PCA and classification

Wines

Dataset

Data on 178 wine samples to be explored belonging to three different types.

Loads the dataset, making sure that the samples observed are on rows and variables on columns, otherwise transpose the entire matrix before making the PCA.

Source: “Multivariate data analysis as discriminating method of the origin of wines” (Forina 1986)

df = data.frame(read.csv('wine.csv'))
df = relocate(df, type, .before = attrib.Alcohol )
df = column_to_rownames(df , var = 'X')
colnames(df) = str_remove(colnames(df),'attrib.')

kable(df)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
  scroll_box( height = "500px")

type	Alcohol	Sugar.free.extract	Fixed.acidity	Tartaric.acid	Malic.acid	Uronic.acids	pH	Ash	Alcalinity.of.ash	Potassium	Calcium	Magnesium	Phosphate	Chloride	Total.phenols	Flavanoids	Nonflavanoid.phenols	Proanthocyanins	Color.intensity	Hue	OD280.OD315.of.diluted.wines	OD280.OD315.of.flavonoids	Glycerol	2.3.butanediol	Total.nitrogen	Proline	Methanol
Barolo	14.23	24.82	73.1	1.21	1.71	0.72	3.38	2.43	15.6	950	62	127	320	82	2.80	3.06	0.28	2.29	5.64	1.04	3.92	4.77	9.29	757	153	1065	113
Barolo	13.20	26.30	72.8	1.84	1.78	0.71	3.30	2.14	11.2	765	75	100	395	90	2.65	2.76	0.26	1.28	4.38	1.05	3.40	3.80	8.93	881	194	1050	94
Barolo	13.16	26.30	68.5	1.94	2.36	0.84	3.48	2.67	18.6	936	70	101	497	67	2.80	3.24	0.30	2.81	5.68	1.03	3.17	3.46	11.74	900	206	1185	125
Barolo	14.37	25.85	74.9	1.59	1.95	0.72	3.43	2.50	16.8	985	47	113	580	49	3.85	3.49	0.24	2.18	7.80	0.86	3.45	3.54	10.13	1119	292	1480	80
Barolo	13.24	26.05	83.5	1.30	2.59	1.10	3.42	2.87	21.0	1088	70	118	408	65	2.80	2.69	0.39	1.82	4.32	1.04	2.93	3.22	10.27	799	215	735	73
Barolo	14.20	28.40	79.9	2.14	1.76	0.96	3.39	2.45	15.2	868	71	112	418	58	3.27	3.39	0.34	1.97	6.75	1.05	2.85	3.16	10.85	865	364	1450	68
Barolo	14.39	27.02	64.3	1.64	1.87	0.95	3.42	2.45	14.6	889	67	96	306	52	2.50	2.52	0.30	1.98	5.25	1.02	3.58	3.94	9.05	931	378	1290	80
Barolo	14.06	26.40	73.5	1.33	2.15	1.14	3.54	2.61	17.6	894	50	121	502	64	2.60	2.51	0.31	1.25	5.05	1.06	3.58	3.94	10.13	865	358	1295	100
Barolo	14.83	26.80	69.5	1.82	1.64	0.67	3.30	2.17	14.0	765	49	97	440	58	2.80	2.98	0.29	1.98	5.20	1.08	2.85	3.03	9.89	825	438	1045	141
Barolo	13.86	27.00	68.5	1.92	1.35	0.67	3.27	2.27	16.0	794	51	98	391	64	2.98	3.15	0.22	1.85	7.22	1.01	3.55	3.75	12.65	788	350	1045	121
Barolo	14.10	26.08	72.5	1.64	2.16	0.62	3.31	2.30	18.0	838	61	105	399	61	2.95	3.32	0.22	2.38	5.75	1.25	3.17	3.27	8.59	964	378	1510	123
Barolo	14.12	28.35	72.9	1.51	1.48	0.96	3.20	2.32	16.8	827	60	95	424	79	2.20	2.43	0.26	1.57	5.00	1.17	2.82	3.04	11.52	894	294	1280	134
Barolo	13.75	30.25	75.1	1.92	1.73	0.64	3.18	2.41	16.0	752	65	89	453	257	2.60	2.76	0.29	1.81	5.60	1.15	2.90	2.92	12.24	784	289	1320	164
Barolo	14.75	30.40	98.9	2.08	1.73	0.72	3.01	2.39	11.4	910	46	91	510	50	3.10	3.69	0.43	2.81	5.40	1.25	2.73	2.82	12.29	766	224	1150	105
Barolo	14.38	27.10	72.3	1.95	1.87	0.67	3.20	2.38	12.0	927	29	102	523	55	3.30	3.64	0.29	2.96	7.50	1.20	3.00	3.32	9.53	1041	324	1547	114
Barolo	13.63	27.15	69.6	1.48	1.81	0.67	3.47	2.70	17.2	905	28	112	385	50	2.85	2.91	0.30	1.46	7.30	1.28	2.88	3.12	7.92	812	229	1310	97
Barolo	14.30	27.90	74.9	1.41	1.92	0.82	3.40	2.72	20.0	860	108	120	513	62	2.80	3.14	0.33	1.97	6.20	1.07	2.65	3.10	9.24	836	308	1280	113
Barolo	13.83	26.30	64.9	1.93	1.57	0.68	3.43	2.62	20.0	905	68	115	419	58	2.95	3.40	0.40	1.72	6.60	1.13	2.57	2.66	9.41	722	274	1130	99
Barolo	14.19	26.40	72.0	1.85	1.59	0.82	3.38	2.48	16.5	964	86	108	488	28	3.30	3.93	0.32	1.86	8.70	1.23	2.82	3.17	9.85	808	230	1680	135
Barolo	13.64	27.72	91.5	1.35	3.10	0.82	3.30	2.56	15.2	1038	111	116	402	67	2.70	3.03	0.17	1.66	5.10	0.96	3.36	4.00	10.39	726	227	845	119
Barolo	14.06	25.32	71.1	1.34	1.63	1.00	3.47	2.28	16.0	905	79	126	323	73	3.00	3.17	0.24	2.10	5.65	1.09	3.71	3.75	10.30	828	225	780	145
Barolo	12.93	28.80	102.1	1.05	3.80	0.89	3.26	2.65	18.6	915	79	102	294	62	2.41	2.41	0.25	1.98	4.50	1.03	3.52	3.66	11.88	589	237	770	123
Barolo	13.71	27.63	80.0	2.23	1.86	1.21	3.33	2.36	16.6	815	89	101	476	134	2.61	2.88	0.27	1.69	3.80	1.11	4.00	4.31	8.81	715	270	1035	109
Barolo	12.85	25.80	69.6	1.54	1.60	0.79	3.45	2.52	17.8	958	101	95	415	73	2.48	2.37	0.26	1.46	3.93	1.09	3.63	3.82	9.14	568	248	1015	102
Barolo	13.50	25.00	81.6	1.55	1.81	0.95	3.42	2.61	20.0	992	62	96	476	47	2.53	2.61	0.28	1.66	3.52	1.12	3.82	4.00	9.45	667	210	845	86
Barolo	13.05	25.72	78.3	1.15	2.05	1.08	3.57	3.22	25.0	1095	63	124	536	82	2.63	2.68	0.47	1.92	3.58	1.13	3.20	3.63	10.34	753	238	830	124
Barolo	13.39	27.10	72.3	1.52	1.77	1.05	3.46	2.62	16.1	936	68	93	395	52	2.85	2.94	0.34	1.45	4.80	0.92	3.22	4.44	9.96	854	285	1195	85
Barolo	13.30	22.70	68.3	1.74	1.72	1.06	3.44	2.14	17.0	882	52	94	434	46	2.40	2.19	0.27	1.35	3.95	1.02	2.77	3.10	9.70	757	350	1285	84
Barolo	13.87	29.30	68.3	1.38	1.90	0.75	3.42	2.80	19.4	1085	68	107	396	76	2.95	2.97	0.37	1.76	4.50	1.25	3.40	3.72	9.53	702	280	915	99
Barolo	14.02	25.20	69.6	1.71	1.68	0.79	3.26	2.21	16.0	780	62	96	510	53	2.65	2.33	0.26	1.98	4.70	1.04	3.59	3.77	9.94	689	293	1035	100
Barolo	13.73	26.75	75.2	1.53	1.50	0.66	3.30	2.70	22.5	1067	76	101	436	53	3.00	3.25	0.29	2.38	5.70	1.19	2.71	3.00	10.44	792	332	1285	120
Barolo	13.58	28.35	62.0	1.14	1.66	0.72	3.28	2.36	19.1	805	58	106	485	498	2.86	3.19	0.22	1.95	6.90	1.09	2.88	3.06	10.73	700	296	1515	108
Barolo	13.68	26.98	64.8	1.60	1.83	0.62	3.40	2.36	17.2	1068	32	104	398	76	2.42	2.69	0.42	1.97	3.84	1.23	2.87	3.04	13.00	733	252	990	141
Barolo	13.76	26.80	77.1	1.81	1.53	0.84	3.40	2.70	19.5	974	39	132	394	128	2.95	2.74	0.50	1.35	5.40	1.25	3.00	3.31	8.33	740	296	1235	109
Barolo	13.51	26.22	65.3	1.28	1.80	0.70	3.36	2.65	19.0	856	53	110	464	53	2.35	2.53	0.29	1.54	4.20	1.10	2.87	2.91	10.10	700	258	1095	86
Barolo	13.48	26.10	70.9	1.44	1.81	0.69	3.45	2.41	20.5	789	49	100	416	35	2.70	2.98	0.26	1.86	5.10	1.04	3.47	4.04	8.21	534	258	920	75
Barolo	13.28	29.70	78.9	1.50	1.64	0.80	3.30	2.84	15.5	964	98	110	431	38	2.60	2.68	0.34	1.36	4.60	1.09	2.78	3.17	13.70	570	224	880	105
Barolo	13.05	25.00	70.9	1.18	1.65	0.89	3.34	2.55	18.0	1025	85	98	382	23	2.45	2.43	0.29	1.44	4.25	1.12	2.51	2.87	8.88	627	220	1105	134
Barolo	13.07	24.30	73.9	1.16	1.50	1.00	3.41	2.10	15.5	930	75	98	386	18	2.40	2.64	0.28	1.37	3.70	1.18	2.69	3.04	9.50	658	212	1020	145
Barolo	14.22	30.20	114.8	1.85	3.99	0.64	3.11	2.51	13.2	895	88	128	280	76	3.00	3.04	0.20	2.08	5.10	0.89	3.53	3.66	12.34	1048	215	760	101
Barolo	13.56	26.60	80.3	1.57	1.71	0.91	3.32	2.31	16.2	890	75	117	316	70	3.15	3.29	0.34	2.34	6.13	0.95	3.38	3.53	9.77	733	246	795	118
Barolo	13.41	27.50	102.7	1.79	3.84	0.92	3.19	2.12	18.8	815	78	90	385	70	2.45	2.68	0.27	1.48	4.28	0.91	3.00	3.36	9.21	565	231	1035	106
Barolo	13.88	27.80	78.9	2.39	1.89	0.65	3.33	2.59	15.0	980	71	101	502	67	3.25	3.56	0.17	1.70	5.43	0.88	3.56	4.00	8.61	665	289	1095	121
Barolo	13.24	25.60	101.3	1.83	3.98	0.62	3.18	2.29	17.5	920	63	103	389	53	2.64	2.63	0.32	1.66	4.36	0.82	3.00	3.15	8.61	576	248	680	105
Barolo	13.05	23.70	80.0	1.22	1.77	0.82	3.33	2.10	17.0	901	49	107	408	50	3.00	3.00	0.28	2.03	5.04	0.88	3.35	3.78	9.96	1044	218	885	155
Barolo	14.21	29.65	104.9	1.74	4.04	0.86	3.35	2.44	18.9	930	63	111	324	46	2.85	2.65	0.30	1.25	5.24	0.87	3.33	3.78	10.08	700	264	1080	90
Barolo	14.38	30.70	90.3	1.24	3.59	0.99	3.16	2.28	16.0	788	71	102	408	70	3.25	3.17	0.27	2.19	4.90	1.04	3.44	3.56	9.48	766	218	1065	91
Barolo	13.90	25.30	75.2	1.93	1.68	0.63	3.16	2.12	16.0	762	81	101	484	56	3.10	3.39	0.21	2.14	6.10	0.91	3.33	3.51	8.78	570	281	985	77
Barolo	14.10	25.98	70.0	1.87	2.02	0.83	3.20	2.40	18.8	880	75	103	480	64	2.75	2.92	0.32	2.38	6.20	1.07	2.75	2.89	10.42	669	249	1060	78
Barolo	13.94	26.80	72.7	2.35	1.73	0.60	3.23	2.27	17.4	868	40	108	420	96	2.88	3.54	0.32	2.08	8.90	1.12	3.10	3.30	13.44	749	383	1260	155
Barolo	13.05	24.30	76.0	2.08	1.73	0.63	3.06	2.04	12.4	792	35	92	638	50	2.72	3.27	0.17	2.91	7.20	1.12	2.91	3.20	9.17	590	224	1150	124
Barolo	13.83	27.60	63.3	1.82	1.65	0.77	3.32	2.60	17.2	968	28	94	411	53	2.45	2.99	0.22	2.29	5.60	1.24	3.37	3.69	9.77	777	330	1265	110
Barolo	13.82	26.25	74.5	1.83	1.75	0.77	3.33	2.42	14.0	785	29	111	472	47	3.88	3.74	0.32	1.87	7.05	1.01	3.26	3.53	7.63	704	360	1190	88
Barolo	13.77	25.20	64.8	1.29	1.90	0.84	3.56	2.68	17.1	927	33	115	405	59	3.00	2.79	0.39	1.68	6.30	1.13	2.93	3.21	7.73	795	313	1375	109
Barolo	13.74	24.80	65.2	1.88	1.67	0.66	3.43	2.25	16.4	784	76	118	502	37	2.60	2.90	0.21	1.62	5.85	0.92	3.20	3.36	7.97	733	292	1060	87
Barolo	13.56	25.00	78.0	1.49	1.73	0.69	3.31	2.46	20.5	808	91	116	411	38	2.96	2.78	0.20	2.45	6.25	0.98	3.03	3.16	7.92	550	266	1120	86
Barolo	14.22	26.60	87.1	1.98	1.70	0.74	3.20	2.30	16.3	768	73	118	465	136	3.20	3.00	0.26	2.03	6.38	0.94	3.31	3.81	13.00	770	248	970	124
Barolo	13.29	26.80	80.0	1.63	1.97	0.96	3.24	2.68	16.8	905	76	102	360	24	3.00	3.23	0.31	1.66	6.00	1.07	2.84	3.21	9.30	676	258	1270	116
Barolo	13.72	27.10	73.3	1.34	1.43	0.93	3.38	2.50	16.7	906	71	108	403	33	3.40	3.67	0.19	2.04	6.80	0.89	2.87	3.10	9.94	755	232	1285	131
Grignolino	12.37	18.30	90.1	2.80	0.94	0.73	3.11	1.36	10.6	580	77	88	296	52	1.98	0.57	0.28	0.42	1.95	1.05	1.82	2.12	5.40	736	287	520	98
Grignolino	12.33	22.90	72.2	2.25	1.10	0.69	3.26	2.28	16.0	715	85	101	365	108	2.05	1.09	0.63	0.41	3.27	1.25	1.67	1.42	6.90	658	345	680	127
Grignolino	12.64	23.90	95.7	1.93	1.36	1.06	3.19	2.02	16.8	688	83	100	395	53	2.02	1.41	0.53	0.62	5.75	0.98	1.59	1.86	8.20	691	321	450	60
Grignolino	13.67	22.20	64.8	2.20	1.25	0.74	3.40	1.92	18.0	725	51	94	301	47	2.10	1.79	0.32	0.73	3.80	1.23	2.46	1.73	8.60	797	262	630	87
Grignolino	12.37	23.50	70.0	2.06	1.13	0.72	3.30	2.16	19.0	785	73	87	422	306	3.50	3.10	0.19	1.87	4.45	1.22	2.87	3.07	7.20	748	141	420	157
Grignolino	12.17	23.03	65.7	1.84	1.45	0.72	3.35	2.53	19.0	790	62	104	411	116	1.89	1.75	0.45	1.03	2.95	1.45	2.23	2.73	7.50	627	219	355	58
Grignolino	12.37	26.80	62.7	1.70	1.21	0.88	3.40	2.56	18.1	978	55	98	310	69	2.42	2.65	0.37	2.08	4.60	1.19	2.30	2.60	7.96	680	259	678	118
Grignolino	13.11	23.70	80.0	1.40	1.01	0.77	3.10	1.70	15.0	730	80	78	297	148	2.98	3.18	0.26	2.28	5.30	1.12	3.18	3.33	8.20	604	100	502	114
Grignolino	12.37	20.90	63.7	1.94	1.17	0.67	3.40	1.92	19.6	785	40	78	212	54	2.11	2.00	0.27	1.04	4.68	1.12	3.48	4.07	7.10	554	425	510	98
Grignolino	13.34	23.72	70.0	2.02	0.94	1.09	3.26	2.36	17.0	760	64	110	451	111	2.53	1.30	0.55	0.42	3.17	1.02	1.93	1.92	8.10	704	363	750	137
Grignolino	12.21	22.70	90.7	3.62	1.19	0.94	3.14	1.75	16.8	795	134	151	448	88	1.85	1.28	0.14	2.50	2.85	1.28	3.07	3.23	6.81	714	195	718	116
Grignolino	12.29	21.40	55.6	1.43	1.61	0.87	3.54	2.21	20.4	682	102	103	324	50	1.10	1.02	0.37	1.46	3.05	0.91	1.82	2.00	6.38	661	301	870	78
Grignolino	13.86	25.25	59.5	1.27	1.51	1.09	3.63	2.67	25.0	785	63	86	383	59	2.95	2.86	0.21	1.87	3.38	1.36	3.16	3.52	7.62	748	170	410	99
Grignolino	13.49	22.30	60.9	1.74	1.66	0.67	3.44	2.24	24.0	680	60	87	300	43	1.88	1.84	0.27	1.03	3.74	0.98	2.78	3.50	8.04	614	160	472	64
Grignolino	12.99	26.10	50.5	1.42	1.67	1.24	3.52	2.60	30.0	974	55	139	473	35	3.30	2.89	0.21	1.96	3.35	1.31	3.50	3.60	8.00	731	293	985	113
Grignolino	11.96	24.50	65.7	2.18	1.09	0.73	3.40	2.30	21.0	681	98	101	366	48	3.38	2.14	0.13	1.65	3.21	0.99	3.13	3.15	7.70	563	183	886	57
Grignolino	11.66	20.30	61.7	1.70	1.88	0.60	3.30	1.92	16.0	785	52	97	312	59	1.61	1.57	0.34	1.15	3.80	1.23	2.14	2.35	6.14	596	109	428	129
Grignolino	13.03	23.50	78.6	1.90	0.90	0.76	3.30	1.71	16.0	790	57	86	396	122	1.95	2.03	0.24	1.46	4.60	1.19	2.48	2.85	8.40	756	167	392	145
Grignolino	11.84	26.40	108.7	1.70	2.89	0.91	3.11	2.23	18.0	790	71	112	350	58	1.72	1.32	0.43	0.95	2.65	0.96	2.52	3.25	5.22	514	246	500	122
Grignolino	12.33	20.60	58.7	2.41	0.99	0.84	3.32	1.95	14.8	680	124	136	438	99	1.90	1.85	0.35	2.76	3.40	1.06	2.31	2.70	7.96	654	259	750	59
Grignolino	12.70	27.15	93.3	1.46	3.87	1.11	3.19	2.40	23.0	890	110	101	321	52	2.83	2.55	0.43	1.95	2.57	1.19	3.13	3.82	8.66	700	227	463	101
Grignolino	12.00	23.20	58.4	1.88	0.92	0.82	3.30	2.00	19.0	680	63	86	408	27	2.42	2.26	0.30	1.43	2.50	1.38	3.12	3.52	5.80	645	199	278	95
Grignolino	12.72	22.90	58.4	1.40	1.81	0.81	3.50	2.20	18.8	890	83	86	418	64	2.20	2.53	0.26	1.77	3.90	1.16	3.14	3.33	7.38	664	199	714	111
Grignolino	12.08	23.50	56.9	1.33	1.13	0.71	3.65	2.51	24.0	980	85	78	215	53	2.00	1.58	0.40	1.40	2.20	1.31	2.72	3.50	8.11	548	203	630	115
Grignolino	13.05	25.50	104.8	1.64	3.86	0.73	3.19	2.32	22.5	938	98	85	195	48	1.65	1.59	0.61	1.62	4.80	0.84	2.01	2.07	8.64	649	207	515	114
Grignolino	11.84	23.40	70.8	1.80	0.89	1.00	3.40	2.58	18.0	922	80	94	378	95	2.20	2.21	0.22	2.35	3.05	0.79	3.08	3.81	6.36	586	138	520	141
Grignolino	12.67	24.30	74.1	1.70	0.98	0.88	3.35	2.24	18.0	840	81	99	336	70	2.20	1.94	0.30	1.46	2.62	1.23	3.16	3.60	7.90	600	217	450	121
