Download Quantum Topological Molecular Descriptors in QSAR Analysis of

Quantum Topological Molecular Descriptors in QSAR Analysis of Organophosphorus
Compounds
Y. Paukku1, G. Hill1*
1
*
Interdisciplinary Center for Nanotoxicity, Department of Chemistry, Jackson State University,
1400 J. R. Lynch Street, P. O. Box 17910, Jackson, MS 39217, USA
To whom correspondence should be addressed.
E-mail address: [email protected].
Phone: (601)-979-1699.
Fax: (601)-979-7823.
Supplementary material
Figure I. Multiple leave-N-out cross-validation plot (10 times reordered data set).
Table I. Results for leave-N-out
N
1
2
3
4
5
6
7
8
9
10
Single Q2LNO
0.81
0.71
0.69
0.70
0.67
0.69
0.71
0.65
0.67
0.67
Av: 0.69
10-times Q2LNO
0.73
0.71
0.69
0.68
0.66
0.67
0.67
0.65
0.65
0.65
Table II. Ten y-randomizations for the real model.
Randomizations
1
2
3
4
5
6
7
8
9
10
Maximum
Average
Real model
Q2
0.393
0.164
0.267
0.122
0.500
0.297
0.389
0.187
0.612
0.309
0.612
0.324
0.737
R2
0.099
0.187
0.145
0.163
0.051
0.187
0.040
0.116
0.008
0.148
0.187
0.114
0.870
Table III. Correlation matrix of the variables in the model
Pcharge
ρR1
P charge
1.000
0.055
ρR1
1.000
K(r)X
-
Analysis of descriptor-Y relations
1) Y = -3.167*Pcharge +4.395
(n=20; R2=0.083; s=1.026; F=7.330; Q2=0.046; SPRESS=1.188)
K(r)X
0.045
0.131
1.000
Analysis of Variance
Source
Intercept
Slope
Error
Adj. Total
Total
DF
1
1
18
19
20
Sum of
Squares
242.4384
7.714039
18.94283
26.65687
269.0953
Mean
Square
242.4384
7.714039
1.05238
1.402993
s = Square Root(1.05238) = 1.025856 T-Value= -2.7074
2) Y = 195.241*ρR1 -32.094
(n=20; R2=0.579; s=0.790; F=24.707; Q2=0.463)
F-Ratio
Prob
Level
Power
(5%)
7.3301
0.0144
0.7260
Analysis of Variance
Source
Intercept
Slope
Error
Adj. Total
Total
DF
1
1
18
19
20
Sum of
Squares
242.4384
15.4216
11.23528
26.65687
269.0953
Mean
Square
242.4384
15.4216
0.6241821
1.402993
s = Square Root(0.6241821) = 0.790052 T-Value=4.9706
3) Y = -34.712*K(r)X +7.797
(n=20; R2=0.259; s=1.047; F=6.297; Q2=0.088)
F-Ratio
Prob
Level
Power
(5%)
24.7069
0.0001
0.9968
Analysis of Variance
Source
Intercept
Slope
Error
Adj. Total
Total
DF
1
1
18
19
20
Sum of
Squares
242.4384
6.908604
19.74827
26.65687
269.0953
Mean
Square
242.4384
6.908604
1.097126
1.402993
s = Square Root(1.097126) = 1.047438 T-Value=-2.5094
F-Ratio
Prob
Level
Power
(5%)
6.2970
0.0219
0.6606
Errors and t-test statistics for regression coefficients for model with all 20
samples:
R2
Adj R2
Coefficient of Variation
Mean Square Error
Square Root of MSE
Ave Abs Pct Error
Variable
Y
Pcharge
ρR1
K(r)X
0.8697
0.8452
0.1338
0.2171545
0.4659984
12.744
Count
20
20
20
20
Regression
Coefficient
b(i)
-14.1527
-3.0611
122.3920
-30.4404
Independent
Variable
Intercept
Pcharge
ρR1
K(r)X
Standard
Deviation
0.2012068
4.614406E-03
1.737173E-02
1.18448
Mean
0.2885081
0.1822146
0.1243126
3.481655
Standard
Error
Sb(i)
5.3177
0.5785
26.4442
6.9844
T-Value
to test
H0:B(i)=0
-2.661
-5.292
4.628
-4.358
Minimum
-0.080117
0.1706071
0.0959985
1.1791
Prob
Level
0.0171
0.0001
0.0003
0.0005
Maximum
0.640682
0.1882551
0.1712337
5.421
Reject
H0 at
5%?
