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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, 10 Dec 2016 19:07:20 +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/10/t1481393343hsc2fgsrvav2d1r.htm/, Retrieved Thu, 03 Apr 2025 20:51:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298740, Retrieved Thu, 03 Apr 2025 20:51:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93

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] [""N2582"" deel 3] [2016-12-10 18:07:20] [afe7f6443461a2cd6ee0b843643e84a9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
4028.8
4076.6
4125.8
4177.2
4183
4222.6
4255.8
4260.8
4279.2
4328.8
4356.6
4393
4419.4
4426.2
4467.2
4517.4
4517
4560.4
4589
4596
4621.2
4654.6
4708.6
4774.4
4824.8
4839
4869.8
4895.8
4895.8
4968.8
5010
5032.4
5054
5083.8
5117.4
5170.8
5182.2
5163.6
5212.6
5288
5303.4
5367.6
5433.8
5465.8
5493.8
5549.4
5590.2
5661.2
5699
5654.2
5671.8
5730.8
5693
5720.4
5747.8
5764.2
5783
5822.4
5836.2
5864.6
5913.4
5906.8
5954
6031.2
6011.2
6059.8
6091.6
6088
6082.2
6108
6151.4
6187
6190
6152.2
6183.8
6222.8
6165.8
6223.4
6292.8
6320.6
6344
6391.2
6443.4
6504
6520.2
6518.8
6563.8
6614
6555.6
6601.8
6632.4
6657.8
6674.4
6687
6697.6
6732
6736.4
6745.8
6805.2
6850.4
6807.2
6844.6
6850.8
6848.2
6837.8
6857.6
6900.8
6940.8
6937.4
6950.4
6978.8
6997.8
6934.8
6946.8
6956.2
6968.2
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
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=298740&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=298740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298740&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)815238Range2969Trim Var.672595
V(Y[t],d=1,D=0)805.703Range140.2Trim Var.384.359
V(Y[t],d=2,D=0)1674.44Range223.2Trim Var.875.38
V(Y[t],d=3,D=0)4777.2Range351.4Trim Var.2508.5
V(Y[t],d=0,D=1)9005.46Range414.6Trim Var.5946.19
V(Y[t],d=1,D=1)544.746Range102.6Trim Var.392.402
V(Y[t],d=2,D=1)470.099Range106.6Trim Var.279.44
V(Y[t],d=3,D=1)975.679Range134.8Trim Var.607.575
V(Y[t],d=0,D=2)12606.4Range537.6Trim Var.7916.36
V(Y[t],d=1,D=2)1675.03Range150.6Trim Var.1276.94
V(Y[t],d=2,D=2)1212.5Range186.4Trim Var.792.105
V(Y[t],d=3,D=2)2264.25Range208Trim Var.1437.21

\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) & 815238 & Range & 2969 & Trim Var. & 672595 \tabularnewline
V(Y[t],d=1,D=0) & 805.703 & Range & 140.2 & Trim Var. & 384.359 \tabularnewline
V(Y[t],d=2,D=0) & 1674.44 & Range & 223.2 & Trim Var. & 875.38 \tabularnewline
V(Y[t],d=3,D=0) & 4777.2 & Range & 351.4 & Trim Var. & 2508.5 \tabularnewline
V(Y[t],d=0,D=1) & 9005.46 & Range & 414.6 & Trim Var. & 5946.19 \tabularnewline
V(Y[t],d=1,D=1) & 544.746 & Range & 102.6 & Trim Var. & 392.402 \tabularnewline
V(Y[t],d=2,D=1) & 470.099 & Range & 106.6 & Trim Var. & 279.44 \tabularnewline
V(Y[t],d=3,D=1) & 975.679 & Range & 134.8 & Trim Var. & 607.575 \tabularnewline
V(Y[t],d=0,D=2) & 12606.4 & Range & 537.6 & Trim Var. & 7916.36 \tabularnewline
V(Y[t],d=1,D=2) & 1675.03 & Range & 150.6 & Trim Var. & 1276.94 \tabularnewline
V(Y[t],d=2,D=2) & 1212.5 & Range & 186.4 & Trim Var. & 792.105 \tabularnewline
V(Y[t],d=3,D=2) & 2264.25 & Range & 208 & Trim Var. & 1437.21 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298740&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]815238[/C][C]Range[/C][C]2969[/C][C]Trim Var.[/C][C]672595[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]805.703[/C][C]Range[/C][C]140.2[/C][C]Trim Var.[/C][C]384.359[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1674.44[/C][C]Range[/C][C]223.2[/C][C]Trim Var.[/C][C]875.38[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4777.2[/C][C]Range[/C][C]351.4[/C][C]Trim Var.[/C][C]2508.5[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]9005.46[/C][C]Range[/C][C]414.6[/C][C]Trim Var.[/C][C]5946.19[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]544.746[/C][C]Range[/C][C]102.6[/C][C]Trim Var.[/C][C]392.402[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]470.099[/C][C]Range[/C][C]106.6[/C][C]Trim Var.[/C][C]279.44[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]975.679[/C][C]Range[/C][C]134.8[/C][C]Trim Var.[/C][C]607.575[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]12606.4[/C][C]Range[/C][C]537.6[/C][C]Trim Var.[/C][C]7916.36[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1675.03[/C][C]Range[/C][C]150.6[/C][C]Trim Var.[/C][C]1276.94[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1212.5[/C][C]Range[/C][C]186.4[/C][C]Trim Var.[/C][C]792.105[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2264.25[/C][C]Range[/C][C]208[/C][C]Trim Var.[/C][C]1437.21[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298740&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)815238Range2969Trim Var.672595
V(Y[t],d=1,D=0)805.703Range140.2Trim Var.384.359
V(Y[t],d=2,D=0)1674.44Range223.2Trim Var.875.38
V(Y[t],d=3,D=0)4777.2Range351.4Trim Var.2508.5
V(Y[t],d=0,D=1)9005.46Range414.6Trim Var.5946.19
V(Y[t],d=1,D=1)544.746Range102.6Trim Var.392.402
V(Y[t],d=2,D=1)470.099Range106.6Trim Var.279.44
V(Y[t],d=3,D=1)975.679Range134.8Trim Var.607.575
V(Y[t],d=0,D=2)12606.4Range537.6Trim Var.7916.36
V(Y[t],d=1,D=2)1675.03Range150.6Trim Var.1276.94
V(Y[t],d=2,D=2)1212.5Range186.4Trim Var.792.105
V(Y[t],d=3,D=2)2264.25Range208Trim Var.1437.21


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()