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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

Sun, 18 Dec 2011 10:11:31 -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/18/t1324221124d8wrls8z6h4mftu.htm/, Retrieved Sun, 05 May 2024 14:34:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156955, Retrieved Sun, 05 May 2024 14:34:54 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

154

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

-     [Paired and Unpaired Two Samples Tests about the Mean] [] [2010-11-18 18:11:09] [2e1e44f0ae3cb9513dc28781dfdb387b]
-    D  [Paired and Unpaired Two Samples Tests about the Mean] [] [2011-10-26 14:24:41] [5c12c14850e1dddd68cd7e26a7cf987c]
- RMPD    [(Partial) Autocorrelation Function] [Auto Correlation ...] [2011-12-18 12:54:39] [5c12c14850e1dddd68cd7e26a7cf987c]
- RMPD        [Kendall tau Correlation Matrix] [Kendall tau Corre...] [2011-12-18 15:11:31] [12a6074303e7dbf450a4f3ff6a9ce824] [Current]

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Dataseries X:

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Histogram

Boxplots

449290	1769	240	118	151036	26258
312831	810	111	55	92556	14881
275326	919	91	67	57803	16957
266451	769	68	60	68701	18717
244190	712	57	39	41152	8464
233497	760	61	82	92596	26641
229437	664	77	55	35728	9724
221399	1118	129	76	54002	20323
218900	624	217	55	62897	22557
215480	694	104	45	57021	14612
214975	861	117	76	58092	4362
204812	910	108	53	29245	6372
200652	975	99	75	47007	13448
200609	742	48	54	42009	14349
191923	890	58	46	36022	10881
191463	697	90	78	83700	20517
189007	651	87	63	46456	13275
186704	456	60	50	38844	8030
184024	815	40	52	40078	16318
183873	726	95	26	46609	11252
182328	526	61	95	73116	11219
178613	483	67	68	74990	19365
178228	628	67	73	49598	14426
176034	597	68	35	40400	2570
174876	584	54	53	29010	9863
174181	616	149	58	58534	15657
173779	588	80	43	66616	21224
172071	611	64	71	52143	20488
168465	426	52	45	33629	10265
166226	880	86	30	57476	7768
164516	496	42	54	31076	10462
161553	734	74	54	63369	5989
156916	562	85	48	20465	6200
155934	297	77	67	44663	15329
154806	301	38	35	27525	10698
153278	606	56	48	57786	6837
152455	474	65	67	41211	9188
151621	427	41	50	34711	9556
150416	384	54	62	31172	8247
148950	407	56	39	37477	7028
148531	395	32	25	23284	5753
147766	535	92	26	28549	6852
146552	875	55	62	41554	10615
146020	771	71	40	29351	9289
144677	452	77	54	59147	6185
144193	627	60	67	92901	12964
143910	496	46	32	48140	8895
143546	569	80	50	36205	5299
141868	497	37	48	44810	9435
140935	375	49	45	28735	5389
140303	756	89	59	75043	9970
139901	282	85	40	37403	13958
139780	513	25	39	30165	7233
139075	587	69	66	76542	13178
136333	539	75	68	66856	14884
136220	518	48	30	40715	7820
134379	498	53	42	33287	10165
134153	391	52	75	78950	24369
131263	449	52	33	100674	7642
130414	454	52	50	33277	13823
129419	495	45	35	53349	13073
128907	843	65	83	29653	9422
126905	538	54	64	34241	11580
126602	597	53	31	44093	15604
125760	471	49	46	26757	9831
125728	298	42	78	33994	12840
124626	466	57	27	53216	6616
124401	405	41	49	31032	7987
122294	721	82	54	46154	17327
122259	618	91	49	25629	8874
121593	629	71	50	49830	8058
121391	468	41	48	28113	8683
120414	661	95	53	74608	7192
120111	273	47	47	39644	13400
119070	465	50	35	23110	8374
115944	360	44	51	32665	8208
115572	535	37	45	65897	12112
115343	347	56	43	61281	10170
113870	381	61	67	30874	12396
113245	287	37	36	38610	6873
111940	315	59	47	35139	14146
111924	497	49	55	41194	4260
109807	372	56	52	32683	10566
108685	341	26	23	22527	5953
106742	366	65	25	37941	5322
104972	352	61	36	50008	5413
102378	248	36	48	64622	12310
102194	384	33	44	25820	7573
102141	673	71	36	31141	7230
101560	442	65	46	13310	3394
100798	312	43	25	28470	8191
98629	560	49	38	33797	5162
97181	438	32	37	28263	10226
95704	322	42	44	60132	11270
95276	410	62	62	52338	10837
94982	391	37	38	35378	9791
94341	249	53	24	19249	7488
94332	350	29	25	84205	9184
94127	386	18	17	23494	8181
93107	483	49	44	23333	8022
90385	360	54	39	41622	8620
89920	229	31	12	13018	1350
88874	241	39	30	22698	5141
86249	574	94	41	21055	7945
85610	306	31	46	98177	10623
84971	395	71	34	42249	10138
84315	248	36	21	61849	1661
82209	244	95	42	22883	6900
81293	212	31	23	24460	7162
80420	211	64	54	42005	14697
72904	190	37	30	15292	4574
72559	251	22	25	27084	7509
71921	345	37	2	10956	3495
71894	287	57	36	34545	1900
64149	305	52	0	13497	70
63952	247	23	15	8019	3080
60373	165	39	3	32689	443
60138	253	23	16	21152	4911
58280	240	20	41	31747	6562
56252	244	26	26	14399	4204
52197	310	52	16	10726	3149
51201	263	27	13	2325	593
50913	256	42	17	17215	3456
49176	291	34	22	40911	9570
48188	205	28	12	22346	2102
43410	292	19	7	2781	4
40248	183	16	8	5444	775
31970	101	15	5	4157	1283
27918	215	24	13	53249	3878
27676	194	22	2	5842	522
19764	75	12	10	5752	2416
19349	67	12	13	3895	786
11796	79	9	1	0	0
10674	33	9	0	0	0
8812	97	13	0	2179	548
7215	72	18	0	1423	603
7131	27	4	0	0	0
6836	11	3	0	0	0
5118	6	3	5	0	0
3616	14	5	0	0	0
0	0	1	0	0	0
0	0	0	0	0	0
0	0	0	0	0	0
0	0	0	0	0	0

