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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 computationMon, 30 Nov 2015 13:42:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/30/t14488912382q2kmt3lvfpqit8.htm/, Retrieved Tue, 14 May 2024 03:03:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284590, Retrieved Tue, 14 May 2024 03:03:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106

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...] [2015-11-30 13:42:23] [f6bae6d252fa79c7f404cd3700ec66e0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
501
488
504
578
545
632
728
725
585
542
480
530
518
489
528
599
572
659
739
758
602
587
497
558
555
523
532
623
598
683
774
780
609
604
531
592
578
543
565
648
615
697
785
830
645
643
551
606
585
553
576
665
656
720
826
838
652
661
584
644
623
553
599
657
680
759
878
881
705
684
577
656
645
593
617
686
679
773
906
934
713
710
600
676
645
602
601
709
706
817
930
983
745
735
620
698
665
626
649
740
729
824
937
994
781
759
643
728
691
649
656
735
748
837
995
1040
809
793
692
763
723
655
658
761
768
885
1067
1038
812
790
692
782
758
709
715
788
794
893
1046
1075
812
822
714
802
748
731
748
827
788
937
1076
1125
840
864
717
813
811
732
745
844
833
935
1110
1124
868
860
762
877
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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=284590&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=284590&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284590&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
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)20351Range645Trim Var.12123.4
V(Y[t],d=1,D=0)8506.67Range467Trim Var.4721.4
V(Y[t],d=2,D=0)16711.6Range643Trim Var.10682
V(Y[t],d=3,D=0)49266.5Range1123Trim Var.31820.8
V(Y[t],d=0,D=1)296.651Range93Trim Var.190.05
V(Y[t],d=1,D=1)501.576Range132Trim Var.289.715
V(Y[t],d=2,D=1)1437.3Range209Trim Var.844.102
V(Y[t],d=3,D=1)4885.6Range359Trim Var.2879.85
V(Y[t],d=0,D=2)783.738Range166Trim Var.491.92
V(Y[t],d=1,D=2)1262.57Range229Trim Var.703.984
V(Y[t],d=2,D=2)3498.64Range361Trim Var.1778.07
V(Y[t],d=3,D=2)11618.4Range676Trim Var.5905.65

\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) & 20351 & Range & 645 & Trim Var. & 12123.4 \tabularnewline
V(Y[t],d=1,D=0) & 8506.67 & Range & 467 & Trim Var. & 4721.4 \tabularnewline
V(Y[t],d=2,D=0) & 16711.6 & Range & 643 & Trim Var. & 10682 \tabularnewline
V(Y[t],d=3,D=0) & 49266.5 & Range & 1123 & Trim Var. & 31820.8 \tabularnewline
V(Y[t],d=0,D=1) & 296.651 & Range & 93 & Trim Var. & 190.05 \tabularnewline
V(Y[t],d=1,D=1) & 501.576 & Range & 132 & Trim Var. & 289.715 \tabularnewline
V(Y[t],d=2,D=1) & 1437.3 & Range & 209 & Trim Var. & 844.102 \tabularnewline
V(Y[t],d=3,D=1) & 4885.6 & Range & 359 & Trim Var. & 2879.85 \tabularnewline
V(Y[t],d=0,D=2) & 783.738 & Range & 166 & Trim Var. & 491.92 \tabularnewline
V(Y[t],d=1,D=2) & 1262.57 & Range & 229 & Trim Var. & 703.984 \tabularnewline
V(Y[t],d=2,D=2) & 3498.64 & Range & 361 & Trim Var. & 1778.07 \tabularnewline
V(Y[t],d=3,D=2) & 11618.4 & Range & 676 & Trim Var. & 5905.65 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284590&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]20351[/C][C]Range[/C][C]645[/C][C]Trim Var.[/C][C]12123.4[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]8506.67[/C][C]Range[/C][C]467[/C][C]Trim Var.[/C][C]4721.4[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]16711.6[/C][C]Range[/C][C]643[/C][C]Trim Var.[/C][C]10682[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]49266.5[/C][C]Range[/C][C]1123[/C][C]Trim Var.[/C][C]31820.8[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]296.651[/C][C]Range[/C][C]93[/C][C]Trim Var.[/C][C]190.05[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]501.576[/C][C]Range[/C][C]132[/C][C]Trim Var.[/C][C]289.715[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1437.3[/C][C]Range[/C][C]209[/C][C]Trim Var.[/C][C]844.102[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]4885.6[/C][C]Range[/C][C]359[/C][C]Trim Var.[/C][C]2879.85[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]783.738[/C][C]Range[/C][C]166[/C][C]Trim Var.[/C][C]491.92[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]1262.57[/C][C]Range[/C][C]229[/C][C]Trim Var.[/C][C]703.984[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]3498.64[/C][C]Range[/C][C]361[/C][C]Trim Var.[/C][C]1778.07[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]11618.4[/C][C]Range[/C][C]676[/C][C]Trim Var.[/C][C]5905.65[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284590&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284590&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)20351Range645Trim Var.12123.4
V(Y[t],d=1,D=0)8506.67Range467Trim Var.4721.4
V(Y[t],d=2,D=0)16711.6Range643Trim Var.10682
V(Y[t],d=3,D=0)49266.5Range1123Trim Var.31820.8
V(Y[t],d=0,D=1)296.651Range93Trim Var.190.05
V(Y[t],d=1,D=1)501.576Range132Trim Var.289.715
V(Y[t],d=2,D=1)1437.3Range209Trim Var.844.102
V(Y[t],d=3,D=1)4885.6Range359Trim Var.2879.85
V(Y[t],d=0,D=2)783.738Range166Trim Var.491.92
V(Y[t],d=1,D=2)1262.57Range229Trim Var.703.984
V(Y[t],d=2,D=2)3498.64Range361Trim Var.1778.07
V(Y[t],d=3,D=2)11618.4Range676Trim Var.5905.65


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()