**3. Results and discussions**

#### **3.1 2D-QSRR study**

#### *3.1.1 Data set for analysis*

A 2D-QSRR study was carried out for a series of 29 alkylated phenols, as indicated above, to determine a quantitative relationship between the structure and the retention property. The values of the 28 descriptors are shown in Table S1 (in Supplementary Material).

## *3.1.2 Stepwise multiple linear regression MLR*

The stepwise multiple linear regression (MLR) procedure based on the forward selection and backward elimination method (including the critical probability: *P*value <0.05 for all descriptors and for the model complete) was employed to determine the best regression model.

The 2D-QSRR model built using stepwise MLR is represented by the following equation:

$$\text{Log}(LRI) = 2.935 + 1.682 \times 10^{-3} \times \text{V} \tag{1}$$

2D-QSRR model as valid. The model's performance was good and was characterized

CV value of 0.977 with the descriptor (V) proposed by the stepwise MLR.

The model created in the calculation process using the alkylated phenols is used to predict the retention property values (Log(LRI)) of the remaining (five molecules). The results obtained by stepwise MLR model are very sufficient to conclude

Evaluation of the applicability domain of the 2D-QSRR model is considered as an important step to establish that the model is reliable to make predictions within the chemical space for which it was developed [31]. In this chapter, we used leverage approach [20]. Leverage of a given chemical compound hi is defined as follows:

�1

where xi is the descriptor row of the query compound and X is the descriptor matrix of the training set compounds used to develop the model. As a prediction

xiði ¼ 1 … nÞ (2)

h� ¼ 3ðP þ 1Þ*=*n (3)

**<sup>2</sup> SE F-t N r<sup>2</sup>**

CoMFA 0.959 0.998 0.003 2937.327 7 0.913

**test**

the performance of models; it is confirmed by the test done with the five

*2D- and 3D-QSRR Studies of Linear Retention Indices for Volatile Alkylated Phenols*

test = 0.880).

hi <sup>¼</sup> xT

tool, the warning leverage h\* is defined as follows:

**r 2**

*Statistical parameters of CoMFA model.*

**Table 3.**

**161**

**Figure 3.**

**CV r**

*Williams plot to evaluate the applicability domain of stepwise MLR model.*

<sup>i</sup> <sup>ð</sup>XTX<sup>Þ</sup>

by r<sup>2</sup>

*3.1.4 External validation*

*DOI: http://dx.doi.org/10.5772/intechopen.89576*

compounds (rtest = 0.938; r2

*3.1.5 Domain of applicability*

N = 24; r = 0.990; r<sup>2</sup> = 0.980; RMSE = 0.008; F = 1085.981; *P* < 0.0001.

In this equation, V is the Connolly solvent-excluded volume, N is the number of compounds, r is the correlation coefficient, r<sup>2</sup> is the coefficient of determination, RMSE is the root mean square of the errors, F is the Fisher's criterion, and *P* is the significance level.

It is observed that the coefficient of correlation r is high, and RMSE is low, which makes it possible to indicate that the model is reliable. A *P* value much smaller than 0.05 indicates that the regression equation is statistically significant; thus, we can conclude, with confidence, that the model provides a significant amount of information [29, 30].

The predicted Log(LRI) values calculated from equation are given in **Table 4** in comparison to the observed values. The correlation between the predicted and observed Log(LRI) is shown in **Figure 2**.

#### *3.1.3 Internal validation (cross-validation)*

The 2D-QSRR model expressed by the equation of stepwise MLR method is validated by its appreciable value of r2 CV obtained using the leave-one-out (LOO) procedure. The value of r2 CV greater than 0.5 is the basic condition for qualifying a

**Figure 2.** *Correlations of observed and predicted Log(LRI) with MLR stepwise (training set in blue; test set in red).*

*2D- and 3D-QSRR Studies of Linear Retention Indices for Volatile Alkylated Phenols DOI: http://dx.doi.org/10.5772/intechopen.89576*

2D-QSRR model as valid. The model's performance was good and was characterized by r<sup>2</sup> CV value of 0.977 with the descriptor (V) proposed by the stepwise MLR.