Grignolino	12.16	25.80	78.9	1.84	1.61	0.78	3.37	2.31	22.8	845	98	90	285	54	1.78	1.69	0.43	1.56	2.45	1.33	2.26	2.92	8.04	643	195	495	116
Grignolino	11.65	22.90	62.9	1.80	1.67	0.64	3.55	2.62	26.0	1045	125	88	281	36	1.92	1.61	0.40	1.34	2.60	1.36	3.21	3.27	9.54	608	262	562	120
Grignolino	11.64	24.20	72.4	1.84	2.06	0.89	3.40	2.46	21.6	962	79	84	304	70	1.95	1.69	0.48	1.35	2.80	1.00	2.75	3.60	7.97	523	223	680	120
Grignolino	12.08	24.00	67.6	1.93	1.33	1.05	3.50	2.30	23.6	932	65	70	278	27	2.20	1.59	0.42	1.38	1.74	1.07	3.21	3.77	8.47	557	200	625	163
Grignolino	12.08	25.50	78.9	1.93	1.83	0.77	3.25	2.32	18.5	960	128	81	329	48	1.60	1.50	0.52	1.64	2.40	1.08	2.27	2.28	8.33	563	314	480	105
Grignolino	12.00	25.30	75.6	1.80	1.51	0.74	3.27	2.42	22.0	915	102	86	342	110	1.45	1.25	0.50	1.63	3.60	1.05	2.65	2.75	8.21	495	170	450	152
Grignolino	12.69	25.00	70.9	1.47	1.53	0.82	3.43	2.26	20.7	845	92	80	214	73	1.38	1.46	0.58	1.62	3.05	0.96	2.06	2.28	8.88	792	198	495	101
Grignolino	12.29	25.00	86.0	1.84	2.83	0.71	3.24	2.22	18.0	915	94	88	329	84	2.45	2.25	0.25	1.99	2.15	1.15	3.30	3.75	5.64	594	190	290	117
Grignolino	11.62	28.40	92.8	1.35	1.99	0.84	3.22	2.28	18.0	794	88	98	372	76	3.02	2.26	0.17	1.35	3.25	1.16	2.96	2.97	13.60	930	200	345	120
Grignolino	12.47	24.95	72.0	1.93	1.52	1.02	3.32	2.20	19.0	790	188	162	464	84	2.50	2.27	0.32	3.28	2.60	1.16	2.63	2.99	6.21	683	268	937	79
Grignolino	11.81	27.50	75.3	1.75	2.12	0.91	3.29	2.74	21.5	942	125	134	375	83	1.60	0.99	0.14	1.56	2.50	0.95	2.26	2.88	7.56	687	179	625	84
Grignolino	12.29	25.30	68.5	1.80	1.41	0.57	3.30	1.98	16.0	890	82	85	440	40	2.55	2.50	0.29	1.77	2.90	1.23	2.74	3.14	8.44	696	335	428	117
Grignolino	12.37	24.80	61.2	1.60	1.07	1.01	3.40	2.10	18.5	845	84	88	385	80	3.52	3.75	0.24	1.95	4.50	1.04	2.77	3.05	7.23	655	180	660	127
Grignolino	12.29	26.50	112.4	2.61	3.17	1.09	2.95	2.21	18.0	845	122	88	438	35	2.85	2.99	0.45	2.81	2.30	1.42	2.83	3.90	8.45	759	159	406	146
Grignolino	12.08	22.90	75.2	2.20	2.08	0.67	3.15	1.70	17.5	805	62	97	212	42	2.23	2.17	0.26	1.40	3.30	1.27	2.96	3.41	7.08	591	399	710	105
Grignolino	12.60	21.90	63.7	2.00	1.34	0.64	3.15	1.90	18.5	870	135	88	224	80	1.45	1.36	0.29	1.35	2.45	1.04	2.77	3.75	8.56	610	195	562	130
Grignolino	12.34	25.80	78.0	2.50	2.45	0.57	3.42	2.46	21.0	915	144	98	146	82	2.56	2.11	0.34	1.31	2.80	0.80	3.38	4.19	8.36	536	306	438	98
Grignolino	11.82	22.70	67.2	2.17	1.72	0.80	3.40	1.88	19.5	874	64	86	442	85	2.50	1.64	0.37	1.42	2.06	0.94	2.44	3.80	7.36	653	194	415	103
Grignolino	12.51	24.50	63.2	1.34	1.73	0.67	3.50	1.98	20.5	905	74	85	254	50	2.20	1.92	0.32	1.48	2.94	1.04	3.57	4.50	10.44	882	158	672	99
Grignolino	12.42	23.50	78.7	1.92	2.55	0.92	3.30	2.27	22.0	980	93	90	342	92	1.68	1.84	0.66	1.42	2.70	0.86	3.30	3.50	7.92	680	219	315	89
Grignolino	12.25	25.00	75.2	1.40	1.73	0.64	3.45	2.12	19.0	890	102	80	265	53	1.65	2.03	0.37	1.63	3.40	1.00	3.17	4.16	10.13	790	207	510	126
Grignolino	12.72	24.10	85.6	2.34	1.75	0.71	3.33	2.28	22.5	910	58	84	159	67	1.38	1.76	0.48	1.63	3.30	0.88	2.42	2.54	7.61	855	194	488	81
Grignolino	12.22	24.50	70.1	1.42	1.29	0.60	3.36	1.94	19.0	897	103	92	157	65	2.36	2.04	0.39	2.08	2.70	0.86	3.02	3.64	7.24	780	132	312	97
Grignolino	11.61	27.60	84.0	1.85	1.35	0.87	3.46	2.70	20.0	950	98	94	408	58	2.74	2.92	0.29	2.49	2.65	0.96	3.26	3.85	6.42	592	386	680	110
Grignolino	11.46	24.84	104.4	2.20	3.74	0.78	3.07	1.82	19.5	685	143	107	322	70	3.18	2.58	0.24	3.58	2.90	0.75	2.81	3.60	7.87	684	196	562	91
Grignolino	12.52	26.35	100.4	1.45	2.43	0.97	3.21	2.17	21.0	680	112	88	339	48	2.55	2.27	0.26	1.22	2.00	0.90	2.78	3.10	8.50	730	171	325	60
Grignolino	11.76	29.60	90.3	2.10	2.68	1.04	3.30	2.92	20.0	1100	115	103	370	38	1.75	2.03	0.60	1.05	3.80	1.23	2.50	2.25	9.94	732	454	607	103
Grignolino	11.41	21.70	100.0	2.04	0.74	0.87	3.50	2.50	21.0	1085	105	88	315	56	2.48	2.01	0.42	1.44	3.08	1.10	2.31	4.16	6.56	638	228	434	81
Grignolino	12.08	23.50	95.7	2.31	1.39	0.66	3.30	2.50	22.5	1025	83	84	235	42	2.56	2.29	0.43	1.04	2.90	0.93	3.19	4.38	7.36	632	247	385	105
Grignolino	11.03	23.30	92.0	3.02	1.51	0.97	3.12	2.20	21.5	835	136	85	358	30	2.46	2.17	0.52	2.01	1.90	1.71	2.87	3.46	6.28	630	175	407	96
Grignolino	11.82	22.90	75.2	2.10	1.47	0.89	3.13	1.99	20.8	754	115	86	264	80	1.98	1.60	0.30	1.53	1.95	0.95	3.33	3.81	7.75	644	386	495	112
Grignolino	12.42	25.30	94.7	1.86	1.61	0.83	3.38	2.19	22.5	964	96	108	268	128	2.00	2.09	0.34	1.61	2.06	1.06	2.96	3.73	9.02	989	227	345	108
Grignolino	12.77	25.50	101.3	2.10	3.43	0.54	3.10	1.98	16.0	720	65	80	224	80	1.63	1.25	0.43	0.83	3.40	0.70	2.12	2.75	6.80	590	251	372	121
Grignolino	12.00	24.20	89.7	1.11	3.43	0.72	3.25	2.00	19.0	865	104	87	107	48	2.00	1.64	0.37	1.87	1.28	0.93	3.05	4.22	7.56	612	182	564	114
Grignolino	11.45	24.30	123.6	1.50	2.40	0.96	3.18	2.42	20.0	915	138	96	262	58	2.90	2.79	0.32	1.83	3.25	0.80	3.39	4.27	9.54	710	311	625	109
Grignolino	11.56	26.60	84.7	1.64	2.05	1.02	3.40	3.23	28.5	1160	92	119	490	94	3.18	5.08	0.47	1.87	6.00	0.93	3.69	4.37	7.68	687	538	465	183
Grignolino	12.42	25.00	110.0	2.13	4.43	0.93	3.23	2.73	26.5	1050	84	102	524	88	2.20	2.13	0.43	1.71	2.08	0.92	3.12	4.33	8.73	560	366	365	118
Grignolino	13.05	24.00	115.0	1.64	5.80	0.85	3.12	2.13	21.5	815	102	86	326	73	2.62	2.65	0.30	2.01	2.60	0.73	3.10	4.29	7.24	610	216	380	114
Grignolino	11.87	27.35	116.7	2.43	4.31	0.81	3.14	2.39	21.0	935	103	82	300	58	2.86	3.03	0.21	2.91	2.80	0.75	3.64	4.50	8.04	635	193	380	66
Grignolino	12.07	24.75	95.3	2.11	2.16	0.89	3.24	2.17	21.0	815	94	85	358	85	2.60	2.65	0.37	1.35	2.76	0.86	3.28	4.29	7.77	558	295	378	86
Grignolino	12.43	23.80	94.1	1.61	1.53	0.65	3.26	2.29	21.5	895	94	86	298	116	2.74	3.15	0.39	1.77	3.94	0.69	2.84	3.40	7.00	628	209	352	79
Grignolino	11.79	21.30	97.2	2.30	2.13	0.81	3.40	2.78	28.5	1075	105	92	345	70	2.13	2.24	0.58	1.76	3.00	0.97	2.44	4.00	7.17	634	173	466	56
Grignolino	12.37	23.30	102.6	1.91	1.63	0.96	3.21	2.30	24.5	925	120	88	302	79	2.22	2.45	0.40	1.90	2.12	0.89	2.78	3.70	8.85	530	166	342	108
Grignolino	12.04	22.80	111.8	1.40	4.30	0.74	3.20	2.38	22.0	930	98	80	138	41	2.10	1.75	0.42	1.35	2.60	0.79	2.57	4.40	6.57	585	144	580	115
Barbera	12.86	26.80	87.3	0.99	1.35	0.92	3.22	2.32	18.0	830	52	122	266	46	1.51	1.25	0.21	0.94	4.10	0.76	1.29	1.26	6.43	673	252	630	122
Barbera	12.88	23.95	78.9	1.85	2.99	0.98	3.50	2.40	20.0	795	55	104	269	72	1.30	1.22	0.24	0.83	5.40	0.74	1.42	1.34	10.10	918	319	530	102
Barbera	12.81	24.45	76.2	2.93	2.31	0.87	3.64	2.40	24.0	785	49	98	266	67	1.15	1.09	0.27	0.83	5.70	0.66	1.36	1.24	10.02	1095	258	560	132
Barbera	12.70	24.75	91.0	1.91	3.55	1.80	3.26	2.36	21.5	805	47	106	356	118	1.70	1.20	0.17	0.84	5.00	0.78	1.29	1.23	8.52	1020	238	600	121
Barbera	12.51	23.50	104.7	1.34	1.24	0.98	3.50	2.25	17.5	975	60	85	273	29	2.00	0.58	0.60	1.25	5.45	0.75	1.51	1.40	8.32	764	178	650	79
Barbera	12.60	23.60	80.6	2.26	2.46	0.97	3.31	2.20	18.5	760	103	94	275	77	1.62	0.66	0.63	0.94	7.10	0.73	1.58	1.37	6.47	573	174	695	100
Barbera	12.25	25.30	91.4	1.42	4.72	1.25	3.40	2.54	21.0	995	105	89	262	144	1.38	0.47	0.53	0.80	3.85	0.75	1.27	1.12	8.25	680	217	720	107
Barbera	12.53	27.10	99.8	1.88	5.51	1.19	3.30	2.64	25.0	930	100	96	360	6	1.79	0.60	0.63	1.10	5.00	0.82	1.69	1.80	8.35	821	230	515	139
Barbera	13.49	25.70	115.5	2.17	3.59	1.47	3.24	2.19	19.5	825	111	88	315	56	1.62	0.48	0.58	0.88	5.70	0.81	1.82	2.23	10.40	700	245	580	150
Barbera	12.84	26.20	82.0	1.79	2.96	1.26	3.50	2.61	24.0	925	48	101	398	15	2.32	0.60	0.53	0.81	4.92	0.89	2.15	2.25	10.60	940	269	590	132
Barbera	12.93	26.78	80.0	1.69	2.81	1.15	3.31	2.70	21.0	965	40	96	351	25	1.54	0.50	0.53	0.75	4.60	0.77	2.31	2.34	10.62	955	260	600	82
Barbera	13.36	24.12	97.8	2.83	2.56	0.77	3.35	2.35	20.0	880	47	89	235	71	1.40	0.50	0.37	0.64	5.60	0.70	2.47	2.60	10.41	814	216	780	106
Barbera	13.52	27.90	85.0	1.46	3.17	1.23	3.28	2.72	23.5	880	38	97	325	21	1.55	0.52	0.50	0.55	4.35	0.89	2.06	2.21	10.20	976	201	520	118
Barbera	13.62	25.52	93.7	2.70	4.95	1.56	3.41	2.35	20.0	805	57	92	191	16	2.00	0.80	0.47	1.02	4.40	0.91	2.05	2.55	8.90	899	205	550	140
Barbera	12.25	23.40	113.5	3.54	3.88	1.04	3.01	2.20	18.5	785	77	112	358	14	1.38	0.78	0.29	1.14	8.21	0.65	2.00	2.23	8.16	521	218	855	97
Barbera	13.16	22.90	117.9	3.15	3.57	1.18	3.14	2.15	21.0	805	88	102	456	17	1.50	0.55	0.43	1.30	4.00	0.60	1.68	2.24	5.61	696	252	830	63
Barbera	13.88	21.40	99.3	2.81	5.04	1.29	3.28	2.23	20.0	750	43	80	171	10	0.98	0.34	0.40	0.68	4.90	0.58	1.33	1.81	7.94	670	156	415	154
Barbera	12.87	24.35	98.9	2.51	4.61	1.25	3.18	2.48	21.5	830	63	86	366	50	1.70	0.65	0.47	0.86	7.65	0.54	1.86	2.10	8.52	806	213	625	122
Barbera	13.32	21.46	96.9	2.85	3.24	1.75	3.30	2.38	21.5	790	42	92	306	21	1.93	0.76	0.45	1.25	8.42	0.55	1.62	2.19	6.12	604	219	650	106
Barbera	13.08	26.80	120.6	2.90	3.90	1.11	3.16	2.36	21.5	790	73	113	303	50	1.41	1.39	0.34	1.14	9.40	0.57	1.33	1.26	7.36	733	164	550	114
Barbera	13.50	26.50	105.5	2.31	3.12	1.31	3.23	2.62	24.0	980	67	123	338	106	1.40	1.57	0.22	1.25	8.60	0.59	1.30	1.29	6.28	568	129	500	107
Barbera	12.79	23.40	117.8	3.12	2.67	0.82	3.21	2.48	22.0	890	53	112	407	127	1.48	1.36	0.24	1.26	10.80	0.48	1.47	1.40	7.00	898	154	480	91
Barbera	13.11	25.20	95.4	2.26	1.90	0.86	3.49	2.75	25.5	1140	74	116	289	55	2.20	1.28	0.26	1.56	7.10	0.61	1.33	1.25	8.57	905	249	425	125
Barbera	13.23	23.85	120.6	2.80	3.30	0.80	3.20	2.28	18.5	915	68	98	351	35	1.80	0.83	0.61	1.87	10.52	0.56	1.51	1.42	10.80	915	154	675	84
Barbera	12.58	21.75	102.7	2.92	1.29	0.79	3.21	2.10	20.0	875	107	103	368	100	1.48	0.58	0.53	1.40	7.60	0.58	1.55	1.34	7.52	924	142	640	100
Barbera	13.17	23.20	129.3	2.28	5.19	1.49	3.58	2.32	22.0	1045	102	93	241	84	1.74	0.63	0.61	1.55	7.90	0.60	1.48	1.31	9.50	969	207	725	84
Barbera	13.84	24.70	122.9	2.76	4.12	1.07	3.19	2.38	19.5	840	108	89	402	6	1.80	0.83	0.48	1.56	9.01	0.57	1.64	1.92	9.29	902	159	480	132
Barbera	12.45	25.35	105.9	2.23	3.03	1.24	3.62	2.64	27.0	1050	118	97	393	53	1.90	0.58	0.63	1.14	7.50	0.67	1.73	2.18	10.20	865	252	880	118
Barbera	14.34	29.10	97.5	2.73	1.68	1.60	3.42	2.70	25.0	1095	78	98	462	49	2.80	1.31	0.53	2.70	13.00	0.57	1.96	2.25	10.82	764	223	660	182
Barbera	13.48	26.95	102.5	3.75	1.67	1.37	3.41	2.64	22.5	1055	79	89	480	35	2.60	1.10	0.52	2.29	11.75	0.57	1.78	2.09	11.09	1080	250	620	160
Barbera	12.36	34.60	116.5	2.25	3.83	0.99	3.32	2.38	21.0	1035	112	88	394	28	2.30	0.92	0.50	1.04	7.65	0.56	1.58	2.00	9.29	636	154	520	127
Barbera	13.69	24.80	74.9	1.04	3.26	0.75	3.36	2.54	20.0	1010	54	107	394	21	1.83	0.56	0.50	0.80	5.88	0.96	1.82	2.61	9.31	653	275	680	130
Barbera	12.85	25.70	86.9	1.79	3.27	0.92	3.33	2.58	22.0	935	46	106	318	48	1.65	0.60	0.60	0.96	5.58	0.87	2.11	2.77	9.77	814	224	570	102
Barbera	12.96	23.30	97.9	2.66	3.45	1.31	3.11	2.35	18.5	795	35	106	257	11	1.39	0.70	0.40	0.94	5.28	0.68	1.75	2.00	10.13	667	212	675	123
Barbera	13.78	25.10	103.5	3.80	2.76	1.23	3.13	2.30	22.0	803	88	90	417	19	1.35	0.68	0.41	1.03	9.58	0.70	1.68	2.05	8.93	677	198	615	109
Barbera	13.73	24.65	92.6	2.91	4.36	1.10	3.31	2.26	22.5	785	96	88	360	34	1.28	0.47	0.52	1.15	6.62	0.78	1.75	2.15	9.67	670	275	520	131
Barbera	13.45	24.90	82.9	1.91	3.70	1.13	3.28	2.60	23.0	890	56	111	386	8	1.70	0.92	0.43	1.46	10.68	0.85	1.56	1.60	10.37	733	196	695	107
Barbera	12.82	22.40	119.9	3.86	3.37	0.96	2.98	2.30	19.5	810	81	88	308	14	1.48	0.66	0.40	0.97	10.26	0.72	1.75	1.90	8.45	589	158	685	132
Barbera	13.58	27.20	119.9	3.04	2.58	0.98	2.98	2.69	24.5	930	80	105	369	38	1.55	0.84	0.39	1.54	8.66	0.74	1.80	1.96	8.90	847	215	750	129
Barbera	13.40	28.15	137.8	3.48	4.60	1.34	3.06	2.86	25.0	1085	92	112	387	27	1.98	0.96	0.27	1.11	8.50	0.67	1.92	2.15	7.80	700	218	630	117
Barbera	12.20	23.70	107.3	3.23	3.03	0.74	3.08	2.32	19.0	845	87	96	265	56	1.25	0.49	0.40	0.73	5.50	0.66	1.83	2.80	7.90	854	224	510	77
Barbera	12.77	23.70	111.5	3.34	2.39	0.79	2.99	2.28	19.5	850	69	86	394	13	1.39	0.51	0.48	0.64	9.90	0.57	1.63	1.69	6.07	579	156	470	152
Barbera	14.16	23.82	118.2	3.63	2.51	1.12	3.10	2.48	20.0	840	73	91	319	15	1.68	0.70	0.44	1.24	9.70	0.62	1.71	1.90	8.93	953	196	660	135
Barbera	13.71	24.95	113.9	2.88	5.65	1.75	3.15	2.45	20.5	1035	72	95	298	12	1.68	0.61	0.52	1.06	7.70	0.64	1.74	1.94	9.90	1120	238	740	120
Barbera	13.40	24.60	126.2	2.94	3.91	1.25	3.12	2.48	23.0	860	84	102	490	15	1.80	0.75	0.43	1.41	7.30	0.70	1.56	1.93	7.58	855	226	750	96
Barbera	13.27	22.75	103.9	2.84	4.28	1.62	3.16	2.26	20.0	760	61	120	526	6	1.59	0.69	0.43	1.35	10.20	0.59	1.56	1.94	7.27	749	157	835	126
Barbera	13.17	23.45	113.9	3.87	2.59	1.59	3.17	2.37	20.0	785	62	120	534	6	1.65	0.68	0.53	1.46	9.30	0.60	1.62	2.05	11.16	1110	160	840	52
Barbera	14.13	27.20	125.9	3.18	4.10	1.43	3.21	2.74	24.5	930	53	96	315	35	2.05	0.76	0.56	1.35	9.20	0.61	1.60	1.87	11.28	857	198	560	112

