INTRODUCTION:
Petroleum and natural gas are modernity
instrument and one of the important methods for economic control over word1.
of all kinds, whether liquid or rock, and although they have positive benefits
as energy for transportation or as household energy2, they have many
negatives on the environment and the life of living organisms of all kinds3,
humans’ animals, plants and water because of inhaled gases4. Chemical
composition is cyclic aromatic toxic hydrogen carbon compounds. Several studies
have been conducted on these compounds that make up the energy tools known as
carbohydrate around: boiling point, toxicitysolubility5, henry
constant, retention index…etc.
Among modern methods is statistical and analysis
graphical analysis (in QSAR analysis) by mathematical algorithms6-10.
In this study, a relationship was evaluated between
molecular structure and toxicity coefficient 
of 16 cyclic aromatic hydrocarbon compounds
by multiple regression method to know the most toxic compounds when abnormal
points (aberant) appear using line plot and how to distribute them using
goodness-of fit graph10-15. Finally, these points are removed to
know the effect of these compounds on improving themodel15-22.
METHODOLOGY:
The Data
Set:
The n-octanol: water partition coefficient
(Log 
) of 16 hydrocarbons compounds22-27,
taken from the scientific article of FrédéricJouannin28-29. The list
of Compounds and experimental value of Log is shown in Table 1.
Table 1. Octanol: water partition
coefficient (log 
) for the selected chemical compounds of
Polycyclic aromatic hydrocarbons (PAHs).
|
S. No°
|
Compounds
|
Log
|
|
1
|
Naphtaléne
|
3.37
|
|
2
|
Acenaphtyléne
|
4.07
|
|
3
|
Acenaphtene
|
4.33
|
|
4
|
Fluorene
|
4.18
|
|
5
|
Phenanthene
|
4.46
|
|
6
|
Anthracene
|
4.45
|
|
7
|
Fluoranthene
|
5.33
|
|
8
|
Pyrene
|
5.32
|
|
9
|
Benzo(a)anthracene
|
5.61
|
|
10
|
Chrysene
|
5.61
|
|
11
|
Benzo(b)fluoranthene
|
6.57
|
|
12
|
Benzo(k)fluoranthene
|
6.84
|
|
13
|
Benzo(a)pyrene
|
6.04
|
|
14
|
Dibenzo(a,h)anthracene
|
5.97
|
|
15
|
Indeno (c, d) pyrene
|
7.66
|
|
16
|
Benzo (g, h, i)
perylene
|
7.23
|
Selection of
descriptors:
The detailed
general formular for a series of cyclic hydrocarbons was obtained by drawing
and placing them in a stable geometric position using the semi - empirical
method (PM3) (Geometry optimization) based on a Hyperchemsoftware33,
including obtaining electronic propriety (HOMO, LUMO, E tot,Enucle
,E buiding, Estab
)and QSAR propriety (Log p Refractivity, Volume ,polarization ,M,…)29-35.
Then we analyse
the relationship of each descriptor with using MINITAB 16 software to choose the best model in term of the
highest value of determination coefficient 
and the smallest standard deviation (S).
Development of the model:
In this study
work, it was relied on mathematical computer software through multi -variable
equation
or linear equations of the multi order in
their general form:
F(x) = a + b1x1 + b2x2+
b3x3 (1)
a:constant of regression
b1, b2 and b3:these
coefficients of regression).
Statistical analysis of the model based on
the following factors:(R 2, R 2 adj,
, r, standard error S, D, VIF, P)34.
r is correlation coefficients:
(2)
For the signific test of
correlation coefficients are using;
(3)
t is student value of 
R2 is
determination coefficients
(4)
S
is the standard deviation:
(5)
R 2adj, is Adjusted R 2:
(6)
VIF is the variance
inflation factors:
(7)
The p-value is the probability of obtaining
a test statistic that is at least as extreme the as actual calculated value, if
the null hypothesis is true.
DW is Durbin-Watson statistic:
(8)
RESULT AND DISCUSSION:
The best model:
(
): HOMO (Highest occupied molecular
orbital), EH (Hydration Energy) and LUMO (Lowest unoccupied molecular orbital)
n=16 compound.
Statistical and graphical analysis:
All indicators
of the theoretical sample selected in Table 2within the statistical conditions
for accepting the model were The standard deviation S=0.635<1(S≪) R2=80.2%
,probability p=0.000
,the variance inflation factor VIF=1.400
,Durbin Watson statistic D=1.90077
and free from any statical problem.
