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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, 23 Dec 2011 05:59:49 -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/23/t13246380162znbpr8teyj2l7q.htm/, Retrieved Mon, 29 Apr 2024 19:50:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160270, Retrieved Mon, 29 Apr 2024 19:50:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

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] [] [2011-12-06 08:04:41] [80bca13c5f9401fbb753952fd2952f4a]
- R  D    [Variance Reduction Matrix] [Paper VRM] [2011-12-23 10:59:49] [c18e83883fa784c15a15b4fbc0636edd] [Current]
- RMPD      [Spectral Analysis] [Paper CP] [2011-12-23 11:12:08] [805a2cd4f7b6665cd8870eed4006f53c]
- RMPD      [(Partial) Autocorrelation Function] [Paper autocorr] [2011-12-23 11:17:12] [805a2cd4f7b6665cd8870eed4006f53c]
- RMPD      [Spectral Analysis] [Paper CP2] [2011-12-23 11:23:33] [805a2cd4f7b6665cd8870eed4006f53c]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379
533590
517945
506174
501866
516141
528222
532638
536322
536535
523597
536214
586570
596594
580523
564478
557560
575093
580112
574761
563250
551531
537034
544686
600991
604378
586111
563668
548604
551174

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160270&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160270&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160270&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)1469750864.43173Range159527Trim Var.995258176.21999
V(Y[t],d=1,D=0)365132020.313481Range88991Trim Var.177521682.134153
V(Y[t],d=2,D=0)548811283.127122Range121994Trim Var.279039899.35193
V(Y[t],d=3,D=0)1254416088.29028Range183118Trim Var.558584325.876503
V(Y[t],d=0,D=1)1541856800.19746Range141263Trim Var.1207846319.76695
V(Y[t],d=1,D=1)77988304.2542373Range37640Trim Var.50857602.4941945
V(Y[t],d=2,D=1)117489777.202964Range61245Trim Var.56667434.5501508
V(Y[t],d=3,D=1)367618242.934211Range107877Trim Var.186264615.016471
V(Y[t],d=0,D=2)3179778656.90381Range178792Trim Var.2595004166.90418
V(Y[t],d=1,D=2)209100616.078631Range67698Trim Var.117520680.697561
V(Y[t],d=2,D=2)351461416.110628Range94798Trim Var.183632211.845513
V(Y[t],d=3,D=2)1122793506.64646Range137188Trim Var.600343882.692308

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1469750864.43173 & Range & 159527 & Trim Var. & 995258176.21999 \tabularnewline
V(Y[t],d=1,D=0) & 365132020.313481 & Range & 88991 & Trim Var. & 177521682.134153 \tabularnewline
V(Y[t],d=2,D=0) & 548811283.127122 & Range & 121994 & Trim Var. & 279039899.35193 \tabularnewline
V(Y[t],d=3,D=0) & 1254416088.29028 & Range & 183118 & Trim Var. & 558584325.876503 \tabularnewline
V(Y[t],d=0,D=1) & 1541856800.19746 & Range & 141263 & Trim Var. & 1207846319.76695 \tabularnewline
V(Y[t],d=1,D=1) & 77988304.2542373 & Range & 37640 & Trim Var. & 50857602.4941945 \tabularnewline
V(Y[t],d=2,D=1) & 117489777.202964 & Range & 61245 & Trim Var. & 56667434.5501508 \tabularnewline
V(Y[t],d=3,D=1) & 367618242.934211 & Range & 107877 & Trim Var. & 186264615.016471 \tabularnewline
V(Y[t],d=0,D=2) & 3179778656.90381 & Range & 178792 & Trim Var. & 2595004166.90418 \tabularnewline
V(Y[t],d=1,D=2) & 209100616.078631 & Range & 67698 & Trim Var. & 117520680.697561 \tabularnewline
V(Y[t],d=2,D=2) & 351461416.110628 & Range & 94798 & Trim Var. & 183632211.845513 \tabularnewline
V(Y[t],d=3,D=2) & 1122793506.64646 & Range & 137188 & Trim Var. & 600343882.692308 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160270&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1469750864.43173[/C][C]Range[/C][C]159527[/C][C]Trim Var.[/C][C]995258176.21999[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]365132020.313481[/C][C]Range[/C][C]88991[/C][C]Trim Var.[/C][C]177521682.134153[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]548811283.127122[/C][C]Range[/C][C]121994[/C][C]Trim Var.[/C][C]279039899.35193[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1254416088.29028[/C][C]Range[/C][C]183118[/C][C]Trim Var.[/C][C]558584325.876503[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1541856800.19746[/C][C]Range[/C][C]141263[/C][C]Trim Var.[/C][C]1207846319.76695[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]77988304.2542373[/C][C]Range[/C][C]37640[/C][C]Trim Var.[/C][C]50857602.4941945[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]117489777.202964[/C][C]Range[/C][C]61245[/C][C]Trim Var.[/C][C]56667434.5501508[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]367618242.934211[/C][C]Range[/C][C]107877[/C][C]Trim Var.[/C][C]186264615.016471[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]3179778656.90381[/C][C]Range[/C][C]178792[/C][C]Trim Var.[/C][C]2595004166.90418[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]209100616.078631[/C][C]Range[/C][C]67698[/C][C]Trim Var.[/C][C]117520680.697561[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]351461416.110628[/C][C]Range[/C][C]94798[/C][C]Trim Var.[/C][C]183632211.845513[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1122793506.64646[/C][C]Range[/C][C]137188[/C][C]Trim Var.[/C][C]600343882.692308[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160270&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160270&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)1469750864.43173Range159527Trim Var.995258176.21999
V(Y[t],d=1,D=0)365132020.313481Range88991Trim Var.177521682.134153
V(Y[t],d=2,D=0)548811283.127122Range121994Trim Var.279039899.35193
V(Y[t],d=3,D=0)1254416088.29028Range183118Trim Var.558584325.876503
V(Y[t],d=0,D=1)1541856800.19746Range141263Trim Var.1207846319.76695
V(Y[t],d=1,D=1)77988304.2542373Range37640Trim Var.50857602.4941945
V(Y[t],d=2,D=1)117489777.202964Range61245Trim Var.56667434.5501508
V(Y[t],d=3,D=1)367618242.934211Range107877Trim Var.186264615.016471
V(Y[t],d=0,D=2)3179778656.90381Range178792Trim Var.2595004166.90418
V(Y[t],d=1,D=2)209100616.078631Range67698Trim Var.117520680.697561
V(Y[t],d=2,D=2)351461416.110628Range94798Trim Var.183632211.845513
V(Y[t],d=3,D=2)1122793506.64646Range137188Trim Var.600343882.692308


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()