3.1. Results of original wood analysis
The original wood analyses conducted on the raw materials and the results obtained are given in Table 2 below.
Table 2
The results of original wood analysis of the samples (wt, %)* and HHVs (MJ/kg).

Moisture

Ash

Volatile compounds

Fixed carbon

Cellulose

Lignin

Extractives

HHV

Zeyrek stem

4.24 ± 0.08

11.82 ± 0.05

62.70 ± 0.04

21.20 ± 0.06

36.07 ± 0.04

22.42 ± 0.08

2.46 ± 0.34

18.33 ± 0.06

Hazelnut shell

5.29 ± 0.06

1.96 ± 0.07

65.12 ± 0.09

27.62 ± 0.05

32.90 ± 0.03

52.78 ± 0.06

1.64 ± 0.42

21.03 ± 0.05

Scotch pine powder

4.49 ± 0.11

1.43 ± 0.08

73.31 ± 0.08

20.82 ± 0.07

35.35 ± 0.06

30.29 ± 0.05

5.07 ± 0.28

20.18 ± 0.03

*The percentages of moisture, ash, volatile compounds, extractives and fixed carbon were calculated based on air dried samples, the percentages of lignin and cellulose were calculated based on extractive free, air dried samples. 
It was found that HHV of cellulose sample isolated from Zeyrek stem was 15.530±0.339, HHV of lignin sample isolated from hazelnut shell was 22.582±0.427, HHV of extractive material isolated from Scotch pine powder was 35.310±0.190 Mj/kg. It seems that higher lignin percentage caused higher HHV value of hazelnut shell. This was followed by the HHV of Scotch pine powder, which had the second higher lignin value. In addition, Scotch pine powder had the highest percentage of extractives among the three samples. It is a known fact that natural lignocellulosic samples with a high percentage of lignin and extractive material show higher HHV values [5, 9, 10].
3.2. Results Of Hhv Values Of Sample Mixtures
Mixture ratios and corresponding HHV values for each sample prepared are given in Table 3.
Table 3
Lignin, cellulose and extractives ratios and measured HHVs of the mixture samples
Sample Code

Cellulose
(%w/w ± SD)

Lignin
(%w/w ± SD)

Extractives (%w/w ± SD)

HHV
(Mj/kg)

S1

44.99 ± 0.01

49.99 ± 0.01

5.02 ± 0.01

20.713 ± 0.049

S2

44.99 ± 0.02

45.01 ± 0.03

10.00 ± 0.04

21.963 ± 0.074

S3

44.97 ± 0.00

40,05 ± 0.00

14.98 ± 0.00

22.663 ± 0.056

S4

44.99 ± 0.03

35.06 ± 0.02

19.95 ± 0.04

22.816 ± 0.200

S5

45.00 ± 0.03

30.11 ± 0.02

24.89 ± 0.04

23.162 ± 0.152

S6

45.07 ± 0.05

25.00 ± 0.03

29.93 ± 0.06

24.520 ± 0.316

S7

44.57 ± 0.03

20.86 ± 0.01

34.57 ± 0.03

25.326 ± 0.131

S8

44.85 ± 0.03

15.39 ± 0.01

39.76 ± 0.03

26.120 ± 0.260

S9

44.96 ± 0.05

10.22 ± 0.01

44.82 ± 0.05

26.378 ± 0.066

As can be seen from the table, although the lignin value shown to increase the HHVs in previous studies decreased from S1 to S9, the HHVs increased. It is seen that the reason for this might be the increasing rate of extractive material, which is another energyintensive component. It is known that the components such as waxes, alkaloids, resins, terpenes in the composition of the extractives provide high HHVs, although it varies according to the kind of biomass [9]. Due to the high variability of its content, it can cause large deviations in the HHV prediction models in which it is included [25, 28].
3.3. Comparative Evaluation Of M(N)lr And Ann Regression Models
The regression models and related statistical data obtained from the literature and the results of this study to be used to determine the effect of lignin and extractive substance ratios on HHVs are presented in Table 4, and Fig. 3 below, respectively.
Table 4
Regression equations used and corresponding statistical data
Prediction Models

Regression Equation

Ref.

MSE

R2

RMSE

MAPE

MAE

DW*

MNLR

HHV = 20.137 + 0.008L + 0.131E0.004E2

[37]

17.326

0.563

4.162

0.128

3.214



MLR1

HHV = 14.3377 + 0.1228L + 0.1353E

[25]

8.102

0.962

2.846

0.097

2.411



MLR2

HHV = 15.605 + 0.074L + 0.172E

[26]

2.938

0.972

1.714

0.066

1.602

1.6193

MLR3

HHV=28.179 + 0.880L + 1.019E

This study

0.077

0.974

0.278

0.012

0.247

2.181

ANN1

HHV = 17.0000 + 0.0337689[L]0.370197[E] + 0.0217811[EL]0.0001237[EL2]0.00026906[LE2]

[26]

124.799

0.864

11.171

0.334

8.431

1.8845

ANN2

HHV = 18.98860.0821496[L]0.788837[E] + 0.047379[LE]0.00044862[EL2]0.000301034[LE2] + 0.00146961[L2]

