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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 computationSat, 17 Dec 2016 20:27:53 +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/17/t14820038448f55udff5cx6p9w.htm/, Retrieved Thu, 02 May 2024 02:30:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300926, Retrieved Thu, 02 May 2024 02:30:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact66

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] [variance reductio...] [2016-12-17 19:27:53] [06fd994a2f2098873ec640c3e39346e5] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4738.4
4687.2
5930.8
5532
5429.8
6107.4
5960.8
5541.8
5362.2
5237
4827
4781.6
4983.2
4718.4
5523.8
5286.6
5389
5810.4
5057.4
5604.4
5285
5215.2
4625.4
4270.4
4685.4
4233.8
5278.4
4978.8
5333.4
5451
5224
5790.2
5079.4
4705.8
4139.6
3720.8
4594
4638.8
4969.4
4764.4
5010.8
5267.8
5312.2
5723.2
4579.6
5015.2
4282.4
3834.2
4523.4
3884.2
3897.8
4845.6
4929
4955.4
5198.4
5122.2
4643.2
4789.8
3950.8
3824.4
4511.8
4262.4
4616.6
5139.6
4972.8
5222
5242
4979.8
4691.8
4821.6
4123.6
4027.4
4365.2
4333.6
4930
5053
5031.4
5342
5191.4
4852.2
4675.6
4689.2
3809.4
4054.2
4409.6
4210.2
4566.4
4907
5021.8
5215.2
4933.6
5197.8
4734.6
4681.8
4172
4037.8
4462.6
4282.6
4962.4
4969.2
5214.6
5416.8
4764.2
5326.2
4545.4
4797.2
4259
4117
4469.2
4203.2
5033.8
4883
5361.6
5044.6
5005.6
5382
4565.4
4825
4290.2
3933.6
4177.6
3949.4
4492.6
4894.2
5224.4
5071
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300926&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300926&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300926&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






Variance Reduction Matrix
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.
V(Y[t],d=0,D=0)263686Range2386.6Trim Var.168587
V(Y[t],d=1,D=0)198665Range2387.2Trim Var.121425
V(Y[t],d=2,D=0)523515Range3221.6Trim Var.351484
V(Y[t],d=3,D=0)1755110Range6071Trim Var.1179800
V(Y[t],d=0,D=1)74585.8Range1790.4Trim Var.38605.6
V(Y[t],d=1,D=1)104833Range1866.8Trim Var.55735.1
V(Y[t],d=2,D=1)288446Range2888.2Trim Var.156082
V(Y[t],d=3,D=1)922313Range4804.6Trim Var.528145
V(Y[t],d=0,D=2)179038Range2950Trim Var.79088.7
V(Y[t],d=1,D=2)243822Range2710Trim Var.113652
V(Y[t],d=2,D=2)629297Range3812.6Trim Var.368467
V(Y[t],d=3,D=2)1964180Range7350.6Trim Var.1175330

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
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. \tabularnewline
V(Y[t],d=0,D=0) & 263686 & Range & 2386.6 & Trim Var. & 168587 \tabularnewline
V(Y[t],d=1,D=0) & 198665 & Range & 2387.2 & Trim Var. & 121425 \tabularnewline
V(Y[t],d=2,D=0) & 523515 & Range & 3221.6 & Trim Var. & 351484 \tabularnewline
V(Y[t],d=3,D=0) & 1755110 & Range & 6071 & Trim Var. & 1179800 \tabularnewline
V(Y[t],d=0,D=1) & 74585.8 & Range & 1790.4 & Trim Var. & 38605.6 \tabularnewline
V(Y[t],d=1,D=1) & 104833 & Range & 1866.8 & Trim Var. & 55735.1 \tabularnewline
V(Y[t],d=2,D=1) & 288446 & Range & 2888.2 & Trim Var. & 156082 \tabularnewline
V(Y[t],d=3,D=1) & 922313 & Range & 4804.6 & Trim Var. & 528145 \tabularnewline
V(Y[t],d=0,D=2) & 179038 & Range & 2950 & Trim Var. & 79088.7 \tabularnewline
V(Y[t],d=1,D=2) & 243822 & Range & 2710 & Trim Var. & 113652 \tabularnewline
V(Y[t],d=2,D=2) & 629297 & Range & 3812.6 & Trim Var. & 368467 \tabularnewline
V(Y[t],d=3,D=2) & 1964180 & Range & 7350.6 & Trim Var. & 1175330 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300926&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]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.[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]263686[/C][C]Range[/C][C]2386.6[/C][C]Trim Var.[/C][C]168587[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]198665[/C][C]Range[/C][C]2387.2[/C][C]Trim Var.[/C][C]121425[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]523515[/C][C]Range[/C][C]3221.6[/C][C]Trim Var.[/C][C]351484[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1755110[/C][C]Range[/C][C]6071[/C][C]Trim Var.[/C][C]1179800[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]74585.8[/C][C]Range[/C][C]1790.4[/C][C]Trim Var.[/C][C]38605.6[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]104833[/C][C]Range[/C][C]1866.8[/C][C]Trim Var.[/C][C]55735.1[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]288446[/C][C]Range[/C][C]2888.2[/C][C]Trim Var.[/C][C]156082[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]922313[/C][C]Range[/C][C]4804.6[/C][C]Trim Var.[/C][C]528145[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]179038[/C][C]Range[/C][C]2950[/C][C]Trim Var.[/C][C]79088.7[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]243822[/C][C]Range[/C][C]2710[/C][C]Trim Var.[/C][C]113652[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]629297[/C][C]Range[/C][C]3812.6[/C][C]Trim Var.[/C][C]368467[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1964180[/C][C]Range[/C][C]7350.6[/C][C]Trim Var.[/C][C]1175330[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300926&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300926&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
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.
V(Y[t],d=0,D=0)263686Range2386.6Trim Var.168587
V(Y[t],d=1,D=0)198665Range2387.2Trim Var.121425
V(Y[t],d=2,D=0)523515Range3221.6Trim Var.351484
V(Y[t],d=3,D=0)1755110Range6071Trim Var.1179800
V(Y[t],d=0,D=1)74585.8Range1790.4Trim Var.38605.6
V(Y[t],d=1,D=1)104833Range1866.8Trim Var.55735.1
V(Y[t],d=2,D=1)288446Range2888.2Trim Var.156082
V(Y[t],d=3,D=1)922313Range4804.6Trim Var.528145
V(Y[t],d=0,D=2)179038Range2950Trim Var.79088.7
V(Y[t],d=1,D=2)243822Range2710Trim Var.113652
V(Y[t],d=2,D=2)629297Range3812.6Trim Var.368467
V(Y[t],d=3,D=2)1964180Range7350.6Trim Var.1175330


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
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()