Data 624 Assignment 7

6.2

Developing a model to predict permeability (see Sect. 1.4) could save significant resources for a pharmaceutical company, while at the same time more rapidly identifying molecules that have a sufficient permeability to become a drug:

A.

Load the data:

data("permeability")
psych::describe(fingerprints) %>% 
  kable() %>% 
  kable_styling(position = "center", full_width = T) %>% 
  scroll_box(height = "200px", width = "200px")

	vars	n	mean	sd	median	trimmed	min	max	range	skew	kurtosis	se
X1	1	165	0.2303030	0.4223084	0	0.1654135	0	1	1	1.2695102	-0.3906011	0.0328767
X2	2	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X3	3	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X4	4	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X5	5	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X6	6	165	0.4484848	0.4988531	0	0.4360902	0	1	1	0.2052826	-1.9696866	0.0388357
X7	7	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X8	8	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X9	9	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X10	10	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X11	11	165	0.1393939	0.3474115	0	0.0526316	0	1	1	2.0633777	2.2714035	0.0270459
X12	12	165	0.7090909	0.4555643	1	0.7593985	0	1	1	-0.9123792	-1.1745728	0.0354656
X13	13	165	0.9575758	0.2021686	1	1.0000000	0	1	1	-4.4992408	18.3545175	0.0157388
X14	14	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X15	15	165	0.1212121	0.3273672	0	0.0300752	0	1	1	2.3001220	3.3107362	0.0254855
X16	16	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X17	17	165	0.9818182	0.1340153	1	1.0000000	0	1	1	-7.1469188	49.3778172	0.0104331
X18	18	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X19	19	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X20	20	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X21	21	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X22	22	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X23	23	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X24	24	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X25	25	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X26	26	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X27	27	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X28	28	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X29	29	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X30	30	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X31	31	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X32	32	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X33	33	165	0.9636364	0.1877631	1	1.0000000	0	1	1	-4.9085939	22.2291256	0.0146173
X34	34	165	0.9636364	0.1877631	1	1.0000000	0	1	1	-4.9085939	22.2291256	0.0146173
X35	35	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X36	36	165	0.1757576	0.3817724	0	0.0977444	0	1	1	1.6883216	0.8557261	0.0297209
X37	37	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X38	38	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X39	39	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X40	40	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X41	41	165	0.3151515	0.4659904	0	0.2706767	0	1	1	0.7885492	-1.3864831	0.0362773
X42	42	165	0.3090909	0.4635255	0	0.2631579	0	1	1	0.8187341	-1.3376716	0.0360854
X43	43	165	0.3090909	0.4635255	0	0.2631579	0	1	1	0.8187341	-1.3376716	0.0360854
X44	44	165	0.3090909	0.4635255	0	0.2631579	0	1	1	0.8187341	-1.3376716	0.0360854
X45	45	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X46	46	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X47	47	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X48	48	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X49	49	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X50	50	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X51	51	165	0.3151515	0.4659904	0	0.2706767	0	1	1	0.7885492	-1.3864831	0.0362773
X52	52	165	0.3090909	0.4635255	0	0.2631579	0	1	1	0.8187341	-1.3376716	0.0360854
X53	53	165	0.3090909	0.4635255	0	0.2631579	0	1	1	0.8187341	-1.3376716	0.0360854
X54	54	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X55	55	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X56	56	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X57	57	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X58	58	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X59	59	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X60	60	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X61	61	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X62	62	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X63	63	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X64	64	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X65	65	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X66	66	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X67	67	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X68	68	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X69	69	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X70	70	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X71	71	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X72	72	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X73	73	165	0.2303030	0.4223084	0	0.1654135	0	1	1	1.2695102	-0.3906011	0.0328767
X74	74	165	0.2303030	0.4223084	0	0.1654135	0	1	1	1.2695102	-0.3906011	0.0328767
X75	75	165	0.2303030	0.4223084	0	0.1654135	0	1	1	1.2695102	-0.3906011	0.0328767
X76	76	165	0.2303030	0.4223084	0	0.1654135	0	1	1	1.2695102	-0.3906011	0.0328767
X77	77	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X78	78	165	0.3151515	0.4659904	0	0.2706767	0	1	1	0.7885492	-1.3864831	0.0362773
X79	79	165	0.3090909	0.4635255	0	0.2631579	0	1	1	0.8187341	-1.3376716	0.0360854
X80	80	165	0.3151515	0.4659904	0	0.2706767	0	1	1	0.7885492	-1.3864831	0.0362773
X81	81	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X82	82	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X83	83	165	0.9636364	0.1877631	1	1.0000000	0	1	1	-4.9085939	22.2291256	0.0146173
X84	84	165	0.9636364	0.1877631	1	1.0000000	0	1	1	-4.9085939	22.2291256	0.0146173
X85	85	165	0.9636364	0.1877631	1	1.0000000	0	1	1	-4.9085939	22.2291256	0.0146173
X86	86	165	0.7030303	0.4583140	1	0.7518797	0	1	1	-0.8806181	-1.2318676	0.0356797
X87	87	165	0.4242424	0.4957320	0	0.4060150	0	1	1	0.3037869	-1.9192353	0.0385927
X88	88	165	0.1696970	0.3765090	0	0.0902256	0	1	1	1.7439220	1.0477237	0.0293112
X89	89	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X90	90	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X91	91	165	0.9636364	0.1877631	1	1.0000000	0	1	1	-4.9085939	22.2291256	0.0146173
X92	92	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X93	93	165	0.2424242	0.4298541	0	0.1804511	0	1	1	1.1911701	-0.5845466	0.0334641
X94	94	165	0.0666667	0.2502032	0	0.0000000	0	1	1	3.4428586	9.9134671	0.0194783
X95	95	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X96	96	165	0.7818182	0.4142688	1	0.8496241	0	1	1	-1.3523114	-0.1721876	0.0322508
X97	97	165	0.5030303	0.5015129	1	0.5037594	0	1	1	-0.0120114	-2.0119393	0.0390427
X98	98	165	0.2484848	0.4334499	0	0.1879699	0	1	1	1.1534936	-0.6734240	0.0337440
X99	99	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X100	100	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X101	101	165	0.7030303	0.4583140	1	0.7518797	0	1	1	-0.8806181	-1.2318676	0.0356797
X102	102	165	0.4121212	0.4937151	0	0.3909774	0	1	1	0.3538323	-1.8861238	0.0384357
X103	103	165	0.1515152	0.3596418	0	0.0676692	0	1	1	1.9262102	1.7208249	0.0279981
X104	104	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X105	105	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X106	106	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X107	107	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X108	108	165	0.1515152	0.3596418	0	0.0676692	0	1	1	1.9262102	1.7208249	0.0279981
X109	109	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X110	110	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X111	111	165	0.4121212	0.4937151	0	0.3909774	0	1	1	0.3538323	-1.8861238	0.0384357
X112	112	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X113	113	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X114	114	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X115	115	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X116	116	165	0.9757576	0.1542691	1	1.0000000	0	1	1	-6.1305096	35.8002286	0.0120098
X117	117	165	0.9575758	0.2021686	1	1.0000000	0	1	1	-4.4992408	18.3545175	0.0157388
X118	118	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X119	119	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X120	120	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X121	121	165	0.3212121	0.4683635	0	0.2781955	0	1	1	0.7588307	-1.4327493	0.0364620
X122	122	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X123	123	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X124	124	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X125	125	165	0.1515152	0.3596418	0	0.0676692	0	1	1	1.9262102	1.7208249	0.0279981
X126	126	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X127	127	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X128	128	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X129	129	165	0.1636364	0.3710714	0	0.0827068	0	1	1	1.8019445	1.2547183	0.0288879
X130	130	165	0.1515152	0.3596418	0	0.0676692	0	1	1	1.9262102	1.7208249	0.0279981
X131	131	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X132	132	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X133	133	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X134	134	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X135	135	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X136	136	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X137	137	165	0.9818182	0.1340153	1	1.0000000	0	1	1	-7.1469188	49.3778172	0.0104331
X138	138	165	0.2727273	0.4467175	0	0.2180451	0	1	1	1.0113564	-0.9830058	0.0347769
X139	139	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X140	140	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X141	141	165	0.3454545	0.4769638	0	0.3082707	0	1	1	0.6441110	-1.5946757	0.0371316
X142	142	165	0.2121212	0.4100547	0	0.1428571	0	1	1	1.3955897	-0.0525378	0.0319227
X143	143	165	0.8848485	0.3201764	1	0.9774436	0	1	1	-2.3894082	3.7319997	0.0249257
X144	144	165	0.9636364	0.1877631	1	1.0000000	0	1	1	-4.9085939	22.2291256	0.0146173
X145	145	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X146	146	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X147	147	165	1.0000000	0.0000000	1	1.0000000	1	1	0	NaN	NaN	0.0000000