Yes
Yes
Yes
Yes
Power
of Test
at 5%
0.7052
0.9986
0.9912
0.9832
Estimated Model
-14.153-3.061*Pcharge+ 122.392* ρR1-30.440* K(r)X
Regression Coefficients
Independent
Regression
Standard
Variable
Coefficient
Error
Intercept
-14.1527
5.3177
Pcharge
-3.0611
0.5785
ρR1
122.3920
26.4442
K(r)X
-30.4404
6.9844
Note: The T-Value used to calculate these confidence limits was 2.120.
Source
Intercept
Model
Error
Total(Adjusted)
DF
1
3
16
19
Analysis of Variance Detail Section
Model
Term
DF
Intercept
1
Model
3
Pcharge
1
ρR1
1
K(r)X
1
Error
16
Total(Adjusted)
19
Normality Tests Section
Test
Name
Shapiro Wilk
Anderson Darling
D'Agostino Skewness
D'Agostino Kurtosis
D'Agostino Omnibus
R2
0.8697
0.1303
1.0000
R2
0.8697
0.2281
0.1745
0.1547
0.1303
1.0000
Test
Value
0.9306
0.5645
0.0647
-1.8500
3.4266
Lower
95% C.L.
-25.4257
-4.2874
66.3329
-45.2467
Sum of
Squares
242.4384
23.1824
3.474472
26.65687
Mean
Square
242.4384
7.727467
0.2171545
1.402993
Sum of
Squares
242.4384
23.1824
6.080916
4.651731
4.124836
3.474472
26.65687
Mean
Square
242.4384
7.727467
6.080916
4.651731
4.124836
0.2171545
1.402993
Prob
Level
0.158365
0.144047
0.948414
0.064318
0.180272
Upper
95% C.L.
-2.8797
-1.8348
178.4512
-15.6340
Standardized
Coefficient
0.0000
-0.5200
0.4768
-0.4464
F-Ratio
Prob
Level
Power
(5%)
35.585
0.0000
1.0000
F-Ratio
Prob
Level
Power
(5%)
35.585
28.003
21.421
18.995
0.0000
0.0001
0.0003
0.0005
1.0000
0.9986
0.9912
0.9832
Reject H0
At Alpha = 20%?
Yes
Yes
No
Yes
Yes
Predicted Values with Confidence Limits of Means
Actual
Predicted
Standard
Error Of
95% Lower
Conf. Limit
95% Upper
Conf. Limit
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Y
3.579
4.533
4.102
2.262
1.179
1.807
3.372
4.553
4.086
3.667
4.246
2.056
5.421
2.107
2.782
2.473
4.333
3.774
5.235
4.067
Y
3.839
4.402
4.564
1.629
1.416
2.096
3.196
4.024
3.829
3.609
4.399
2.488
4.937
2.891
2.170
2.767
4.743
3.336
4.800
4.498
Actual
Y
3.579
4.533
4.102
2.262
1.179
1.807
3.372
4.553
4.086
3.667
4.246
2.056
5.421
2.107
2.782
2.473
4.333
3.774
5.235
4.067
Predicted
Y
3.839
4.402
4.564
1.629
1.416
2.096
3.196
4.024
3.829
3.609
4.399
2.488
4.937
2.891
2.170
2.767
4.743
3.336
4.800
4.498
Predicted
0.158
0.249
0.164
0.306
0.306
0.232
0.132
0.119
0.143
0.108
0.138
0.144
0.201
0.132
0.349
0.326
0.214
0.129
0.194
0.154
Of Mean
3.503
3.873
4.215
0.981
0.768
1.604
2.915
3.773
3.526
3.380
4.106
2.182
4.511
2.612
1.430
2.076
4.289
3.062
4.390
4.171
Of Mean
4.175
4.930
4.912
2.277
2.065
2.589
3.476
4.275
4.132
3.839
4.692
2.794
5.363
3.170
2.910
3.458
5.196
3.610
5.211
4.825
Residual
-0.260
0.131
-0.462
0.633
-0.237
-0.290
0.176
0.529
0.257
0.057
-0.153
-0.432
0.484
-0.784
0.612
-0.294
-0.410
0.438
0.435
-0.431
Absolute
