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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, 20 Dec 2016 13:17:11 +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/20/t1482236431v4pqfba70dy9jnd.htm/, Retrieved Sun, 28 Apr 2024 07:41:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301625, Retrieved Sun, 28 Apr 2024 07:41:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact60

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] [] [2016-12-20 12:17:11] [672675941468e072e71d9fb024f2b817] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5248.8
5149.6
5712.8
5649.4
5718.4
5989.8
5635.2
5954
5253.6
5923.6
4830.6
4042.4
4941.6
5258.2
5853.6
5356.6
5486.8
5603.4
5203.4
5584
4965.4
5566
4199.4
3677.6
4757.2
4889.8
5500.6
5227
5198.2
5055.2
4938.2
5530
4854
5204.8
4315.4
3347.6
4687
5095.2
5104.6
5003.6
5048.6
5213
5190.2
5527.4
4656.4
5222.6
4291.4
3296.4
4461.8
3933
4059.4
4785.4
4844
4801.8
4929
5047.2
4651.8
5083.2
4525.4
3617
4596.6
4729.8
5060.8
5039
5165
5223.6
5099.6
5156
4690.6
5088.4
4461.8
3539.4
4609.8
4560.4
5115.8
4966.6
5080.2
5174
5070.2
5114
4518
5053.8
4004.6
3738.6
4355.4
4493.4
4961.2
5048.2
5070
5016.4
5156.4
5139
4620.6
5241
4301.4
3491.6
4520.8
4571
5121
5002.6
5288.4
5176.4
4960
5304.4
4489.8
5164.6
4306.4
3596.8
4450.2
4494.2
5150
4947.6
5231.8
5037.4
5094.4
5228.2
5092.4
5187.4
4376.4
3650.8
4472.6
4452.6
4823.2
4858.6
5045.6
4869.8

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=301625&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=301625&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301625&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)302925Range2693.4Trim Var.162764
V(Y[t],d=1,D=0)302673Range2706Trim Var.194535
V(Y[t],d=2,D=0)788552Range4274.4Trim Var.470191
V(Y[t],d=3,D=0)2529610Range6666.6Trim Var.1771150
V(Y[t],d=0,D=1)80980.8Range2163.6Trim Var.32140
V(Y[t],d=1,D=1)77839Range1764Trim Var.36134.2
V(Y[t],d=2,D=1)214078Range2337.6Trim Var.125190
V(Y[t],d=3,D=1)688460Range4074.6Trim Var.395977
V(Y[t],d=0,D=2)216633Range3414.2Trim Var.77320.9
V(Y[t],d=1,D=2)229918Range3173.8Trim Var.115783
V(Y[t],d=2,D=2)633093Range3798.6Trim Var.384967
V(Y[t],d=3,D=2)2029260Range7006Trim Var.1278450

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 302925 & Range & 2693.4 & Trim Var. & 162764 \tabularnewline
V(Y[t],d=1,D=0) & 302673 & Range & 2706 & Trim Var. & 194535 \tabularnewline
V(Y[t],d=2,D=0) & 788552 & Range & 4274.4 & Trim Var. & 470191 \tabularnewline
V(Y[t],d=3,D=0) & 2529610 & Range & 6666.6 & Trim Var. & 1771150 \tabularnewline
V(Y[t],d=0,D=1) & 80980.8 & Range & 2163.6 & Trim Var. & 32140 \tabularnewline
V(Y[t],d=1,D=1) & 77839 & Range & 1764 & Trim Var. & 36134.2 \tabularnewline
V(Y[t],d=2,D=1) & 214078 & Range & 2337.6 & Trim Var. & 125190 \tabularnewline
V(Y[t],d=3,D=1) & 688460 & Range & 4074.6 & Trim Var. & 395977 \tabularnewline
V(Y[t],d=0,D=2) & 216633 & Range & 3414.2 & Trim Var. & 77320.9 \tabularnewline
V(Y[t],d=1,D=2) & 229918 & Range & 3173.8 & Trim Var. & 115783 \tabularnewline
V(Y[t],d=2,D=2) & 633093 & Range & 3798.6 & Trim Var. & 384967 \tabularnewline
V(Y[t],d=3,D=2) & 2029260 & Range & 7006 & Trim Var. & 1278450 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301625&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]302925[/C][C]Range[/C][C]2693.4[/C][C]Trim Var.[/C][C]162764[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]302673[/C][C]Range[/C][C]2706[/C][C]Trim Var.[/C][C]194535[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]788552[/C][C]Range[/C][C]4274.4[/C][C]Trim Var.[/C][C]470191[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]2529610[/C][C]Range[/C][C]6666.6[/C][C]Trim Var.[/C][C]1771150[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]80980.8[/C][C]Range[/C][C]2163.6[/C][C]Trim Var.[/C][C]32140[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]77839[/C][C]Range[/C][C]1764[/C][C]Trim Var.[/C][C]36134.2[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]214078[/C][C]Range[/C][C]2337.6[/C][C]Trim Var.[/C][C]125190[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]688460[/C][C]Range[/C][C]4074.6[/C][C]Trim Var.[/C][C]395977[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]216633[/C][C]Range[/C][C]3414.2[/C][C]Trim Var.[/C][C]77320.9[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]229918[/C][C]Range[/C][C]3173.8[/C][C]Trim Var.[/C][C]115783[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]633093[/C][C]Range[/C][C]3798.6[/C][C]Trim Var.[/C][C]384967[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2029260[/C][C]Range[/C][C]7006[/C][C]Trim Var.[/C][C]1278450[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301625&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301625&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)302925Range2693.4Trim Var.162764
V(Y[t],d=1,D=0)302673Range2706Trim Var.194535
V(Y[t],d=2,D=0)788552Range4274.4Trim Var.470191
V(Y[t],d=3,D=0)2529610Range6666.6Trim Var.1771150
V(Y[t],d=0,D=1)80980.8Range2163.6Trim Var.32140
V(Y[t],d=1,D=1)77839Range1764Trim Var.36134.2
V(Y[t],d=2,D=1)214078Range2337.6Trim Var.125190
V(Y[t],d=3,D=1)688460Range4074.6Trim Var.395977
V(Y[t],d=0,D=2)216633Range3414.2Trim Var.77320.9
V(Y[t],d=1,D=2)229918Range3173.8Trim Var.115783
V(Y[t],d=2,D=2)633093Range3798.6Trim Var.384967
V(Y[t],d=3,D=2)2029260Range7006Trim Var.1278450


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()