X148	148	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X149	149	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X150	150	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X151	151	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X152	152	165	0.6606061	0.4749451	1	0.6992481	0	1	1	-0.6722154	-1.5574556	0.0369744
X153	153	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X154	154	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X155	155	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X156	156	165	0.7939394	0.4057058	1	0.8646617	0	1	1	-1.4402454	0.0748704	0.0315842
X157	157	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X158	158	165	0.5878788	0.4937151	1	0.6090226	0	1	1	-0.3538323	-1.8861238	0.0384357
X159	159	165	0.5272727	0.5007755	1	0.5338346	0	1	1	-0.1082618	-2.0002924	0.0389853
X160	160	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X161	161	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X162	162	165	0.6606061	0.4749451	1	0.6992481	0	1	1	-0.6722154	-1.5574556	0.0369744
X163	163	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X164	164	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X165	165	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X166	166	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X167	167	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X168	168	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X169	169	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X170	170	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X171	171	165	0.9454545	0.2277821	1	1.0000000	0	1	1	-3.8875290	13.1929486	0.0177328
X172	172	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X173	173	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X174	174	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X175	175	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X176	176	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X177	177	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X178	178	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X179	179	165	0.6606061	0.4749451	1	0.6992481	0	1	1	-0.6722154	-1.5574556	0.0369744
X180	180	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X181	181	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X182	182	165	0.6787879	0.4683635	1	0.7218045	0	1	1	-0.7588307	-1.4327493	0.0364620
X183	183	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X184	184	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X185	185	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X186	186	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X187	187	165	0.6606061	0.4749451	1	0.6992481	0	1	1	-0.6722154	-1.5574556	0.0369744
X188	188	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X189	189	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X190	190	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X191	191	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X192	192	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X193	193	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X194	194	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X195	195	165	0.6606061	0.4749451	1	0.6992481	0	1	1	-0.6722154	-1.5574556	0.0369744
X196	196	165	0.6606061	0.4749451	1	0.6992481	0	1	1	-0.6722154	-1.5574556	0.0369744
X197	197	165	0.6606061	0.4749451	1	0.6992481	0	1	1	-0.6722154	-1.5574556	0.0369744
X198	198	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X199	199	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X200	200	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X201	201	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X202	202	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X203	203	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X204	204	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X205	205	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X206	206	165	0.6787879	0.4683635	1	0.7218045	0	1	1	-0.7588307	-1.4327493	0.0364620
X207	207	165	0.6787879	0.4683635	1	0.7218045	0	1	1	-0.7588307	-1.4327493	0.0364620
X208	208	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X209	209	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X210	210	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X211	211	165	0.6424242	0.4807453	1	0.6766917	0	1	1	-0.5889234	-1.6631389	0.0374260
X212	212	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X213	213	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X214	214	165	0.6484848	0.4788969	1	0.6842105	0	1	1	-0.6163538	-1.6298761	0.0372821
X215	215	165	0.9454545	0.2277821	1	1.0000000	0	1	1	-3.8875290	13.1929486	0.0177328
X216	216	165	0.9818182	0.1340153	1	1.0000000	0	1	1	-7.1469188	49.3778172	0.0104331
X217	217	165	0.9515152	0.2154423	1	1.0000000	0	1	1	-4.1661155	15.4502662	0.0167722
X218	218	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X219	219	165	0.9818182	0.1340153	1	1.0000000	0	1	1	-7.1469188	49.3778172	0.0104331
X220	220	165	0.9515152	0.2154423	1	1.0000000	0	1	1	-4.1661155	15.4502662	0.0167722
X221	221	165	0.7212121	0.4497679	1	0.7744361	0	1	1	-0.9777106	-1.0503377	0.0350144
X222	222	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X223	223	165	0.7212121	0.4497679	1	0.7744361	0	1	1	-0.9777106	-1.0503377	0.0350144
X224	224	165	0.7212121	0.4497679	1	0.7744361	0	1	1	-0.9777106	-1.0503377	0.0350144
X225	225	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X226	226	165	0.7818182	0.4142688	1	0.8496241	0	1	1	-1.3523114	-0.1721876	0.0322508
X227	227	165	0.7818182	0.4142688	1	0.8496241	0	1	1	-1.3523114	-0.1721876	0.0322508
X228	228	165	0.7818182	0.4142688	1	0.8496241	0	1	1	-1.3523114	-0.1721876	0.0322508
X229	229	165	0.6060606	0.4901091	1	0.6315789	0	1	1	-0.4301810	-1.8259004	0.0381549
X230	230	165	0.2545455	0.4369314	0	0.1954887	0	1	1	1.1167287	-0.7573974	0.0340151
X231	231	165	0.8242424	0.3817724	1	0.9022556	0	1	1	-1.6883216	0.8557261	0.0297209
X232	232	165	0.8242424	0.3817724	1	0.9022556	0	1	1	-1.6883216	0.8557261	0.0297209
X233	233	165	0.8242424	0.3817724	1	0.9022556	0	1	1	-1.6883216	0.8557261	0.0297209
X234	234	165	0.8242424	0.3817724	1	0.9022556	0	1	1	-1.6883216	0.8557261	0.0297209
X235	235	165	0.5575758	0.4981859	1	0.5714286	0	1	1	-0.2297408	-1.9589818	0.0387837
X236	236	165	0.6121212	0.4887500	1	0.6390977	0	1	1	-0.4560274	-1.8028555	0.0380491
X237	237	165	0.5333333	0.5004063	1	0.5413534	0	1	1	-0.1324176	-1.9944431	0.0389566
X238	238	165	0.2969697	0.4583140	0	0.2481203	0	1	1	0.8806181	-1.2318676	0.0356797
X239	239	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X240	240	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X241	241	165	0.7515152	0.4334499	1	0.8120301	0	1	1	-1.1534936	-0.6734240	0.0337440
X242	242	165	0.4484848	0.4988531	0	0.4360902	0	1	1	0.2052826	-1.9696866	0.0388357
X243	243	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X244	244	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X245	245	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X246	246	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X247	247	165	0.7333333	0.4435628	1	0.7894737	0	1	1	-1.0457107	-0.9119058	0.0345313
X248	248	165	0.5878788	0.4937151	1	0.6090226	0	1	1	-0.3538323	-1.8861238	0.0384357
X249	249	165	0.7515152	0.4334499	1	0.8120301	0	1	1	-1.1534936	-0.6734240	0.0337440
X250	250	165	0.4484848	0.4988531	0	0.4360902	0	1	1	0.2052826	-1.9696866	0.0388357
X251	251	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X252	252	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X253	253	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X254	254	165	0.8060606	0.3965856	1	0.8796992	0	1	1	-1.5341238	0.3558023	0.0308741
X255	255	165	0.7333333	0.4435628	1	0.7894737	0	1	1	-1.0457107	-0.9119058	0.0345313
X256	256	165	0.5878788	0.4937151	1	0.6090226	0	1	1	-0.3538323	-1.8861238	0.0384357
X257	257	165	0.5515152	0.4988531	1	0.5639098	0	1	1	-0.2052826	-1.9696866	0.0388357
X258	258	165	0.1030303	0.3049239	0	0.0075188	0	1	1	2.5879497	4.7262375	0.0237383
X259	259	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X260	260	165	0.7393939	0.4403016	1	0.7969925	0	1	1	-1.0808186	-0.8367927	0.0342774
X261	261	165	0.7515152	0.4334499	1	0.8120301	0	1	1	-1.1534936	-0.6734240	0.0337440
X262	262	165	0.7636364	0.4261414	1	0.8270677	0	1	1	-1.2298199	-0.4904051	0.0331751
X263	263	165	0.6727273	0.4706461	1	0.7142857	0	1	1	-0.7295522	-1.4765927	0.0366397
X264	264	165	0.3757576	0.4857922	0	0.3458647	0	1	1	0.5084043	-1.7520334	0.0378189
X265	265	165	0.7393939	0.4403016	1	0.7969925	0	1	1	-1.0808186	-0.8367927	0.0342774
X266	266	165	0.7636364	0.4261414	1	0.8270677	0	1	1	-1.2298199	-0.4904051	0.0331751
X267	267	165	0.5151515	0.5012918	1	0.5187970	0	1	1	-0.0600835	-2.0084524	0.0390255
X268	268	165	0.6909091	0.4635255	1	0.7368421	0	1	1	-0.8187341	-1.3376716	0.0360854
X269	269	165	0.5272727	0.5007755	1	0.5338346	0	1	1	-0.1082618	-2.0002924	0.0389853
X270	270	165	0.4787879	0.5010705	0	0.4736842	0	1	1	0.0841541	-2.0049594	0.0390083
X271	271	165	0.3454545	0.4769638	0	0.3082707	0	1	1	0.6441110	-1.5946757	0.0371316
X272	272	165	0.4060606	0.4925911	0	0.3834586	0	1	1	0.3790977	-1.8674931	0.0383482
X273	273	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X274	274	165	0.6545455	0.4769638	1	0.6917293	0	1	1	-0.6441110	-1.5946757	0.0371316
X275	275	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X276	276	165	0.1757576	0.3817724	0	0.0977444	0	1	1	1.6883216	0.8557261	0.0297209
X277	277	165	0.9878788	0.1097602	1	1.0000000	0	1	1	-8.8360249	76.5393209	0.0085448
X278	278	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X279	279	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X280	280	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
X281	281	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
X282	282	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X283	283	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X284	284	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X285	285	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X286	286	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X287	287	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X288	288	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X289	289	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X290	290	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X291	291	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X292	292	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X293	293	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X294	294	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X295	295	165	0.1030303	0.3049239	0	0.0075188	0	1	1	2.5879497	4.7262375	0.0237383
