3. FOOD ChEMISTRy & bIOTEChNOLOGy 3.1. Lectures

Chem. Listy, 102, s265–s1311 (2008) Food Chemistry & Biotechnology
Table III
Antifungal screening summary
log 1/c
Compound MIC log 1/cMIC exp. predict.
Usually, lipophilicity parameters are linearly related to
pharmacological activity (MICs), but in the more general
case this relationship is not linear 28 . Therefore, it was made
a complete regression analysis resorting to linear, quadratic
and cubic relationships. The statistical quality of the resulting
models is determined by correlation coefficient (r), standard
error of estimation (s), and probability factor related to Fratio
(F). Good quality of mathematical models was obtained
in cases of quadratic and cubic relationships, as depicted
in Eqs.(1) and (2). It is noteworthy that both equations were
derived using entire data set of compounds (n = 14) and no
outliers were identified. The F-value obtained in Eqs.(1)
and (2) is found statistically significant at 99 % level since
all the calculated F values are higher as compared to tabulated
values. It is apparent from the data that fitting equations
improve when resorting to second order polynomial.
For the estimation of the quality with regard to predictive
ability of the best model (2), the cross-validation statistical
technique has been applied. The simplest and most general
cross-validation procedure is the leave-one-out technique
(LOO technique). This method uses cross-validated fewer
parameters: PRESS (predicted residual sum of squares), SSY
(total sum of squares deviation), r 2 CV and r2 adj
Residuals
1 3.726 3.772 –0.046
2 4.854 4.946 –0.092
3 4.579 4.498 0.081
4 4.615 4.632 –0.017
5 4.880 4.986 –0.106
6 4.604 4.657 –0.053
7 4.638 4.568 0.07
8 4.325 4.231 0.094
9 4.551 4.483 0.068
10 3.277 3.435 –0.158
11 3.313 3.229 0.084
12 4.577 4.645 –0.068
13 3.602 3.778 –0.176
14 3.637 3.573 0.064
Ketoconazole 4.628 – –
Amphotericin 4.869 – –
log 1/c MIC = –0.748 log P 2 + 3.654 log P + 0.712 (1)
r = 0.962; s = 0.171; F = 69.32
log1/cMIC = –0.201 log P3 + 0.863 log P2 –
0.263 log P + 3.382
r = 0.979; s = 0.134; F = 77.56
(Table IV).
PRESS is an important cross-validation parameter as it is a
good approximation of the real predictive error of the models.
Its value being less than SSY points out that the model pre-
(2)
s755
dicts better than chance and can be considered statistically
significant. The present models have PRESS