Percent
Error
7.275
2.900
11.261
27.976
20.115
16.050
5.211
11.622
6.285
1.560
3.602
21.003
8.932
37.218
22.001
11.895
9.456
11.613
8.309
10.592
Sqrt(MSE)
Without
This Row
0.476
0.480
0.464
0.430
0.474
0.473
0.479
0.460
0.476
0.481
0.480
0.467
0.461
0.433
0.418
0.469
0.466
0.467
0.465
0.467
Residual Report
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Regression Diagnostics Section
Standardized
Row
Residual
RStudent
1
-0.5940
-0.5816
2
0.3339
0.3244
3
-1.0592
-1.0635
4
1.7996
1.9510
5
-0.6747
-0.6628
6
-0.7179
-0.7066
7
0.3932
0.3826
8
1.1741
1.1892
9
0.5790
0.5666
10
0.1262
0.1222
11
-0.3436
-0.3339
12
-0.9747
-0.9730
13
1.1517
1.1645
14
-1.7541
-1.8898
15
1.9826
2.2102
16
-0.8836
-0.8773
17
-0.9898
-0.9891
Hat
Diagonal
0.1155
0.2860
0.1243
0.4304
0.4310
0.2489
0.0807
0.0647
0.0942
0.0538
0.0878
0.0961
0.1861
0.0799
0.5610
0.4897
0.2109
Cook's D
0.0115
0.0112
0.0398
0.6118
0.0862
0.0427
0.0034
0.0238
0.0087
0.0002
0.0028
0.0253
0.0758
0.0668
1.2556
0.1874
0.0654
Dffits
-0.2102
0.2053
-0.4007
1.6960
-0.5768
-0.4067
0.1133
0.3127
0.1828
0.0291
-0.1036
-0.3173
0.5568
-0.5567
2.4984
-0.8595
-0.5113
CovRatio
1.3387
1.7632
1.1052
0.9198
2.0269
1.5119
1.3545
0.9652
1.3131
1.3627
1.3777
1.1212
1.1251
0.5988
0.9548
2.0769
1.2741
18
19
20
0.9788
1.0262
-0.9798
0.9775
1.0281
-0.9785
0.0767
0.1726
0.1097
0.0199
0.0549
0.0296
0.2818
0.4696
-0.3434
1.0952
1.1916
1.1352
Plots Section
Histogram of Residuals of Y
Normal Probability Plot of Residuals of Y
8.0
1.0
Residuals of Y
6.0
0.5
Coun
4.0
0.0
2.0
-0.5
0.0
-1.0
-1.0
-0.5
0.0
0.5
1.0
-2.0
Residuals of Y
-1.0
0.0
1.0
2.0
Expected Normals
Residuals of Y vs Pcharge
Residuals of Y vs Row
1.0
1.0
0.5
Residuals of Y
0.5
Residuals of Y
0.0
0.0
-0.5
-0.5
-1.0
-0.2
-1.0
0.0
5.0
10.0
15.0
0.1
20.0
0.3
0.6
0.8
0.2
0.2
Pcharge
Row
Residuals of Y vs ρR1
Residuals of Y vs K(r)X
1.0
1.0
Residuals of Y0.5
Residuals of Y
0.5
0.0
0.0
-0.5
-0.5
-1.0
-1.0
0.2
0.2
0.2
ρR1
0.2
0.2
0.1
0.1
0.1
K(r)X
Errors and t-test statistics for regression coefficients for model with 16
samples:
R2
Adj R2
Coefficient of Variation
Mean Square Error
Square Root of MSE
Ave Abs Pct Error
Variable
Y
Pcharge
ρR1
K(r)X
0.9005
0.8757
0.1175
0.1798956
0.424141
10.580
Count
16
16
16
16
Independent
Variable
Intercept
Pcharge
ρR1
K(r)X
Standard
Deviation
0.2010285
4.987871E-03
8.273194E-03
1.202886
Mean
0.305139
0.1825122
0.1187495
3.610556
Regression
Coefficient
b(i)
-5.6115
-3.2546
89.8508
-52.0736
Standard
Error
Sb(i)
6.4000
0.5836
27.9870
15.9346
T-Value
to test
H0:B(i)=0
-0.877
-5.577
3.210
-3.268
Minimum
-0.041429
0.1706071
0.0959985
1.1791
Prob
Level
0.3978
0.0001
0.0075
0.0067
Maximum
0.640682
0.1882551
0.1295073
5.421
Reject
H0 at
5%?
