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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, 19 Dec 2016 15:07:24 +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/19/t1482156496gij0qqw80jqq3u5.htm/, Retrieved Sat, 18 May 2024 02:53:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301359, Retrieved Sat, 18 May 2024 02:53:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71

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...] [2016-12-19 14:07:24] [2e2b863c9581eba851d0277c64dc678f] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3440
3620
3600
4140
4820
3940
3860
4680
5000
4480
4600
3660
3660
3780
4140
4000
4340
6440
3880
4780
4960
5340
4640
4180
3860
3760
3860
3460
3620
7220
4480
4440
4940
4820
4420
3940
3560
3660
4140
3680
4540
3820
5680
4520
4640
4820
4740
3900
3300
3520
3840
3500
3300
3840
4000
4180
5020
4540
4520
3680
3580
3500
3440
3560
3320
3220
4180
4460
4420
4620
4220
3660
3440
3700
3500
3240
3200
4180
4100
4120
4240
4020
3780
3560
3360
3240
3540
3300
3280
4200
3340
3900
4380
4120
3780
3380
3260
3320
3380
3100
3240
3100
3240
3640
4140
4240
4040
3760
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA
NA

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time0 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 time0 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301359&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]0 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301359&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301359&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 time0 seconds
R ServerBig Analytics Cloud Computing Center






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)450841Range4120Trim Var.215057
V(Y[t],d=1,D=0)512270Range6340Trim Var.137548
V(Y[t],d=2,D=0)1427050Range9800Trim Var.298310
V(Y[t],d=3,D=0)4678600Range18820Trim Var.903074
V(Y[t],d=0,D=1)363978Range5900Trim Var.80825
V(Y[t],d=1,D=1)874721Range8920Trim Var.184885
V(Y[t],d=2,D=1)2806680Range14640Trim Var.581314
V(Y[t],d=3,D=1)9664400Range28580Trim Var.2126830
V(Y[t],d=0,D=2)870803Range7600Trim Var.209635
V(Y[t],d=1,D=2)2356050Range11880Trim Var.527275
V(Y[t],d=2,D=2)7745540Range22480Trim Var.1595840
V(Y[t],d=3,D=2)26944300Range39860Trim Var.6092770

\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) & 450841 & Range & 4120 & Trim Var. & 215057 \tabularnewline
V(Y[t],d=1,D=0) & 512270 & Range & 6340 & Trim Var. & 137548 \tabularnewline
V(Y[t],d=2,D=0) & 1427050 & Range & 9800 & Trim Var. & 298310 \tabularnewline
V(Y[t],d=3,D=0) & 4678600 & Range & 18820 & Trim Var. & 903074 \tabularnewline
V(Y[t],d=0,D=1) & 363978 & Range & 5900 & Trim Var. & 80825 \tabularnewline
V(Y[t],d=1,D=1) & 874721 & Range & 8920 & Trim Var. & 184885 \tabularnewline
V(Y[t],d=2,D=1) & 2806680 & Range & 14640 & Trim Var. & 581314 \tabularnewline
V(Y[t],d=3,D=1) & 9664400 & Range & 28580 & Trim Var. & 2126830 \tabularnewline
V(Y[t],d=0,D=2) & 870803 & Range & 7600 & Trim Var. & 209635 \tabularnewline
V(Y[t],d=1,D=2) & 2356050 & Range & 11880 & Trim Var. & 527275 \tabularnewline
V(Y[t],d=2,D=2) & 7745540 & Range & 22480 & Trim Var. & 1595840 \tabularnewline
V(Y[t],d=3,D=2) & 26944300 & Range & 39860 & Trim Var. & 6092770 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301359&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]450841[/C][C]Range[/C][C]4120[/C][C]Trim Var.[/C][C]215057[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]512270[/C][C]Range[/C][C]6340[/C][C]Trim Var.[/C][C]137548[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1427050[/C][C]Range[/C][C]9800[/C][C]Trim Var.[/C][C]298310[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]4678600[/C][C]Range[/C][C]18820[/C][C]Trim Var.[/C][C]903074[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]363978[/C][C]Range[/C][C]5900[/C][C]Trim Var.[/C][C]80825[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]874721[/C][C]Range[/C][C]8920[/C][C]Trim Var.[/C][C]184885[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]2806680[/C][C]Range[/C][C]14640[/C][C]Trim Var.[/C][C]581314[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]9664400[/C][C]Range[/C][C]28580[/C][C]Trim Var.[/C][C]2126830[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]870803[/C][C]Range[/C][C]7600[/C][C]Trim Var.[/C][C]209635[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]2356050[/C][C]Range[/C][C]11880[/C][C]Trim Var.[/C][C]527275[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]7745540[/C][C]Range[/C][C]22480[/C][C]Trim Var.[/C][C]1595840[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]26944300[/C][C]Range[/C][C]39860[/C][C]Trim Var.[/C][C]6092770[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301359&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301359&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)450841Range4120Trim Var.215057
V(Y[t],d=1,D=0)512270Range6340Trim Var.137548
V(Y[t],d=2,D=0)1427050Range9800Trim Var.298310
V(Y[t],d=3,D=0)4678600Range18820Trim Var.903074
V(Y[t],d=0,D=1)363978Range5900Trim Var.80825
V(Y[t],d=1,D=1)874721Range8920Trim Var.184885
V(Y[t],d=2,D=1)2806680Range14640Trim Var.581314
V(Y[t],d=3,D=1)9664400Range28580Trim Var.2126830
V(Y[t],d=0,D=2)870803Range7600Trim Var.209635
V(Y[t],d=1,D=2)2356050Range11880Trim Var.527275
V(Y[t],d=2,D=2)7745540Range22480Trim Var.1595840
V(Y[t],d=3,D=2)26944300Range39860Trim Var.6092770


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()