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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 computationThu, 01 Dec 2011 07:26:38 -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/01/t1322742449uhj0t3h2xc4w4hu.htm/, Retrieved Wed, 24 Apr 2024 01:31:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149281, Retrieved Wed, 24 Apr 2024 01:31:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

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] [ws9 ] [2011-12-01 12:26:38] [76a85a4cc6ea7903d92a0f5b9d2872d3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1825038,884
1833613,892
1841394,72
1846337,44
1846636,388
1848811,284
1854308,593
1859350,416
1863607,22
1863388,804
1868989,752
1873914,588
1879476,484
1881890,112
1887876
1890047,544
1893926,44
1895770,997
1894421,904
1893706,254
1895605,776
1898112,398
1901613,42
1903930,829
1904289,602
1901999,557
1900014,128
1894917,434
1888508,093
1883619,003
1877283,62
1869974,201
1858123,397
1844272,642
1822554
1805879,069
1783907,497
1764566,857
1743482,568
1726096,716
1715969,003
1702842,305
1695021,725
1689012,144
1682883,508
1677154,503
1675730,25
1672366,24
1671357,696
1670452,852
1675419,584
1682598,123
1694500,993
1689506,036
1688232,462
1686699,613
1685946,434
1690390,023
1692809,166
1696766,76

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time0 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 0 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149281&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]0 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149281&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 time0 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)8133953235.80174Range233836.75Trim Var.7502688708.34943
V(Y[t],d=1,D=0)64919536.3255572Range33874.442Trim Var.42511726.0448353
V(Y[t],d=2,D=0)15301910.3689682Range24155.966Trim Var.7357831.90894173
V(Y[t],d=3,D=0)39742388.6100635Range42241.3680000002Trim Var.16963400.5812827
V(Y[t],d=0,D=1)6434513991.71359Range236699.495Trim Var.5321279809.23464
V(Y[t],d=1,D=1)150875799.271603Range51270.6850000001Trim Var.91523985.3331154
V(Y[t],d=2,D=1)28083194.6933161Range26071.4809999997Trim Var.16896061.0224649
V(Y[t],d=3,D=1)66477066.0735475Range34245.7179999992Trim Var.43789307.891682
V(Y[t],d=0,D=2)15626895255.1862Range354044.267Trim Var.13575741529.2108
V(Y[t],d=1,D=2)389558587.577708Range68633.7909999995Trim Var.287240658.877008
V(Y[t],d=2,D=2)82158356.8845238Range39536.7629999993Trim Var.55754130.3771588
V(Y[t],d=3,D=2)185674119.46228Range63209.230999999Trim Var.103695477.268016

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 8133953235.80174 & Range & 233836.75 & Trim Var. & 7502688708.34943 \tabularnewline
V(Y[t],d=1,D=0) & 64919536.3255572 & Range & 33874.442 & Trim Var. & 42511726.0448353 \tabularnewline
V(Y[t],d=2,D=0) & 15301910.3689682 & Range & 24155.966 & Trim Var. & 7357831.90894173 \tabularnewline
V(Y[t],d=3,D=0) & 39742388.6100635 & Range & 42241.3680000002 & Trim Var. & 16963400.5812827 \tabularnewline
V(Y[t],d=0,D=1) & 6434513991.71359 & Range & 236699.495 & Trim Var. & 5321279809.23464 \tabularnewline
V(Y[t],d=1,D=1) & 150875799.271603 & Range & 51270.6850000001 & Trim Var. & 91523985.3331154 \tabularnewline
V(Y[t],d=2,D=1) & 28083194.6933161 & Range & 26071.4809999997 & Trim Var. & 16896061.0224649 \tabularnewline
V(Y[t],d=3,D=1) & 66477066.0735475 & Range & 34245.7179999992 & Trim Var. & 43789307.891682 \tabularnewline
V(Y[t],d=0,D=2) & 15626895255.1862 & Range & 354044.267 & Trim Var. & 13575741529.2108 \tabularnewline
V(Y[t],d=1,D=2) & 389558587.577708 & Range & 68633.7909999995 & Trim Var. & 287240658.877008 \tabularnewline
V(Y[t],d=2,D=2) & 82158356.8845238 & Range & 39536.7629999993 & Trim Var. & 55754130.3771588 \tabularnewline
V(Y[t],d=3,D=2) & 185674119.46228 & Range & 63209.230999999 & Trim Var. & 103695477.268016 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149281&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]8133953235.80174[/C][C]Range[/C][C]233836.75[/C][C]Trim Var.[/C][C]7502688708.34943[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]64919536.3255572[/C][C]Range[/C][C]33874.442[/C][C]Trim Var.[/C][C]42511726.0448353[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]15301910.3689682[/C][C]Range[/C][C]24155.966[/C][C]Trim Var.[/C][C]7357831.90894173[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]39742388.6100635[/C][C]Range[/C][C]42241.3680000002[/C][C]Trim Var.[/C][C]16963400.5812827[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]6434513991.71359[/C][C]Range[/C][C]236699.495[/C][C]Trim Var.[/C][C]5321279809.23464[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]150875799.271603[/C][C]Range[/C][C]51270.6850000001[/C][C]Trim Var.[/C][C]91523985.3331154[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]28083194.6933161[/C][C]Range[/C][C]26071.4809999997[/C][C]Trim Var.[/C][C]16896061.0224649[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]66477066.0735475[/C][C]Range[/C][C]34245.7179999992[/C][C]Trim Var.[/C][C]43789307.891682[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]15626895255.1862[/C][C]Range[/C][C]354044.267[/C][C]Trim Var.[/C][C]13575741529.2108[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]389558587.577708[/C][C]Range[/C][C]68633.7909999995[/C][C]Trim Var.[/C][C]287240658.877008[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]82158356.8845238[/C][C]Range[/C][C]39536.7629999993[/C][C]Trim Var.[/C][C]55754130.3771588[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]185674119.46228[/C][C]Range[/C][C]63209.230999999[/C][C]Trim Var.[/C][C]103695477.268016[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149281&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)8133953235.80174Range233836.75Trim Var.7502688708.34943
V(Y[t],d=1,D=0)64919536.3255572Range33874.442Trim Var.42511726.0448353
V(Y[t],d=2,D=0)15301910.3689682Range24155.966Trim Var.7357831.90894173
V(Y[t],d=3,D=0)39742388.6100635Range42241.3680000002Trim Var.16963400.5812827
V(Y[t],d=0,D=1)6434513991.71359Range236699.495Trim Var.5321279809.23464
V(Y[t],d=1,D=1)150875799.271603Range51270.6850000001Trim Var.91523985.3331154
V(Y[t],d=2,D=1)28083194.6933161Range26071.4809999997Trim Var.16896061.0224649
V(Y[t],d=3,D=1)66477066.0735475Range34245.7179999992Trim Var.43789307.891682
V(Y[t],d=0,D=2)15626895255.1862Range354044.267Trim Var.13575741529.2108
V(Y[t],d=1,D=2)389558587.577708Range68633.7909999995Trim Var.287240658.877008
V(Y[t],d=2,D=2)82158356.8845238Range39536.7629999993Trim Var.55754130.3771588
V(Y[t],d=3,D=2)185674119.46228Range63209.230999999Trim Var.103695477.268016


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()