No
Yes
Yes
Yes
Power
of Test
at 5%
0.1276
0.9991
0.8378
0.8503
Estimated Model
-5.612-3.255*Pcharge+ 89.851* ρR1-52.073* K(r)X
Regression Coefficients
Independent
Regression
Standard
Variable
Coefficient
Error
Intercept
-5.6115
6.4000
Pcharge
-3.2546
0.5836
ρR1
89.8508
27.9870
K(r)X
-52.0736
15.9346
Note: The T-Value used to calculate these confidence limits was 2.179.
Lower
95% C.L.
-19.5559
-4.5262
28.8722
-86.7921
Upper
95% C.L.
8.3329
-1.9830
150.8293
-17.3551
Standardized
Coefficient
0.0000
-0.5439
0.3726
-0.3582
F-Ratio
Prob
Level
Power
(5%)
36.216
0.0000
1.0000
F-Ratio
Prob
Level
Power
(5%)
36.216
31.098
10.307
10.680
0.0000
0.0001
0.0075
0.0067
1.0000
0.9991
0.8378
0.8503
Analysis of Variance Section
Source
Intercept
Model
Error
Total(Adjusted)
DF
1
3
12
15
Analysis of Variance Detail Section
Model
Term
DF
Intercept
1
Model
3
Pcharge
1
ρR1
1
K(r)X
1
Error
12
Total(Adjusted)
15
Normality Tests Section
Test
Name
Shapiro Wilk
Anderson Darling
D'Agostino Skewness
D'Agostino Kurtosis
R2
0.9005
0.0995
1.0000
R2
0.9005
0.2578
0.0854
0.0885
0.0995
1.0000
Test
Value
0.9354
0.3552
-0.0485
-1.7839
Sum of
Squares
208.5779
19.54526
2.158747
21.70401
Mean
Square
208.5779
6.515087
0.1798956
1.446934
Sum of
Squares
208.5779
19.54526
5.594337
1.854171
1.921203
2.158747
21.70401
Mean
Square
208.5779
6.515087
5.594337
1.854171
1.921203
0.1798956
1.446934
Prob
Level
0.296507
0.460112
0.961284
0.074447
Reject H0
At Alpha = 20%?