Observed variables are:

colnames(df)

##  [1] "type"                         "Alcohol"                     
##  [3] "Sugar.free.extract"           "Fixed.acidity"               
##  [5] "Tartaric.acid"                "Malic.acid"                  
##  [7] "Uronic.acids"                 "pH"                          
##  [9] "Ash"                          "Alcalinity.of.ash"           
## [11] "Potassium"                    "Calcium"                     
## [13] "Magnesium"                    "Phosphate"                   
## [15] "Chloride"                     "Total.phenols"               
## [17] "Flavanoids"                   "Nonflavanoid.phenols"        
## [19] "Proanthocyanins"              "Color.intensity"             
## [21] "Hue"                          "OD280.OD315.of.diluted.wines"
## [23] "OD280.OD315.of.flavonoids"    "Glycerol"                    
## [25] "2.3.butanediol"               "Total.nitrogen"              
## [27] "Proline"                      "Methanol"

We can also divide the samples in three classes:

df %>% group_by(type) %>% summarise(count = n()) %>% kable() %>% kable_minimal(full_width = F)

type	count
Barbera	48
Barolo	59
Grignolino	71

#PCA

Preprocessing

Befor performing PCA you need to autoscale in order to have a dataset where all the columns have mean = 0 and standard deviation = 1

\[ X^*_{i,j} = \frac{X_{i,j} - \overline{X_i}}{S_{X_i}} \]

For all values within each column subtract their mean and then divide by their standard deviation

dfa = df[,-1]

dfa = data.frame(scale(dfa))
kable(dfa)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
  scroll_box( height = "600px", width = '910px')

