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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, 16 Dec 2016 17:52:32 +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/16/t14819071775vu5758ilb279tg.htm/, Retrieved Fri, 21 Feb 2025 18:26:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300449, Retrieved Fri, 21 Feb 2025 18:26:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- R  D    [ARIMA Backward Selection] [] [2016-12-16 14:51:40] [683f400e1b95307fc738e729f07c4fce]
- RM D        [Variance Reduction Matrix] [] [2016-12-16 16:52:32] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2931
3626
4098
3473
3606
4174
4451
3321
3678
4583
5062
5028
5592
6210
6568
5836
6424
6452
6480
2493
2738
2939
3094
2750
2874
3239
3247
2496
2363
2397
2666
2365
2870
2783
2664
1979

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=300449&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=300449&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300449&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)1991240Range4589Trim Var.1594160
V(Y[t],d=1,D=0)689185Range4892Trim Var.159027
V(Y[t],d=2,D=0)1455420Range8247Trim Var.336901
V(Y[t],d=3,D=0)4362260Range12523Trim Var.1016130
V(Y[t],d=0,D=1)5737290Range6879Trim Var.4512560
V(Y[t],d=1,D=1)1083520Range6543Trim Var.57427.6
V(Y[t],d=2,D=1)1970400Range6871Trim Var.201742
V(Y[t],d=3,D=1)6175870Range12224Trim Var.1628690
V(Y[t],d=0,D=2)13889600Range8417Trim Var.13022100
V(Y[t],d=1,D=2)4083070Range7719Trim Var.86394.9
V(Y[t],d=2,D=2)8837230Range12224Trim Var.686928
V(Y[t],d=3,D=2)30046000Range18439Trim Var.7865600

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1991240 & Range & 4589 & Trim Var. & 1594160 \tabularnewline
V(Y[t],d=1,D=0) & 689185 & Range & 4892 & Trim Var. & 159027 \tabularnewline
V(Y[t],d=2,D=0) & 1455420 & Range & 8247 & Trim Var. & 336901 \tabularnewline
V(Y[t],d=3,D=0) & 4362260 & Range & 12523 & Trim Var. & 1016130 \tabularnewline
V(Y[t],d=0,D=1) & 5737290 & Range & 6879 & Trim Var. & 4512560 \tabularnewline
V(Y[t],d=1,D=1) & 1083520 & Range & 6543 & Trim Var. & 57427.6 \tabularnewline
V(Y[t],d=2,D=1) & 1970400 & Range & 6871 & Trim Var. & 201742 \tabularnewline
V(Y[t],d=3,D=1) & 6175870 & Range & 12224 & Trim Var. & 1628690 \tabularnewline
V(Y[t],d=0,D=2) & 13889600 & Range & 8417 & Trim Var. & 13022100 \tabularnewline
V(Y[t],d=1,D=2) & 4083070 & Range & 7719 & Trim Var. & 86394.9 \tabularnewline
V(Y[t],d=2,D=2) & 8837230 & Range & 12224 & Trim Var. & 686928 \tabularnewline
V(Y[t],d=3,D=2) & 30046000 & Range & 18439 & Trim Var. & 7865600 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300449&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1991240[/C][C]Range[/C][C]4589[/C][C]Trim Var.[/C][C]1594160[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]689185[/C][C]Range[/C][C]4892[/C][C]Trim Var.[/C][C]159027[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1455420[/C][C]Range[/C][C]8247[/C][C]Trim Var.[/C][C]336901[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4362260[/C][C]Range[/C][C]12523[/C][C]Trim Var.[/C][C]1016130[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]5737290[/C][C]Range[/C][C]6879[/C][C]Trim Var.[/C][C]4512560[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1083520[/C][C]Range[/C][C]6543[/C][C]Trim Var.[/C][C]57427.6[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]1970400[/C][C]Range[/C][C]6871[/C][C]Trim Var.[/C][C]201742[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]6175870[/C][C]Range[/C][C]12224[/C][C]Trim Var.[/C][C]1628690[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]13889600[/C][C]Range[/C][C]8417[/C][C]Trim Var.[/C][C]13022100[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]4083070[/C][C]Range[/C][C]7719[/C][C]Trim Var.[/C][C]86394.9[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]8837230[/C][C]Range[/C][C]12224[/C][C]Trim Var.[/C][C]686928[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]30046000[/C][C]Range[/C][C]18439[/C][C]Trim Var.[/C][C]7865600[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300449&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300449&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)1991240Range4589Trim Var.1594160
V(Y[t],d=1,D=0)689185Range4892Trim Var.159027
V(Y[t],d=2,D=0)1455420Range8247Trim Var.336901
V(Y[t],d=3,D=0)4362260Range12523Trim Var.1016130
V(Y[t],d=0,D=1)5737290Range6879Trim Var.4512560
V(Y[t],d=1,D=1)1083520Range6543Trim Var.57427.6
V(Y[t],d=2,D=1)1970400Range6871Trim Var.201742
V(Y[t],d=3,D=1)6175870Range12224Trim Var.1628690
V(Y[t],d=0,D=2)13889600Range8417Trim Var.13022100
V(Y[t],d=1,D=2)4083070Range7719Trim Var.86394.9
V(Y[t],d=2,D=2)8837230Range12224Trim Var.686928
V(Y[t],d=3,D=2)30046000Range18439Trim Var.7865600


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
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()