. 2011 Dec 20;12(12):9533–9569. doi: 10.3390/ijms12129533

Table 6.

Correlation equations for the Group-II models of Table 3 and the molecular structures and data of Table 4.

Catastrophe	QSAR Model	R_Pearson^(a)	R_ALG^(b)	r^(c)	t-Stud.	t^(d)	Fisher	f^(e)	Π^(f)
QSAR (II)	$\| Y_{I I}^{L o g P, P O L} 〉 = - 2.044 \| 1 〉 + 0.051 \| L o g P 〉 + 0.242 \| P O L 〉$	0.556	0.989	1.778	−0.702	−0.245	4.464	0.763	1.9504
	$\| Y_{I I}^{L o g P, H} 〉 = 5.379 \| 1 〉 + 0.304 \| L o g P 〉 - 0.023 \| H 〉$	0.556	0.989	1.778	18.564	6.489	4.468	0.764	6.771
	$\| Y_{I I}^{P O L, H} 〉 = - 2.637 \| 1 〉 + 0.248 \| P O L 〉 - 0.021 \| H 〉$	0.728	0.992	1.363	−1.151	−0.402	11.302	1.932	2.398
Hyperbolic umbilic (HU)	$\begin{array}{l} \| Y_{H U}^{L o g P, P O L} 〉 = - 39.499 \| 1 〉 - 2.463 \| L o g P 〉 + 2.043 \| P O L 〉 \\ + 0.104 \| (L o g P) (P O L) 〉 - 0.145 \| L o g P^{3} 〉 - 6 \cdot 10^{- 4} \| P O L^{3} 〉 \end{array}$	0.715	0.992	1.387	−2.215	−0.774	3.561	0.609	1.701
	$\begin{array}{l} \| Y_{H U}^{L o g P, H} 〉 = 5.319 \| 1 〉 + 1.083 \| L o g P 〉 - 0.002 \| H 〉 \\ - 0.003 \| (L o g P) (H) 〉 - 0.161 \| L o g P^{3} 〉 - 9 \cdot 10^{- 6} \| H^{3} 〉 \end{array}$	0.736	0.992	1.3485	19.328	6.756	4.019	0.687	6.923
	$\begin{array}{l} \| Y_{H U}^{P O L, H} 〉 = - 13.192 \| 1 〉 + 0.766 \| P O L 〉 + 0.122 \| H 〉 \\ - 0.004 \| (P O L) (H) 〉 - 2 \cdot 10^{- 4} \| P O L^{3} 〉 - 5.1 \cdot 10^{- 7} \| H^{3} 〉 \end{array}$	0.755	0.993	1.315	−0.79	−0.276	4.503	0.770	1.549
Elliptic umbilic (EU)	$\begin{array}{l} {\| Y_{E U}^{L o g P, P O L} 〉}_{A} = - 69.262 \| 1 〉 - 0.556 \| L o g P 〉 + 4.531 \| P O L 〉 \\ + 0.443 \| L o g P^{2} 〉 - 0.068 \| P O L^{2} 〉 \\ + 0.002 \| (L o g P) (P O L^{2}) 〉 - 0.322 \| L o g P^{3} 〉 \end{array}$	0.757	0.993	1.312	−2.548	−0.891	3.582	0.612	1.670
	$\begin{array}{l} {\| Y_{E U}^{L o g P, P O L} 〉}_{B} = 644.623 \| 1 〉 + 0.022 \| L o g P 〉 - 59.934 \| P O L 〉 \\ + 0.467 \| L o g P^{2} 〉 + 1.855 \| P O L^{2} 〉 \\ - 0.015 \| (P O L) (L o g P^{2}) 〉 - 0.019 \| P O L^{3} 〉 \end{array}$	0.722	0.992	1.374	1.866	0.652	2.908	0.497	1.600
	$\begin{array}{l} {\| Y_{E U}^{L o g P, H} 〉}_{A} = 5.022 \| 1 〉 + 0.974 \| L o g P 〉 + 0.025 \| H 〉 \\ + 0.530 \| L o g P^{2} 〉 + 0.001 \| H^{2} 〉 \\ + 2.87 \cdot 10^{- 4} \| (L o g P) (H^{2}) 〉 - 0.359 \| L o g P^{3} 〉 \end{array}$	0.843	0.995	1.181	20.638	7.214	6.542	1.118	7.395
Elliptic umbilic (EU)	$\begin{array}{l} {\| Y_{E U}^{L o g P, H} 〉}_{B} = 4.779 \| 1 〉 + 0.643 \| L o g P 〉 + 0.029 \| H 〉 \\ - 0.211 \| L o g P^{2} 〉 + 0.004 \| H^{2} 〉 \\ + 0.001 \| (H) (L o g P^{2}) 〉 + 5 \cdot 10^{- 5} \| H^{3} 〉 \end{array}$	0.851	0.995	1.170	17.047	5.958	7.015	1.199	6.189