Alcohol	Sugar.free.extract	Fixed.acidity	Tartaric.acid	Malic.acid	Uronic.acids	pH	Ash	Alcalinity.of.ash	Potassium	Calcium	Magnesium	Phosphate	Chloride	Total.phenols	Flavanoids	Nonflavanoid.phenols	Proanthocyanins	Color.intensity	Hue	OD280.OD315.of.diluted.wines	OD280.OD315.of.flavonoids	Glycerol	X2.3.butanediol	Total.nitrogen	Proline	Methanol
1.5143408	-0.2053617	-0.6700454	-1.2514422	-0.5606682	-0.7715621	0.5368170	0.2313998	-1.1663032	0.6446457	-0.5940655	1.9085215	-0.4861718	0.3696880	0.8067217	1.0319081	-0.6577078	1.2214385	0.2510088	0.3610679	1.8427215	2.0160386	0.2856855	0.1788922	-1.2542737	1.0101594	0.1257762
0.2455968	0.4558517	-0.6860711	-0.2528886	-0.4980086	-0.8111865	-0.0240248	-0.8256672	-2.4838405	-1.0830488	-0.1100276	0.0180940	0.3253303	0.5295045	0.5670481	0.7315653	-0.8184106	-0.5431887	-0.2924962	0.4048188	1.1103172	0.9232054	0.0712206	1.0708073	-0.6715702	0.9625263	-0.6420487
0.1963252	0.4558517	-0.9157718	-0.0943880	0.0211715	-0.2960697	1.2378692	1.1062139	-0.2679823	0.5139012	-0.2961961	0.0881098	1.4289731	0.0700320	0.8067217	1.2121137	-0.4970050	2.1299594	0.2682629	0.3173170	0.7863692	0.5401505	1.7452386	1.2074717	-0.5010228	1.3912237	0.6107181
1.6867914	0.2548071	-0.5738916	-0.6491400	-0.3458351	-0.7715621	0.8873431	0.4865539	-0.8069748	0.9715068	-1.1525708	0.9282998	2.3270354	-0.2895553	2.4844372	1.4623994	-0.9791134	1.0292513	1.1827317	-0.4264485	1.1807407	0.6302811	0.7861037	2.7827089	0.7212333	2.3280068	-1.2078143
0.2948684	0.3441603	-0.1144902	-1.1087916	0.2270533	0.7341638	0.8172379	1.8352256	0.4506745	1.9334124	-0.2961961	1.2783790	0.4659906	0.0300778	0.8067217	0.6614853	0.2261576	0.4002753	-0.3183774	0.3610679	0.4483365	0.2697588	0.8695068	0.4809925	-0.3731123	-0.0377675	-1.4906972
1.4773871	1.3940599	-0.3067978	0.2226132	-0.5159113	0.1794227	0.6069222	0.3043010	-1.2860793	-0.1211432	-0.2589624	0.8582840	0.5741909	-0.1097616	1.5576991	1.3622851	-0.1755994	0.6623487	0.7298108	0.4048188	0.3356589	0.2021608	1.2150336	0.9557215	1.7445176	2.2327407	-1.6927563
1.7114272	0.7775231	-1.1401306	-0.5698897	-0.4174461	0.1397983	0.8172379	0.3043010	-1.4657435	0.0749734	-0.4078971	-0.2619694	-0.6376522	-0.2296240	0.3273744	0.4912911	-0.4970050	0.6798202	0.0827810	0.2735661	1.3638418	1.0809339	0.1427089	1.4304505	1.9434895	1.7246550	-1.2078143
1.3049364	0.5005283	-0.6486779	-1.0612415	-0.1668075	0.8926613	1.6585005	0.8875103	-0.5674226	0.1216679	-1.0408697	1.4884265	1.4830732	0.0101008	0.4871569	0.4812796	-0.4166536	-0.5956034	-0.0034896	0.4485697	1.3638418	1.0809339	0.7861037	0.9557215	1.6592439	1.7405327	-0.3995777
2.2534149	0.6792346	-0.8623530	-0.2845887	-0.6233279	-0.9696839	-0.0240248	-0.7163155	-1.6454077	-1.0830488	-1.0781034	-0.1919535	0.8122315	-0.1097616	0.8067217	0.9518167	-0.5773564	0.6798202	0.0612134	0.5360715	0.3356589	0.0556987	0.6431271	0.6680069	2.7962264	0.9466487	1.2573075
1.0585784	0.7685878	-0.9157718	-0.1260881	-0.8829179	-0.9696839	-0.2343405	-0.3518096	-1.0465271	-0.8122210	-1.0036361	-0.1219377	0.2820502	0.0101008	1.0943301	1.1220109	-1.1398162	0.4526900	0.9325468	0.2298152	1.3215877	0.8668738	2.2873583	0.4018710	1.5455457	0.9466487	0.4490708
1.3542080	0.3575632	-0.7020967	-0.5698897	-0.1578561	-1.1678058	0.0460804	-0.2424578	-0.4476464	-0.4013099	-0.6312992	0.3681732	0.3686104	-0.0498304	1.0463954	1.2922052	-1.1398162	1.3786825	0.2984576	1.2798370	0.7863692	0.3260904	-0.1313297	1.6678150	1.9434895	2.4232729	0.5298945
1.3788438	1.3717216	-0.6807292	-0.7759404	-0.7665500	0.1794227	-0.7250771	-0.1695567	-0.8069748	-0.5040377	-0.6685329	-0.3319852	0.6391111	0.3097568	-0.1519728	0.4011882	-0.8184106	-0.0365136	-0.0250573	0.9298297	0.2934048	0.0669650	1.6141767	1.1643145	0.7496579	1.6928996	0.9744246
0.9230815	2.2205766	-0.5632079	-0.1260881	-0.5427655	-1.0885570	-0.8652875	0.1584986	-1.0465271	-1.2044544	-0.4823645	-0.7520802	0.9528919	3.8656749	0.4871569	0.7315653	-0.5773564	0.3828038	0.2337547	0.8423279	0.4060824	-0.0682309	2.0431066	0.3730995	0.6785965	1.8199211	2.1867796
2.1548717	2.2875915	0.7081588	0.1275128	-0.5427655	-0.7715621	-2.0570763	0.0855974	-2.4239525	0.2710901	-1.1898045	-0.6120485	1.5696335	-0.2695782	1.2860690	1.6626279	0.5475632	2.1299594	0.1474840	1.2798370	0.1666425	-0.1808941	2.0728934	0.2436280	-0.2452018	1.2800799	-0.1975185
1.6991093	0.8132643	-0.7127804	-0.0785379	-0.4174461	-0.9696839	-0.7250771	0.0491469	-2.2442883	0.4298512	-1.8227771	0.1581256	1.7102938	-0.1696928	1.6056339	1.6125708	-0.5773564	2.3920327	1.0533257	1.0610825	0.5469294	0.3824220	0.4286621	2.2216655	1.1760263	2.5407677	0.1661880
0.7752666	0.8356026	-0.8570111	-0.8234906	-0.4711544	-0.9696839	1.1677640	1.2155656	-0.6871987	0.2243957	-1.8600108	0.8582840	0.2171300	-0.2695782	0.8866129	0.8817367	-0.4970050	-0.2287007	0.9670551	1.4110897	0.3779130	0.1570956	-0.5304728	0.5744997	-0.1741404	1.7881657	-0.5208132
1.6005661	1.1706770	-0.5738916	-0.9344410	-0.3726892	-0.3753184	0.6770274	1.2884668	0.1512342	-0.1958543	1.1186840	1.4184107	1.6020936	-0.0298534	0.8067217	1.1119995	-0.2559508	0.6623487	0.4925666	0.4923206	0.0539650	0.1345629	0.2558987	0.7471284	0.9486298	1.6928996	0.1257762
1.0216247	0.4558517	-1.1080793	-0.1102380	-0.6859876	-0.9300596	0.8873431	0.9239609	0.1512342	0.2243957	-0.3706634	1.0683315	0.5850109	-0.1097616	1.0463954	1.3722966	0.3065090	0.2255598	0.6651078	0.7548261	-0.0587126	-0.3611552	0.3571738	-0.0728581	0.4654123	1.2165692	-0.4399895
1.4650692	0.5005283	-0.7288061	-0.2370385	-0.6680848	-0.3753184	0.5368170	0.4136527	-0.8968069	0.7753901	0.2995429	0.5782207	1.3315929	-0.7090737	1.6056339	1.9029021	-0.3363022	0.4701615	1.5709495	1.1923352	0.2934048	0.2134272	0.6192977	0.5457282	-0.1599281	2.9631140	1.0148365
0.7875845	1.0902591	0.3128599	-1.0295414	0.6835737	-0.3753184	-0.0240248	0.7052574	-1.2860793	1.4664679	1.2303850	1.1383473	0.4010705	0.0700320	0.6469393	1.0018738	-1.5415732	0.1207304	0.0180781	0.0110606	1.0539784	1.1485318	0.9409951	-0.0440866	-0.2025649	0.3115415	0.3682472
1.3049364	0.0180212	-0.7768830	-1.0453914	-0.6322793	0.3379202	1.1677640	-0.3153590	-1.0465271	0.2243957	0.0389071	1.8385057	-0.4537117	0.1898944	1.1262866	1.1420338	-0.9791134	0.8894789	0.2553223	0.5798225	1.5469428	0.8668738	0.8873788	0.6895855	-0.2309895	0.1051316	1.4189548
-0.0869865	1.5727662	0.8790989	-1.5050431	1.3101703	-0.0979479	-0.3044457	1.0333127	-0.2679823	0.3177846	0.0389071	0.1581256	-0.7674925	-0.0298534	0.1835703	0.3811654	-0.8987620	0.6798202	-0.2407339	0.3173170	1.2793336	0.7654769	1.8286416	-1.0295090	-0.0604421	0.0733763	0.5298945
0.8738098	1.0500502	-0.3014559	0.3652637	-0.4263975	1.1700319	0.1862908	-0.0237543	-0.8668629	-0.6161044	0.4112440	0.0881098	1.2017525	1.4084955	0.5031351	0.8517024	-0.7380592	0.1731451	-0.5426811	0.6673243	1.9553990	1.4977878	-0.0002677	-0.1232081	0.4085632	0.9148933	-0.0358712
-0.1855298	0.2324688	-0.8570111	-0.7283903	-0.6591334	-0.4941915	1.0275535	0.5594551	-0.5075345	0.7193568	0.8580482	-0.3319852	0.5417308	0.1898944	0.2954180	0.3411197	-0.8184106	-0.2287007	-0.4866052	0.5798225	1.4342653	0.9457381	0.1963251	-1.1805591	0.0958930	0.8513826	-0.3187540
0.6151339	-0.1249438	-0.2159859	-0.7125402	-0.4711544	0.1397983	0.8172379	0.8875103	0.1512342	1.0368790	-0.5940655	-0.2619694	1.2017525	-0.3295094	0.3753092	0.5813939	-0.6577078	0.1207304	-0.6634600	0.7110752	1.7018745	1.1485318	0.3810033	-0.4684656	-0.4441737	0.3115415	-0.9653433
0.0608283	0.1967275	-0.3922678	-1.3465425	-0.2563213	0.6549151	1.8688162	3.1109961	1.6484357	1.9987846	-0.5568318	1.6984740	1.8509542	0.3696880	0.5350916	0.6514739	0.8689688	0.5749909	-0.6375788	0.7548261	0.8286233	0.7316779	0.9112083	0.1501207	-0.0462298	0.2639084	0.5703063
0.4796370	0.8132643	-0.7127804	-0.7600904	-0.5069599	0.5360420	1.0976587	0.9239609	-1.0165830	0.5139012	-0.3706634	-0.4720169	0.3253303	-0.2296240	0.8866129	0.9117710	-0.1755994	-0.2461723	-0.1113279	-0.1639430	0.8567927	1.6442500	0.6848286	0.8766000	0.6217474	1.4229791	-1.0057552
0.3687759	-1.1525052	-0.9264555	-0.4113891	-0.5517168	0.5756664	0.9574483	-0.8256672	-0.7470867	0.0096012	-0.9664024	-0.4020010	0.7473114	-0.3494865	0.1675920	0.1609140	-0.7380592	-0.4208878	-0.4779781	0.2735661	0.2229813	0.1345629	0.5299373	0.1788922	1.5455457	1.7087773	-1.0461670
1.0708963	1.7961491	-0.9264555	-0.9819912	-0.3905920	-0.6526890	0.8172379	1.5800715	-0.0284300	1.9053957	-0.3706634	0.5082048	0.3361503	0.2498256	1.0463954	0.9418052	0.0654548	0.2954460	-0.2407339	1.2798370	1.1103172	0.8330748	0.4286621	-0.2167153	0.5506860	0.5338290	-0.4399895
1.2556648	-0.0355907	-0.8570111	-0.4589393	-0.5875224	-0.4941915	-0.3044457	-0.5705131	-1.0465271	-0.9429655	-0.5940655	-0.2619694	1.5696335	-0.2096470	0.5670481	0.3010740	-0.8184106	0.6798202	-0.1544632	0.3610679	1.3779265	0.8894064	0.6729139	-0.3102226	0.7354456	0.9148933	-0.3995777
0.8984457	0.6568963	-0.5578660	-0.7442403	-0.7486472	-1.0093083	-0.0240248	1.2155656	0.8998349	1.7372957	-0.0727939	0.0881098	0.7689514	-0.2096470	1.1262866	1.2221252	-0.5773564	1.3786825	0.2768900	1.0173315	0.1384731	0.0218997	0.9707819	0.4306424	1.2897246	1.7087773	0.4086590
0.7136771	1.3717216	-1.2629938	-1.3623926	-0.6054251	-0.7715621	-0.1642353	-0.0237543	-0.1182621	-0.7094933	-0.7430003	0.4381890	1.2991328	8.6801482	0.9025912	1.1620566	-1.1398162	0.6274055	0.7945138	0.5798225	0.3779130	0.0894976	1.1435453	-0.2311011	0.7780825	2.4391506	-0.0762830
0.8368561	0.7596525	-1.1134212	-0.6332899	-0.4532517	-1.1678058	0.6770274	-0.0237543	-0.6871987	1.7466346	-1.7110761	0.2981573	0.3577904	0.2498256	0.1995485	0.6614853	0.4672118	0.6623487	-0.5254270	1.1923352	0.3638283	0.0669650	2.4958659	0.0062634	0.1527421	0.7719942	1.2573075
0.9353994	0.6792346	-0.4563703	-0.3004387	-0.7217931	-0.2960697	0.6770274	1.2155656	0.0015140	0.8687790	-1.4504403	2.2586007	0.3145102	1.2886331	1.0463954	0.7115424	1.1100230	-0.4208878	0.1474840	1.2798370	0.5469294	0.3711557	-0.2862210	0.0566135	0.7780825	1.5500005	-0.0358712
0.6274518	0.4201104	-1.0867118	-1.1404918	-0.4801058	-0.8508108	0.3966065	1.0333127	-0.1482061	-0.2332099	-0.9291687	0.7182523	1.0719122	-0.2096470	0.0877008	0.5013025	-0.5773564	-0.0889283	-0.3701398	0.6235734	0.3638283	-0.0794972	0.7682316	-0.2311011	0.2380158	1.1054255	-0.9653433
0.5904981	0.3664985	-0.7875667	-0.8868908	-0.4711544	-0.8904352	1.0275535	0.1584986	0.3009543	-0.8589155	-1.0781034	0.0180940	0.5525509	-0.5692342	0.6469393	0.9518167	-0.8184106	0.4701615	0.0180781	0.3610679	1.2089101	1.1935971	-0.3577093	-1.4251165	0.2380158	0.5497067	-1.4098735
0.3441400	1.9748554	-0.3602166	-0.7917905	-0.6233279	-0.4545672	-0.0240248	1.7258738	-1.1962472	0.7753901	0.7463471	0.7182523	0.7148513	-0.5093030	0.4871569	0.6514739	-0.1755994	-0.4034163	-0.1975985	0.5798225	0.2370660	0.2134272	2.9128811	-1.1661734	-0.2452018	0.4226852	-0.1975185
0.0608283	-0.1249438	-0.7875667	-1.2989923	-0.6143765	-0.0979479	0.2563961	0.6688068	-0.4476464	1.3450624	0.2623092	-0.1219377	0.1846699	-0.8089590	0.2474832	0.4011882	-0.5773564	-0.2636438	-0.3485721	0.7110752	-0.1432208	-0.1245625	0.0414338	-0.7561801	-0.3020509	1.1371808	0.9744246
0.0854641	-0.4376799	-0.6273104	-1.3306924	-0.7486472	0.3379202	0.7471326	-0.9714696	-1.1962472	0.4578679	-0.1100276	-0.1219377	0.2279500	-0.9088444	0.1675920	0.6114282	-0.6577078	-0.3859447	-0.5858164	0.9735806	0.1103037	0.0669650	0.4107901	-0.5332013	-0.4157491	0.8672603	1.4189548
1.5020229	2.1982383	1.5575172	-0.2370385	1.4802466	-1.0885570	-1.3560241	0.5230045	-1.8849599	0.1310068	0.3740103	1.9785373	-0.9189729	0.2498256	1.1262866	1.0118852	-1.3005190	0.8545358	0.0180781	-0.2951957	1.2934183	0.7654769	2.1026802	2.2720156	-0.3731123	0.0416209	-0.3591658
0.6890413	0.5898814	-0.2854303	-0.6808401	-0.5606682	-0.0186991	0.1161856	-0.2060072	-0.9866390	0.0843123	-0.1100276	1.2083632	-0.5294519	0.1299632	1.3659602	1.2621709	-0.1755994	1.3087962	0.4623718	-0.0326903	1.0821478	0.6190147	0.5716388	0.0062634	0.0674684	0.1527647	0.3278353
0.5042728	0.9919707	0.9111501	-0.3321388	1.3459759	0.0209252	-0.7951823	-0.8985684	-0.2080942	-0.6161044	0.0016734	-0.6820644	0.2171300	0.1299632	0.2474832	0.6514739	-0.7380592	-0.1937576	-0.3356316	-0.2076939	0.5469294	0.4274873	0.2380266	-1.2021377	-0.1457158	0.9148933	-0.1571067
1.0832142	1.1260004	-0.3602166	0.6188646	-0.3995434	-1.0489327	0.1862908	0.8146092	-1.3459674	0.9248124	-0.2589624	0.0881098	1.4830732	0.0700320	1.5257427	1.5324794	-1.5415732	0.1906166	0.1604246	-0.3389467	1.3356724	1.1485318	-0.1194149	-0.4828513	0.6785965	1.1054255	0.4490708
0.2948684	0.1431157	0.8363639	-0.2687386	1.4712952	-1.1678058	-0.8652875	-0.2789084	-0.5973666	0.3644790	-0.5568318	0.2281415	0.2604101	-0.2096470	0.5510698	0.6014167	-0.3363022	0.1207304	-0.3011233	-0.6014521	0.5469294	0.1908945	-0.1194149	-1.1230162	0.0958930	-0.2124219	-0.1975185
0.0608283	-0.7057394	-0.3014559	-1.2355921	-0.5069599	-0.3753184	0.1862908	-0.9714696	-0.7470867	0.1870401	-1.0781034	0.5082048	0.4659906	-0.2695782	1.1262866	0.9718395	-0.6577078	0.7671780	-0.0078031	-0.3389467	1.0398937	0.9006728	0.6848286	2.2432441	-0.3304755	0.4385629	1.8230731
1.4897050	1.9525171	1.0286714	-0.4113891	1.5250035	-0.2168210	0.3265013	0.2678504	-0.1781502	0.4578679	-0.5568318	0.7882682	-0.4428917	-0.3494865	0.8866129	0.6214396	-0.4970050	-0.5956034	0.0784675	-0.3826976	1.0117244	0.9006728	0.7563169	-0.2311011	0.3232895	1.0577924	-0.8036960
1.6991093	2.4216212	0.2487574	-1.2038920	1.1221913	0.2982958	-1.0054980	-0.3153590	-1.0465271	-0.8682544	-0.2589624	0.1581256	0.4659906	0.1299632	1.5257427	1.1420338	-0.7380592	1.0467229	-0.0681926	0.3610679	1.1666560	0.6528137	0.3988753	0.2436280	-0.3304755	1.0101594	-0.7632842
1.1078500	0.0090859	-0.5578660	-0.1102380	-0.5875224	-1.1281814	-1.0054980	-0.8985684	-1.0465271	-1.1110655	0.1133745	0.0881098	1.2883127	-0.1497158	1.2860690	1.3622851	-1.2201676	0.9593651	0.4494312	-0.2076939	1.0117244	0.5964821	-0.0181398	-1.1661734	0.5648983	0.7561165	-1.3290498
1.3542080	0.3128867	-0.8356436	-0.2053384	-0.2831754	-0.3356941	-0.7250771	0.1220480	-0.2080942	-0.0090766	-0.1100276	0.2281415	1.2450326	0.0101008	0.7268305	0.8917481	-0.3363022	1.3786825	0.4925666	0.4923206	0.1948119	-0.1020298	0.9588671	-0.4540798	0.1101053	0.9942817	-1.2886380
1.1571216	0.6792346	-0.6914129	0.5554644	-0.5427655	-1.2470545	-0.5147614	-0.3518096	-0.6273106	-0.1211432	-1.4132066	0.5782207	0.5958310	0.6493669	0.9345477	1.5124565	-0.3363022	0.8545358	1.6572202	0.7110752	0.6877763	0.3598893	2.7579897	0.1213493	2.0145509	1.6293889	1.8230731
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1.0093068	0.4335134	-0.5952591	-0.2687386	-0.5248627	-0.5734403	0.1862908	0.1949492	-1.6454077	-0.8962710	-1.8227771	0.7882682	1.1584724	-0.3295094	2.5323719	1.7126851	-0.3363022	0.4876331	0.8592168	0.2298152	0.9131315	0.6190147	-0.7032362	-0.2023296	1.6876685	1.4071014	-0.8845197
0.9477173	-0.0355907	-1.1134212	-1.1246417	-0.3905920	-0.2960697	1.7987110	1.1426644	-0.7171427	0.4298512	-1.6738424	1.0683315	0.4335306	-0.0897846	1.1262866	0.7615996	0.2261576	0.1556735	0.5357019	0.7548261	0.4483365	0.2584925	-0.6436626	0.4522210	1.0196912	1.9945755	-0.0358712
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-0.1855298	0.1877922	0.0671336	-0.3321388	0.8357472	0.0209252	0.1862908	0.7781586	0.7501148	0.5045623	-1.1898045	0.4381890	-0.5078119	-0.3095323	-1.0307762	-1.4309028	1.9135370	-1.1022785	0.2251276	-0.3826976	-0.7066087	-0.2372257	0.5716388	0.5888854	-0.2452018	-0.5617309	-0.3187540
-0.0500328	-0.8844457	0.6547400	1.0468161	0.9968720	1.5662755	-1.3560241	-0.0602049	-0.2979263	-0.8028821	-1.5993750	0.4381890	-1.1678336	-1.0486838	-1.4462105	-1.3307885	0.3065090	-1.1372216	0.0957216	-1.2139649	-1.2136578	-1.1047324	0.7861037	-0.4684656	-0.4157491	-0.2282996	0.5298945
0.9600352	-0.0802672	0.9538852	2.8537227	0.3792268	1.2492806	-1.2158136	-0.2424578	0.7501148	-0.7281710	0.3740103	-0.6820644	0.5633709	-0.8888673	-1.5101235	-1.3508114	0.3868604	-0.9799776	1.9505403	-1.1264630	-1.3122506	-1.0484008	0.0712206	-0.3965369	-0.6147211	-0.4188318	-0.0358712
0.8984457	-0.2813119	0.3716206	1.4430676	1.8114477	0.7341638	0.0460804	-0.3882602	0.8998349	-0.8962710	0.6718797	-0.8220960	-0.0533707	-0.5892113	-1.6219712	-1.5610513	1.2707258	-0.7703189	0.6737349	-0.7764558	-1.2136578	-0.9357376	0.5120652	-0.4468870	0.4796246	-0.7205077	0.8531891
0.5535444	-0.1696204	-0.1465415	-0.1419382	1.2206565	0.8530369	-0.1642353	0.8510598	1.0495551	0.0843123	-0.8174676	0.7882682	0.2279500	-1.1086150	-0.9508850	-1.1105371	0.5475632	-0.2287007	2.4250288	-0.4701994	-1.4812670	-1.5553853	0.9290803	0.0062634	-0.6431456	-0.1647889	-0.1166948
-0.2224835	-1.2865349	1.8299530	2.9488230	0.9252610	0.1794227	-2.2673920	-0.2424578	0.0015140	-0.6627988	0.1133745	-0.8220960	-0.6160121	-0.9887526	-1.3024063	-1.3708342	0.3065090	-1.0848070	2.2438605	-1.0389612	-1.2136578	-1.2173956	-0.2147327	-1.0295090	-1.1832123	-0.1965443	0.8936010
0.7136771	0.8579409	1.8299530	1.6491183	0.2181019	0.2586714	-2.2673920	1.1791150	1.4987156	0.4578679	0.0761408	0.3681732	0.0440096	-0.5093030	-1.1905586	-1.1906285	0.2261576	-0.0889283	1.5536954	-0.9514594	-1.1432343	-1.1497977	0.0533485	0.8262499	-0.3731123	0.0098656	0.7723655
0.4919549	1.2823684	2.7861489	2.3465208	2.0262808	1.6851486	-1.7065502	1.7987750	1.6484357	1.9053957	0.5229450	0.8582840	0.2387701	-0.7290507	-0.5034942	-1.0704914	-0.7380592	-0.8402052	1.4846789	-1.2577158	-0.9742179	-0.9357376	-0.6019611	-0.2311011	-0.3304755	-0.3711987	0.2874235
-0.9861934	-0.7057394	1.1568765	1.9502694	0.6209140	-0.6923134	-1.5663397	-0.1695567	-0.1482061	-0.3359377	0.3367766	-0.2619694	-1.0812733	-0.1497158	-1.6699059	-1.5410285	0.3065090	-1.5041243	0.1906193	-1.3014667	-1.1009802	-0.2034267	-0.5423875	0.8766000	-0.2452018	-0.7522631	-1.3290498
-0.2840730	-0.7057394	1.3812353	2.1246200	0.0480257	-0.4941915	-2.1972867	-0.3153590	0.0015140	-0.2892432	-0.3334297	-0.9621277	0.3145102	-1.0087297	-1.4462105	-1.5210056	0.9493202	-1.6613683	2.0885733	-1.6952249	-1.3826741	-1.4539884	-1.6325843	-1.1014376	-1.2116369	-0.8792845	1.7018376
1.4281155	-0.6521275	1.7391411	2.5842717	0.1554422	0.8134126	-1.4261293	0.4136527	0.1512342	-0.3826321	-0.1844950	-0.6120485	-0.4969918	-0.9687756	-0.9828415	-1.3307885	0.6279146	-0.6130749	2.0023027	-1.4764703	-1.2699965	-1.2173956	0.0712206	1.5886935	-0.6431456	-0.2759327	1.0148365
0.8738098	-0.1472821	1.5094403	1.3955174	2.9661758	3.3097477	-1.0756032	0.3043010	0.3009543	1.4384513	-0.2217287	-0.3319852	-0.7242124	-1.0287068	-0.9828415	-1.4208913	1.2707258	-0.9275630	1.1395963	-1.3889685	-1.2277425	-1.1723304	0.6490844	2.7899018	-0.0462298	-0.0218898	0.4086590
0.4919549	-0.3036501	2.1664912	1.4906177	1.4086355	1.3285293	-1.2859188	0.4136527	1.0495551	-0.1958543	0.2250755	0.1581256	1.3532329	-0.9687756	-0.7911025	-1.2807314	0.5475632	-0.3160585	0.9670551	-1.1264630	-1.4812670	-1.1835967	-0.7330230	0.8837928	-0.2167772	0.0098656	-0.5612250
0.3318221	-1.1301669	0.9752527	1.3321172	1.7398366	2.7946309	-1.0054980	-0.3882602	0.1512342	-1.1297433	-0.6312992	1.4184107	1.7427539	-1.1485692	-1.1266456	-1.3407999	0.5475632	-0.4208878	2.2179793	-1.6077230	-1.4812670	-1.1723304	-0.9177011	0.1213493	-1.1974246	0.2797861	0.6511300
0.2086431	-0.8174308	1.5094403	2.9646731	0.2270533	2.6757578	-0.9353927	0.0126963	0.1512342	-0.8962710	-0.5940655	1.4184107	1.8293141	-1.1485692	-1.0307762	-1.3508114	1.3510772	-0.2287007	1.8297614	-1.5639721	-1.3967588	-1.0484008	1.3997118	2.7179731	-1.1547878	0.2956638	-2.3393456
1.3911617	0.8579409	2.1504656	1.8710191	1.5787118	2.0417679	-0.6549718	1.3613680	1.4987156	0.4578679	-0.9291687	-0.2619694	-0.5402719	-0.5692342	-0.3916465	-1.2707200	1.5921314	-0.4208878	1.7866261	-1.5202212	-1.4249282	-1.2511946	1.4712001	0.8981786	-0.6147211	-0.5934863	0.0853643

