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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_variancereduction.wasp
Title produced by softwareVariance Reduction Matrix
Date of computationTue, 06 Dec 2011 14:45:50 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/06/t13232007776z2vxxwix9e4d9e.htm/, Retrieved Mon, 12 May 2025 17:56:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151836, Retrieved Mon, 12 May 2025 17:56:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact222

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP     [Variance Reduction Matrix] [] [2011-12-06 19:45:50] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
-           [Variance Reduction Matrix] [variance reductio...] [2011-12-08 13:13:19] [d5821fed422662f85834b1edae505ce2]
- RM        [Variance Reduction Matrix] [] [2011-12-13 16:57:03] [4f851df07e928502141e501e960f13e4]
- R         [Variance Reduction Matrix] [] [2011-12-14 10:20:49] [5b1044653d12da6c563533920760fdbb]
- RMP       [Spectral Analysis] [] [2011-12-14 10:25:56] [5b1044653d12da6c563533920760fdbb]
-           [Variance Reduction Matrix] [Variance Reductio...] [2011-12-14 13:43:09] [2c6fcdc40ef3b1a27716d75d6f478b32]
-           [Variance Reduction Matrix] [Variance Reductio...] [2011-12-14 13:43:09] [2c6fcdc40ef3b1a27716d75d6f478b32]
- RM          [Variance Reduction Matrix] [] [2012-12-21 13:44:26] [74be16979710d4c4e7c6647856088456]
- RM        [Variance Reduction Matrix] [] [2011-12-18 11:16:26] [4c0148be6b1ebc4ef8d5b4e23a77fcfa]
- R         [Variance Reduction Matrix] [variance reductio...] [2011-12-18 12:30:04] [2e8e2c135ae7a1d1ed044e87454acf31]
- RM        [Variance Reduction Matrix] [] [2011-12-19 12:07:31] [182e2e10fa38557ff81755a04c8c64c0]
- R         [Variance Reduction Matrix] [] [2011-12-19 17:30:39] [880b2848ba77f3f5ee007f117bbf00fe]
- RM        [Variance Reduction Matrix] [] [2011-12-21 17:32:56] [0f1ce50ec9632e206f4325c3ca8926e2]
- R         [Variance Reduction Matrix] [Paper VRM] [2011-12-22 09:16:10] [98f3ba974ec9d6d754dcc83206539a91]
- RM        [Variance Reduction Matrix] [] [2011-12-22 14:22:52] [2d3d135c7070430a7cc2b1c9a86f42b1]
- RM        [Variance Reduction Matrix] [VRM] [2011-12-22 17:51:32] [c035d973aa8488be257660c2dc4ec375]
- R         [Variance Reduction Matrix] [paper deel 2 vari...] [2011-12-22 21:16:19] [d5821fed422662f85834b1edae505ce2]
- R         [Variance Reduction Matrix] [paper deel 2 vari...] [2011-12-22 21:16:19] [d5821fed422662f85834b1edae505ce2]
- RM        [Variance Reduction Matrix] [Variance Reductio...] [2011-12-22 22:57:32] [0b0939f48f9203aad97203a2adcb743b]
- R         [Variance Reduction Matrix] [VRM] [2011-12-23 01:07:08] [7e17e0c557325a60eb6c8af681a1c273]
- R         [Variance Reduction Matrix] [WS9 variance redu...] [2012-11-16 20:11:05] [bc2c61a583a6186666a33616ccc196e4]
- RM        [Variance Reduction Matrix] [] [2012-11-18 13:38:31] [8fcd082199f7dbedf65d69a953eb5ad7]
- RM        [Variance Reduction Matrix] [VRM] [2012-11-23 15:41:11] [74be16979710d4c4e7c6647856088456]
- RMP       [Spectral Analysis] [spectral analysis] [2012-11-23 15:49:48] [fa543719fe3f8358943b948de15add90]