X296	296	165	0.3151515	0.4659904	0	0.2706767	0	1	1	0.7885492	-1.3864831	0.0362773
X297	297	165	0.1333333	0.3409694	0	0.0451128	0	1	1	2.1376956	2.5855224	0.0265444
X298	298	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
X299	299	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
X300	300	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
X301	301	165	0.3151515	0.4659904	0	0.2706767	0	1	1	0.7885492	-1.3864831	0.0362773
X302	302	165	0.3151515	0.4659904	0	0.2706767	0	1	1	0.7885492	-1.3864831	0.0362773
X303	303	165	0.1333333	0.3409694	0	0.0451128	0	1	1	2.1376956	2.5855224	0.0265444
X304	304	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
X305	305	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
X306	306	165	0.0787879	0.2702275	0	0.0000000	0	1	1	3.0985691	7.6475895	0.0210372
X307	307	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X308	308	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X309	309	165	0.1272727	0.3342928	0	0.0375940	0	1	1	2.2164303	2.9304333	0.0260247
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X311	311	165	0.2363636	0.4261414	0	0.1729323	0	1	1	1.2298199	-0.4904051	0.0331751
X312	312	165	0.2787879	0.4497679	0	0.2255639	0	1	1	0.9777106	-1.0503377	0.0350144
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X318	318	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
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X337	337	165	0.0787879	0.2702275	0	0.0000000	0	1	1	3.0985691	7.6475895	0.0210372
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X472	472	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X473	473	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X474	474	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X475	475	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X476	476	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X477	477	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X478	478	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X479	479	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X480	480	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X481	481	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X482	482	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X483	483	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X484	484	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X485	485	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X486	486	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X487	487	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X488	488	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X489	489	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X490	490	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X491	491	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X492	492	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X493	493	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X494	494	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X495	495	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X496	496	165	0.1393939	0.3474115	0	0.0526316	0	1	1	2.0633777	2.2714035	0.0270459
X497	497	165	0.1454545	0.3536318	0	0.0601504	0	1	1	1.9930149	1.9842440	0.0275302
X498	498	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X499	499	165	0.1515152	0.3596418	0	0.0676692	0	1	1	1.9262102	1.7208249	0.0279981
X500	500	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X501	501	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X502	502	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X503	503	165	0.1212121	0.3273672	0	0.0300752	0	1	1	2.3001220	3.3107362	0.0254855
X504	504	165	0.2181818	0.4142688	0	0.1503759	0	1	1	1.3523114	-0.1721876	0.0322508
X505	505	165	0.2181818	0.4142688	0	0.1503759	0	1	1	1.3523114	-0.1721876	0.0322508
X506	506	165	0.2181818	0.4142688	0	0.1503759	0	1	1	1.3523114	-0.1721876	0.0322508
X507	507	165	0.1696970	0.3765090	0	0.0902256	0	1	1	1.7439220	1.0477237	0.0293112
X508	508	165	0.1515152	0.3596418	0	0.0676692	0	1	1	1.9262102	1.7208249	0.0279981
X509	509	165	0.1939394	0.3965856	0	0.1203008	0	1	1	1.5341238	0.3558023	0.0308741
X510	510	165	0.0969697	0.2968173	0	0.0000000	0	1	1	2.6992205	5.3181326	0.0231072
X511	511	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X512	512	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X513	513	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X514	514	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X515	515	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X516	516	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X517	517	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X518	518	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X519	519	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X520	520	165	0.1030303	0.3049239	0	0.0075188	0	1	1	2.5879497	4.7262375	0.0237383
X521	521	165	0.1030303	0.3049239	0	0.0075188	0	1	1	2.5879497	4.7262375	0.0237383
X522	522	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X523	523	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X524	524	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X525	525	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X526	526	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X527	527	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X528	528	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X529	529	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X530	530	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X531	531	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X532	532	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X533	533	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X534	534	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X535	535	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X536	536	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X537	537	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X538	538	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X539	539	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X540	540	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X541	541	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X542	542	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X543	543	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X544	544	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X545	545	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X546	546	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X547	547	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X548	548	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X549	549	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X550	550	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X551	551	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X552	552	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X553	553	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X554	554	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X555	555	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X556	556	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X557	557	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X558	558	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X559	559	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X560	560	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X561	561	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X562	562	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X563	563	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X564	564	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X565	565	165	0.2242424	0.4183521	0	0.1578947	0	1	1	1.3103141	-0.2846925	0.0325687
X566	566	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X567	567	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X568	568	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X569	569	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X570	570	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X571	571	165	0.1575758	0.3654519	0	0.0751880	0	1	1	1.8626198	1.4784228	0.0284504
X572	572	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X573	573	165	0.1878788	0.3918044	0	0.1127820	0	1	1	1.5835940	0.5109766	0.0305019
X574	574	165	0.1575758	0.3654519	0	0.0751880	0	1	1	1.8626198	1.4784228	0.0284504
X575	575	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X576	576	165	0.1575758	0.3654519	0	0.0751880	0	1	1	1.8626198	1.4784228	0.0284504
X577	577	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X578	578	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X579	579	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X580	580	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X581	581	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X582	582	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X583	583	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X584	584	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X585	585	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X586	586	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X587	587	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X588	588	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X589	589	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X590	590	165	0.0666667	0.2502032	0	0.0000000	0	1	1	3.4428586	9.9134671	0.0194783
X591	591	165	0.0666667	0.2502032	0	0.0000000	0	1	1	3.4428586	9.9134671	0.0194783
X592	592	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X593	593	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X594	594	165	0.0787879	0.2702275	0	0.0000000	0	1	1	3.0985691	7.6475895	0.0210372
X595	595	165	0.0666667	0.2502032	0	0.0000000	0	1	1	3.4428586	9.9134671	0.0194783
X596	596	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X597	597	165	0.1272727	0.3342928	0	0.0375940	0	1	1	2.2164303	2.9304333	0.0260247
X598	598	165	0.1333333	0.3409694	0	0.0451128	0	1	1	2.1376956	2.5855224	0.0265444
X599	599	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
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X601	601	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
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X603	603	165	0.1818182	0.3868687	0	0.1052632	0	1	1	1.6349393	0.6772411	0.0301177