Correlation matrix

Let’s generate the correlation matrix (27 rows and 27 columns)

dfa_cor = data.frame(cor(dfa))
#datatable(dfa_cor,extensions = 'FixedColumns',options = list( scrollX = TRUE, pageLength= 10)) %>%
 # formatStyle(1:27,backgroundColor = styleEqual(c(1:20), 'yellow'))

kable(dfa_cor)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
  scroll_box( height = "600px", width = '910px')

	Alcohol	Sugar.free.extract	Fixed.acidity	Tartaric.acid	Malic.acid	Uronic.acids	pH	Ash	Alcalinity.of.ash	Potassium	Calcium	Magnesium	Phosphate	Chloride	Total.phenols	Flavanoids	Nonflavanoid.phenols	Proanthocyanins	Color.intensity	Hue	OD280.OD315.of.diluted.wines	OD280.OD315.of.flavonoids	Glycerol	X2.3.butanediol	Total.nitrogen	Proline	Methanol
Alcohol	1.0000000	0.4124031	-0.0400770	-0.0195719	0.0943969	0.1072329	0.0080560	0.2115446	-0.3102351	0.0005526	-0.5035553	0.2707982	0.3788148	-0.0421810	0.2891011	0.2368149	-0.1559295	0.1366979	0.5463642	-0.0718353	0.0723432	-0.0878576	0.5074500	0.4074027	0.1607410	0.6437200	0.0898249
Sugar.free.extract	0.4124031	1.0000000	0.0719314	-0.2400749	0.1484639	0.0187298	-0.0202150	0.4945495	-0.0897664	0.3384123	-0.0706575	0.2209219	0.2889401	0.0870562	0.4061156	0.3680170	-0.1184863	0.2523949	0.1906822	0.0693538	0.2403449	0.1216317	0.5405946	0.1888727	0.2040697	0.3786292	0.1605151
Fixed.acidity	-0.0400770	0.0719314	1.0000000	0.5675909	0.6877515	0.4355117	-0.5569699	0.0779802	0.2523674	0.1202581	0.2198174	-0.0732503	-0.1621801	-0.2209237	-0.3272809	-0.4425712	0.3384899	-0.1769754	0.3688295	-0.6675706	-0.4667117	-0.3368467	-0.0257136	0.1332041	-0.2860797	-0.3335044	0.0187283
Tartaric.acid	-0.0195719	-0.2400749	0.5675909	1.0000000	0.2839947	0.3666198	-0.4543328	-0.1131098	0.1612928	-0.1506238	0.0854281	-0.0509865	0.0129849	-0.2071491	-0.4184790	-0.5143300	0.2504155	-0.1916546	0.4793438	-0.4826248	-0.5115558	-0.4453052	-0.1356825	0.1464582	-0.1675758	-0.2295639	0.0373755
Malic.acid	0.0943969	0.1484639	0.6877515	0.2839947	1.0000000	0.4819607	-0.3267622	0.1640455	0.2885004	0.0997244	0.0551196	-0.0545751	-0.1990815	-0.2423567	-0.3351670	-0.4110066	0.2929771	-0.2207462	0.2489853	-0.5613720	-0.3687104	-0.2767655	0.0558314	0.1251496	-0.1843969	-0.1920106	0.0548492
Uronic.acids	0.1072329	0.0187298	0.4355117	0.3666198	0.4819607	1.0000000	-0.0298627	0.2534374	0.3697245	0.1008272	-0.0258082	0.0991191	0.0568225	-0.2387192	-0.2908666	-0.4634240	0.3367068	-0.2397020	0.3564417	-0.4395001	-0.4785483	-0.4327349	0.0304916	0.2835991	-0.1350174	-0.1226900	0.1326399
pH	0.0080560	-0.0202150	-0.5569699	-0.4543328	-0.3267622	-0.0298627	1.0000000	0.3211003	0.2346881	0.3369130	-0.1353547	0.0502152	-0.0238014	0.0298760	0.1543275	0.1472205	0.0091876	-0.0260850	-0.1669499	0.2250022	0.1862118	0.1432470	0.0893005	0.1274578	0.1633942	0.1562395	-0.0497973
Ash	0.2115446	0.4945495	0.0779802	-0.1131098	0.1640455	0.2534374	0.3211003	1.0000000	0.4433672	0.6807299	-0.1149148	0.2865867	0.2491846	-0.0836635	0.1289795	0.1150773	0.1862304	0.0096519	0.2588873	-0.0747249	0.0039112	-0.0147851	0.3044197	0.1605515	0.1822634	0.2236263	0.0781793
Alcalinity.of.ash	-0.3102351	-0.0897664	0.2523674	0.1612928	0.2885004	0.3697245	0.2346881	0.4433672	1.0000000	0.3954162	0.2064289	-0.0833331	-0.2031736	-0.1061559	-0.3211133	-0.3513699	0.3619217	-0.1973268	0.0187320	-0.2739343	-0.2767685	-0.1535432	-0.1513507	-0.0471761	-0.1320424	-0.4405969	0.0444520
Potassium	0.0005526	0.3384123	0.1202581	-0.1506238	0.0997244	0.1008272	0.3369130	0.6807299	0.3954162	1.0000000	0.0514741	0.0774548	0.0431303	-0.0995655	0.1106805	0.1118491	0.2501900	0.1206613	0.1028338	-0.0404874	0.0851523	0.1286263	0.2419732	0.1162352	0.0782048	0.0587181	0.1894566
Calcium	-0.5035553	-0.0706575	0.2198174	0.0854281	0.0551196	-0.0258082	-0.1353547	-0.1149148	0.2064289	0.0514741	1.0000000	-0.0070412	-0.1917079	0.0288365	-0.0889970	-0.0821943	0.1154874	0.1967054	-0.3327608	-0.0083293	0.0297866	0.1370642	-0.2333020	-0.2853701	-0.1399953	-0.3463332	-0.1056329
Magnesium	0.2707982	0.2209219	-0.0732503	-0.0509865	-0.0545751	0.0991191	0.0502152	0.2865867	-0.0833331	0.0774548	-0.0070412	1.0000000	0.4132108	0.0627266	0.2144012	0.1957838	-0.2562940	0.2364406	0.1999500	0.0554219	0.0660039	-0.0430884	0.1096198	0.2021825	0.1842797	0.3933508	-0.1282879
Phosphate	0.3788148	0.2889401	-0.1621801	0.0129849	-0.1990815	0.0568225	-0.0238014	0.2491846	-0.2031736	0.0431303	-0.1917079	0.4132108	1.0000000	0.0970560	0.4530556	0.3952801	-0.2074820	0.3673048	0.3063964	0.2002422	0.1915034	0.0774151	0.2403397	0.1419035	0.2482478	0.5253342	0.0163679
Chloride	-0.0421810	0.0870562	-0.2209237	-0.2071491	-0.2423567	-0.2387192	0.0298760	-0.0836635	-0.1061559	-0.0995655	0.0288365	0.0627266	0.0970560	1.0000000	0.1883902	0.2641855	-0.2071262	0.1478057	-0.1303209	0.1869861	0.1832014	0.1221586	0.0399425	-0.0464040	0.0453626	0.0882419	0.0727942
Total.phenols	0.2891011	0.4061156	-0.3272809	-0.4184790	-0.3351670	-0.2908666	0.1543275	0.1289795	-0.3211133	0.1106805	-0.0889970	0.2144012	0.4530556	0.1883902	1.0000000	0.8645635	-0.4499353	0.6124131	-0.0551364	0.4335018	0.6999494	0.5966330	0.2499350	0.0310428	0.2813534	0.4981149	-0.0060915
Flavanoids	0.2368149	0.3680170	-0.4425712	-0.5143300	-0.4110066	-0.4634240	0.1472205	0.1150773	-0.3513699	0.1118491	-0.0821943	0.1957838	0.3952801	0.2641855	0.8645635	1.0000000	-0.5378996	0.6526918	-0.1723794	0.5433903	0.7871939	0.6785504	0.2113079	-0.0784984	0.3346486	0.4941931	-0.0108081
Nonflavanoid.phenols	-0.1559295	-0.1184863	0.3384899	0.2504155	0.2929771	0.3367068	0.0091876	0.1862304	0.3619217	0.2501900	0.1154874	-0.2562940	-0.2074820	-0.2071262	-0.4499353	-0.5378996	1.0000000	-0.3658451	0.1390570	-0.2626388	-0.5032696	-0.3991033	-0.0204900	0.0649589	-0.0695854	-0.3113852	0.0529947
Proanthocyanins	0.1366979	0.2523949	-0.1769754	-0.1916546	-0.2207462	-0.2397020	-0.0260850	0.0096519	-0.1973268	0.1206613	0.1967054	0.2364406	0.3673048	0.1478057	0.6124131	0.6526918	-0.3658451	1.0000000	-0.0252499	0.2955280	0.5190671	0.4673242	0.1559191	0.0110107	0.0385652	0.3304167	-0.0114812
Color.intensity	0.5463642	0.1906822	0.3688295	0.4793438	0.2489853	0.3564417	-0.1669499	0.2588873	0.0187320	0.1028338	-0.3327608	0.1999500	0.3063964	-0.1303209	-0.0551364	-0.1723794	0.1390570	-0.0252499	1.0000000	-0.5219100	-0.4288149	-0.5067624	0.2945091	0.3831965	-0.0622228	0.3161001	0.1906663
Hue	-0.0718353	0.0693538	-0.6675706	-0.4826248	-0.5613720	-0.4395001	0.2250022	-0.0747249	-0.2739343	-0.0404874	-0.0083293	0.0554219	0.2002422	0.1869861	0.4335018	0.5433903	-0.2626388	0.2955280	-0.5219100	1.0000000	0.5653701	0.4711945	0.0339406	-0.2026795	0.2473513	0.2362272	-0.0037564
OD280.OD315.of.diluted.wines	0.0723432	0.2403449	-0.4667117	-0.5115558	-0.3687104	-0.4785483	0.1862118	0.0039112	-0.2767685	0.0851523	0.0297866	0.0660039	0.1915034	0.1832014	0.6999494	0.7871939	-0.5032696	0.5190671	-0.4288149	0.5653701	1.0000000	0.9138155	0.1725603	-0.1817294	0.2778624	0.3127611	-0.0660986
OD280.OD315.of.flavonoids	-0.0878576	0.1216317	-0.3368467	-0.4453052	-0.2767655	-0.4327349	0.1432470	-0.0147851	-0.1535432	0.1286263	0.1370642	-0.0430884	0.0774151	0.1221586	0.5966330	0.6785504	-0.3991033	0.4673242	-0.5067624	0.4711945	0.9138155	1.0000000	0.0451278	-0.2645117	0.1834899	0.1494997	-0.0827086
Glycerol	0.5074500	0.5405946	-0.0257136	-0.1356825	0.0558314	0.0304916	0.0893005	0.3044197	-0.1513507	0.2419732	-0.2333020	0.1096198	0.2403397	0.0399425	0.2499350	0.2113079	-0.0204900	0.1559191	0.2945091	0.0339406	0.1725603	0.0451278	1.0000000	0.4489515	0.1633914	0.4150893	0.1868202
X2.3.butanediol	0.4074027	0.1888727	0.1332041	0.1464582	0.1251496	0.2835991	0.1274578	0.1605515	-0.0471761	0.1162352	-0.2853701	0.2021825	0.1419035	-0.0464040	0.0310428	-0.0784984	0.0649589	0.0110107	0.3831965	-0.2026795	-0.1817294	-0.2645117	0.4489515	1.0000000	0.0507209	0.2425320	0.0424956
Total.nitrogen	0.1607410	0.2040697	-0.2860797	-0.1675758	-0.1843969	-0.1350174	0.1633942	0.1822634	-0.1320424	0.0782048	-0.1399953	0.1842797	0.2482478	0.0453626	0.2813534	0.3346486	-0.0695854	0.0385652	-0.0622228	0.2473513	0.2778624	0.1834899	0.1633914	0.0507209	1.0000000	0.3847329	0.0248949
Proline	0.6437200	0.3786292	-0.3335044	-0.2295639	-0.1920106	-0.1226900	0.1562395	0.2236263	-0.4405969	0.0587181	-0.3463332	0.3933508	0.5253342	0.0882419	0.4981149	0.4941931	-0.3113852	0.3304167	0.3161001	0.2362272	0.3127611	0.1494997	0.4150893	0.2425320	0.3847329	1.0000000	-0.0282840
Methanol	0.0898249	0.1605151	0.0187283	0.0373755	0.0548492	0.1326399	-0.0497973	0.0781793	0.0444520	0.1894566	-0.1056329	-0.1282879	0.0163679	0.0727942	-0.0060915	-0.0108081	0.0529947	-0.0114812	0.1906663	-0.0037564	-0.0660986	-0.0827086	0.1868202	0.0424956	0.0248949	-0.0282840	1.0000000

Eigenvalues

Find eigenvalues of the correlation matrix,i.e., given the matrix \({\bf C}\) finding all the scalars \(\lambda\) and vectors \({\bf v}\) for which

\[ {\bf Cv} = {\bf \lambda v} \]

\({\bf C}\) is a simmetric matrix, so his eigenvalues will belong to \(\mathbb{R}\)

autovalori = eigen(dfa_cor)
autovalori_df = data.frame('PC'= c(1:length(autovalori$values)), 'Eigenvalues' = autovalori$values )

kable(autovalori_df)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
 scroll_box( height = "600px")

PC	Eigenvalues
1	6.8317794
2	4.2515407
3	2.5280146
4	1.9778221
5	1.3932847
6	1.1251778
7	1.0024894
8	0.9500365
9	0.8529229
10	0.7537384
11	0.7253604
12	0.6385046
13	0.5406406
14	0.4784583
15	0.4391382
16	0.3789690
17	0.3399381
18	0.3200851
19	0.2755318
20	0.2431034
21	0.2144411
22	0.2000665
23	0.1654097
24	0.1323651
25	0.1093742
26	0.0813498
27	0.0504575

Scree plot

You can repesent eigenvalues in relative terms as well

pca = prcomp(dfa)
var = pca$sdev^2
pca_var = round(var/sum(var)*100, 2)

pc = pca(dfa, scale = F)

a = c(1:length(autovalori$values))
pc_names = c()

for (i in a) {
  pc_names = append(pc_names, paste('PC',i,sep ='' ))
}


autovalori_df = data.frame('PC' = c(1:length(autovalori$values)),'Eigenvalues' = pca_var )
autovalori_df1 = autovalori_df

rownames(autovalori_df) = pc_names
autovalori_df1[2] = lapply(autovalori_df1[2], paste0, '%')

kable(autovalori_df1)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
  scroll_box( height = "600px")

PC	Eigenvalues
1	25.3%
2	15.75%
3	9.36%
4	7.33%
5	5.16%
6	4.17%
7	3.71%
8	3.52%
9	3.16%
10	2.79%
11	2.69%
12	2.36%
13	2%
14	1.77%
15	1.63%
16	1.4%
17	1.26%
18	1.19%
19	1.02%
20	0.9%
21	0.79%
22	0.74%
23	0.61%
24	0.49%
25	0.41%
26	0.3%
27	0.19%

autovalori_df2 = autovalori_df[1:9,]

p = ggplot(autovalori_df, aes(y=Eigenvalues,x = reorder(PC, -Eigenvalues)))+ 
  geom_col(width = 0.8, fill = 'cornflowerblue')+ 
  geom_line(aes(x=PC))+
  geom_point()+
  theme_classic()+
  geom_text(label = autovalori_df1$Eigenvalues, size = 3, nudge_y = 1.5, nudge_x = 0.6, angle = 30)+
  ylim(0,27)+
  labs(x='PC',y='Explained variance (%)')+
  theme(axis.text.x = element_text(size = 9, angle = 0))+
  ggtitle('Scree Plot')

ggplotly(p)

---

Loadings

We talk before about eigenvectors, in PCA they’re called loadings. For the first two principal components loading vectors are

loadingdf = data.frame(autovalori$vectors[,1:2])

colnames(loadingdf) = c('V1', 'V2')
loadingdf$Variable = colnames(df[-1])

kable(loadingdf)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
 scroll_box( height = "500px")

V1	V2	Variable
0.0947178	-0.3605457	Alcohol
0.1305410	-0.2789443	Sugar.free.extract
-0.2572863	-0.1233457	Fixed.acidity
-0.2410748	-0.0847243	Tartaric.acid
-0.2178324	-0.1480722	Malic.acid
-0.2101676	-0.2022898	Uronic.acids
0.1112612	-0.0026499	pH
0.0224119	-0.2757054	Ash
-0.1699383	0.0046834	Alcalinity.of.ash
0.0206117	-0.1636632	Potassium
-0.0491952	0.1995560	Calcium
0.0940340	-0.1974412	Magnesium
0.1588299	-0.2366248	Phosphate
0.1153329	0.0555492	Chloride
0.3126062	-0.0906483	Total.phenols
0.3462961	-0.0310953	Flavanoids
-0.2233480	-0.0340345	Nonflavanoid.phenols
0.2278198	-0.0454079	Proanthocyanins
-0.1133362	-0.3693302	Color.intensity
0.2662477	0.1508639	Hue
0.3246313	0.0866188	OD280.OD315.of.diluted.wines
0.2716018	0.1477125	OD280.OD315.of.flavonoids
0.1008240	-0.2996720	Glycerol
-0.0285027	-0.2892599	2.3.butanediol
0.1510805	-0.0892620	Total.nitrogen
0.2228657	-0.2727261	Proline
-0.0169842	-0.0976458	Methanol

loadings = as.matrix(loadingdf[,1:2])

---

Scores

Dot product between each loading vector \({\bf v}\) and each row \(\bf{x}\) of the dataset gives the so-called score vectors \(\bf{t}\). For the first PC score vector will be

\[ {\bf t_1} = PC1 = { \bf v1 \cdot X} \] For \(m\) variables  

\[ PC_{1,m} = v_{1,1}x_1+v_{1,2}x_2+...+v_{1,m}x_m \]

Or, in scalar notation

\[ {\bf PC1_i} = || {\bf v1} ||*|| {\bf x_i} ||*\cos\theta \qquad \qquad \textrm{con} \quad \theta \in [0,\pi] \]

---

For \(PC1\) and \(PC2\) score vectors are

scoredf = as.matrix(dfa) %*% loadings

pca_df = data.frame(scoredf)
colnames(pca_df) = c('PC1','PC2')
pca_df$Type = df$type


kable(pca_df)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
 scroll_box( height = "600px")

