0.578 | 0.416 | 44.25 | 0.812 | 0.583 | |

trans-anethole yield | The best ANN (with all input) | 79.41 | 0.246 | 0.334 | 46.72 | 0.448 | 0.452 |

ANN without SY/m^{2} | 61.43 | 0.332 | 0.487 | 35.52 | 0.532 | 0.471 | |

ANN without NS/U | 66.40 | 0.316 | 0.459 | 37.14 | 0.431 | 0.384 | |

ANN without NDM | 68.40 | 0.308 | 0.445 | 38.76 | 0.416 | 0.335 |

^{a}: Determination coefficient;

^{b}: root mean square error;

^{c}: mean absolute error.

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## Share and Cite

**MDPI and ACS Style**

Sabzi-Nojadeh, M.; Niedbała, G.; Younessi-Hamzekhanlu, M.; Aharizad, S.; Esmaeilpour, M.; Abdipour, M.; Kujawa, S.; Niazian, M.
Modeling the Essential Oil and *Trans*-Anethole Yield of Fennel (*Foeniculum vulgare* Mill. var. *vulgare*) by Application Artificial Neural Network and Multiple Linear Regression Methods. *Agriculture* **2021**, *11*, 1191.
https://doi.org/10.3390/agriculture11121191

**AMA Style**

Sabzi-Nojadeh M, Niedbała G, Younessi-Hamzekhanlu M, Aharizad S, Esmaeilpour M, Abdipour M, Kujawa S, Niazian M.
Modeling the Essential Oil and *Trans*-Anethole Yield of Fennel (*Foeniculum vulgare* Mill. var. *vulgare*) by Application Artificial Neural Network and Multiple Linear Regression Methods. *Agriculture*. 2021; 11(12):1191.
https://doi.org/10.3390/agriculture11121191

**Chicago/Turabian Style**

Sabzi-Nojadeh, Mohsen, Gniewko Niedbała, Mehdi Younessi-Hamzekhanlu, Saeid Aharizad, Mohammad Esmaeilpour, Moslem Abdipour, Sebastian Kujawa, and Mohsen Niazian.
2021. "Modeling the Essential Oil and *Trans*-Anethole Yield of Fennel (*Foeniculum vulgare* Mill. var. *vulgare*) by Application Artificial Neural Network and Multiple Linear Regression Methods" *Agriculture* 11, no. 12: 1191.
https://doi.org/10.3390/agriculture11121191