	$\begin{array}{l} {\| Y_{E U}^{P O L, H} 〉}_{A} = 802.877 \| 1 〉 - 74.631 \| P O L 〉 - 0.02 \| H 〉 \\ + 2.291 \| P O L^{2} 〉 + 0.005 \| H^{2} 〉 \\ - 2 \cdot 10^{- 4} \| (P O L) (H^{2}) 〉 - 0.023 \| P O L^{3} 〉 \end{array}$	0.857	0.996	1.162	3.124	1.092	7.346	1.256	2.029
	$\begin{array}{l} {\| Y_{E U}^{P O L, H} 〉}_{B} = 11.888 \| 1 〉 - 0.562 \| P O L 〉 + 0.068 \| H 〉 \\ + 0.011 \| P O L^{2} 〉 + 0.004 \| H^{2} 〉 \\ - 4 \cdot 10^{- 5} \| (H) (P O L^{2}) 〉 + 4 \cdot 10^{- 5} \| H^{3} 〉 \end{array}$	0.853	0.996	1.167	0.532	0.186	7.120	1.217	1.696
Parabolic umbilic (PU)	$\begin{array}{l} {\| Y_{P U}^{L o g P, P O L} 〉}_{A} = 474.915 \| 1 〉 + 0.021 \| L o g P 〉 - 39.256 \| P O L 〉 \\ + 0.454 \| L o g P^{2} 〉 + 0.914 \| P O L^{2} 〉 \\ - 0.015 \| (L o g P^{2}) (P O L) 〉 - 10^{- 4} \| P O L^{4} 〉 \end{array}$	0.722	0.992	1.374	1.817	0.635	2.905	0.497	1.593
Parabolic umbilic (PU)	$\begin{array}{l} {\| Y_{P U}^{L o g P, P O L} 〉}_{B} = - 67.522 \| 1 〉 - 1.539 \| L o g P 〉 + 4.444 \| P O L 〉 \\ + 0.573 \| L o g P^{2} 〉 - 0.067 \| P O L^{2} 〉 \\ + 0.002 \| (P O L^{2}) (L o g P) 〉 - 0.115 \| L o g P^{4} 〉 \end{array}$	0.703	0.992	1.411	−2.219	−0.776	2.611	0.446	1.671
Parabolic umbilic (PU)	$\begin{array}{l} {\| Y_{P U}^{L o g P, H} 〉}_{A} = 4.852 \| 1 〉 + 0.700 \| L o g P 〉 + 0.041 \| H 〉 \\ - 0.240 \| L o g P^{2} 〉 + 0.004 \| H^{2} 〉 \\ + 0.002 \| (L o g P^{2}) (H) 〉 - 10^{- 6} \| H^{4} 〉 \end{array}$	0.874	0.996	1.140	20.243	7.075	8.645	1.478	7.317
	$\begin{array}{l} {\| Y_{P U}^{L o g P, H} 〉}_{B} = 5.10 \| 1 〉 + 0.552 \| L o g P 〉 + 0.020 \| H 〉 \\ + 0.460 \| L o g P^{2} 〉 + 9.57 \cdot 10^{- 4} \| H^{2} 〉 \\ + 1.93 \cdot 10^{- 4} \| (H^{2}) (L o g P^{2}) 〉 - 0.099 \| L o g P^{4} 〉 \end{array}$	0.767	0.993	1.295	16.828	5.882	3.815	0.652	6.058
	$\begin{array}{l} {\| Y_{P U}^{P O L, H} 〉}_{A} = 8.876 \| 1 〉 - 0.366 \| P O L 〉 + 0.069 \| H 〉 \\ + 0.008 \| P O L^{2} 〉 + 0.003 \| H^{2} 〉 \\ - 3.7 \cdot 10^{- 5} \| (P O L^{2}) (H) 〉 - 4.5 \cdot 10^{- 7} \| H^{4} 〉 \end{array}$	0.841	0.995	1.183	0.386	0.135	6.447	1.102	1.623
	$\begin{array}{l} {\| Y_{P U}^{P O L, H} 〉}_{B} = 595.212 \| 1 〉 - 48.906 \| P O L 〉 - 0.019 \| H 〉 \\ + 1.129 \| P O L^{2} 〉 + 5 \cdot 10^{- 3} \| H^{2} 〉 \\ - 1.49 \cdot 10^{- 4} \| (H^{2}) (P O L) 〉 - 1.73 \cdot 10^{- 4} \| P O L^{4} 〉 \end{array}$	0.856	0.996	1.163	3.074	1.074	7.292	1.246	2.015

^(a)

the statistical Pearson correlation factor;

^(b)

computed from Equation (7);

^(c)

computed from Equation (9);

^(d)

computed from Equation (10) with $t_{\begin{array}{l} T a b u l a t e d \\ (0.99; 19) \end{array}} = 2.861$ ;

^(e)

computed from Equation (11) with $F_{\begin{array}{l} T a b u l a t e d \\ (0.99; 2, 20) \end{array}} = 5.85$ ;

^(f)

computed from Equation (8).