Table 2. Diagnostic statistical sample.
|
S
|
R 2
|
R 2(adj)
|
R 2(préd)
|
|
0.616007
|
80.2%
|
75.3%
|
75.3%
|
|
P
|
VIF
|
DW
|
|
|
0.00
|
1.400
|
1.90077
|
|
The model based
on three descriptors is for equation using the Minitab 16 software 34:
(9)
t student value for model is:
=4.608(acceptthe model).
Relationship between Y and X:
The matrix of the compatibility
relationship or the proportions shown in the table 3 and figure 2 . positive direct proportion(r=0.8955)
between HOMO and Log and negative
direct proportion between two descriptors EH, LUMO) and
Using test of student for correlation
coefficient of the model 
(14 ;0.05) =2.1448<
=6.54. The correlation coefficient has
statistically significant and was not the result of chance, but rather
represents the reality of the strength of the relationship at Level % 95.
Table 3. Relationshipmatrix
|
Log kow
|
HOMO
|
EH
|
|
HOMO
|
0,868
|
|
|
|
0.000
|
|
|
|
EH
|
-0,465
|
-0,361
|
|
|
0,07
|
0,170
|
|
|
LUMO
|
-0,348
|
-0,471
|
0,482
|
|
0,186
|
0,062
|
0,059
|
Figure 1.
Histogram of coefficient correlation.
The goodness-of-fit:
As shown in Figure 3 that the points are
far apart, but within the field between the lines of the continuous confidence
bands around the regression for the 95th percentiles, the distribution of
points can be modified by the equation39-49.
As shown in Figure 4 that it right of
adjustment y=f(x) is a line linear, the y expeimental and Y calculated values are very close. This model fits well the
y calcu data (R² = 100%) and 
=100% between the y experimental and Y
Calculated.
The Relationship between Log and HOMO is statisticaly significant
(p<0.05)
Figure 2. diagram of the goodness-of-fit.
One
compound has a big residue, which indicate a data compound that is not well fit
by the equation in figure 5. This compound is clear in inflamed on the plots
and is in distrurbance 7 (Fluoranthene) of the worksheet For abnormal (aberant)
data can have a healthy power on the consequences (scores), estimate to detect
the source for its abnormal (abnormal) class. Adjust important data entry or
measurement errors. Consider
The compounds in Figure 6:
2(Acénaphtylene),3(Acenaphtene)
12 (Benzo (k)fluoranthene) has a major
power (
>
=0.52), and it is important.
Removing data that are
associated with special cause and redoing the analysis
Figure 3. Line plot of the MLR model.
After two redoing the analysis for removing the
aberrantcompounds:
7(Fluoranthene),14(Dibenzo(a,h)anthracene)Thesecompounds are power toxicity compounds
because not well fit by the equation.
New model is Very good statistical value: The standard
deviation S =0.431636
(
),
, =89,3
=79.75
.
Probability p=0.000 , the variance inflation factor VIF=1.310 ,Durbin Watson statistic D=2.37329
( 
)his adjustment power (Table 4).
Table 4: Diagnostic statistical Sample (after removing
the aberrant compounds).
|
S
|
R-sq
|
R-sq(adj)
|
R-sq(prév)
|
|
0,431636
|
91,8%
|
89.3%
|
79.75%
|
|
P
|
VIF
|
DW
|
|
|
0.000
|
1.31
|
2.37329
|
|
Removing the aberrant compounds).
(10)
The parfaithly of The positive correlation (r=0.9581)
in Table 5 and figure 4 indicates that when HOMO increases, Log also tends to increase and the negative
correlation by two descriptors (
=-0.455,
).
Table 5; Correlation matrix (After removing the
aberrant compounds).
|
|
Log kow
|
HOMO
|
EH
|
|
HOMO
|
0,947
|
|
|
|
0.000
|
|
|
|
EH
|
-0,455
|
-0,356
|
|
|
0,102
|
0,212
|
|
|
LUMO
|
-0,342
|
-0,38
|
0,472
|
|
|
0,231
|
0,181
|
0,089
|
Figure 4: Histogram of coefficient correlation (After
removing the aberant compounds).