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=156955&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=156955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156955&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=pearson)
	Y	X1	X2	X3	X4	X5
Y	1	0.879	0.772	0.784	0.704	0.737
X1	0.879	1	0.777	0.741	0.649	0.646
X2	0.772	0.777	1	0.667	0.613	0.621
X3	0.784	0.741	0.667	1	0.705	0.787
X4	0.704	0.649	0.613	0.705	1	0.722
X5	0.737	0.646	0.621	0.787	0.722	1

\begin{tabular}{lllllllll}
\hline
Correlations for all pairs of data series (method=pearson) \tabularnewline
  & Y & X1 & X2 & X3 & X4 & X5 \tabularnewline
Y & 1 & 0.879 & 0.772 & 0.784 & 0.704 & 0.737 \tabularnewline
X1 & 0.879 & 1 & 0.777 & 0.741 & 0.649 & 0.646 \tabularnewline
X2 & 0.772 & 0.777 & 1 & 0.667 & 0.613 & 0.621 \tabularnewline
X3 & 0.784 & 0.741 & 0.667 & 1 & 0.705 & 0.787 \tabularnewline
X4 & 0.704 & 0.649 & 0.613 & 0.705 & 1 & 0.722 \tabularnewline
X5 & 0.737 & 0.646 & 0.621 & 0.787 & 0.722 & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156955&T=1

[TABLE]
[ROW][C]Correlations for all pairs of data series (method=pearson)[/C][/ROW]
[ROW][C] [/C][C]Y[/C][C]X1[/C][C]X2[/C][C]X3[/C][C]X4[/C][C]X5[/C][/ROW]
[ROW][C]Y[/C][C]1[/C][C]0.879[/C][C]0.772[/C][C]0.784[/C][C]0.704[/C][C]0.737[/C][/ROW]
[ROW][C]X1[/C][C]0.879[/C][C]1[/C][C]0.777[/C][C]0.741[/C][C]0.649[/C][C]0.646[/C][/ROW]
[ROW][C]X2[/C][C]0.772[/C][C]0.777[/C][C]1[/C][C]0.667[/C][C]0.613[/C][C]0.621[/C][/ROW]
[ROW][C]X3[/C][C]0.784[/C][C]0.741[/C][C]0.667[/C][C]1[/C][C]0.705[/C][C]0.787[/C][/ROW]
[ROW][C]X4[/C][C]0.704[/C][C]0.649[/C][C]0.613[/C][C]0.705[/C][C]1[/C][C]0.722[/C][/ROW]
[ROW][C]X5[/C][C]0.737[/C][C]0.646[/C][C]0.621[/C][C]0.787[/C][C]0.722[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156955&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=pearson)
	Y	X1	X2	X3	X4	X5
Y	1	0.879	0.772	0.784	0.704	0.737
X1	0.879	1	0.777	0.741	0.649	0.646
X2	0.772	0.777	1	0.667	0.613	0.621
X3	0.784	0.741	0.667	1	0.705	0.787
X4	0.704	0.649	0.613	0.705	1	0.722
X5	0.737	0.646	0.621	0.787	0.722	1