- RMP       [Spectral Analysis] [spectral analysis 2] [2012-11-23 15:52:45] [fa543719fe3f8358943b948de15add90]
- RMP       [(Partial) Autocorrelation Function] [ACF] [2012-11-23 15:55:29] [fa543719fe3f8358943b948de15add90]
-   P         [(Partial) Autocorrelation Function] [ACF 2] [2012-11-23 16:02:05] [fa543719fe3f8358943b948de15add90]
- RMP         [Standard Deviation-Mean Plot] [SDMP] [2012-11-23 16:11:43] [fa543719fe3f8358943b948de15add90]
- R         [Variance Reduction Matrix] [variance reductio...] [2012-11-26 21:22:23] [dbdfdab7c884aa7a69290945f2923e51]
- RM        [Variance Reduction Matrix] [] [2012-12-08 18:56:34] [8c6900b6affe5ced50ee5724b2e31c80]
- RMP       [Spectral Analysis] [CP met 1] [2012-12-13 09:12:06] [a87a0df67d47b041e4d219678c935cd7]
- RMP       [(Partial) Autocorrelation Function] [ACF ] [2012-12-13 09:18:10] [a87a0df67d47b041e4d219678c935cd7]
- RMP       [(Partial) Autocorrelation Function] [ACF 2] [2012-12-13 09:22:09] [a87a0df67d47b041e4d219678c935cd7]
- RMP       [(Partial) Autocorrelation Function] [ACF na diff ] [2012-12-13 09:28:09] [a87a0df67d47b041e4d219678c935cd7]
- RM        [Standard Deviation-Mean Plot] [STDV ] [2012-12-13 09:37:59] [a87a0df67d47b041e4d219678c935cd7]
- RMP         [ARIMA Backward Selection] [arima backward] [2012-12-13 10:15:18] [a87a0df67d47b041e4d219678c935cd7]
- RMPD        [Skewness and Kurtosis Test] [skewness en kurt ] [2012-12-13 10:35:52] [a87a0df67d47b041e4d219678c935cd7]
- RMPD        [Central Tendency] [2de test op norma...] [2012-12-13 10:40:58] [a87a0df67d47b041e4d219678c935cd7]
- RMP         [ARIMA Forecasting] [arima forcast ] [2012-12-13 10:50:07] [a87a0df67d47b041e4d219678c935cd7]
- R         [Variance Reduction Matrix] [Variantie reducti...] [2012-12-17 16:03:50] [6c4cddab89f59a22f4fb07e80256756e]
- R         [Variance Reduction Matrix] [VRM aantal overna...] [2012-12-17 16:12:05] [6c4cddab89f59a22f4fb07e80256756e]
- R         [Variance Reduction Matrix] [VRM overnachtingen] [2012-12-17 16:19:24] [6c4cddab89f59a22f4fb07e80256756e]
-             [Variance Reduction Matrix] [VRM overnachtingen] [2012-12-17 16:21:50] [6c4cddab89f59a22f4fb07e80256756e]
- R         [Variance Reduction Matrix] [dfsdgsdg] [2012-12-17 16:20:20] [6c4cddab89f59a22f4fb07e80256756e]
- R  D      [Variance Reduction Matrix] [paper deel 4 vari...] [2012-12-18 16:22:20] [97c624f8202925579dccb4f50bae925c]
- RM        [Variance Reduction Matrix] [blog 13 paper 2012] [2012-12-19 00:55:20] [9e08e0bf3a846135420010fecb8b28cd]
- RM        [Variance Reduction Matrix] [] [2012-12-20 17:46:02] [07135448e3e28ff93d39332c64d7f130]
- RM        [Variance Reduction Matrix] [Paper Deel 4 Arima 1] [2012-12-21 13:50:34] [2972d443360a042d7188069add54b356]
- R  D      [Variance Reduction Matrix] [Variance reduction] [2012-12-21 15:58:39] [4acb2b89f689cf743a6b65cec03f73b4]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
655362
873127
1107897
1555964
1671159
1493308
2957796
2638691
1305669
1280496
921900
867888
652586
913831
1108544
1555827
1699283
1509458
3268975
2425016
1312703
1365498
934453
775019
651142
843192
1146766
1652601
1465906
1652734
2922334
2702805
1458956
1410363
1019279
936574
708917
885295
1099663
1576220
1487870
1488635
2882530
2677026
1404398
1344370
936865
