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Author

*The author of this computation has been verified*

R Software Module

rwasp_pairs.wasp

Title produced by software

Kendall tau Correlation Matrix

Date of computation

Mon, 12 Dec 2011 10:13:43 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/12/t132370283484cechu3m6so3q4.htm/, Retrieved Fri, 03 May 2024 06:34:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=154015, Retrieved Fri, 03 May 2024 06:34:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

101

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Kendall tau Correlation Matrix] [] [2010-12-05 18:04:16] [b98453cac15ba1066b407e146608df68]
- RMPD    [Kendall tau Correlation Matrix] [] [2011-12-12 15:13:43] [05d3841c0e91f0207133db830e88168b] [Current]

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Dataseries X:

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1418	56	30	79	210907
869	56	28	58	120982
1530	54	38	60	176508
2172	89	30	108	179321
901	40	22	49	123185
463	25	26	0	52746
3201	92	25	121	385534
371	18	18	1	33170
1192	63	11	20	101645
1583	44	26	43	149061
1439	33	25	69	165446
1764	84	38	78	237213
1495	88	44	86	173326
1373	55	30	44	133131
2187	60	40	104	258873
1491	66	34	63	180083
4041	154	47	158	324799
1706	53	30	102	230964
2152	119	31	77	236785
1036	41	23	82	135473
1882	61	36	115	202925
1929	58	36	101	215147
2242	75	30	80	344297
1220	33	25	50	153935
1289	40	39	83	132943
2515	92	34	123	174724
2147	100	31	73	174415
2352	112	31	81	225548
1638	73	33	105	223632
1222	40	25	47	124817
1812	45	33	105	221698
1677	60	35	94	210767
1579	62	42	44	170266
1731	75	43	114	260561
807	31	30	38	84853
2452	77	33	107	294424
829	34	13	30	101011
1940	46	32	71	215641
2662	99	36	84	325107
186	17	0	0	7176
1499	66	28	59	167542
865	30	14	33	106408
1793	76	17	42	96560
2527	146	32	96	265769
2747	67	30	106	269651
1324	56	35	56	149112
2702	107	20	57	175824
1383	58	28	59	152871
1179	34	28	39	111665
2099	61	39	34	116408
4308	119	34	76	362301
918	42	26	20	78800
1831	66	39	91	183167
3373	89	39	115	277965
1713	44	33	85	150629
1438	66	28	76	168809
496	24	4	8	24188
2253	259	39	79	329267
744	17	18	21	65029
1161	64	14	30	101097
2352	41	29	76	218946
2144	68	44	101	244052
4691	168	21	94	341570
1112	43	16	27	103597
2694	132	28	92	233328
1973	105	35	123	256462
1769	71	28	75	206161
3148	112	38	128	311473
2474	94	23	105	235800
2084	82	36	55	177939
1954	70	32	56	207176
1226	57	29	41	196553
1389	53	25	72	174184
1496	103	27	67	143246
2269	121	36	75	187559
1833	62	28	114	187681
1268	52	23	118	119016
1943	52	40	77	182192
893	32	23	22	73566
1762	62	40	66	194979
1403	45	28	69	167488
1425	46	34	105	143756
1857	63	33	116	275541
1840	75	28	88	243199
1502	88	34	73	182999
1441	46	30	99	135649
1420	53	33	62	152299
1416	37	22	53	120221
2970	90	38	118	346485
1317	63	26	30	145790
1644	78	35	100	193339
870	25	8	49	80953
1654	45	24	24	122774
1054	46	29	67	130585
937	41	20	46	112611
3004	144	29	57	286468
2008	82	45	75	241066
2547	91	37	135	148446
1885	71	33	68	204713
1626	63	33	124	182079
1468	53	25	33	140344
2445	62	32	98	220516
1964	63	29	58	243060
1381	32	28	68	162765
1369	39	28	81	182613
1659	62	31	131	232138
2888	117	52	110	265318
1290	34	21	37	85574
2845	92	24	130	310839
1982	93	41	93	225060
1904	54	33	118	232317
1391	144	32	39	144966
602	14	19	13	43287
1743	61	20	74	155754
1559	109	31	81	164709
2014	38	31	109	201940
2143	73	32	151	235454
2146	75	18	51	220801
874	50	23	28	99466
1590	61	17	40	92661
1590	55	20	56	133328
1210	77	12	27	61361
2072	75	17	37	125930
1281	72	30	83	100750
1401	50	31	54	224549
834	32	10	27	82316
1105	53	13	28	102010
1272	42	22	59	101523
1944	71	42	133	243511
391	10	1	12	22938
761	35	9	0	41566
1605	65	32	106	152474
