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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 17:12:11 -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/t1323209597iv996qozo8i7dxi.htm/, Retrieved Mon, 29 Apr 2024 03:55:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151988, Retrieved Mon, 29 Apr 2024 03:55:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact89

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 20:53:20] [f5fdea4413921432bb019d1f20c4f2ec]
- R P   [(Partial) Autocorrelation Function] [WS 9 Partial Auto...] [2011-12-06 21:05:30] [f5fdea4413921432bb019d1f20c4f2ec]
- RMP     [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-06 21:16:41] [f5fdea4413921432bb019d1f20c4f2ec]
- R P       [Spectral Analysis] [WS 9 Spectral Ana...] [2011-12-06 21:35:07] [f5fdea4413921432bb019d1f20c4f2ec]
- RMP           [Variance Reduction Matrix] [WS 9 Variance Red...] [2011-12-06 22:12:11] [6140f0163e532fc168d2f211324acd0a] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1015407
1039210
1258049
1469445
1552346
1549144
1785895
1662335
1629440
1467430
1202209
1076982
1039367
1063449
1335135
1491602
1591972
1641248
1898849
1798580
1762444
1622044
1368955
1262973
1195650
1269530
1479279
1607819
1712466
1721766
1949843
1821326
1757802
1590367
1260647
1149235
1016367
1027885
1262159
1520854
1544144
1564709
1821776
1741365
1623386
1498658
1241822
1136029
1035030
1078521
1279431
1171023
1573377
1589514
1859878
1783191
1689849
1619868
1323443
1177481

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=151988&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=151988&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151988&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)73118345838.7345Range934436Trim Var.59246423020.0311
V(Y[t],d=1,D=0)27946591822.0859Range732074Trim Var.20103832183.0914
V(Y[t],d=2,D=0)36606687860.9997Range896979Trim Var.25354623011.279
V(Y[t],d=3,D=0)110377945717.232Range1717059Trim Var.67365988774.1302
V(Y[t],d=0,D=1)15001882088.0833Range555912Trim Var.8891073437.76771
V(Y[t],d=1,D=1)7909631810.14431Range746167Trim Var.1265341951.19024
V(Y[t],d=2,D=1)21973687731.4609Range1129659Trim Var.2774641221.37436
V(Y[t],d=3,D=1)72376742688.4273Range2209565Trim Var.8311383510.92038
V(Y[t],d=0,D=2)41349317083.0635Range740007Trim Var.31852683751.8942
V(Y[t],d=1,D=2)18816324225.3529Range957679Trim Var.4742692161.93118
V(Y[t],d=2,D=2)49886096130.8565Range1433793Trim Var.9186651939.72989
V(Y[t],d=3,D=2)160032336614.364Range2830841Trim Var.28165368839.8103

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 73118345838.7345 & Range & 934436 & Trim Var. & 59246423020.0311 \tabularnewline
V(Y[t],d=1,D=0) & 27946591822.0859 & Range & 732074 & Trim Var. & 20103832183.0914 \tabularnewline
V(Y[t],d=2,D=0) & 36606687860.9997 & Range & 896979 & Trim Var. & 25354623011.279 \tabularnewline
V(Y[t],d=3,D=0) & 110377945717.232 & Range & 1717059 & Trim Var. & 67365988774.1302 \tabularnewline
V(Y[t],d=0,D=1) & 15001882088.0833 & Range & 555912 & Trim Var. & 8891073437.76771 \tabularnewline
V(Y[t],d=1,D=1) & 7909631810.14431 & Range & 746167 & Trim Var. & 1265341951.19024 \tabularnewline
V(Y[t],d=2,D=1) & 21973687731.4609 & Range & 1129659 & Trim Var. & 2774641221.37436 \tabularnewline
V(Y[t],d=3,D=1) & 72376742688.4273 & Range & 2209565 & Trim Var. & 8311383510.92038 \tabularnewline
V(Y[t],d=0,D=2) & 41349317083.0635 & Range & 740007 & Trim Var. & 31852683751.8942 \tabularnewline
V(Y[t],d=1,D=2) & 18816324225.3529 & Range & 957679 & Trim Var. & 4742692161.93118 \tabularnewline
V(Y[t],d=2,D=2) & 49886096130.8565 & Range & 1433793 & Trim Var. & 9186651939.72989 \tabularnewline
V(Y[t],d=3,D=2) & 160032336614.364 & Range & 2830841 & Trim Var. & 28165368839.8103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151988&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]73118345838.7345[/C][C]Range[/C][C]934436[/C][C]Trim Var.[/C][C]59246423020.0311[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]27946591822.0859[/C][C]Range[/C][C]732074[/C][C]Trim Var.[/C][C]20103832183.0914[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]36606687860.9997[/C][C]Range[/C][C]896979[/C][C]Trim Var.[/C][C]25354623011.279[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]110377945717.232[/C][C]Range[/C][C]1717059[/C][C]Trim Var.[/C][C]67365988774.1302[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]15001882088.0833[/C][C]Range[/C][C]555912[/C][C]Trim Var.[/C][C]8891073437.76771[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]7909631810.14431[/C][C]Range[/C][C]746167[/C][C]Trim Var.[/C][C]1265341951.19024[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]21973687731.4609[/C][C]Range[/C][C]1129659[/C][C]Trim Var.[/C][C]2774641221.37436[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]72376742688.4273[/C][C]Range[/C][C]2209565[/C][C]Trim Var.[/C][C]8311383510.92038[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]41349317083.0635[/C][C]Range[/C][C]740007[/C][C]Trim Var.[/C][C]31852683751.8942[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]18816324225.3529[/C][C]Range[/C][C]957679[/C][C]Trim Var.[/C][C]4742692161.93118[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]49886096130.8565[/C][C]Range[/C][C]1433793[/C][C]Trim Var.[/C][C]9186651939.72989[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]160032336614.364[/C][C]Range[/C][C]2830841[/C][C]Trim Var.[/C][C]28165368839.8103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151988&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151988&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)73118345838.7345Range934436Trim Var.59246423020.0311
V(Y[t],d=1,D=0)27946591822.0859Range732074Trim Var.20103832183.0914
V(Y[t],d=2,D=0)36606687860.9997Range896979Trim Var.25354623011.279
V(Y[t],d=3,D=0)110377945717.232Range1717059Trim Var.67365988774.1302
V(Y[t],d=0,D=1)15001882088.0833Range555912Trim Var.8891073437.76771
V(Y[t],d=1,D=1)7909631810.14431Range746167Trim Var.1265341951.19024
V(Y[t],d=2,D=1)21973687731.4609Range1129659Trim Var.2774641221.37436
V(Y[t],d=3,D=1)72376742688.4273Range2209565Trim Var.8311383510.92038
V(Y[t],d=0,D=2)41349317083.0635Range740007Trim Var.31852683751.8942
V(Y[t],d=1,D=2)18816324225.3529Range957679Trim Var.4742692161.93118
V(Y[t],d=2,D=2)49886096130.8565Range1433793Trim Var.9186651939.72989
V(Y[t],d=3,D=2)160032336614.364Range2830841Trim Var.28165368839.8103


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()