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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 17:20:43 +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/t14819053278u58ghc5hsva7vf.htm/, Retrieved Thu, 02 May 2024 21:35:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300420, Retrieved Thu, 02 May 2024 21:35:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61

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 16:20:43] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
512
308
396
532
442
818
350
598
446
684
622
794
618
624
672
640
734
1042
760
682
1352
1196
1140
1134
1008
1262
842
890
792
1138
800
1212
1606
1686
1374
1670
1350
1056
1914
928
1296
966
1302
1822
1308
2030
2824
1342
1562
1278
2340
1826
1412
3068
1448
1202
2094
2408
2344
2386
3020
1990
2570
3664
2272
1596
3282
3870
3950
4292
3056
3170
3138
3232
3660
3310
2160
4444
2654
3226
5788
4288
4446
2778
3398
3896
2078
3230
2926
4746
2236
4306
3278
3498
2964
4184
3344
4152
2220
3520
2872
2900
1430
2730
3226
5472
4664
4566

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=300420&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=300420&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300420&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)1763580Range5480Trim Var.1283570
V(Y[t],d=1,D=0)827570Range5072Trim Var.410473
V(Y[t],d=2,D=0)2549070Range8910Trim Var.1253070
V(Y[t],d=3,D=0)8797600Range16588Trim Var.4642930
V(Y[t],d=0,D=1)824831Range5358Trim Var.409983
V(Y[t],d=1,D=1)1502680Range6896Trim Var.758050
V(Y[t],d=2,D=1)4404040Range12074Trim Var.2293030
V(Y[t],d=3,D=1)14387800Range19552Trim Var.7868190
V(Y[t],d=0,D=2)2343980Range8668Trim Var.1140840
V(Y[t],d=1,D=2)5010080Range12074Trim Var.2271910
V(Y[t],d=2,D=2)14525400Range21708Trim Var.7662750
V(Y[t],d=3,D=2)46617800Range34152Trim Var.23357900

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1763580 & Range & 5480 & Trim Var. & 1283570 \tabularnewline
V(Y[t],d=1,D=0) & 827570 & Range & 5072 & Trim Var. & 410473 \tabularnewline
V(Y[t],d=2,D=0) & 2549070 & Range & 8910 & Trim Var. & 1253070 \tabularnewline
V(Y[t],d=3,D=0) & 8797600 & Range & 16588 & Trim Var. & 4642930 \tabularnewline
V(Y[t],d=0,D=1) & 824831 & Range & 5358 & Trim Var. & 409983 \tabularnewline
V(Y[t],d=1,D=1) & 1502680 & Range & 6896 & Trim Var. & 758050 \tabularnewline
V(Y[t],d=2,D=1) & 4404040 & Range & 12074 & Trim Var. & 2293030 \tabularnewline
V(Y[t],d=3,D=1) & 14387800 & Range & 19552 & Trim Var. & 7868190 \tabularnewline
V(Y[t],d=0,D=2) & 2343980 & Range & 8668 & Trim Var. & 1140840 \tabularnewline
V(Y[t],d=1,D=2) & 5010080 & Range & 12074 & Trim Var. & 2271910 \tabularnewline
V(Y[t],d=2,D=2) & 14525400 & Range & 21708 & Trim Var. & 7662750 \tabularnewline
V(Y[t],d=3,D=2) & 46617800 & Range & 34152 & Trim Var. & 23357900 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300420&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1763580[/C][C]Range[/C][C]5480[/C][C]Trim Var.[/C][C]1283570[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]827570[/C][C]Range[/C][C]5072[/C][C]Trim Var.[/C][C]410473[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]2549070[/C][C]Range[/C][C]8910[/C][C]Trim Var.[/C][C]1253070[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]8797600[/C][C]Range[/C][C]16588[/C][C]Trim Var.[/C][C]4642930[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]824831[/C][C]Range[/C][C]5358[/C][C]Trim Var.[/C][C]409983[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]1502680[/C][C]Range[/C][C]6896[/C][C]Trim Var.[/C][C]758050[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]4404040[/C][C]Range[/C][C]12074[/C][C]Trim Var.[/C][C]2293030[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]14387800[/C][C]Range[/C][C]19552[/C][C]Trim Var.[/C][C]7868190[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2343980[/C][C]Range[/C][C]8668[/C][C]Trim Var.[/C][C]1140840[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]5010080[/C][C]Range[/C][C]12074[/C][C]Trim Var.[/C][C]2271910[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]14525400[/C][C]Range[/C][C]21708[/C][C]Trim Var.[/C][C]7662750[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]46617800[/C][C]Range[/C][C]34152[/C][C]Trim Var.[/C][C]23357900[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300420&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300420&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)1763580Range5480Trim Var.1283570
V(Y[t],d=1,D=0)827570Range5072Trim Var.410473
V(Y[t],d=2,D=0)2549070Range8910Trim Var.1253070
V(Y[t],d=3,D=0)8797600Range16588Trim Var.4642930
V(Y[t],d=0,D=1)824831Range5358Trim Var.409983
V(Y[t],d=1,D=1)1502680Range6896Trim Var.758050
V(Y[t],d=2,D=1)4404040Range12074Trim Var.2293030
V(Y[t],d=3,D=1)14387800Range19552Trim Var.7868190
V(Y[t],d=0,D=2)2343980Range8668Trim Var.1140840
V(Y[t],d=1,D=2)5010080Range12074Trim Var.2271910
V(Y[t],d=2,D=2)14525400Range21708Trim Var.7662750
V(Y[t],d=3,D=2)46617800Range34152Trim Var.23357900


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()