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X605	605	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X606	606	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X607	607	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X608	608	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X609	609	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X610	610	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X611	611	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X612	612	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X613	613	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X614	614	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X615	615	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X616	616	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X617	617	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X618	618	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X619	619	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X620	620	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X621	621	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X622	622	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X623	623	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X624	624	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X625	625	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X626	626	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X627	627	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X628	628	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X629	629	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X630	630	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X631	631	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X632	632	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
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X634	634	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X635	635	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X636	636	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X637	637	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X638	638	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X639	639	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X640	640	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
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X642	642	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X643	643	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X644	644	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X645	645	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X646	646	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X647	647	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X648	648	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X649	649	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X650	650	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X651	651	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X652	652	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X653	653	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X654	654	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X655	655	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X656	656	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X657	657	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X658	658	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X659	659	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X660	660	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X661	661	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X662	662	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X663	663	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X664	664	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X665	665	165	0.0484848	0.2154423	0	0.0000000	0	1	1	4.1661155	15.4502662	0.0167722
X666	666	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X667	667	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X668	668	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X669	669	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X670	670	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X671	671	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X672	672	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X673	673	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X674	674	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X675	675	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X676	676	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X677	677	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X678	678	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X679	679	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X680	680	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X681	681	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X682	682	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X683	683	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X684	684	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X685	685	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X686	686	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X687	687	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X688	688	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X689	689	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X690	690	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X691	691	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X692	692	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X693	693	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X694	694	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X695	695	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X696	696	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X697	697	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X698	698	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X699	699	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X700	700	165	0.1090909	0.3127023	0	0.0150376	0	1	1	2.4850472	4.2010305	0.0243438
X701	701	165	0.1090909	0.3127023	0	0.0150376	0	1	1	2.4850472	4.2010305	0.0243438
X702	702	165	0.1090909	0.3127023	0	0.0150376	0	1	1	2.4850472	4.2010305	0.0243438
X703	703	165	0.0909091	0.2883549	0	0.0000000	0	1	1	2.8202160	5.9900312	0.0224484
X704	704	165	0.0848485	0.2795044	0	0.0000000	0	1	1	2.9526225	6.7590538	0.0217594
X705	705	165	0.1090909	0.3127023	0	0.0150376	0	1	1	2.4850472	4.2010305	0.0243438
X706	706	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X707	707	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X708	708	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X709	709	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X710	710	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X711	711	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X712	712	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X713	713	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X714	714	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X715	715	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X716	716	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X717	717	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X718	718	165	0.0363636	0.1877631	0	0.0000000	0	1	1	4.9085939	22.2291256	0.0146173
X719	719	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X720	720	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X721	721	165	0.0242424	0.1542691	0	0.0000000	0	1	1	6.1305096	35.8002286	0.0120098
X722	722	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X723	723	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X724	724	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X725	725	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X726	726	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X727	727	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X728	728	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X729	729	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X730	730	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X731	731	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X732	732	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X733	733	165	0.0606061	0.2393327	0	0.0000000	0	1	1	3.6495726	11.3885115	0.0186320
X734	734	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X735	735	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X736	736	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X737	737	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X738	738	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X739	739	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X740	740	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X741	741	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X742	742	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X743	743	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X744	744	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X745	745	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X746	746	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X747	747	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X748	748	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X749	749	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X750	750	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X751	751	165	0.0787879	0.2702275	0	0.0000000	0	1	1	3.0985691	7.6475895	0.0210372
X752	752	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X753	753	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X754	754	165	0.0787879	0.2702275	0	0.0000000	0	1	1	3.0985691	7.6475895	0.0210372
X755	755	165	0.0787879	0.2702275	0	0.0000000	0	1	1	3.0985691	7.6475895	0.0210372
X756	756	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X757	757	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X758	758	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X759	759	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X760	760	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X761	761	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X762	762	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X763	763	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X764	764	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X765	765	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X766	766	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X767	767	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
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X769	769	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X770	770	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X771	771	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X772	772	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X773	773	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X774	774	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X775	775	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X776	776	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X777	777	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X778	778	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X779	779	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