872705
628151
953712
1160384
1400618
1661511
1495347
2918786
2775677
1407026
1370199
964526
850851
683118
847224
1073256
1514326
1503734
1507712
2865698
2788128
1391596
1366378
946295
859626

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151836&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151836&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151836&T=0

As an alternative you can also use a QR Code:  
QR Code


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)468240377400.069Range2640824Trim Var.328076329333.678
V(Y[t],d=1,D=0)384287209760.755Range3156049Trim Var.168829966800.806
V(Y[t],d=2,D=0)780671548226.982Range4552818Trim Var.457770959918.714
V(Y[t],d=3,D=0)2177117639858.82Range7243094Trim Var.1195081325442.09
V(Y[t],d=0,D=1)12196107477.809Range657820Trim Var.5567909805.6478
V(Y[t],d=1,D=1)32668245680.7954Range1149284Trim Var.11856129743.0189
V(Y[t],d=2,D=1)112466808107.788Range1980917Trim Var.41537059932.7553
V(Y[t],d=3,D=1)405657208851.6Range3851230Trim Var.157975674327.594
V(Y[t],d=0,D=2)38817776859.2123Range1149284Trim Var.18797714215.9053
V(Y[t],d=1,D=2)104471406393.447Range1934230Trim Var.38546476181.9122
V(Y[t],d=2,D=2)364770805831.82Range3435759Trim Var.134362066768.356
V(Y[t],d=3,D=2)1330720488090.72Range6543562Trim Var.496505179182.41

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 468240377400.069 & Range & 2640824 & Trim Var. & 328076329333.678 \tabularnewline
V(Y[t],d=1,D=0) & 384287209760.755 & Range & 3156049 & Trim Var. & 168829966800.806 \tabularnewline
V(Y[t],d=2,D=0) & 780671548226.982 & Range & 4552818 & Trim Var. & 457770959918.714 \tabularnewline
V(Y[t],d=3,D=0) & 2177117639858.82 & Range & 7243094 & Trim Var. & 1195081325442.09 \tabularnewline
V(Y[t],d=0,D=1) & 12196107477.809 & Range & 657820 & Trim Var. & 5567909805.6478 \tabularnewline
V(Y[t],d=1,D=1) & 32668245680.7954 & Range & 1149284 & Trim Var. & 11856129743.0189 \tabularnewline
V(Y[t],d=2,D=1) & 112466808107.788 & Range & 1980917 & Trim Var. & 41537059932.7553 \tabularnewline
V(Y[t],d=3,D=1) & 405657208851.6 & Range & 3851230 & Trim Var. & 157975674327.594 \tabularnewline
V(Y[t],d=0,D=2) & 38817776859.2123 & Range & 1149284 & Trim Var. & 18797714215.9053 \tabularnewline
V(Y[t],d=1,D=2) & 104471406393.447 & Range & 1934230 & Trim Var. & 38546476181.9122 \tabularnewline
V(Y[t],d=2,D=2) & 364770805831.82 & Range & 3435759 & Trim Var. & 134362066768.356 \tabularnewline
V(Y[t],d=3,D=2) & 1330720488090.72 & Range & 6543562 & Trim Var. & 496505179182.41 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151836&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]468240377400.069[/C][C]Range[/C][C]2640824[/C][C]Trim Var.[/C][C]328076329333.678[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]384287209760.755[/C][C]Range[/C][C]3156049[/C][C]Trim Var.[/C][C]168829966800.806[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]780671548226.982[/C][C]Range[/C][C]4552818[/C][C]Trim Var.[/C][C]457770959918.714[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2177117639858.82[/C][C]Range[/C][C]7243094[/C][C]Trim Var.[/C][C]1195081325442.09[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12196107477.809[/C][C]Range[/C][C]657820[/C][C]Trim Var.