530	25	11	23	61857
1988	66	25	44	99923
1386	41	36	71	132487
2395	86	31	116	317394
387	16	0	4	21054
1742	42	24	62	209641
620	19	13	12	22648
449	19	8	18	31414
800	45	13	14	46698
1684	65	19	60	131698
1050	35	18	7	91735
2699	95	33	98	244749
1606	49	40	64	184510
1502	37	22	29	79863
1204	64	38	32	128423
1138	38	24	25	97839
568	34	8	16	38214
1459	32	35	48	151101
2158	65	43	100	272458
1111	52	43	46	172494
1421	62	14	45	108043
2833	65	41	129	328107
1955	83	38	130	250579
2922	95	45	136	351067
1002	29	31	59	158015
1060	18	13	25	98866
956	33	28	32	85439
2186	247	31	63	229242
3604	139	40	95	351619
1035	29	30	14	84207
1417	118	16	36	120445
3261	110	37	113	324598
1587	67	30	47	131069
1424	42	35	92	204271
1701	65	32	70	165543
1249	94	27	19	141722
946	64	20	50	116048
1926	81	18	41	250047
3352	95	31	91	299775
1641	67	31	111	195838
2035	63	21	41	173260
2312	83	39	120	254488
1369	45	41	135	104389
1577	30	13	27	136084
2201	70	32	87	199476
961	32	18	25	92499
1900	83	39	131	224330
1254	31	14	45	135781
1335	67	7	29	74408
1597	66	17	58	81240
207	10	0	4	14688
1645	70	30	47	181633
2429	103	37	109	271856
151	5	0	7	7199
474	20	5	12	46660
141	5	1	0	17547
1639	36	16	37	133368
872	34	32	37	95227
1318	48	24	46	152601
1018	40	17	15	98146
1383	43	11	42	79619
1314	31	24	7	59194
1335	42	22	54	139942
1403	46	12	54	118612
910	33	19	14	72880
616	18	13	16	65475
1407	55	17	33	99643
771	35	15	32	71965
766	59	16	21	77272
473	19	24	15	49289
1376	66	15	38	135131
1232	60	17	22	108446
1521	36	18	28	89746
572	25	20	10	44296
1059	47	16	31	77648
1544	54	16	32	181528
1230	53	18	32	134019
1206	40	22	43	124064
1205	40	8	27	92630
1255	39	17	37	121848
613	14	18	20	52915
721	45	16	32	81872
1109	36	23	0	58981
740	28	22	5	53515
1126	44	13	26	60812
728	30	13	10	56375
689	22	16	27	65490
592	17	16	11	80949
995	31	20	29	76302
1613	55	22	25	104011
2048	54	17	55	98104
705	21	18	23	67989
301	14	17	5	30989
1803	81	12	43	135458
799	35	7	23	73504
861	43	17	34	63123
1186	46	14	36	61254
1451	30	23	35	74914
628	23	17	0	31774
1161	38	14	37	81437
1463	54	15	28	87186
742	20	17	16	50090
979	53	21	26	65745
675	45	18	38	56653
1241	39	18	23	158399
676	20	17	22	46455
1049	24	17	30	73624
620	31	16	16	38395
1081	35	15	18	91899
1688	151	21	28	139526
736	52	16	32	52164
617	30	14	21	51567
812	31	15	23	70551
1051	29	17	29	84856
1656	57	15	50	102538
705	40	15	12	86678
945	44	10	21	85709
554	25	6	18	34662
1597	77	22	27	150580
982	35	21	41	99611
222	11	1	13	19349
1212	63	18	12	99373
1143	44	17	21	86230
435	19	4	8	30837
532	13	10	26	31706
882	42	16	27	89806
608	38	16	13	62088
459	29	9	16	40151
578	20	16	2	27634
826	27	17	42	76990
509	20	7	5	37460
717	19	15	37	54157
637	37	14	17	49862
857	26	14	38	84337
830	42	18	37	64175
652	49	12	29	59382
707	30	16	32	119308
954	49	21	35	76702
1461	67	19	17	103425
672	28	16	20	70344
778	19	1	7	43410
1141	49	16	46	104838
680	27	10	24	62215
1090	30	19	40	69304
616	22	12	3	53117
285	12	2	10	19764
1145	31	14	37	86680
733	20	17	17	84105
888	20	19	28	77945
849	39	14	19	89113
1182	29	11	29	91005
528	16	4	8	40248
642	27	16	10	64187
947	21	20	15	50857
819	19	12	15	56613
757	35	15	28	62792
894	14	16	17	72535

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154015&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154015&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154015&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Gwilym Jenkins' @ jenkins.wessa.net

Correlations for all pairs of data series (method=kendall)
	pageviews	logins	compendiums_reviewed	blogged_computations	time_in_rfc
pageviews	1	0.661	0.527	0.627	0.739
logins	0.661	1	0.453	0.523	0.609
compendiums_reviewed	0.527	0.453	1	0.574	0.59
blogged_computations	0.627	0.523	0.574	1	0.683
time_in_rfc	0.739	0.609	0.59	0.683	1