PC1	PC2	Type
3.6308600	-0.6292087	Barolo
2.4400531	0.3574711	Barolo
2.9604247	-2.1851389	Barolo
4.1730598	-3.8371757	Barolo
1.3808962	-1.5983210	Barolo
3.1071849	-2.8943718	Barolo
2.9821856	-1.3610763	Barolo
3.0215099	-2.4866169	Barolo
3.1054514	-1.6262975	Barolo
3.4380875	-1.5870281	Barolo
3.7167079	-1.6407545	Barolo
2.2156140	-1.9559817	Barolo
3.1093151	-1.8686257	Barolo
3.1033252	-3.0104960	Barolo
4.3312544	-3.3834754	Barolo
2.7461945	-1.6536923	Barolo
2.7388679	-2.4480227	Barolo
2.2908597	-1.5470332	Barolo
3.3815226	-2.8328371	Barolo
2.3994991	-1.2343417	Barolo
3.1369044	-0.9624110	Barolo
1.4898105	-0.7279734	Barolo
2.7595049	-0.4237672	Barolo
2.4550198	0.8141001	Barolo
2.2989926	-0.1393205	Barolo
2.1381058	-2.0901235	Barolo
2.5831589	-1.2601220	Barolo
1.6179669	-0.2181538	Barolo
3.2716582	-1.3456544	Barolo
2.8389313	-0.3431892	Barolo
3.0493534	-2.0541357	Barolo
4.5437015	-1.3312017	Barolo
2.6637058	-1.5407107	Barolo
2.4543365	-1.8096604	Barolo
2.2961557	-0.8516623	Barolo
2.7553028	0.5545296	Barolo
2.1705141	-1.6150722	Barolo
1.3692965	-0.0587028	Barolo
1.5903138	0.4884558	Barolo
2.0673947	-2.7657933	Barolo
2.4894792	-0.7831143	Barolo
0.5674966	-0.0561462	Barolo
3.4274759	-1.4377863	Barolo
0.4706982	0.0417069	Barolo
2.2770015	-0.8318321	Barolo
1.3278129	-2.0080217	Barolo
2.7108450	-1.6829857	Barolo
2.9112307	0.1441564	Barolo
2.1546086	-1.2992650	Barolo
3.2743058	-2.8366165	Barolo
3.0882041	-0.4708518	Barolo
3.5516567	-1.6564722	Barolo
3.7187677	-1.5063930	Barolo
2.8659766	-1.7443776	Barolo
2.5899480	-0.3590137	Barolo
2.4616163	-0.0495328	Barolo
3.0401335	-1.9680481	Barolo
2.0032499	-1.2597682	Barolo
3.0641206	-2.0006794	Barolo
-2.0884339	4.4367256	Grignolino
-1.3118828	1.9565697	Grignolino
-2.0524475	1.1059742	Grignolino
-0.1551462	1.5256468	Grignolino
2.2757136	2.1411336	Grignolino
0.1549999	2.4972307	Grignolino
1.2584024	0.4249755	Grignolino
1.7766068	2.8242968	Grignolino
1.0332506	3.5687698	Grignolino
-0.5003386	-0.0020774	Grignolino
0.4549277	2.0188020	Grignolino
-1.0632387	2.6541637	Grignolino
2.1970273	0.9252274	Grignolino
-0.0876740	2.6350332	Grignolino
3.2407141	-0.9291790	Grignolino
1.7422561	2.4818928	Grignolino
-0.9264655	3.7936989	Grignolino
0.4068257	1.9654843	Grignolino
-1.5180199	2.0946467	Grignolino
0.9719135	2.3654701	Grignolino
0.4253382	0.8473329	Grignolino
1.0466202	3.8455100	Grignolino
1.6257835	2.0034056	Grignolino
0.6179027	3.1502434	Grignolino
-2.7661843	0.7623246	Grignolino
0.8984946	2.1500607	Grignolino
1.0797038	2.3574108	Grignolino
-0.4853396	2.4245825	Grignolino
0.4198705	2.6541453	Grignolino
-0.3943813	2.2573790	Grignolino
-0.0561648	2.4184422	Grignolino
-0.9645965	2.2614618	Grignolino
-0.9821298	2.3090858	Grignolino
-1.4558716	1.8565688	Grignolino
0.7607398	3.0168495	Grignolino
1.3367742	0.1995947	Grignolino
2.0049181	1.2904155	Grignolino
-0.2593154	0.9354176	Grignolino
1.7906397	2.0275219	Grignolino
2.1392142	1.6159967	Grignolino
0.2836264	1.1006212	Grignolino
0.7908182	3.1525499	Grignolino
-0.3382040	3.7858558	Grignolino
0.3722644	2.6817709	Grignolino
0.0476232	2.9021583	Grignolino
1.4347165	2.0307499	Grignolino
-1.1586059	2.0504316	Grignolino
0.6078082	2.2181697	Grignolino
-1.8286098	1.7093764	Grignolino
0.2843367	3.4061021	Grignolino
2.2556971	1.2524388	Grignolino
0.4295913	2.4880918	Grignolino
-0.4663111	2.1866433	Grignolino
-0.5838877	-0.8999848	Grignolino
-0.3006135	2.8731598	Grignolino
-0.2337933	2.4665992	Grignolino
-0.4619611	3.9714932	Grignolino
0.0589802	3.5258207	Grignolino
0.2074522	1.3310928	Grignolino
-2.4080265	2.3841260	Grignolino
-0.3702052	3.6531893	Grignolino
0.4498231	1.5467709	Grignolino
2.7407280	-1.4536995	Grignolino
-0.2252235	0.0779608	Grignolino
-0.6646233	1.7130359	Grignolino
0.4922118	1.6112849	Grignolino
0.3029392	2.5584966	Grignolino
0.1965154	2.3740318	Grignolino
-1.3228126	2.1620338	Grignolino
-0.7170673	2.5394542	Grignolino
-1.9196053	2.9246339	Grignolino
-1.5573691	0.3752379	Barbera
-2.2055050	-0.5847499	Barbera
-2.9884890	-1.0340765	Barbera
-3.1004210	-1.5971030	Barbera
-2.7300472	0.4903295	Barbera
-3.5971717	1.3538013	Barbera
-3.8366155	0.1940621	Barbera
-4.0212313	-1.2236204	Barbera
-3.7957193	-0.8228648	Barbera
-1.8872972	-1.9205438	Barbera
-2.1643027	-1.6168873	Barbera
-2.4710001	-0.3665622	Barbera
-2.6102608	-1.8628066	Barbera
-3.3918646	-1.0758938	Barbera
-3.7504996	-0.1591000	Barbera
-3.8912280	0.1874222	Barbera
-5.6010922	0.2597836	Barbera
-4.1348640	-1.2994407	Barbera
-4.3420472	-0.6589090	Barbera
-4.4426665	-1.5560849	Barbera
-3.5038037	-1.5298532	Barbera
-3.7355479	-1.5568556	Barbera
-2.2378501	-1.9207520	Barbera
-3.8957122	-2.2757988	Barbera
-3.8346097	0.2765473	Barbera
-4.8687403	-2.0711920	Barbera
-4.1931138	-2.0368152	Barbera
-3.2751077	-1.9981468	Barbera
-1.7592127	-5.1243595	Barbera
-2.5974194	-4.6675257	Barbera
-3.1312710	-1.8884911	Barbera
-1.1345177	-0.9471860	Barbera
-2.2456814	-0.8584042	Barbera
-3.6906983	-0.7321010	Barbera
-4.2252261	-1.4553541	Barbera
-3.7821678	-0.6720054	Barbera
-2.6940927	-2.5314831	Barbera
-4.8594426	-0.3894455	Barbera
-3.3361836	-2.5746286	Barbera
-4.0655334	-3.1446850	Barbera
-3.8424993	0.8950589	Barbera
-4.9337046	0.0243347	Barbera
-4.2722408	-2.4156104	Barbera
-4.9345429	-3.6757807	Barbera
-3.9221483	-2.0850240	Barbera
-4.2542812	-2.4593670	Barbera
-4.1401235	-3.6508823	Barbera
-4.4790529	-3.9402470	Barbera

Plots

scoreplot = ggplot(pca_df, aes(PC1,PC2*-1, color=Type))+geom_point(size = 0.8)+
  xlab(paste('PC1 - ', pca_var[1], '%'))+
  ylab(paste('PC2 - ', pca_var[2], '%'))+
  theme_bw()+
  theme(plot.title = element_text(hjust = 0.5))+
  geom_hline(yintercept = 0, alpha= 0.2, linetype = 'dashed')+
  geom_vline(xintercept = 0, alpha= 0.2, linetype = 'dashed')+
  stat_ellipse()

ggplotly(scoreplot)

---

From the graph you can appreciate how the three types of wine are arranged in 3 main clusters

However, there is no further information concerning the original variables and their influence onto the data variability along major components

Then a loading plot will be useful

nomi = colnames(df[2:28])

loadingplot = ggplot(loadingdf, aes(V1,V2*-1))+geom_point(color= 'white')+
  xlab(paste('PC1 - ', pca_var[1], '%'))+
  ylab(paste('PC2 - ', pca_var[2], '%'))+
  geom_text(label=nomi, color='black', size=3)+
  #geom_label(label=nomi,size= 3, fill= 'cornflowerblue', color= 'white', fontface= 'bold')+
  geom_segment(aes(xend=0, yend=0), color="orange", alpha= 0.3) +
  ggtitle('Loading plot')+theme_bw()+
  theme(plot.title = element_text(hjust = 0.5))+
  geom_hline(yintercept = 0, alpha= 0.2, linetype = 'dashed')+
  geom_vline(xintercept = 0, alpha= 0.2, linetype = 'dashed')

ggplotly(loadingplot)

biplot = ggplot()+geom_point(data=pca_df, aes(PC1,PC2*-1, color=Type))+
  xlab(paste('PC1 - ', pca_var[1], '%'))+
  ylab(paste('PC2 - ', pca_var[2], '%'))+
  ggtitle('Biplot')+theme_bw()+
  geom_text(data = loadingdf,aes(V1*12,V2*-12), label = nomi, size=2.5)+
  theme(plot.title = element_text(hjust = 0.5))+
  geom_hline(yintercept = 0, alpha= 0.2, linetype = 'dashed')+
  geom_vline(xintercept = 0, alpha= 0.2, linetype = 'dashed')  

ggplotly(biplot)

---

Classification

We’re going to use PLS Discriminant Analysis method (PLS-DA)

Start by splitting the dataset in train and test set

set.seed(100)

trts = sample(c('TR', 'TS'), nrow(df), replace = T, prob = c(0.7,0.3))
df1 = cbind('TR/TS' = trts, df)

df1TR = df1[df1$`TR/TS` == 'TR',]
df1TS = df1[df1$`TR/TS` == 'TS',]

kable(df1)  %>% kable_styling(fixed_thead = T, full_width = FALSE) %>%
  scroll_box( height = "500px")