[26]

195.114

0.779

13.968

0.382

9.721

1.8455

ANN3

HHV = 20.71650.141898[L]1.78999[E] + 0.0763139[LE]0.0006305[EL2]0.00244972[LE2] + 0.00194996[L2] + 0.112698[E2]

[26]

0.003

0.813

53.576

1.379

35.296

1.8179

*: DW values are taken from the relevant literature. 
When looked at Table 4 and Fig. 3, it is seen that R2 values increased and MAPE values decreased as one goes from MLR1 to MLR3. The R2 value of the MNLR Eq. (0.563) is smaller than those of these equations, while the MAPE value (0.128) is higher. It is also seen that the R2 values of the ANN equations were lower than those of MLR equations, and the MAPE values were much higher. However, a more fundamental problem here was that the R2 values of the ANN1 and ANN2 equations, which were relatively comparable to the others, corresponded to a negative correlation. The graphs of the experimental HHVs against the predicted values drawn for each model are given below in order to be able to see the situation in this respect.
As can be seen in Fig. 4, the relationship calculated by using the MNLR model was a negative relationship. Therefore, since the expected positive linear relationship could not be obtained, the calculated statistical parameters did not fully define the fitting of the model.
When the MLR equations were evaluated among themselves, MLR3, which revealed a positive linear relationship, gave the highest R2 (0.974), the lowest MAPE (0.012) and RMSE (0.278) values, which were expected in terms of representing the sample. The standard error of the estimation in the model was 0.339. In addition, 46.26% of the variation in HHV could be explained by the lignin content, while 53.74% could be explicated by the extractive content. While these values were 62.4% and 37.6%, respectively, in the MLR2 model [26], which revealed the closest prediction performance to this model, these values are 56.4% and 43.6% in the MLR1 model [25]. A greater part of the change in HHV, in MLR1 and MLR2 models was caused by lignin, while it was caused by the extractives in the model obtained from this study (MLR3). Among the possible reasons for this situation, the extractive material used in the current study was obtained from a single type (Scotch pine) sample, and the extractive ratios were up to 45% in contrast to the samples used in MLR1 and MLR2 studies (generally below 15%).
It is important that there is no autocorrelation in the creation of MLR models. DurbinWatson statistic is used to determine this situation. It is also applied to optimize model stability and distinguish important independent variables from unimportant ones [26, 38]. If there is a random distribution in the model, the value of the DW statistic will be close to 2. In general, it is desirable for this value to be between 1.5–2.5. The value of the DW coefficient obtained in this study is 2.181, which reveals that there is no autocorrelation in the study. The obtained DW coefficient stands out as the best value among the examined models.
Theoretical HHV values calculated by applying the mixture ratios prepared in this study to the equations selected from the literature are given in Table S1 in comparison with the experimental HHV values.
The percantege relative error between the experimental and calculated HHVs of the MNLR and MLR equations did not exceed 15.71% for the samples in which the extractive substance value was below 30% (Table S1). However, it is noteworthy that larger estimation deviations occured in samples where the extractive substance value exceeds 30% (especially in MNLR model). When the relevant studies in the literature were examined, it would be seen that the extractive substance percentages were generally below 30%. The lignin and extractive substance contents of the samples used in all three studies varied between 14.66–57.36%, and 1.23–28.28%, respectively, and these changes did not show homogeneity in each group of the samples. In addition, considering the limited number of samples in each group (N = 12, 17 and 11) from which the relevant estimation equations were obtained, it could be concluded that the derived equations reflected the character of these samples in a way. Sheng and Azevedo (2005) [35] also obtained the results supporting this idea in their study.
When the model fit of the ANN equations in Fig. 4 and Table 4 were considered, ANN1 and ANN2 models showed a negative relationship, while ANN3 showed a positive linear relationship but had very large deviations in the estimation results (RMSE = 53.576, MAPE = 1.379). Considering the experimental and calculated HHVs of the ANNbased equations, it was seen that the percentage relative error increased in samples with 20% or more extractive substance percentage (Table S1). For instance, the relative error rates of the ANN equations reached 40% for samples with extractive substance ratios of 30% and above, and even reached 132.6% for the ANN3 model.
While it is possible that the inclusion of quadratic terms in the equations can make a positive contribution to the accuracy of the estimation results calculated from the model obtained in the relevant study using a limited number of samples [26], it is obvious that these models will create large deviations when applied to samples where the distribution of lignin and extractive substance ratios are more homogeneous as in the current study. In fact, the main purpose of deriving such equations is to obtain the highest estimation model fit by using the least number of independent variables [36]. It can even be seen from the low R2 and high MAPE values obtained from the MNLR equation that the contribution of such terms can significantly alter the estimation accuracy. It is worthy of note that a quadratic term (E2) that is not in the other MLR equations is included in this equation.
Since the samples, from which the estimation models are derived, are limited, their estimation performances are also limited [35]. In addition, the addition of quadratic terms to the model causes large deviations in the estimation results obtained when the model is applied to different samples, unless it is studied with sufficiently large and homogeneous samples as much as possible.