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X782	782	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
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X785	785	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
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X787	787	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
X788	788	165	0.0000000	0.0000000	0	0.0000000	0	0	0	NaN	NaN	0.0000000
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X793	793	165	0.0545455	0.2277821	0	0.0000000	0	1	1	3.8875290	13.1929486	0.0177328
X794	794	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X795	795	165	0.0727273	0.2604788	0	0.0000000	0	1	1	3.2607885	8.6854909	0.0202782
X796	796	165	0.0303030	0.1719417	0	0.0000000	0	1	1	5.4303342	27.6562534	0.0133856
X797	797	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
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X961	961	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X962	962	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X963	963	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X964	964	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X965	965	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X966	966	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X967	967	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X968	968	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X969	969	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X970	970	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X971	971	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X972	972	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X973	973	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X974	974	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X975	975	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X976	976	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X977	977	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X978	978	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X979	979	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X980	980	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X981	981	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X982	982	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X983	983	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X984	984	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X985	985	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X986	986	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X987	987	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X988	988	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X989	989	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X990	990	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X991	991	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X992	992	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X993	993	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X994	994	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X995	995	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X996	996	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X997	997	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X998	998	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X999	999	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1000	1000	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X1001	1001	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X1002	1002	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1003	1003	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1004	1004	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1005	1005	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1006	1006	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1007	1007	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1008	1008	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1009	1009	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1010	1010	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1011	1011	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X1012	1012	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X1013	1013	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1014	1014	165	0.0181818	0.1340153	0	0.0000000	0	1	1	7.1469188	49.3778172	0.0104331
X1015	1015	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1016	1016	165	0.0424242	0.2021686	0	0.0000000	0	1	1	4.4992408	18.3545175	0.0157388
X1017	1017	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1018	1018	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1019	1019	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1020	1020	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1021	1021	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1022	1022	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1023	1023	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1024	1024	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1025	1025	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1026	1026	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1027	1027	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1028	1028	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1029	1029	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1030	1030	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1031	1031	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1032	1032	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1033	1033	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1034	1034	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1035	1035	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1036	1036	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1037	1037	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1038	1038	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1039	1039	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1040	1040	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1041	1041	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1042	1042	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1043	1043	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1044	1044	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1045	1045	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1046	1046	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1047	1047	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1048	1048	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1049	1049	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1050	1050	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1051	1051	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1052	1052	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1053	1053	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1054	1054	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1055	1055	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1056	1056	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1057	1057	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1058	1058	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1059	1059	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1060	1060	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1061	1061	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1062	1062	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1063	1063	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1064	1064	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1065	1065	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1066	1066	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1067	1067	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1068	1068	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1069	1069	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1070	1070	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1071	1071	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1072	1072	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1073	1073	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1074	1074	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1075	1075	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1076	1076	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1077	1077	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1078	1078	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1079	1079	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1080	1080	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1081	1081	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1082	1082	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1083	1083	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1084	1084	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1085	1085	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1086	1086	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1087	1087	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1088	1088	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1089	1089	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1090	1090	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1091	1091	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1092	1092	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1093	1093	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1094	1094	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1095	1095	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1096	1096	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1097	1097	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1098	1098	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1099	1099	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1100	1100	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1101	1101	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1102	1102	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1103	1103	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1104	1104	165	0.0121212	0.1097602	0	0.0000000	0	1	1	8.8360249	76.5393209	0.0085448
X1105	1105	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1106	1106	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606
X1107	1107	165	0.0060606	0.0778499	0	0.0000000	0	1	1	12.6126265	158.0362534	0.0060606