Figure (5) has a n symetry distribution from
coefficient of Skewness(-0.1451
) which defined by 
=(3*(x ̅-Med)/s) (when 
,Median =0.0225) and coefficient of
Kurtosis (-0.711
)also the coefficient of Skewness with the
coefficient of Kurtosis Jarque and Bera test give which presented like of
Normality test of Residues has two degrees of freedom (JB test= 0.343=n
5.99)indicates that the resting pulse data
follow a normal distribution .
The mean of the students’ resting pulse is 0 (95%
confidance intervals of -0.2185and0.2185).
The standard deviation is 0.3785(95% confidance
intervals of 0.274and0.690).
Using a significance level of 0.05 ,the Anderson
-Darling normality test (A-squared=0.20
)indicates that the resting puls data
follow a normality distribution.
The boxplot shows: 1st Quartie is -0.3264,Median is
0.0225 (95% confidance intervals of 0.305 and 0.193), 3rd Quartie is 0.2359
maximum is 0.616 and no outhiers compounds (aberant) are present.
Figure 5. Summary of RESI (After removing the aberrant
compounds).
A normal distribution in Figure 6
Figure 6. diagram of the goodness-of-fit. (After
removing the aberrant compounds)
There are no abnormal data compounds
(aberrant) in figure 7. Abnormal data compounds can have a healthy power on the
consequences(score):2(Fluorene) ,3 (Acenaphtene)has a
major power (
) and it is important.
Figure 7. Line plot of the MLR model (After
removing the aberrant compounds)
Interpretation of the mode:
The hydrophobicity is expressed by the
octanol-water partition coefficient (
); which estimate the solubility in both
aqueous and organic phases (in general n-octanol-water is used)27.
Three descriptors were able to model the Octanol-Water
Partition Coefficient. The value of coefficient by electronic descriptor
HOMO (4.41) in equation (9) for the correlation coefficient (
= 0.868) in table 3show the regularity of
the positive impact of this descriptor to the value of 
.
The value of coefficient by two descriptors
(QSAR descriptor EH (-0.509) and electronic descriptor (QSER
descriptor) LUMO (0.337)) in equation (9) for the correlation coefficient (=-0.465 and 
= -0.348) in table 3indicate the negative
correlation of these descriptors to the value of
The value of coefficient by the electronic
descriptor HOMO after removing the aberrant points (5.22) in equation (10) for
the correlation coefficient (r=0.947) in table 5show the regularity of positive
impact of this descriptor to the value of 
.
The value of two descriptors (QSAR
descriptor EH (-0.362) and electronic descriptor (QSER descriptor)
LUMO (0.170) in equation (10) for the correlation coefficient (=-0.455 and =-0.345) in table 5indicate the negative
correlation of these descriptor to the value of 
.
CONCLUSION:
The octa-water constants (Log) of 16 Polycyclic aromatic hydrocarbons
(PAHs). Among three descriptors (two electronic descriptor (QSER) HOMO is
Highest occupied molecular orbital, LUMO is lowest unoccupied molecular orbital
and one QSAR descriptor EHis Hydration Energy selected to model the
n-Octanol: water partition coefficient (Log ) by set of 16 Polycyclic aromatic
hydrocarbons (PAHs) on a linear model of regression used the method of least
squares.
The Multilinear model with three variablespresent is robust, and a good quality of fit after
removing the aberrant points:
7(Fluoranthene),14(Dibenzo (a,h) anthracene)
and good result statistic of r=0.9581for the retention time, S = 0.4316R2
= 91.8% = 89.3%, Durbin-Watson statistic =
2.373.
2(Fluorene),3(Acenaphtene)is influential
and important the model and no aberrant point.
CONFLICTS OF INTEREST:
The author declare that is no conflictof
interest.
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(Hydration Energy) by Least Squares with
correlation coefficient r=0.868, S=0.635, R2 =
75.4%, R2ajd=73.7% and Durbin-Watson statistic =1.85277
and graphical analysis by diagram of goodness of fit and line plot. The results
statistical of new model after removing the aberrant compounds (Toxicity
compounds) shows high Coefficient of correlation r=0.9581, S=0.4316,
determination coefficient R2
=91. 8%, ajustemed R2ajd = 89.3%, Durbin-Watson statistic D=2.373,
Three explanatory Variable model selected is robust and has good fitness.
Two influential compounds detected and important the model and absence aberant
compounds of the studied sample.