Correlations for all pairs of data series with p-values
pair	Pearson r	Spearman rho	Kendall tau
Y;X1	0.8789	0.8542	0.6822
p-value	(0)	(0)	(0)
Y;X2	0.7716	0.7354	0.5684
p-value	(0)	(0)	(0)
Y;X3	0.7841	0.7596	0.5836
p-value	(0)	(0)	(0)
Y;X4	0.7036	0.6521	0.4906
p-value	(0)	(0)	(0)
Y;X5	0.7372	0.6973	0.5272
p-value	(0)	(0)	(0)
X1;X2	0.7766	0.7705	0.5992
p-value	(0)	(0)	(0)
X1;X3	0.7406	0.7122	0.5385
p-value	(0)	(0)	(0)
X1;X4	0.6493	0.6242	0.4558
p-value	(0)	(0)	(0)
X1;X5	0.6458	0.6237	0.4568
p-value	(0)	(0)	(0)
X2;X3	0.6667	0.7003	0.5231
p-value	(0)	(0)	(0)
X2;X4	0.6129	0.6073	0.4588
p-value	(0)	(0)	(0)
X2;X5	0.6212	0.5786	0.4249
p-value	(0)	(0)	(0)
X3;X4	0.7049	0.6715	0.5064
p-value	(0)	(0)	(0)
X3;X5	0.787	0.7662	0.5974
p-value	(0)	(0)	(0)
X4;X5	0.7216	0.7084	0.5493
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
Y;X1 & 0.8789 & 0.8542 & 0.6822 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
Y;X2 & 0.7716 & 0.7354 & 0.5684 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
Y;X3 & 0.7841 & 0.7596 & 0.5836 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
Y;X4 & 0.7036 & 0.6521 & 0.4906 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
Y;X5 & 0.7372 & 0.6973 & 0.5272 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X1;X2 & 0.7766 & 0.7705 & 0.5992 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X1;X3 & 0.7406 & 0.7122 & 0.5385 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X1;X4 & 0.6493 & 0.6242 & 0.4558 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X1;X5 & 0.6458 & 0.6237 & 0.4568 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X2;X3 & 0.6667 & 0.7003 & 0.5231 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X2;X4 & 0.6129 & 0.6073 & 0.4588 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X2;X5 & 0.6212 & 0.5786 & 0.4249 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X3;X4 & 0.7049 & 0.6715 & 0.5064 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X3;X5 & 0.787 & 0.7662 & 0.5974 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
X4;X5 & 0.7216 & 0.7084 & 0.5493 \tabularnewline
p-value & (0) & (0) & (0) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156955&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]Y;X1[/C][C]0.8789[/C][C]0.8542[/C][C]0.6822[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]Y;X2[/C][C]0.7716[/C][C]0.7354[/C][C]0.5684[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]Y;X3[/C][C]0.7841[/C][C]0.7596[/C][C]0.5836[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]Y;X4[/C][C]0.7036[/C][C]0.6521[/C][C]0.4906[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]Y;X5[/C][C]0.7372[/C][C]0.6973[/C][C]0.5272[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X1;X2[/C][C]0.7766[/C][C]0.7705[/C][C]0.5992[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X1;X3[/C][C]0.7406[/C][C]0.7122[/C][C]0.5385[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X1;X4[/C][C]0.6493[/C][C]0.6242[/C][C]0.4558[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X1;X5[/C][C]0.6458[/C][C]0.6237[/C][C]0.4568[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X2;X3[/C][C]0.6667[/C][C]0.7003[/C][C]0.5231[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X2;X4[/C][C]0.6129[/C][C]0.6073[/C][C]0.4588[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X2;X5[/C][C]0.6212[/C][C]0.5786[/C][C]0.4249[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X3;X4[/C][C]0.7049[/C][C]0.6715[/C][C]0.5064[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X3;X5[/C][C]0.787[/C][C]0.7662[/C][C]0.5974[/C][/ROW]
[ROW][C]p-value[/C][C](0)[/C][C](0)[/C][C](0)[/C][/ROW]
[ROW][C]X4;X5[/C][C]0.7216[/C][C]0.7084[/C][C]0.5493[/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=156955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156955&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
Y;X1	0.8789	0.8542	0.6822
p-value	(0)	(0)	(0)
Y;X2	0.7716	0.7354	0.5684
p-value	(0)	(0)	(0)
Y;X3	0.7841	0.7596	0.5836
p-value	(0)	(0)	(0)
Y;X4	0.7036	0.6521	0.4906
p-value	(0)	(0)	(0)
Y;X5	0.7372	0.6973	0.5272
p-value	(0)	(0)	(0)
X1;X2	0.7766	0.7705	0.5992
p-value	(0)	(0)	(0)
X1;X3	0.7406	0.7122	0.5385
p-value	(0)	(0)	(0)
X1;X4	0.6493	0.6242	0.4558
p-value	(0)	(0)	(0)
X1;X5	0.6458	0.6237	0.4568
p-value	(0)	(0)	(0)
X2;X3	0.6667	0.7003	0.5231
p-value	(0)	(0)	(0)
X2;X4	0.6129	0.6073	0.4588
p-value	(0)	(0)	(0)
X2;X5	0.6212	0.5786	0.4249
p-value	(0)	(0)	(0)
X3;X4	0.7049	0.6715	0.5064
p-value	(0)	(0)	(0)
X3;X5	0.787	0.7662	0.5974
p-value	(0)	(0)	(0)
X4;X5	0.7216	0.7084	0.5493
p-value	(0)	(0)	(0)

Figure 1

PNG link

Postscript link

PDF link

Parameters (Session):

Parameters (R input):

par1 = pearson ;

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