A Statistical Estimation Approach for Quantitative Concentrations of Compounds Lacking Authentic Standards/Surrogates Based on Linear Correlations between Directly Measured Detector Responses and Carbon Number of Different Functional Groups

Table 6

Assessment of the PD values between the actual and projected RF values for arbitrarily divided chemical groups.

Order	Type of VOC groups	Number of chemical	Projected equation^a		𝑅^2	P value	PD values^b of all and six individual (nonmodified) groups^c
			Slope	Intercept			All	I	II	III	IV	V	VI
(A) 6 original functional groups
1	All	18	34,175	−82,472	0.9396	3.58𝐸−11	17.9	43.6	3.52	16.5	7.75	41.8	2.62
2	Aldehyde (I)	4	24,836	−60,290	0.9725	1.39𝐸−02	9.83	9.83
3	Aromatic (II)	6	29,456	−43,139	0.9713	3.13𝐸−04	2.03		2.03
4	Carboxylic (III)	4	29,818	−58,701	0.9012	5.07𝐸−02	12.7			12.7
5	Ketone (IV)^d	2	*	*	*	*	*	*	*	*	*	*	*
6	Alcohol (V)^d	1	*	*	*	*	*	*	*	*	*	*	*
7	Ester (VI)^d	1	*	*	*	*	*	*	*	*	*	*	*
(B) 25 arbitrary groups
1	II + V	7	25,484	−12,686	0.9823	1.42𝐸−05	2.83	—^e	2.60	—	—	4.26	—
2	II + VI	6	32,806	−69,569	0.9668	6.89𝐸−05	3.17	—	2.61	—	—	—	6.54
3	II + IV	8	35,411	−89,325	0.9856	9.35𝐸−07	3.97	—	3.29	—	6.03	—	—
4	II + III + VI	11	32,994	−71,393	0.9857	1.31𝐸−09	5.63	—	2.74	9.87	—	—	5.96
5	II + III	10	32,949	−70,402	0.9872	7.36𝐸−09	5.73	—	2.59	10.4	—	—	—
6	II + III + IV	12	33,650	−76,475	0.9845	2.18𝐸−10	7.33	—	2.94	11.1	13.0	—	—
7	II + III + V	11	31,181	−56,899	0.9654	6.96𝐸−08	9.89	—	2.11	17.2	—	27.2	—
8	III + VI	5	29,615	−57,914	0.9445	5.65𝐸−03	10.3	—	—	12.9	—	—	0.27
9	III + IV	6	30,661	−64,601	0.8746	1.96𝐸−02	12.0	—	—	10.3	19.0	—	—
10	I + IV	6	31,804	−85,229	0.9241	2.22𝐸−03	13.1	13.6	—	—	12.0	—	—
11	III + V	5	27,486	−42,376	0.6568	9.62𝐸−02	13.1	—	—	19.3	—	27.5	—
12	I + II + IV	12	37,696	−108,341	0.9787	1.09𝐸−09	13.1	29.7	4.26	—	6.63	—	—
13	I + II + III + IV	16	35,474	−91,942	0.9664	1.04𝐸−11	14.3	27.1	3.77	23.2	2.65	—	—
14	I + II + VI	11	38,121	−111,370	0.9773	1.05𝐸−08	14.7	33.4	4.32	—	—	—	1.75
15	I + II + III + VI	15	35,445	−91,569	0.9646	8.12𝐸−11	15.2	28.1	3.73	22.8	—	—	1.38
16	I + II	10	38,135	−111,661	0.9774	7.25𝐸−08	16.2	33.9	4.37	—	—	—	—
17	I + II + III	14	35,458	−91,524	0.9646	4.50𝐸−10	16.2	28.4	3.71	22.7	—	—	—
18	I + II + V	11	35,227	−89,454	0.9322	1.47𝐸−06	17.9	32.6	3.58	—	—	44.8	—
19	I + VI	5	33,109	−92,201	0.9272	8.52𝐸−03	18.7	20.6	—	—	—	—	10.9
20	I + II + III + V	15	34,080	−81,036	0.9372	3.43𝐸−09	20.7	47.4	3.34	15.1	—	40.7	—
21	I + III + IV	10	29,862	−69,448	0.8341	2.22𝐸−04	21.7	34.5	—	17.5	4.57	—	—
22	I + III + VI	9	30,162	−70,431	0.8311	6.19𝐸−04	24.1	34.9	—	17.5	—	—	7.46
23	I + III	8	27,327	−59,496	0.7476	5.59𝐸−03	26.8	37.1	—	16.5	—	—	—
24	I + III + V	9	25,591	−47,341	0.5444	2.32𝐸−02	35.8	57.4	—	12.9	—	41.0	—
25	I + V	5	20,967	−33,206	0.3434	2.99𝐸−01	47.7	48.3	—	—	—	45.7	—
Statistics	Mean				0.8955	0.0188	14.9	33.0	3.26	15.8	8.95	34.1	4.61
(n = 29)^d	SD				0.1490	0.0586	9.90	12.1	0.74	4.45	5.36	14.0	3.67
	Min						2.03	9.83	2.03	9.87	2.65	4.26	0.27
	N						29	17	17	17	8	8	8

aThe projected equations are derived from linear regression analysis between the number of carbon (x-axis) and actual RF values (y-axis).
^bPercent difference (PD) = |(RF(Projected)−RF(Actual))|/RF(Actual) * 100.
^cI: aldehyde, II: aromatic, III: carboxylic, IV: ketone, V: alcohol, and VI: ester.
^dAs three groups (ketone (IV), alcohol (V), and ester (VI)) have only the limited number of components (less than 2), their predictive equations cannot be made and are not considered from counting of total group numbers (7(A) + 25(B) − 3(A) = 29).
^eNot computed.