psych::describe(permeability) %>% 
  kable() %>% 
  kable_styling(position = "center", full_width = T) %>% 
  scroll_box(height = "200px", width = "200px")

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
X1	1	165	12.23744	15.57865	4.91	9.322838	6.086073	0.06	55.6	55.54	1.396559	0.5589865	1.212797

The matrix fingerprints contains the 1,107 binary molecular predictors for the 165 compounds, while permeability contains permeability response. The tables are presented above.

B.

The fingerprint predictors indicate the presence or absence of substructures of a molecule and are often sparse meaning that relatively few of the molecules contain each substructure. Filter out the predictors that have low frequencies using the nearZeroVar function from the caret package. How many predictors are left for modeling?

B<-fingerprints[,-nearZeroVar(fingerprints)]
ncol(B)

[1] 388

The number of predictors left for modeling based on the nearZeroVar function from caret is 388. This is down from 1107.

C.

Split the data into a training and a test set, pre-process the data, and tune a PLS model. How many latent variables are optimal and what is the corresponding resampled estimate of R2?

#adding permeability
dataset<-B %>% as.data.frame() %>% 
  mutate(permeability = permeability)

histogram(permeability)

set.seed(1)

datasplit<-initial_split(dataset, prop =.75)
datatrain<-training(datasplit)
datatest<-testing(datasplit)
answer<-(datatrain %>% select(permeability))[,1][,1]


plstest <- train(x=datatrain %>% select(-permeability), 
                 y=answer,
                 method = "pls",
                 center = T,
                 preProcess = c("center","scale"),
                 tuneGrid = expand.grid(ncomp = 1:10),
                 trControl = trainControl(method = "cv", number = 10)
)


plstest_graph <- data.frame(plstest$results$ncomp,plstest$results$RMSE)

ggplot(plstest_graph, aes(x=plstest.results.ncomp, y=plstest.results.RMSE))+
  geom_line(color = "skyblue3")+
  geom_point(pch = 21, fill = NA, color = "skyblue3", size = 2)+
  geom_vline(xintercept = plstest$bestTune$ncomp, linetype = 2, color = "grey70")+
  labs(x = "Components",
       y = "RMSE",
       title = "Tuning Grid for PLS No. of Components")+
  scale_x_continuous(breaks = seq(0,10,1))+
  defaulttheme

Based on the tuning grid, the optimal number of components is 9

plstest$results %>% filter(ncomp ==plstest$bestTune$ncomp) %>% 
  kable() %>% 
  kable_classic_2()

ncomp	RMSE	Rsquared	MAE	RMSESD	RsquaredSD	MAESD
9	10.83249	0.5505667	7.914403	2.24633	0.1964194	1.774683

D.

Predict the response for the test set. What is the test set estimate of R2?

response<-predict(plstest,datatrain)

plsresults <- data.frame(Model = "PLS",
                      RMSE = RMSE(response, datatrain$permeability),
                      Rsquared = caret::R2(response, datatrain$permeability),
                      MAE = MAE(response, datatrain$permeability))

plsresults %>% 
  kable() %>% 
  kable_classic_2()

	Model	RMSE	Rsquared	MAE
permeability	PLS	6.160214	0.837707	4.565464

Doing this evaluation on the test set shows an r2 of 0.83.

E.