TR/TS	type	Alcohol	Sugar.free.extract	Fixed.acidity	Tartaric.acid	Malic.acid	Uronic.acids	pH	Ash	Alcalinity.of.ash	Potassium	Calcium	Magnesium	Phosphate	Chloride	Total.phenols	Flavanoids	Nonflavanoid.phenols	Proanthocyanins	Color.intensity	Hue	OD280.OD315.of.diluted.wines	OD280.OD315.of.flavonoids	Glycerol	2.3.butanediol	Total.nitrogen	Proline	Methanol
TR	Barolo	14.23	24.82	73.1	1.21	1.71	0.72	3.38	2.43	15.6	950	62	127	320	82	2.80	3.06	0.28	2.29	5.64	1.04	3.92	4.77	9.29	757	153	1065	113
TR	Barolo	13.20	26.30	72.8	1.84	1.78	0.71	3.30	2.14	11.2	765	75	100	395	90	2.65	2.76	0.26	1.28	4.38	1.05	3.40	3.80	8.93	881	194	1050	94
TR	Barolo	13.16	26.30	68.5	1.94	2.36	0.84	3.48	2.67	18.6	936	70	101	497	67	2.80	3.24	0.30	2.81	5.68	1.03	3.17	3.46	11.74	900	206	1185	125
TR	Barolo	14.37	25.85	74.9	1.59	1.95	0.72	3.43	2.50	16.8	985	47	113	580	49	3.85	3.49	0.24	2.18	7.80	0.86	3.45	3.54	10.13	1119	292	1480	80
TR	Barolo	13.24	26.05	83.5	1.30	2.59	1.10	3.42	2.87	21.0	1088	70	118	408	65	2.80	2.69	0.39	1.82	4.32	1.04	2.93	3.22	10.27	799	215	735	73
TR	Barolo	14.20	28.40	79.9	2.14	1.76	0.96	3.39	2.45	15.2	868	71	112	418	58	3.27	3.39	0.34	1.97	6.75	1.05	2.85	3.16	10.85	865	364	1450	68
TS	Barolo	14.39	27.02	64.3	1.64	1.87	0.95	3.42	2.45	14.6	889	67	96	306	52	2.50	2.52	0.30	1.98	5.25	1.02	3.58	3.94	9.05	931	378	1290	80
TR	Barolo	14.06	26.40	73.5	1.33	2.15	1.14	3.54	2.61	17.6	894	50	121	502	64	2.60	2.51	0.31	1.25	5.05	1.06	3.58	3.94	10.13	865	358	1295	100
TR	Barolo	14.83	26.80	69.5	1.82	1.64	0.67	3.30	2.17	14.0	765	49	97	440	58	2.80	2.98	0.29	1.98	5.20	1.08	2.85	3.03	9.89	825	438	1045	141
TR	Barolo	13.86	27.00	68.5	1.92	1.35	0.67	3.27	2.27	16.0	794	51	98	391	64	2.98	3.15	0.22	1.85	7.22	1.01	3.55	3.75	12.65	788	350	1045	121
TR	Barolo	14.10	26.08	72.5	1.64	2.16	0.62	3.31	2.30	18.0	838	61	105	399	61	2.95	3.32	0.22	2.38	5.75	1.25	3.17	3.27	8.59	964	378	1510	123
TS	Barolo	14.12	28.35	72.9	1.51	1.48	0.96	3.20	2.32	16.8	827	60	95	424	79	2.20	2.43	0.26	1.57	5.00	1.17	2.82	3.04	11.52	894	294	1280	134
TR	Barolo	13.75	30.25	75.1	1.92	1.73	0.64	3.18	2.41	16.0	752	65	89	453	257	2.60	2.76	0.29	1.81	5.60	1.15	2.90	2.92	12.24	784	289	1320	164
TR	Barolo	14.75	30.40	98.9	2.08	1.73	0.72	3.01	2.39	11.4	910	46	91	510	50	3.10	3.69	0.43	2.81	5.40	1.25	2.73	2.82	12.29	766	224	1150	105
TS	Barolo	14.38	27.10	72.3	1.95	1.87	0.67	3.20	2.38	12.0	927	29	102	523	55	3.30	3.64	0.29	2.96	7.50	1.20	3.00	3.32	9.53	1041	324	1547	114
TR	Barolo	13.63	27.15	69.6	1.48	1.81	0.67	3.47	2.70	17.2	905	28	112	385	50	2.85	2.91	0.30	1.46	7.30	1.28	2.88	3.12	7.92	812	229	1310	97
TR	Barolo	14.30	27.90	74.9	1.41	1.92	0.82	3.40	2.72	20.0	860	108	120	513	62	2.80	3.14	0.33	1.97	6.20	1.07	2.65	3.10	9.24	836	308	1280	113
TR	Barolo	13.83	26.30	64.9	1.93	1.57	0.68	3.43	2.62	20.0	905	68	115	419	58	2.95	3.40	0.40	1.72	6.60	1.13	2.57	2.66	9.41	722	274	1130	99
TR	Barolo	14.19	26.40	72.0	1.85	1.59	0.82	3.38	2.48	16.5	964	86	108	488	28	3.30	3.93	0.32	1.86	8.70	1.23	2.82	3.17	9.85	808	230	1680	135
TR	Barolo	13.64	27.72	91.5	1.35	3.10	0.82	3.30	2.56	15.2	1038	111	116	402	67	2.70	3.03	0.17	1.66	5.10	0.96	3.36	4.00	10.39	726	227	845	119
TR	Barolo	14.06	25.32	71.1	1.34	1.63	1.00	3.47	2.28	16.0	905	79	126	323	73	3.00	3.17	0.24	2.10	5.65	1.09	3.71	3.75	10.30	828	225	780	145
TS	Barolo	12.93	28.80	102.1	1.05	3.80	0.89	3.26	2.65	18.6	915	79	102	294	62	2.41	2.41	0.25	1.98	4.50	1.03	3.52	3.66	11.88	589	237	770	123
TR	Barolo	13.71	27.63	80.0	2.23	1.86	1.21	3.33	2.36	16.6	815	89	101	476	134	2.61	2.88	0.27	1.69	3.80	1.11	4.00	4.31	8.81	715	270	1035	109
TS	Barolo	12.85	25.80	69.6	1.54	1.60	0.79	3.45	2.52	17.8	958	101	95	415	73	2.48	2.37	0.26	1.46	3.93	1.09	3.63	3.82	9.14	568	248	1015	102
TR	Barolo	13.50	25.00	81.6	1.55	1.81	0.95	3.42	2.61	20.0	992	62	96	476	47	2.53	2.61	0.28	1.66	3.52	1.12	3.82	4.00	9.45	667	210	845	86
TR	Barolo	13.05	25.72	78.3	1.15	2.05	1.08	3.57	3.22	25.0	1095	63	124	536	82	2.63	2.68	0.47	1.92	3.58	1.13	3.20	3.63	10.34	753	238	830	124
TS	Barolo	13.39	27.10	72.3	1.52	1.77	1.05	3.46	2.62	16.1	936	68	93	395	52	2.85	2.94	0.34	1.45	4.80	0.92	3.22	4.44	9.96	854	285	1195	85
TS	Barolo	13.30	22.70	68.3	1.74	1.72	1.06	3.44	2.14	17.0	882	52	94	434	46	2.40	2.19	0.27	1.35	3.95	1.02	2.77	3.10	9.70	757	350	1285	84
TR	Barolo	13.87	29.30	68.3	1.38	1.90	0.75	3.42	2.80	19.4	1085	68	107	396	76	2.95	2.97	0.37	1.76	4.50	1.25	3.40	3.72	9.53	702	280	915	99
TR	Barolo	14.02	25.20	69.6	1.71	1.68	0.79	3.26	2.21	16.0	780	62	96	510	53	2.65	2.33	0.26	1.98	4.70	1.04	3.59	3.77	9.94	689	293	1035	100
TR	Barolo	13.73	26.75	75.2	1.53	1.50	0.66	3.30	2.70	22.5	1067	76	101	436	53	3.00	3.25	0.29	2.38	5.70	1.19	2.71	3.00	10.44	792	332	1285	120
TS	Barolo	13.58	28.35	62.0	1.14	1.66	0.72	3.28	2.36	19.1	805	58	106	485	498	2.86	3.19	0.22	1.95	6.90	1.09	2.88	3.06	10.73	700	296	1515	108
TR	Barolo	13.68	26.98	64.8	1.60	1.83	0.62	3.40	2.36	17.2	1068	32	104	398	76	2.42	2.69	0.42	1.97	3.84	1.23	2.87	3.04	13.00	733	252	990	141
TS	Barolo	13.76	26.80	77.1	1.81	1.53	0.84	3.40	2.70	19.5	974	39	132	394	128	2.95	2.74	0.50	1.35	5.40	1.25	3.00	3.31	8.33	740	296	1235	109
TR	Barolo	13.51	26.22	65.3	1.28	1.80	0.70	3.36	2.65	19.0	856	53	110	464	53	2.35	2.53	0.29	1.54	4.20	1.10	2.87	2.91	10.10	700	258	1095	86
TS	Barolo	13.48	26.10	70.9	1.44	1.81	0.69	3.45	2.41	20.5	789	49	100	416	35	2.70	2.98	0.26	1.86	5.10	1.04	3.47	4.04	8.21	534	258	920	75
TR	Barolo	13.28	29.70	78.9	1.50	1.64	0.80	3.30	2.84	15.5	964	98	110	431	38	2.60	2.68	0.34	1.36	4.60	1.09	2.78	3.17	13.70	570	224	880	105
TR	Barolo	13.05	25.00	70.9	1.18	1.65	0.89	3.34	2.55	18.0	1025	85	98	382	23	2.45	2.43	0.29	1.44	4.25	1.12	2.51	2.87	8.88	627	220	1105	134
TS	Barolo	13.07	24.30	73.9	1.16	1.50	1.00	3.41	2.10	15.5	930	75	98	386	18	2.40	2.64	0.28	1.37	3.70	1.18	2.69	3.04	9.50	658	212	1020	145
TR	Barolo	14.22	30.20	114.8	1.85	3.99	0.64	3.11	2.51	13.2	895	88	128	280	76	3.00	3.04	0.20	2.08	5.10	0.89	3.53	3.66	12.34	1048	215	760	101
TR	Barolo	13.56	26.60	80.3	1.57	1.71	0.91	3.32	2.31	16.2	890	75	117	316	70	3.15	3.29	0.34	2.34	6.13	0.95	3.38	3.53	9.77	733	246	795	118
TS	Barolo	13.41	27.50	102.7	1.79	3.84	0.92	3.19	2.12	18.8	815	78	90	385	70	2.45	2.68	0.27	1.48	4.28	0.91	3.00	3.36	9.21	565	231	1035	106
TS	Barolo	13.88	27.80	78.9	2.39	1.89	0.65	3.33	2.59	15.0	980	71	101	502	67	3.25	3.56	0.17	1.70	5.43	0.88	3.56	4.00	8.61	665	289	1095	121
TS	Barolo	13.24	25.60	101.3	1.83	3.98	0.62	3.18	2.29	17.5	920	63	103	389	53	2.64	2.63	0.32	1.66	4.36	0.82	3.00	3.15	8.61	576	248	680	105
TR	Barolo	13.05	23.70	80.0	1.22	1.77	0.82	3.33	2.10	17.0	901	49	107	408	50	3.00	3.00	0.28	2.03	5.04	0.88	3.35	3.78	9.96	1044	218	885	155
TR	Barolo	14.21	29.65	104.9	1.74	4.04	0.86	3.35	2.44	18.9	930	63	111	324	46	2.85	2.65	0.30	1.25	5.24	0.87	3.33	3.78	10.08	700	264	1080	90
TS	Barolo	14.38	30.70	90.3	1.24	3.59	0.99	3.16	2.28	16.0	788	71	102	408	70	3.25	3.17	0.27	2.19	4.90	1.04	3.44	3.56	9.48	766	218	1065	91
TS	Barolo	13.90	25.30	75.2	1.93	1.68	0.63	3.16	2.12	16.0	762	81	101	484	56	3.10	3.39	0.21	2.14	6.10	0.91	3.33	3.51	8.78	570	281	985	77
TR	Barolo	14.10	25.98	70.0	1.87	2.02	0.83	3.20	2.40	18.8	880	75	103	480	64	2.75	2.92	0.32	2.38	6.20	1.07	2.75	2.89	10.42	669	249	1060	78
TR	Barolo	13.94	26.80	72.7	2.35	1.73	0.60	3.23	2.27	17.4	868	40	108	420	96	2.88	3.54	0.32	2.08	8.90	1.12	3.10	3.30	13.44	749	383	1260	155
TR	Barolo	13.05	24.30	76.0	2.08	1.73	0.63	3.06	2.04	12.4	792	35	92	638	50	2.72	3.27	0.17	2.91	7.20	1.12	2.91	3.20	9.17	590	224	1150	124
TR	Barolo	13.83	27.60	63.3	1.82	1.65	0.77	3.32	2.60	17.2	968	28	94	411	53	2.45	2.99	0.22	2.29	5.60	1.24	3.37	3.69	9.77	777	330	1265	110
TR	Barolo	13.82	26.25	74.5	1.83	1.75	0.77	3.33	2.42	14.0	785	29	111	472	47	3.88	3.74	0.32	1.87	7.05	1.01	3.26	3.53	7.63	704	360	1190	88
TR	Barolo	13.77	25.20	64.8	1.29	1.90	0.84	3.56	2.68	17.1	927	33	115	405	59	3.00	2.79	0.39	1.68	6.30	1.13	2.93	3.21	7.73	795	313	1375	109
TR	Barolo	13.74	24.80	65.2	1.88	1.67	0.66	3.43	2.25	16.4	784	76	118	502	37	2.60	2.90	0.21	1.62	5.85	0.92	3.20	3.36	7.97	733	292	1060	87
TR	Barolo	13.56	25.00	78.0	1.49	1.73	0.69	3.31	2.46	20.5	808	91	116	411	38	2.96	2.78	0.20	2.45	6.25	0.98	3.03	3.16	7.92	550	266	1120	86
TR	Barolo	14.22	26.60	87.1	1.98	1.70	0.74	3.20	2.30	16.3	768	73	118	465	136	3.20	3.00	0.26	2.03	6.38	0.94	3.31	3.81	13.00	770	248	970	124
TR	Barolo	13.29	26.80	80.0	1.63	1.97	0.96	3.24	2.68	16.8	905	76	102	360	24	3.00	3.23	0.31	1.66	6.00	1.07	2.84	3.21	9.30	676	258	1270	116
TR	Barolo	13.72	27.10	73.3	1.34	1.43	0.93	3.38	2.50	16.7	906	71	108	403	33	3.40	3.67	0.19	2.04	6.80	0.89	2.87	3.10	9.94	755	232	1285	131
TR	Grignolino	12.37	18.30	90.1	2.80	0.94	0.73	3.11	1.36	10.6	580	77	88	296	52	1.98	0.57	0.28	0.42	1.95	1.05	1.82	2.12	5.40	736	287	520	98
TR	Grignolino	12.33	22.90	72.2	2.25	1.10	0.69	3.26	2.28	16.0	715	85	101	365	108	2.05	1.09	0.63	0.41	3.27	1.25	1.67	1.42	6.90	658	345	680	127
TR	Grignolino	12.64	23.90	95.7	1.93	1.36	1.06	3.19	2.02	16.8	688	83	100	395	53	2.02	1.41	0.53	0.62	5.75	0.98	1.59	1.86	8.20	691	321	450	60
TS	Grignolino	13.67	22.20	64.8	2.20	1.25	0.74	3.40	1.92	18.0	725	51	94	301	47	2.10	1.79	0.32	0.73	3.80	1.23	2.46	1.73	8.60	797	262	630	87
TR	Grignolino	12.37	23.50	70.0	2.06	1.13	0.72	3.30	2.16	19.0	785	73	87	422	306	3.50	3.10	0.19	1.87	4.45	1.22	2.87	3.07	7.20	748	141	420	157
TR	Grignolino	12.17	23.03	65.7	1.84	1.45	0.72	3.35	2.53	19.0	790	62	104	411	116	1.89	1.75	0.45	1.03	2.95	1.45	2.23	2.73	7.50	627	219	355	58
TR	Grignolino	12.37	26.80	62.7	1.70	1.21	0.88	3.40	2.56	18.1	978	55	98	310	69	2.42	2.65	0.37	2.08	4.60	1.19	2.30	2.60	7.96	680	259	678	118
TR	Grignolino	13.11	23.70	80.0	1.40	1.01	0.77	3.10	1.70	15.0	730	80	78	297	148	2.98	3.18	0.26	2.28	5.30	1.12	3.18	3.33	8.20	604	100	502	114
TR	Grignolino	12.37	20.90	63.7	1.94	1.17	0.67	3.40	1.92	19.6	785	40	78	212	54	2.11	2.00	0.27	1.04	4.68	1.12	3.48	4.07	7.10	554	425	510	98
TR	Grignolino	13.34	23.72	70.0	2.02	0.94	1.09	3.26	2.36	17.0	760	64	110	451	111	2.53	1.30	0.55	0.42	3.17	1.02	1.93	1.92	8.10	704	363	750	137
TR	Grignolino	12.21	22.70	90.7	3.62	1.19	0.94	3.14	1.75	16.8	795	134	151	448	88	1.85	1.28	0.14	2.50	2.85	1.28	3.07	3.23	6.81	714	195	718	116
TR	Grignolino	12.29	21.40	55.6	1.43	1.61	0.87	3.54	2.21	20.4	682	102	103	324	50	1.10	1.02	0.37	1.46	3.05	0.91	1.82	2.00	6.38	661	301	870	78
TR	Grignolino	13.86	25.25	59.5	1.27	1.51	1.09	3.63	2.67	25.0	785	63	86	383	59	2.95	2.86	0.21	1.87	3.38	1.36	3.16	3.52	7.62	748	170	410	99
TR	Grignolino	13.49	22.30	60.9	1.74	1.66	0.67	3.44	2.24	24.0	680	60	87	300	43	1.88	1.84	0.27	1.03	3.74	0.98	2.78	3.50	8.04	614	160	472	64
TS	Grignolino	12.99	26.10	50.5	1.42	1.67	1.24	3.52	2.60	30.0	974	55	139	473	35	3.30	2.89	0.21	1.96	3.35	1.31	3.50	3.60	8.00	731	293	985	113
TR	Grignolino	11.96	24.50	65.7	2.18	1.09	0.73	3.40	2.30	21.0	681	98	101	366	48	3.38	2.14	0.13	1.65	3.21	0.99	3.13	3.15	7.70	563	183	886	57
TR	Grignolino	11.66	20.30	61.7	1.70	1.88	0.60	3.30	1.92	16.0	785	52	97	312	59	1.61	1.57	0.34	1.15	3.80	1.23	2.14	2.35	6.14	596	109	428	129
TS	Grignolino	13.03	23.50	78.6	1.90	0.90	0.76	3.30	1.71	16.0	790	57	86	396	122	1.95	2.03	0.24	1.46	4.60	1.19	2.48	2.85	8.40	756	167	392	145
TS	Grignolino	11.84	26.40	108.7	1.70	2.89	0.91	3.11	2.23	18.0	790	71	112	350	58	1.72	1.32	0.43	0.95	2.65	0.96	2.52	3.25	5.22	514	246	500	122
TS	Grignolino	12.33	20.60	58.7	2.41	0.99	0.84	3.32	1.95	14.8	680	124	136	438	99	1.90	1.85	0.35	2.76	3.40	1.06	2.31	2.70	7.96	654	259	750	59
TR	Grignolino	12.70	27.15	93.3	1.46	3.87	1.11	3.19	2.40	23.0	890	110	101	321	52	2.83	2.55	0.43	1.95	2.57	1.19	3.13	3.82	8.66	700	227	463	101
TR	Grignolino	12.00	23.20	58.4	1.88	0.92	0.82	3.30	2.00	19.0	680	63	86	408	27	2.42	2.26	0.30	1.43	2.50	1.38	3.12	3.52	5.80	645	199	278	95
TR	Grignolino	12.72	22.90	58.4	1.40	1.81	0.81	3.50	2.20	18.8	890	83	86	418	64	2.20	2.53	0.26	1.77	3.90	1.16	3.14	3.33	7.38	664	199	714	111
TS	Grignolino	12.08	23.50	56.9	1.33	1.13	0.71	3.65	2.51	24.0	980	85	78	215	53	2.00	1.58	0.40	1.40	2.20	1.31	2.72	3.50	8.11	548	203	630	115
TS	Grignolino	13.05	25.50	104.8	1.64	3.86	0.73	3.19	2.32	22.5	938	98	85	195	48	1.65	1.59	0.61	1.62	4.80	0.84	2.01	2.07	8.64	649	207	515	114
TR	Grignolino	11.84	23.40	70.8	1.80	0.89	1.00	3.40	2.58	18.0	922	80	94	378	95	2.20	2.21	0.22	2.35	3.05	0.79	3.08	3.81	6.36	586	138	520	141
TR	Grignolino	12.67	24.30	74.1	1.70	0.98	0.88	3.35	2.24	18.0	840	81	99	336	70	2.20	1.94	0.30	1.46	2.62	1.23	3.16	3.60	7.90	600	217	450	121
TS	Grignolino	12.16	25.80	78.9	1.84	1.61	0.78	3.37	2.31	22.8	845	98	90	285	54	1.78	1.69	0.43	1.56	2.45	1.33	2.26	2.92	8.04	643	195	495	116
TR	Grignolino	11.65	22.90	62.9	1.80	1.67	0.64	3.55	2.62	26.0	1045	125	88	281	36	1.92	1.61	0.40	1.34	2.60	1.36	3.21	3.27	9.54	608	262	562	120
TR	Grignolino	11.64	24.20	72.4	1.84	2.06	0.89	3.40	2.46	21.6	962	79	84	304	70	1.95	1.69	0.48	1.35	2.80	1.00	2.75	3.60	7.97	523	223	680	120
TS	Grignolino	12.08	24.00	67.6	1.93	1.33	1.05	3.50	2.30	23.6	932	65	70	278	27	2.20	1.59	0.42	1.38	1.74	1.07	3.21	3.77	8.47	557	200	625	163
TS	Grignolino	12.08	25.50	78.9	1.93	1.83	0.77	3.25	2.32	18.5	960	128	81	329	48	1.60	1.50	0.52	1.64	2.40	1.08	2.27	2.28	8.33	563	314	480	105
