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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 computationFri, 16 Dec 2016 14:34:36 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481895316yneeog2feyk2zir.htm/, Retrieved Fri, 03 May 2024 02:05:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300257, Retrieved Fri, 03 May 2024 02:05:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact72

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Variance Reduction Matrix] [] [2016-12-16 13:34:36] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6086
6090.5
6103.5
6144
6190.5
6225
6272
6294
6366
6426
6477
6500
6538
6581
6615.5
6639.5
6651
6665
6684
6684.5
6666.5
6666.5
6651
6652
6647
6618.5
6604.5
6572
6556
6535
6515.5
6515
6489
6491
6483.5
6486.5
6486.5
6478.5
6461
6458.5
6446
6420
6397.5
6408
6408.5
6401.5
6408.5
6417.5
6406.5
6426.5
6431.5
6441.5
6446
6450
6468
6488.5
6512
6525
6551
6567.5
6560.5
6572
6574.5
6583.5
6589.5
6600
6601
6586
6590
6616
6641.5
6647
6662
6663.5
6663
6653.5
6642.5
6624.5
6605.5
6604.5
6575
6566
6562.5
6560.5
6502
6552.5
6542.5
6536
6516.5
6506.5
6491.5
6469.5
6445
6426
6355.5
6340
6307.5
6254.5
6230.5
6213
6212.5
6203
6204
6220.5
6205
6199.5
6184.5
6169
6140.5
6144.5
6145.5
6148.5
6145
6133
6138
6104.5
6090.5

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300257&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300257&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300257&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
V(Y[t],d=0,D=0)30704.7Range598.5Trim Var.24373.4
V(Y[t],d=1,D=0)529.405Range142.5Trim Var.273.029
V(Y[t],d=2,D=0)453.375Range169.5Trim Var.179.564
V(Y[t],d=3,D=0)1415.02Range335Trim Var.571.816
V(Y[t],d=0,D=1)35915.1Range835Trim Var.19283.2
V(Y[t],d=1,D=1)860.708Range160.5Trim Var.424.719
V(Y[t],d=2,D=1)1051.57Range252Trim Var.426.442
V(Y[t],d=3,D=1)3173.1Range400Trim Var.1188.28
V(Y[t],d=0,D=2)45517.4Range839Trim Var.29997.6
V(Y[t],d=1,D=2)2131.75Range313Trim Var.868.65
V(Y[t],d=2,D=2)3324.81Range434.5Trim Var.1168.43
V(Y[t],d=3,D=2)10136.2Range757.5Trim Var.3178.5

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 30704.7 & Range & 598.5 & Trim Var. & 24373.4 \tabularnewline
V(Y[t],d=1,D=0) & 529.405 & Range & 142.5 & Trim Var. & 273.029 \tabularnewline
V(Y[t],d=2,D=0) & 453.375 & Range & 169.5 & Trim Var. & 179.564 \tabularnewline
V(Y[t],d=3,D=0) & 1415.02 & Range & 335 & Trim Var. & 571.816 \tabularnewline
V(Y[t],d=0,D=1) & 35915.1 & Range & 835 & Trim Var. & 19283.2 \tabularnewline
V(Y[t],d=1,D=1) & 860.708 & Range & 160.5 & Trim Var. & 424.719 \tabularnewline
V(Y[t],d=2,D=1) & 1051.57 & Range & 252 & Trim Var. & 426.442 \tabularnewline
V(Y[t],d=3,D=1) & 3173.1 & Range & 400 & Trim Var. & 1188.28 \tabularnewline
V(Y[t],d=0,D=2) & 45517.4 & Range & 839 & Trim Var. & 29997.6 \tabularnewline
V(Y[t],d=1,D=2) & 2131.75 & Range & 313 & Trim Var. & 868.65 \tabularnewline
V(Y[t],d=2,D=2) & 3324.81 & Range & 434.5 & Trim Var. & 1168.43 \tabularnewline
V(Y[t],d=3,D=2) & 10136.2 & Range & 757.5 & Trim Var. & 3178.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300257&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]30704.7[/C][C]Range[/C][C]598.5[/C][C]Trim Var.[/C][C]24373.4[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]529.405[/C][C]Range[/C][C]142.5[/C][C]Trim Var.[/C][C]273.029[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]453.375[/C][C]Range[/C][C]169.5[/C][C]Trim Var.[/C][C]179.564[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1415.02[/C][C]Range[/C][C]335[/C][C]Trim Var.[/C][C]571.816[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]35915.1[/C][C]Range[/C][C]835[/C][C]Trim Var.[/C][C]19283.2[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]860.708[/C][C]Range[/C][C]160.5[/C][C]Trim Var.[/C][C]424.719[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1051.57[/C][C]Range[/C][C]252[/C][C]Trim Var.[/C][C]426.442[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]3173.1[/C][C]Range[/C][C]400[/C][C]Trim Var.[/C][C]1188.28[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]45517.4[/C][C]Range[/C][C]839[/C][C]Trim Var.[/C][C]29997.6[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2131.75[/C][C]Range[/C][C]313[/C][C]Trim Var.[/C][C]868.65[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3324.81[/C][C]Range[/C][C]434.5[/C][C]Trim Var.[/C][C]1168.43[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]10136.2[/C][C]Range[/C][C]757.5[/C][C]Trim Var.[/C][C]3178.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300257&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300257&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)30704.7Range598.5Trim Var.24373.4
V(Y[t],d=1,D=0)529.405Range142.5Trim Var.273.029
V(Y[t],d=2,D=0)453.375Range169.5Trim Var.179.564
V(Y[t],d=3,D=0)1415.02Range335Trim Var.571.816
V(Y[t],d=0,D=1)35915.1Range835Trim Var.19283.2
V(Y[t],d=1,D=1)860.708Range160.5Trim Var.424.719
V(Y[t],d=2,D=1)1051.57Range252Trim Var.426.442
V(Y[t],d=3,D=1)3173.1Range400Trim Var.1188.28
V(Y[t],d=0,D=2)45517.4Range839Trim Var.29997.6
V(Y[t],d=1,D=2)2131.75Range313Trim Var.868.65
V(Y[t],d=2,D=2)3324.81Range434.5Trim Var.1168.43
V(Y[t],d=3,D=2)10136.2Range757.5Trim Var.3178.5


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.orig <- length(x)
x <- na.omit(x)
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)
if(n.orig!=n) {
a<-table.row.start(a)
a<-table.element(a,'Warning: NAs were removed from the time series! The results shown below will only be correct if the NAs are all located at the start and/or end of the time series.',6,F)
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,signif(var(myx), digits=6))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,signif(max(myx)-min(myx), digits=6))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,signif(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()