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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 17:41:31 +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/t1481906531ia7oaviaedosdv6.htm/, Retrieved Thu, 02 May 2024 20:21:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300438, Retrieved Thu, 02 May 2024 20:21:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57

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 16:41:31] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5190
4805
4935
3675
3805
5260
6735
5435
3090
4750
3110
3135
4985
3665
3535
4195
3960
3150
3330
4265
4240
4255
3685
3525
4000
3050
3800
3035
3095
2820
2760
4435
3665
4140
2890
3295
2660
2950
2770
3365
3090
3275
3370
2685
2760
3030
2410
2570
2675
3100
3025

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=300438&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=300438&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300438&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)798882Range4325Trim Var.469070
V(Y[t],d=1,D=0)735655Range4195Trim Var.398396
V(Y[t],d=2,D=0)1986250Range7305Trim Var.1053080
V(Y[t],d=3,D=0)6286870Range12355Trim Var.3183600
V(Y[t],d=0,D=1)756186Range4555Trim Var.398987
V(Y[t],d=1,D=1)1253420Range4680Trim Var.766560
V(Y[t],d=2,D=1)3210660Range7495Trim Var.2212960
V(Y[t],d=3,D=1)9934040Range11200Trim Var.7402170
V(Y[t],d=0,D=2)1578170Range4755Trim Var.1061690
V(Y[t],d=1,D=2)3047470Range6145Trim Var.1884130
V(Y[t],d=2,D=2)8740780Range9655Trim Var.6296390
V(Y[t],d=3,D=2)29463200Range17515Trim Var.20675600

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 798882 & Range & 4325 & Trim Var. & 469070 \tabularnewline
V(Y[t],d=1,D=0) & 735655 & Range & 4195 & Trim Var. & 398396 \tabularnewline
V(Y[t],d=2,D=0) & 1986250 & Range & 7305 & Trim Var. & 1053080 \tabularnewline
V(Y[t],d=3,D=0) & 6286870 & Range & 12355 & Trim Var. & 3183600 \tabularnewline
V(Y[t],d=0,D=1) & 756186 & Range & 4555 & Trim Var. & 398987 \tabularnewline
V(Y[t],d=1,D=1) & 1253420 & Range & 4680 & Trim Var. & 766560 \tabularnewline
V(Y[t],d=2,D=1) & 3210660 & Range & 7495 & Trim Var. & 2212960 \tabularnewline
V(Y[t],d=3,D=1) & 9934040 & Range & 11200 & Trim Var. & 7402170 \tabularnewline
V(Y[t],d=0,D=2) & 1578170 & Range & 4755 & Trim Var. & 1061690 \tabularnewline
V(Y[t],d=1,D=2) & 3047470 & Range & 6145 & Trim Var. & 1884130 \tabularnewline
V(Y[t],d=2,D=2) & 8740780 & Range & 9655 & Trim Var. & 6296390 \tabularnewline
V(Y[t],d=3,D=2) & 29463200 & Range & 17515 & Trim Var. & 20675600 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300438&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]798882[/C][C]Range[/C][C]4325[/C][C]Trim Var.[/C][C]469070[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]735655[/C][C]Range[/C][C]4195[/C][C]Trim Var.[/C][C]398396[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1986250[/C][C]Range[/C][C]7305[/C][C]Trim Var.[/C][C]1053080[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]6286870[/C][C]Range[/C][C]12355[/C][C]Trim Var.[/C][C]3183600[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]756186[/C][C]Range[/C][C]4555[/C][C]Trim Var.[/C][C]398987[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1253420[/C][C]Range[/C][C]4680[/C][C]Trim Var.[/C][C]766560[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3210660[/C][C]Range[/C][C]7495[/C][C]Trim Var.[/C][C]2212960[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]9934040[/C][C]Range[/C][C]11200[/C][C]Trim Var.[/C][C]7402170[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1578170[/C][C]Range[/C][C]4755[/C][C]Trim Var.[/C][C]1061690[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]3047470[/C][C]Range[/C][C]6145[/C][C]Trim Var.[/C][C]1884130[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]8740780[/C][C]Range[/C][C]9655[/C][C]Trim Var.[/C][C]6296390[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]29463200[/C][C]Range[/C][C]17515[/C][C]Trim Var.[/C][C]20675600[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300438&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300438&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)798882Range4325Trim Var.469070
V(Y[t],d=1,D=0)735655Range4195Trim Var.398396
V(Y[t],d=2,D=0)1986250Range7305Trim Var.1053080
V(Y[t],d=3,D=0)6286870Range12355Trim Var.3183600
V(Y[t],d=0,D=1)756186Range4555Trim Var.398987
V(Y[t],d=1,D=1)1253420Range4680Trim Var.766560
V(Y[t],d=2,D=1)3210660Range7495Trim Var.2212960
V(Y[t],d=3,D=1)9934040Range11200Trim Var.7402170
V(Y[t],d=0,D=2)1578170Range4755Trim Var.1061690
V(Y[t],d=1,D=2)3047470Range6145Trim Var.1884130
V(Y[t],d=2,D=2)8740780Range9655Trim Var.6296390
V(Y[t],d=3,D=2)29463200Range17515Trim Var.20675600


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()