TR	Grignolino	12.00	25.30	75.6	1.80	1.51	0.74	3.27	2.42	22.0	915	102	86	342	110	1.45	1.25	0.50	1.63	3.60	1.05	2.65	2.75	8.21	495	170	450	152
TR	Grignolino	12.69	25.00	70.9	1.47	1.53	0.82	3.43	2.26	20.7	845	92	80	214	73	1.38	1.46	0.58	1.62	3.05	0.96	2.06	2.28	8.88	792	198	495	101
TR	Grignolino	12.29	25.00	86.0	1.84	2.83	0.71	3.24	2.22	18.0	915	94	88	329	84	2.45	2.25	0.25	1.99	2.15	1.15	3.30	3.75	5.64	594	190	290	117
TS	Grignolino	11.62	28.40	92.8	1.35	1.99	0.84	3.22	2.28	18.0	794	88	98	372	76	3.02	2.26	0.17	1.35	3.25	1.16	2.96	2.97	13.60	930	200	345	120
TR	Grignolino	12.47	24.95	72.0	1.93	1.52	1.02	3.32	2.20	19.0	790	188	162	464	84	2.50	2.27	0.32	3.28	2.60	1.16	2.63	2.99	6.21	683	268	937	79
TR	Grignolino	11.81	27.50	75.3	1.75	2.12	0.91	3.29	2.74	21.5	942	125	134	375	83	1.60	0.99	0.14	1.56	2.50	0.95	2.26	2.88	7.56	687	179	625	84
TR	Grignolino	12.29	25.30	68.5	1.80	1.41	0.57	3.30	1.98	16.0	890	82	85	440	40	2.55	2.50	0.29	1.77	2.90	1.23	2.74	3.14	8.44	696	335	428	117
TR	Grignolino	12.37	24.80	61.2	1.60	1.07	1.01	3.40	2.10	18.5	845	84	88	385	80	3.52	3.75	0.24	1.95	4.50	1.04	2.77	3.05	7.23	655	180	660	127
TS	Grignolino	12.29	26.50	112.4	2.61	3.17	1.09	2.95	2.21	18.0	845	122	88	438	35	2.85	2.99	0.45	2.81	2.30	1.42	2.83	3.90	8.45	759	159	406	146
TR	Grignolino	12.08	22.90	75.2	2.20	2.08	0.67	3.15	1.70	17.5	805	62	97	212	42	2.23	2.17	0.26	1.40	3.30	1.27	2.96	3.41	7.08	591	399	710	105
TR	Grignolino	12.60	21.90	63.7	2.00	1.34	0.64	3.15	1.90	18.5	870	135	88	224	80	1.45	1.36	0.29	1.35	2.45	1.04	2.77	3.75	8.56	610	195	562	130
TR	Grignolino	12.34	25.80	78.0	2.50	2.45	0.57	3.42	2.46	21.0	915	144	98	146	82	2.56	2.11	0.34	1.31	2.80	0.80	3.38	4.19	8.36	536	306	438	98
TR	Grignolino	11.82	22.70	67.2	2.17	1.72	0.80	3.40	1.88	19.5	874	64	86	442	85	2.50	1.64	0.37	1.42	2.06	0.94	2.44	3.80	7.36	653	194	415	103
TR	Grignolino	12.51	24.50	63.2	1.34	1.73	0.67	3.50	1.98	20.5	905	74	85	254	50	2.20	1.92	0.32	1.48	2.94	1.04	3.57	4.50	10.44	882	158	672	99
TR	Grignolino	12.42	23.50	78.7	1.92	2.55	0.92	3.30	2.27	22.0	980	93	90	342	92	1.68	1.84	0.66	1.42	2.70	0.86	3.30	3.50	7.92	680	219	315	89
TS	Grignolino	12.25	25.00	75.2	1.40	1.73	0.64	3.45	2.12	19.0	890	102	80	265	53	1.65	2.03	0.37	1.63	3.40	1.00	3.17	4.16	10.13	790	207	510	126
TS	Grignolino	12.72	24.10	85.6	2.34	1.75	0.71	3.33	2.28	22.5	910	58	84	159	67	1.38	1.76	0.48	1.63	3.30	0.88	2.42	2.54	7.61	855	194	488	81
TR	Grignolino	12.22	24.50	70.1	1.42	1.29	0.60	3.36	1.94	19.0	897	103	92	157	65	2.36	2.04	0.39	2.08	2.70	0.86	3.02	3.64	7.24	780	132	312	97
TR	Grignolino	11.61	27.60	84.0	1.85	1.35	0.87	3.46	2.70	20.0	950	98	94	408	58	2.74	2.92	0.29	2.49	2.65	0.96	3.26	3.85	6.42	592	386	680	110
TS	Grignolino	11.46	24.84	104.4	2.20	3.74	0.78	3.07	1.82	19.5	685	143	107	322	70	3.18	2.58	0.24	3.58	2.90	0.75	2.81	3.60	7.87	684	196	562	91
TS	Grignolino	12.52	26.35	100.4	1.45	2.43	0.97	3.21	2.17	21.0	680	112	88	339	48	2.55	2.27	0.26	1.22	2.00	0.90	2.78	3.10	8.50	730	171	325	60
TR	Grignolino	11.76	29.60	90.3	2.10	2.68	1.04	3.30	2.92	20.0	1100	115	103	370	38	1.75	2.03	0.60	1.05	3.80	1.23	2.50	2.25	9.94	732	454	607	103
TR	Grignolino	11.41	21.70	100.0	2.04	0.74	0.87	3.50	2.50	21.0	1085	105	88	315	56	2.48	2.01	0.42	1.44	3.08	1.10	2.31	4.16	6.56	638	228	434	81
TS	Grignolino	12.08	23.50	95.7	2.31	1.39	0.66	3.30	2.50	22.5	1025	83	84	235	42	2.56	2.29	0.43	1.04	2.90	0.93	3.19	4.38	7.36	632	247	385	105
TR	Grignolino	11.03	23.30	92.0	3.02	1.51	0.97	3.12	2.20	21.5	835	136	85	358	30	2.46	2.17	0.52	2.01	1.90	1.71	2.87	3.46	6.28	630	175	407	96
TS	Grignolino	11.82	22.90	75.2	2.10	1.47	0.89	3.13	1.99	20.8	754	115	86	264	80	1.98	1.60	0.30	1.53	1.95	0.95	3.33	3.81	7.75	644	386	495	112
TS	Grignolino	12.42	25.30	94.7	1.86	1.61	0.83	3.38	2.19	22.5	964	96	108	268	128	2.00	2.09	0.34	1.61	2.06	1.06	2.96	3.73	9.02	989	227	345	108
TR	Grignolino	12.77	25.50	101.3	2.10	3.43	0.54	3.10	1.98	16.0	720	65	80	224	80	1.63	1.25	0.43	0.83	3.40	0.70	2.12	2.75	6.80	590	251	372	121
TS	Grignolino	12.00	24.20	89.7	1.11	3.43	0.72	3.25	2.00	19.0	865	104	87	107	48	2.00	1.64	0.37	1.87	1.28	0.93	3.05	4.22	7.56	612	182	564	114
TR	Grignolino	11.45	24.30	123.6	1.50	2.40	0.96	3.18	2.42	20.0	915	138	96	262	58	2.90	2.79	0.32	1.83	3.25	0.80	3.39	4.27	9.54	710	311	625	109
TR	Grignolino	11.56	26.60	84.7	1.64	2.05	1.02	3.40	3.23	28.5	1160	92	119	490	94	3.18	5.08	0.47	1.87	6.00	0.93	3.69	4.37	7.68	687	538	465	183
TR	Grignolino	12.42	25.00	110.0	2.13	4.43	0.93	3.23	2.73	26.5	1050	84	102	524	88	2.20	2.13	0.43	1.71	2.08	0.92	3.12	4.33	8.73	560	366	365	118
TR	Grignolino	13.05	24.00	115.0	1.64	5.80	0.85	3.12	2.13	21.5	815	102	86	326	73	2.62	2.65	0.30	2.01	2.60	0.73	3.10	4.29	7.24	610	216	380	114
TR	Grignolino	11.87	27.35	116.7	2.43	4.31	0.81	3.14	2.39	21.0	935	103	82	300	58	2.86	3.03	0.21	2.91	2.80	0.75	3.64	4.50	8.04	635	193	380	66
TR	Grignolino	12.07	24.75	95.3	2.11	2.16	0.89	3.24	2.17	21.0	815	94	85	358	85	2.60	2.65	0.37	1.35	2.76	0.86	3.28	4.29	7.77	558	295	378	86
TS	Grignolino	12.43	23.80	94.1	1.61	1.53	0.65	3.26	2.29	21.5	895	94	86	298	116	2.74	3.15	0.39	1.77	3.94	0.69	2.84	3.40	7.00	628	209	352	79
TS	Grignolino	11.79	21.30	97.2	2.30	2.13	0.81	3.40	2.78	28.5	1075	105	92	345	70	2.13	2.24	0.58	1.76	3.00	0.97	2.44	4.00	7.17	634	173	466	56
TR	Grignolino	12.37	23.30	102.6	1.91	1.63	0.96	3.21	2.30	24.5	925	120	88	302	79	2.22	2.45	0.40	1.90	2.12	0.89	2.78	3.70	8.85	530	166	342	108
TR	Grignolino	12.04	22.80	111.8	1.40	4.30	0.74	3.20	2.38	22.0	930	98	80	138	41	2.10	1.75	0.42	1.35	2.60	0.79	2.57	4.40	6.57	585	144	580	115
TR	Barbera	12.86	26.80	87.3	0.99	1.35	0.92	3.22	2.32	18.0	830	52	122	266	46	1.51	1.25	0.21	0.94	4.10	0.76	1.29	1.26	6.43	673	252	630	122
TS	Barbera	12.88	23.95	78.9	1.85	2.99	0.98	3.50	2.40	20.0	795	55	104	269	72	1.30	1.22	0.24	0.83	5.40	0.74	1.42	1.34	10.10	918	319	530	102
TS	Barbera	12.81	24.45	76.2	2.93	2.31	0.87	3.64	2.40	24.0	785	49	98	266	67	1.15	1.09	0.27	0.83	5.70	0.66	1.36	1.24	10.02	1095	258	560	132
TR	Barbera	12.70	24.75	91.0	1.91	3.55	1.80	3.26	2.36	21.5	805	47	106	356	118	1.70	1.20	0.17	0.84	5.00	0.78	1.29	1.23	8.52	1020	238	600	121
TR	Barbera	12.51	23.50	104.7	1.34	1.24	0.98	3.50	2.25	17.5	975	60	85	273	29	2.00	0.58	0.60	1.25	5.45	0.75	1.51	1.40	8.32	764	178	650	79
TR	Barbera	12.60	23.60	80.6	2.26	2.46	0.97	3.31	2.20	18.5	760	103	94	275	77	1.62	0.66	0.63	0.94	7.10	0.73	1.58	1.37	6.47	573	174	695	100
TR	Barbera	12.25	25.30	91.4	1.42	4.72	1.25	3.40	2.54	21.0	995	105	89	262	144	1.38	0.47	0.53	0.80	3.85	0.75	1.27	1.12	8.25	680	217	720	107
TR	Barbera	12.53	27.10	99.8	1.88	5.51	1.19	3.30	2.64	25.0	930	100	96	360	6	1.79	0.60	0.63	1.10	5.00	0.82	1.69	1.80	8.35	821	230	515	139
TR	Barbera	13.49	25.70	115.5	2.17	3.59	1.47	3.24	2.19	19.5	825	111	88	315	56	1.62	0.48	0.58	0.88	5.70	0.81	1.82	2.23	10.40	700	245	580	150
TR	Barbera	12.84	26.20	82.0	1.79	2.96	1.26	3.50	2.61	24.0	925	48	101	398	15	2.32	0.60	0.53	0.81	4.92	0.89	2.15	2.25	10.60	940	269	590	132
TR	Barbera	12.93	26.78	80.0	1.69	2.81	1.15	3.31	2.70	21.0	965	40	96	351	25	1.54	0.50	0.53	0.75	4.60	0.77	2.31	2.34	10.62	955	260	600	82
TR	Barbera	13.36	24.12	97.8	2.83	2.56	0.77	3.35	2.35	20.0	880	47	89	235	71	1.40	0.50	0.37	0.64	5.60	0.70	2.47	2.60	10.41	814	216	780	106
TR	Barbera	13.52	27.90	85.0	1.46	3.17	1.23	3.28	2.72	23.5	880	38	97	325	21	1.55	0.52	0.50	0.55	4.35	0.89	2.06	2.21	10.20	976	201	520	118
TS	Barbera	13.62	25.52	93.7	2.70	4.95	1.56	3.41	2.35	20.0	805	57	92	191	16	2.00	0.80	0.47	1.02	4.40	0.91	2.05	2.55	8.90	899	205	550	140
TR	Barbera	12.25	23.40	113.5	3.54	3.88	1.04	3.01	2.20	18.5	785	77	112	358	14	1.38	0.78	0.29	1.14	8.21	0.65	2.00	2.23	8.16	521	218	855	97
TS	Barbera	13.16	22.90	117.9	3.15	3.57	1.18	3.14	2.15	21.0	805	88	102	456	17	1.50	0.55	0.43	1.30	4.00	0.60	1.68	2.24	5.61	696	252	830	63
TS	Barbera	13.88	21.40	99.3	2.81	5.04	1.29	3.28	2.23	20.0	750	43	80	171	10	0.98	0.34	0.40	0.68	4.90	0.58	1.33	1.81	7.94	670	156	415	154
TR	Barbera	12.87	24.35	98.9	2.51	4.61	1.25	3.18	2.48	21.5	830	63	86	366	50	1.70	0.65	0.47	0.86	7.65	0.54	1.86	2.10	8.52	806	213	625	122
TR	Barbera	13.32	21.46	96.9	2.85	3.24	1.75	3.30	2.38	21.5	790	42	92	306	21	1.93	0.76	0.45	1.25	8.42	0.55	1.62	2.19	6.12	604	219	650	106
TR	Barbera	13.08	26.80	120.6	2.90	3.90	1.11	3.16	2.36	21.5	790	73	113	303	50	1.41	1.39	0.34	1.14	9.40	0.57	1.33	1.26	7.36	733	164	550	114
TR	Barbera	13.50	26.50	105.5	2.31	3.12	1.31	3.23	2.62	24.0	980	67	123	338	106	1.40	1.57	0.22	1.25	8.60	0.59	1.30	1.29	6.28	568	129	500	107
TS	Barbera	12.79	23.40	117.8	3.12	2.67	0.82	3.21	2.48	22.0	890	53	112	407	127	1.48	1.36	0.24	1.26	10.80	0.48	1.47	1.40	7.00	898	154	480	91
TR	Barbera	13.11	25.20	95.4	2.26	1.90	0.86	3.49	2.75	25.5	1140	74	116	289	55	2.20	1.28	0.26	1.56	7.10	0.61	1.33	1.25	8.57	905	249	425	125
TR	Barbera	13.23	23.85	120.6	2.80	3.30	0.80	3.20	2.28	18.5	915	68	98	351	35	1.80	0.83	0.61	1.87	10.52	0.56	1.51	1.42	10.80	915	154	675	84
TR	Barbera	12.58	21.75	102.7	2.92	1.29	0.79	3.21	2.10	20.0	875	107	103	368	100	1.48	0.58	0.53	1.40	7.60	0.58	1.55	1.34	7.52	924	142	640	100
TS	Barbera	13.17	23.20	129.3	2.28	5.19	1.49	3.58	2.32	22.0	1045	102	93	241	84	1.74	0.63	0.61	1.55	7.90	0.60	1.48	1.31	9.50	969	207	725	84
TS	Barbera	13.84	24.70	122.9	2.76	4.12	1.07	3.19	2.38	19.5	840	108	89	402	6	1.80	0.83	0.48	1.56	9.01	0.57	1.64	1.92	9.29	902	159	480	132
TS	Barbera	12.45	25.35	105.9	2.23	3.03	1.24	3.62	2.64	27.0	1050	118	97	393	53	1.90	0.58	0.63	1.14	7.50	0.67	1.73	2.18	10.20	865	252	880	118
TR	Barbera	14.34	29.10	97.5	2.73	1.68	1.60	3.42	2.70	25.0	1095	78	98	462	49	2.80	1.31	0.53	2.70	13.00	0.57	1.96	2.25	10.82	764	223	660	182
TR	Barbera	13.48	26.95	102.5	3.75	1.67	1.37	3.41	2.64	22.5	1055	79	89	480	35	2.60	1.10	0.52	2.29	11.75	0.57	1.78	2.09	11.09	1080	250	620	160
TS	Barbera	12.36	34.60	116.5	2.25	3.83	0.99	3.32	2.38	21.0	1035	112	88	394	28	2.30	0.92	0.50	1.04	7.65	0.56	1.58	2.00	9.29	636	154	520	127
TR	Barbera	13.69	24.80	74.9	1.04	3.26	0.75	3.36	2.54	20.0	1010	54	107	394	21	1.83	0.56	0.50	0.80	5.88	0.96	1.82	2.61	9.31	653	275	680	130
TR	Barbera	12.85	25.70	86.9	1.79	3.27	0.92	3.33	2.58	22.0	935	46	106	318	48	1.65	0.60	0.60	0.96	5.58	0.87	2.11	2.77	9.77	814	224	570	102
TR	Barbera	12.96	23.30	97.9	2.66	3.45	1.31	3.11	2.35	18.5	795	35	106	257	11	1.39	0.70	0.40	0.94	5.28	0.68	1.75	2.00	10.13	667	212	675	123
TR	Barbera	13.78	25.10	103.5	3.80	2.76	1.23	3.13	2.30	22.0	803	88	90	417	19	1.35	0.68	0.41	1.03	9.58	0.70	1.68	2.05	8.93	677	198	615	109
TR	Barbera	13.73	24.65	92.6	2.91	4.36	1.10	3.31	2.26	22.5	785	96	88	360	34	1.28	0.47	0.52	1.15	6.62	0.78	1.75	2.15	9.67	670	275	520	131
TR	Barbera	13.45	24.90	82.9	1.91	3.70	1.13	3.28	2.60	23.0	890	56	111	386	8	1.70	0.92	0.43	1.46	10.68	0.85	1.56	1.60	10.37	733	196	695	107
TS	Barbera	12.82	22.40	119.9	3.86	3.37	0.96	2.98	2.30	19.5	810	81	88	308	14	1.48	0.66	0.40	0.97	10.26	0.72	1.75	1.90	8.45	589	158	685	132
TS	Barbera	13.58	27.20	119.9	3.04	2.58	0.98	2.98	2.69	24.5	930	80	105	369	38	1.55	0.84	0.39	1.54	8.66	0.74	1.80	1.96	8.90	847	215	750	129
TS	Barbera	13.40	28.15	137.8	3.48	4.60	1.34	3.06	2.86	25.0	1085	92	112	387	27	1.98	0.96	0.27	1.11	8.50	0.67	1.92	2.15	7.80	700	218	630	117
TR	Barbera	12.20	23.70	107.3	3.23	3.03	0.74	3.08	2.32	19.0	845	87	96	265	56	1.25	0.49	0.40	0.73	5.50	0.66	1.83	2.80	7.90	854	224	510	77
TR	Barbera	12.77	23.70	111.5	3.34	2.39	0.79	2.99	2.28	19.5	850	69	86	394	13	1.39	0.51	0.48	0.64	9.90	0.57	1.63	1.69	6.07	579	156	470	152
TR	Barbera	14.16	23.82	118.2	3.63	2.51	1.12	3.10	2.48	20.0	840	73	91	319	15	1.68	0.70	0.44	1.24	9.70	0.62	1.71	1.90	8.93	953	196	660	135
TS	Barbera	13.71	24.95	113.9	2.88	5.65	1.75	3.15	2.45	20.5	1035	72	95	298	12	1.68	0.61	0.52	1.06	7.70	0.64	1.74	1.94	9.90	1120	238	740	120
TS	Barbera	13.40	24.60	126.2	2.94	3.91	1.25	3.12	2.48	23.0	860	84	102	490	15	1.80	0.75	0.43	1.41	7.30	0.70	1.56	1.93	7.58	855	226	750	96
TR	Barbera	13.27	22.75	103.9	2.84	4.28	1.62	3.16	2.26	20.0	760	61	120	526	6	1.59	0.69	0.43	1.35	10.20	0.59	1.56	1.94	7.27	749	157	835	126
TS	Barbera	13.17	23.45	113.9	3.87	2.59	1.59	3.17	2.37	20.0	785	62	120	534	6	1.65	0.68	0.53	1.46	9.30	0.60	1.62	2.05	11.16	1110	160	840	52
TR	Barbera	14.13	27.20	125.9	3.18	4.10	1.43	3.21	2.74	24.5	930	53	96	315	35	2.05	0.76	0.56	1.35	9.20	0.61	1.60	1.87	11.28	857	198	560	112

model = plsda(df1TR[-(1:2)], df1TR$type, cv = list('ven', 5), lim.type = 'jm', scale = T, method = 'simpls')

dfrmse = model$cvres$rmse %>% data.frame()

dfrmse = sapply(dfrmse, mean) %>% data.frame()
colnames(dfrmse) = 'Mean'

plotRMSE(model)

model = selectCompNum(model, 3)

par(mfrow = c(2,2))

plotPredictions(model, nc = 1)
plotPredictions(model, nc = 2)
plotPredictions(model, nc = 3)

plot(model)

plotRegcoeffs(model, show.labels = T)

pred = predict(model, df1TS[-(1:2)], df1TS$type)
plot(pred)

\(R^2\) of the prediction is 0.8761831

References

Forina, Michele. 1986. “Wines M.Forina, C.Armanino, M.Castino, M.Ubigli, “Multivariate Data Analysis as Discriminating Method of the Origin of Wines”, Vitis, 25, 189-201 (1986).” https://doi.org/10.13140/2.1.4312.6560.