No
No
No
Yes
D'Agostino Omnibus
3.1845
0.203468
No
Predicted Values with Confidence Limits of Means
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Actual
Y
3.579
4.533
4.102
2.262
1.179
1.807
3.372
4.086
3.667
4.246
5.421
2.107
4.333
3.774
5.235
4.067
Predicted
Y
3.690
4.641
4.489
1.842
1.610
1.822
3.133
3.726
3.565
4.298
5.062
2.643
4.683
3.202
4.739
4.624
Actual
Y
3.579
4.533
4.102
2.262
1.179
1.807
3.372
4.086
3.667
4.246
5.421
2.107
4.333
3.774
5.235
4.067
Predicted
Y
3.690
4.641
4.489
1.842
1.610
1.822
3.133
3.726
3.565
4.298
5.062
2.643
4.683
3.202
4.739
4.624
Standard
Error Of
Predicted
0.161
0.353
0.171
0.294
0.292
0.270
0.131
0.141
0.108
0.141
0.206
0.201
0.226
0.141
0.199
0.182
95% Lower
Conf. Limit
Of Mean
3.339
3.872
4.117
1.201
0.973
1.233
2.847
3.419
3.329
3.992
4.614
2.205
4.190
2.895
4.306
4.228
95% Upper
Conf. Limit
Of Mean
4.042
5.411
4.861
2.483
2.247
2.411
3.418
4.034
3.801
4.604
5.510
3.081
5.175
3.508
5.171
5.019
Residual
-0.112
-0.108
-0.387
0.420
-0.431
-0.016
0.239
0.360
0.101
-0.052
0.359
-0.537
-0.350
0.573
0.497
-0.557
Absolute
Percent
Error
3.118
2.383
9.439
18.572
36.520
0.866
7.086
8.804
2.764
1.226
6.615
25.467
8.075
15.171
9.487
13.683
Sqrt(MSE)
Without
This Row
0.442
0.439
0.424
0.407
0.405
0.443
0.436
0.428
0.442
0.443
0.425
0.403
0.425
0.403
0.409
0.402
Residual Report
Row
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Regression Diagnostics Section
Standardized
Row
Residual
RStudent
1
-0.2844
-0.2732
2
-0.4600
-0.4444
3
-0.9972
-0.9970
4
1.3752
1.4346
5
-1.4012
-1.4670
6
-0.0478
-0.0458
7
0.5922
0.5754
8
0.8994
0.8916
9
0.2471
0.2372
10
-0.1301
-0.1246
11
0.9666
0.9637
12
-1.4368
-1.5118
13
-0.9748
-0.9726
14
1.4312
1.5046
15
1.3253
1.3733
16
-1.4520
-1.5312
Hat
Diagonal
0.1447
0.6934
0.1621
0.4812
0.4750
0.4060
0.0953
0.1107
0.0651
0.1099
0.2350
0.2249
0.2839
0.1101
0.2193
0.1834
Cook's D
0.0034
0.1196
0.0481
0.4385
0.4442
0.0004
0.0092
0.0252
0.0011
0.0005
0.0718
0.1498
0.0942
0.0634
0.1233
0.1184
Dffits
-0.1124
-0.6682
-0.4385
1.3815
-1.3955
-0.0379
0.1867
0.3146
0.0626
-0.0438
0.5342
-0.8144
-0.6124
0.5293
0.7278
-0.7256
CovRatio
1.6117
4.3019
1.1959
1.3746
1.3202
2.3823
1.3903
1.2047
1.4844
1.5822
1.3388
0.8588
1.4219
0.7529
0.9633
0.8008
Histogram of Residuals of Y
Normal Probability Plot of Residuals of Y
4.0
0.6
Residuals of Y
3.0
0.3
Count
2.0
0.0
1.0
-0.3
0.0
-0.6
-0.6
-0.3
0.0
0.3
0.6
-2.0
Residuals of Y
-1.0
0.0
1.0
2.0
Expected Normals
Residuals of Y vs Pcharge
Residuals of Y vs Row
0.6
0.6
Residuals of Y
Residuals of Y
0.3
0.3
0.0
0.0
-0.3
-0.3
-0.6
-0.2
-0.6
0.0
5.0
10.0
15.0
0.1
20.0
0.3
0.6
0.8
0.1
0.1
Pcharge
Row
Residuals of Y vs ρR1
Residuals of Y vs K(r)X
0.6
0.6
0.3
Residuals of Y0.3
0.0
0.0
-0.3
-0.3
Residuals of Y
-0.6
-0.6
0.2
0.2
0.2
ρR1
0.2
0.2
0.1
0.1
0.1
K(r)X