[/C][C]5567909805.6478[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]32668245680.7954[/C][C]Range[/C][C]1149284[/C][C]Trim Var.[/C][C]11856129743.0189[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]112466808107.788[/C][C]Range[/C][C]1980917[/C][C]Trim Var.[/C][C]41537059932.7553[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]405657208851.6[/C][C]Range[/C][C]3851230[/C][C]Trim Var.[/C][C]157975674327.594[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]38817776859.2123[/C][C]Range[/C][C]1149284[/C][C]Trim Var.[/C][C]18797714215.9053[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]104471406393.447[/C][C]Range[/C][C]1934230[/C][C]Trim Var.[/C][C]38546476181.9122[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]364770805831.82[/C][C]Range[/C][C]3435759[/C][C]Trim Var.[/C][C]134362066768.356[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1330720488090.72[/C][C]Range[/C][C]6543562[/C][C]Trim Var.[/C][C]496505179182.41[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151836&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151836&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Variance Reduction Matrix
V(Y[t],d=0,D=0)468240377400.069Range2640824Trim Var.328076329333.678
V(Y[t],d=1,D=0)384287209760.755Range3156049Trim Var.168829966800.806
V(Y[t],d=2,D=0)780671548226.982Range4552818Trim Var.457770959918.714
V(Y[t],d=3,D=0)2177117639858.82Range7243094Trim Var.1195081325442.09
V(Y[t],d=0,D=1)12196107477.809Range657820Trim Var.5567909805.6478
V(Y[t],d=1,D=1)32668245680.7954Range1149284Trim Var.11856129743.0189
V(Y[t],d=2,D=1)112466808107.788Range1980917Trim Var.41537059932.7553
V(Y[t],d=3,D=1)405657208851.6Range3851230Trim Var.157975674327.594
V(Y[t],d=0,D=2)38817776859.2123Range1149284Trim Var.18797714215.9053
V(Y[t],d=1,D=2)104471406393.447Range1934230Trim Var.38546476181.9122
V(Y[t],d=2,D=2)364770805831.82Range3435759Trim Var.134362066768.356
V(Y[t],d=3,D=2)1330720488090.72Range6543562Trim Var.496505179182.41


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
n <- length(x)
sx <- sort(x)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Variance Reduction Matrix',6,TRUE)
a<-table.row.end(a)
for (bigd in 0:2) {
for (smalld in 0:3) {
mylabel <- 'V(Y[t],d='
mylabel <- paste(mylabel,as.character(smalld),sep='')
mylabel <- paste(mylabel,',D=',sep='')
mylabel <- paste(mylabel,as.character(bigd),sep='')
mylabel <- paste(mylabel,')',sep='')
a<-table.row.start(a)
a<-table.element(a,mylabel,header=TRUE)
myx <- x
if (smalld > 0) myx <- diff(myx,lag=1,differences=smalld)
if (bigd > 0) myx <- diff(myx,lag=par1,differences=bigd)
a<-table.element(a,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,var(smyx[smyx>quantile(smyx,0.05) & smyxa<-table.row.end(a)
}
}
a<-table.end(a)
table.save(a,file='mytable.tab')
bitmap(file='pic0.png')
op <- par(mfrow=c(2,2))
plot(x,type='l',xlab='time',ylab='value',main='d=0, D=0')
plot(diff(x,lag=1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=0')
plot(diff(x,lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=0, D=1')
plot(diff(diff(x,lag=1,differences=1),lag=par1,differences=1),type='l',xlab='time',ylab='value',main='d=1, D=1')
par(op)
dev.off()