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=kendall) \tabularnewline
  & pageviews & logins & compendiums_reviewed & blogged_computations & time_in_rfc \tabularnewline
pageviews & 1 & 0.661 & 0.527 & 0.627 & 0.739 \tabularnewline
logins & 0.661 & 1 & 0.453 & 0.523 & 0.609 \tabularnewline
compendiums_reviewed & 0.527 & 0.453 & 1 & 0.574 & 0.59 \tabularnewline
blogged_computations & 0.627 & 0.523 & 0.574 & 1 & 0.683 \tabularnewline
time_in_rfc & 0.739 & 0.609 & 0.59 & 0.683 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154015&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=kendall)[/C][/ROW]
[ROW][C] [/C][C]pageviews[/C][C]logins[/C][C]compendiums_reviewed[/C][C]blogged_computations[/C][C]time_in_rfc[/C][/ROW]
[ROW][C]pageviews[/C][C]1[/C][C]0.661[/C][C]0.527[/C][C]0.627[/C][C]0.739[/C][/ROW]
[ROW][C]logins[/C][C]0.661[/C][C]1[/C][C]0.453[/C][C]0.523[/C][C]0.609[/C][/ROW]
[ROW][C]compendiums_reviewed[/C][C]0.527[/C][C]0.453[/C][C]1[/C][C]0.574[/C][C]0.59[/C][/ROW]
[ROW][C]blogged_computations[/C][C]0.627[/C][C]0.523[/C][C]0.574[/C][C]1[/C][C]0.683[/C][/ROW]
[ROW][C]time_in_rfc[/C][C]0.739[/C][C]0.609[/C][C]0.59[/C][C]0.683[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154015&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154015&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Correlations for all pairs of data series (method=kendall)
	pageviews	logins	compendiums_reviewed	blogged_computations	time_in_rfc
pageviews	1	0.661	0.527	0.627	0.739
logins	0.661	1	0.453	0.523	0.609
compendiums_reviewed	0.527	0.453	1	0.574	0.59
blogged_computations	0.627	0.523	0.574	1	0.683
time_in_rfc	0.739	0.609	0.59	0.683	1

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
pageviews;logins	0.7588	0.845	0.6609
p-value	(0)	(0)	(0)
pageviews;compendiums_reviewed	0.6652	0.7185	0.5273
p-value	(0)	(0)	(0)
pageviews;blogged_computations	0.7606	0.8249	0.6272
p-value	(0)	(0)	(0)
pageviews;time_in_rfc	0.8928	0.9025	0.7387
p-value	(0)	(0)	(0)
logins;compendiums_reviewed	0.5488	0.6284	0.4525
p-value	(0)	(0)	(0)
logins;blogged_computations	0.5661	0.7178	0.523
p-value	(0)	(0)	(0)
logins;time_in_rfc	0.716	0.7982	0.609
p-value	(0)	(0)	(0)
compendiums_reviewed;blogged_computations	0.7623	0.7722	0.574
p-value	(0)	(0)	(0)
compendiums_reviewed;time_in_rfc	0.758	0.7892	0.5899
p-value	(0)	(0)	(0)
blogged_computations;time_in_rfc	0.8309	0.8717	0.683
p-value	(0)	(0)	(0)

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series with p-values \tabularnewline
pair & Pearson r & Spearman rho & Kendall tau \tabularnewline
pageviews;logins & 0.7588 & 0.845 & 0.6609 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
pageviews;compendiums_reviewed & 0.6652 & 0.7185 & 0.5273 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
pageviews;blogged_computations & 0.7606 & 0.8249 & 0.6272 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
pageviews;time_in_rfc & 0.8928 & 0.9025 & 0.7387 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
logins;compendiums_reviewed & 0.5488 & 0.6284 & 0.4525 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
logins;blogged_computations & 0.5661 & 0.7178 & 0.523 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
logins;time_in_rfc & 0.716 & 0.7982 & 0.609 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
compendiums_reviewed;blogged_computations & 0.7623 & 0.7722 & 0.574 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
compendiums_reviewed;time_in_rfc & 0.758 & 0.7892 & 0.5899 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
blogged_computations;time_in_rfc & 0.8309 & 0.8717 & 0.683 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=154015&T=2