Try building other models discussed in this chapter. Do any have better predictive performance?

pcr_model <- train(
  permeability ~ ., data = datatrain, method = "pcr",
  center = TRUE,
  trControl = trainControl("cv", number = 10)
)

pcr_out <- predict(pcr_model, datatest)

pcr_results <- data.frame(
  Model = "PCR",
  RMSE = RMSE(pcr_out, datatest$permeability),
  Rsquared =caret::R2(pcr_out, datatest$permeability)
)

r <- model.matrix(permeability ~ ., data = datatrain)
r_test <- model.matrix(permeability ~ ., data = datatest)

ridge_cv <- cv.glmnet(r, datatrain$permeability, alpha=0)
ridge_model <- glmnet(r, datatrain$permeability, alpha = 0, lambda = ridge_cv$lambda.min)

ridge_out <- as.vector(predict(ridge_model, r_test))

ridge_results <- data.frame(
  Model = "RIDGE",
  RMSE = RMSE(ridge_out, datatest$permeability),
  Rsquared = caret::R2(ridge_out, datatest$permeability)
)


fractionTune = seq(.3,.9,.1)
lambdaTune = seq(.05, .3, .1)

elastic_model <- train(x=datatrain %>% select(-permeability), 
                 y=answer,
                  method = "enet", 
                  trControl = trainControl(method = "repeatedcv"), 
                  preProcess = c("center", "scale"), 
                  tuneGrid = expand.grid(lambda = lambdaTune,
                                         fraction = fractionTune)
                )

elastic_out <- elastic_model%>%
  predict(datatest %>% select(-permeability))

elastic_results <- data.frame(
  Model = "ElasticNet",
  RMSE = RMSE(elastic_out, datatest$permeability),
  Rsquared = caret::R2(elastic_out, datatest$permeability)
 )



results<-bind_rows(pcr_results,ridge_results,elastic_results,plsresults)

kable(results) %>% 
  kable_classic_2()

	Model	RMSE	Rsquared	MAE
permeability…1	PCR	14.766874	0.1724866	NA
permeability…2	RIDGE	12.417815	0.4130966	NA
permeability…3	ElasticNet	12.522396	0.4477899	NA
permeability…4	PLS	6.160214	0.8377070	4.565464

Testing this on the other models show that our best model was based on the PLS.

F.

Would you recommend any of your models to replace the permeability laboratory experiment?

The model with the PLS could replace the laboratory experiment with as it explains 84% of the variance exhibited in the dataset. none of the other models come close to this.

6.3

A chemical manufacturing process for a pharmaceutical product was discussed in Sect. 1.4. In this problem, the objective is to understand the relationship between biological measurements of the raw materials (predictors), measurements of the manufacturing process (predictors), and the response of product yield. Biological predictors cannot be changed but can be used to assess the quality of the raw material before processing. On the other hand, manufacturing process predictors can be changed in the manufacturing process. Improving product yield by 1 % will boost revenue by approximately one hundred thousand dollars per batch:

A.

Start R and use these commands to load the data:

library(RANN)

data(ChemicalManufacturingProcess)

head(ChemicalManufacturingProcess,5)

  Yield BiologicalMaterial01 BiologicalMaterial02 BiologicalMaterial03
1 38.00                 6.25                49.58                56.97
2 42.44                 8.01                60.97                67.48
3 42.03                 8.01                60.97                67.48
4 41.42                 8.01                60.97                67.48
5 42.49                 7.47                63.33                72.25
  BiologicalMaterial04 BiologicalMaterial05 BiologicalMaterial06
1                12.74                19.51                43.73
2                14.65                19.36                53.14
3                14.65                19.36                53.14
4                14.65                19.36                53.14
5                14.02                17.91                54.66
  BiologicalMaterial07 BiologicalMaterial08 BiologicalMaterial09
1                  100                16.66                11.44
2                  100                19.04                12.55
3                  100                19.04                12.55
4                  100                19.04                12.55
5                  100                18.22                12.80
  BiologicalMaterial10 BiologicalMaterial11 BiologicalMaterial12
1                 3.46               138.09                18.83
2                 3.46               153.67                21.05
3                 3.46               153.67                21.05
4                 3.46               153.67                21.05
5                 3.05               147.61                21.05
  ManufacturingProcess01 ManufacturingProcess02 ManufacturingProcess03
1                     NA                     NA                     NA
2                    0.0                      0                     NA
3                    0.0                      0                     NA
4                    0.0                      0                     NA
5                   10.7                      0                     NA
  ManufacturingProcess04 ManufacturingProcess05 ManufacturingProcess06
1                     NA                     NA                     NA
2                    917                 1032.2                  210.0
3                    912                 1003.6                  207.1
4                    911                 1014.6                  213.3
5                    918                 1027.5                  205.7
  ManufacturingProcess07 ManufacturingProcess08 ManufacturingProcess09
1                     NA                     NA                  43.00
2                    177                    178                  46.57
3                    178                    178                  45.07
4                    177                    177                  44.92
5                    178                    178                  44.96
  ManufacturingProcess10 ManufacturingProcess11 ManufacturingProcess12
1                     NA                     NA                     NA
2                     NA                     NA                      0
3                     NA                     NA                      0
4                     NA                     NA                      0
5                     NA                     NA                      0
  ManufacturingProcess13 ManufacturingProcess14 ManufacturingProcess15
1                   35.5                   4898                   6108
2                   34.0                   4869                   6095
3                   34.8                   4878                   6087
4                   34.8                   4897                   6102
5                   34.6                   4992                   6233
  ManufacturingProcess16 ManufacturingProcess17 ManufacturingProcess18
1                   4682                   35.5                   4865
2                   4617                   34.0                   4867
3                   4617                   34.8                   4877
4                   4635                   34.8                   4872
5                   4733                   33.9                   4886
  ManufacturingProcess19 ManufacturingProcess20 ManufacturingProcess21
1                   6049                   4665                    0.0
2                   6097                   4621                    0.0
3                   6078                   4621                    0.0
4                   6073                   4611                    0.0
5                   6102                   4659                   -0.7
  ManufacturingProcess22 ManufacturingProcess23 ManufacturingProcess24
1                     NA                     NA                     NA
2                      3                      0                      3
3                      4                      1                      4
4                      5                      2                      5
5                      8                      4                     18
  ManufacturingProcess25 ManufacturingProcess26 ManufacturingProcess27
1                   4873                   6074                   4685
2                   4869                   6107                   4630
3                   4897                   6116                   4637
4                   4892                   6111                   4630
5                   4930                   6151                   4684
  ManufacturingProcess28 ManufacturingProcess29 ManufacturingProcess30
1                   10.7                   21.0                    9.9
2                   11.2                   21.4                    9.9
3                   11.1                   21.3                    9.4
4                   11.1                   21.3                    9.4
5                   11.3                   21.6                    9.0
  ManufacturingProcess31 ManufacturingProcess32 ManufacturingProcess33
1                   69.1                    156                     66
2                   68.7                    169                     66
3                   69.3                    173                     66
4                   69.3                    171                     68
5                   69.4                    171                     70
  ManufacturingProcess34 ManufacturingProcess35 ManufacturingProcess36
1                    2.4                    486                  0.019
2                    2.6                    508                  0.019
3                    2.6                    509                  0.018
4                    2.5                    496                  0.018
5                    2.5                    468                  0.017
  ManufacturingProcess37 ManufacturingProcess38 ManufacturingProcess39
1                    0.5                      3                    7.2
2                    2.0                      2                    7.2
3                    0.7                      2                    7.2
4                    1.2                      2                    7.2
5                    0.2                      2                    7.3
  ManufacturingProcess40 ManufacturingProcess41 ManufacturingProcess42
1                     NA                     NA                   11.6
2                    0.1                   0.15                   11.1
3                    0.0                   0.00                   12.0
4                    0.0                   0.00                   10.6
5                    0.0                   0.00                   11.0
  ManufacturingProcess43 ManufacturingProcess44 ManufacturingProcess45
1                    3.0                    1.8                    2.4
2                    0.9                    1.9                    2.2
3                    1.0                    1.8                    2.3
4                    1.1                    1.8                    2.1
5                    1.1                    1.7                    2.1

The matrix processPredictors contains the 57 predictors (12 describing the input biological material and 45 describing the process predictors) for the 176 manufacturing runs. yield contains the percent yield for each run.

B.

A small percentage of cells in the predictor set contain missing values. Use an imputation function to fill in these missing values (e.g., see Sect. 3.8).

ChemicalManufacturingProcess %>% 
  naniar::miss_var_summary() %>% 
  filter(n_miss > 0) %>% 
  ggplot(aes( x = fct_reorder(variable, n_miss), y = pct_miss))+
  coord_flip()+
  geom_col(alpha = 0.5, fill = "skyblue3", color = "darkblue")+
  defaulttheme+
  labs(title = "Top Features with Missing Data",
       y = "Percent Missing",
       x = "Feature")

df<-
ChemicalManufacturingProcess %>% 
  recipe(~.) %>% 
  step_impute_knn(all_predictors()) %>% 
  prep() %>% 
  bake(ChemicalManufacturingProcess)


paste0("Old Percent Missing from Dataframe is: ",
round(ChemicalManufacturingProcess %>% 
  naniar::pct_miss(),2),"%"
)

[1] "Old Percent Missing from Dataframe is: 1.04%"

paste0("New Percent Missing from Dataframe is: ",
round(df %>% 
  naniar::pct_miss(),2),"%"
)

[1] "New Percent Missing from Dataframe is: 0%"

The figure above shows the amount of features with missing data. The imputation method that was done is based on KNN imputation (K-nearest neighbors). As shown above, we have reduced the missingness of the dataset from 1.04% to 0%.

C.

Split the data into a training and a test set, pre-process the data, and tune a model of your choice from this chapter. What is the optimal value of the performance metric?

set.seed(1)
split<-initial_split(df, prop = .75)
datatrain<-training(split)
datatest<-testing(split)

answer<-(datatrain %>% select(Yield))[,1][[1]]

plstest <- train(x=datatrain %>% select(-Yield), 
                 y=answer,
                 method = "pls",
                 center = T,
                 preProcess = c("center","scale"),
                 tuneGrid = expand.grid(ncomp = 1:10),
                 trControl = trainControl(method = "cv", number = 10)
)


plstest_graph <- data.frame(plstest$results$ncomp,plstest$results$RMSE)

ggplot(plstest_graph, aes(x=plstest.results.ncomp, y=plstest.results.RMSE))+
  geom_line(color = "skyblue3")+
  geom_point(pch = 21, fill = NA, color = "skyblue3", size = 2)+
  geom_vline(xintercept = plstest$bestTune$ncomp, linetype = 2, color = "grey70")+
  labs(x = "Components",
       y = "RMSE",
       title = "Tuning Grid for PLS No. of Components")+
  scale_x_continuous(breaks = seq(0,10,1))+
  defaulttheme

Optimal number of components is 2 as shown in the above figure.

plstest$results %>% filter(ncomp ==plstest$bestTune$ncomp) %>% 
  kable() %>% 
  kable_classic_2()

ncomp	RMSE	Rsquared	MAE	RMSESD	RsquaredSD	MAESD
3	1.391805	0.5712031	1.061595	0.6923412	0.1951998	0.3491816

D.

Predict the response for the test set. What is the value of the performance metric and how does this compare with the resampled performance metric on the training set?

response<-predict(plstest,datatrain)

results <- data.frame(Model = "PLS",
                      RMSE = RMSE(response, datatrain$Yield),
                      Rsquared = R2(response, datatrain$Yield),
                      MAE = MAE(response, datatrain$Yield))


results %>% kable() %>% 
  kable_classic_2()

Model	RMSE	Rsquared	MAE
PLS	0.9980421	0.7105195	0.7954016

Test set result show that the model explains 71% of the variance in the dataset

E.

Which predictors are most important in the model you have trained? Do either the biological or process predictors dominate the list?

varImp(plstest) %>% plot

The figure above shows the most important features. Manufacturing process 32 is overwhelmingly important

F.

Explore the relationships between each of the top predictors and the response. How could this information be helpful in improving yield in future runs of the manufacturing process?

vars<-varImp(plstest)[1] %>% as.data.frame() %>% 
  slice_max(order_by = Overall, n = 5)

df %>% select(c(rownames(vars),"Yield")) %>% 
  GGally::ggpairs(progress = F)+defaulttheme

scatter matrix of the top 6 features above show including our predictor variable Yield where we can see that there is a clear relationship that can be used to simplify predictions