[TABLE]
[ROW][C]Correlations for all pairs of data series with p-values[/C][/ROW]
[ROW][C]pair[/C][C]Pearson r[/C][C]Spearman rho[/C][C]Kendall tau[/C][/ROW]
[ROW][C]pageviews;logins[/C][C]0.7588[/C][C]0.845[/C][C]0.6609[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]pageviews;compendiums_reviewed[/C][C]0.6652[/C][C]0.7185[/C][C]0.5273[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]pageviews;blogged_computations[/C][C]0.7606[/C][C]0.8249[/C][C]0.6272[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]pageviews;time_in_rfc[/C][C]0.8928[/C][C]0.9025[/C][C]0.7387[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]logins;compendiums_reviewed[/C][C]0.5488[/C][C]0.6284[/C][C]0.4525[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]logins;blogged_computations[/C][C]0.5661[/C][C]0.7178[/C][C]0.523[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]logins;time_in_rfc[/C][C]0.716[/C][C]0.7982[/C][C]0.609[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]compendiums_reviewed;blogged_computations[/C][C]0.7623[/C][C]0.7722[/C][C]0.574[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]compendiums_reviewed;time_in_rfc[/C][C]0.758[/C][C]0.7892[/C][C]0.5899[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]blogged_computations;time_in_rfc[/C][C]0.8309[/C][C]0.8717[/C][C]0.683[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=154015&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=154015&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
pageviews;logins	0.7588	0.845	0.6609
p-value	(0)	(0)	(0)
pageviews;compendiums_reviewed	0.6652	0.7185	0.5273
p-value	(0)	(0)	(0)
pageviews;blogged_computations	0.7606	0.8249	0.6272
p-value	(0)	(0)	(0)
pageviews;time_in_rfc	0.8928	0.9025	0.7387
p-value	(0)	(0)	(0)
logins;compendiums_reviewed	0.5488	0.6284	0.4525
p-value	(0)	(0)	(0)
logins;blogged_computations	0.5661	0.7178	0.523
p-value	(0)	(0)	(0)
logins;time_in_rfc	0.716	0.7982	0.609
p-value	(0)	(0)	(0)
compendiums_reviewed;blogged_computations	0.7623	0.7722	0.574
p-value	(0)	(0)	(0)
compendiums_reviewed;time_in_rfc	0.758	0.7892	0.5899
p-value	(0)	(0)	(0)
blogged_computations;time_in_rfc	0.8309	0.8717	0.683
p-value	(0)	(0)	(0)

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = kendall ;

Parameters (R input):

par1 = kendall ;

R code (references can be found in the software module):

panel.tau <- function(x, y, digits=2, prefix='', cex.cor)
{
usr <- par('usr'); on.exit(par(usr))
par(usr = c(0, 1, 0, 1))
rr <- cor.test(x, y, method=par1)
r <- round(rr$p.value,2)
txt <- format(c(r, 0.123456789), digits=digits)[1]
txt <- paste(prefix, txt, sep='')
if(missing(cex.cor)) cex <- 0.5/strwidth(txt)
text(0.5, 0.5, txt, cex = cex)
}
panel.hist <- function(x, ...)
{
usr <- par('usr'); on.exit(par(usr))
par(usr = c(usr[1:2], 0, 1.5) )
h <- hist(x, plot = FALSE)
breaks <- h$breaks; nB <- length(breaks)
y <- h$counts; y <- y/max(y)
rect(breaks[-nB], 0, breaks[-1], y, col='grey', ...)
}
bitmap(file='test1.png')
pairs(t(y),diag.panel=panel.hist, upper.panel=panel.smooth, lower.panel=panel.tau, main=main)
dev.off()
load(file='createtable')
n <- length(y[,1])
n
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,paste('Correlations for all pairs of data series (method=',par1,')',sep=''),n+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,' ',header=TRUE)
for (i in 1:n) {
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
}
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,dimnames(t(x))[[2]][i],header=TRUE)
for (j in 1:n) {
r <- cor.test(y[i,],y[j,],method=par1)
a<-table.element(a,round(r$estimate,3))
}
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Correlations for all pairs of data series with p-values',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'pair',1,TRUE)
a<-table.element(a,'Pearson r',1,TRUE)
a<-table.element(a,'Spearman rho',1,TRUE)
a<-table.element(a,'Kendall tau',1,TRUE)
a<-table.row.end(a)
cor.test(y[1,],y[2,],method=par1)
for (i in 1:(n-1))
{
for (j in (i+1):n)
{
a<-table.row.start(a)
dum <- paste(dimnames(t(x))[[2]][i],';',dimnames(t(x))[[2]][j],sep='')
a<-table.element(a,dum,header=TRUE)
rp <- cor.test(y[i,],y[j,],method='pearson')
a<-table.element(a,round(rp$estimate,4))
rs <- cor.test(y[i,],y[j,],method='spearman')
a<-table.element(a,round(rs$estimate,4))
rk <- cor.test(y[i,],y[j,],method='kendall')
a<-table.element(a,round(rk$estimate,4))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=T)
a<-table.element(a,paste('(',round(rp$p.value,4),')',sep=''))
a<-table.element(a,paste('(',round(rs$p.value,4),')',sep=''))
a<-table.element(a,paste('(',round(rk$p.value,4),')',sep=''))
a<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code