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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 computationSat, 10 Dec 2016 11:40:29 +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/10/t1481366776kxti26rz89cmfwy.htm/, Retrieved Mon, 06 May 2024 02:22:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298633, Retrieved Mon, 06 May 2024 02:22:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD    [Variance Reduction Matrix] [N1993 Variance Re...] [2016-12-10 10:40:29] [1eb03b74c4069f30e782d39ada1a3213] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6970
6455
8005
8115
8180
7930
7275
7865
7610
7435
8480
8850
8345
8275
8595
8430
8395
7735
7890
8435
7620
7610
8005
8935
8320
7670
8660
8485
8160
7910
7725
7555
7685
7740
7455
7850
6930
6600
7290
7625
7755
6915
6145
5985
6100
5955
5800
5905
5705
5430
6435
6025
5815
5160
4985
5585
5790
6190
6300
6340
6610
6685
7450
7410
7255
6460
6035
6745
6655
7070
7415
7720
7815
7260
7925
7825
7805
7530
7015
6575
6640
7075
6405
6720
6385
6085
6475
6555
6500
5790
5195
5680
5745
6010
5705
6310
6870
6260
7210
7090
7055
6535
6320
6010
6165
6985
6760
7220
6995
6475
7225
7325
7515
6925
7165
6895
6400
6685
6955
7550
7645
6710
7470
7355
7525
7165

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=298633&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=298633&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298633&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)760335Range3950Trim Var.506659
V(Y[t],d=1,D=0)229932Range2485Trim Var.143205
V(Y[t],d=2,D=0)523095Range3610Trim Var.316499
V(Y[t],d=3,D=0)1513200Range6235Trim Var.934979
V(Y[t],d=0,D=1)874203Range3765Trim Var.654198
V(Y[t],d=1,D=1)192692Range2175Trim Var.116200
V(Y[t],d=2,D=1)418068Range3335Trim Var.276661
V(Y[t],d=3,D=1)1204460Range5170Trim Var.796474
V(Y[t],d=0,D=2)2064180Range6190Trim Var.1339600
V(Y[t],d=1,D=2)564837Range3795Trim Var.334514
V(Y[t],d=2,D=2)1255240Range5155Trim Var.851171
V(Y[t],d=3,D=2)3622340Range8550Trim Var.2536920

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 760335 & Range & 3950 & Trim Var. & 506659 \tabularnewline
V(Y[t],d=1,D=0) & 229932 & Range & 2485 & Trim Var. & 143205 \tabularnewline
V(Y[t],d=2,D=0) & 523095 & Range & 3610 & Trim Var. & 316499 \tabularnewline
V(Y[t],d=3,D=0) & 1513200 & Range & 6235 & Trim Var. & 934979 \tabularnewline
V(Y[t],d=0,D=1) & 874203 & Range & 3765 & Trim Var. & 654198 \tabularnewline
V(Y[t],d=1,D=1) & 192692 & Range & 2175 & Trim Var. & 116200 \tabularnewline
V(Y[t],d=2,D=1) & 418068 & Range & 3335 & Trim Var. & 276661 \tabularnewline
V(Y[t],d=3,D=1) & 1204460 & Range & 5170 & Trim Var. & 796474 \tabularnewline
V(Y[t],d=0,D=2) & 2064180 & Range & 6190 & Trim Var. & 1339600 \tabularnewline
V(Y[t],d=1,D=2) & 564837 & Range & 3795 & Trim Var. & 334514 \tabularnewline
V(Y[t],d=2,D=2) & 1255240 & Range & 5155 & Trim Var. & 851171 \tabularnewline
V(Y[t],d=3,D=2) & 3622340 & Range & 8550 & Trim Var. & 2536920 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298633&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]760335[/C][C]Range[/C][C]3950[/C][C]Trim Var.[/C][C]506659[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]229932[/C][C]Range[/C][C]2485[/C][C]Trim Var.[/C][C]143205[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]523095[/C][C]Range[/C][C]3610[/C][C]Trim Var.[/C][C]316499[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1513200[/C][C]Range[/C][C]6235[/C][C]Trim Var.[/C][C]934979[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]874203[/C][C]Range[/C][C]3765[/C][C]Trim Var.[/C][C]654198[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]192692[/C][C]Range[/C][C]2175[/C][C]Trim Var.[/C][C]116200[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]418068[/C][C]Range[/C][C]3335[/C][C]Trim Var.[/C][C]276661[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1204460[/C][C]Range[/C][C]5170[/C][C]Trim Var.[/C][C]796474[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]2064180[/C][C]Range[/C][C]6190[/C][C]Trim Var.[/C][C]1339600[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]564837[/C][C]Range[/C][C]3795[/C][C]Trim Var.[/C][C]334514[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1255240[/C][C]Range[/C][C]5155[/C][C]Trim Var.[/C][C]851171[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]3622340[/C][C]Range[/C][C]8550[/C][C]Trim Var.[/C][C]2536920[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298633&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298633&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)760335Range3950Trim Var.506659
V(Y[t],d=1,D=0)229932Range2485Trim Var.143205
V(Y[t],d=2,D=0)523095Range3610Trim Var.316499
V(Y[t],d=3,D=0)1513200Range6235Trim Var.934979
V(Y[t],d=0,D=1)874203Range3765Trim Var.654198
V(Y[t],d=1,D=1)192692Range2175Trim Var.116200
V(Y[t],d=2,D=1)418068Range3335Trim Var.276661
V(Y[t],d=3,D=1)1204460Range5170Trim Var.796474
V(Y[t],d=0,D=2)2064180Range6190Trim Var.1339600
V(Y[t],d=1,D=2)564837Range3795Trim Var.334514
V(Y[t],d=2,D=2)1255240Range5155Trim Var.851171
V(Y[t],d=3,D=2)3622340Range8550Trim Var.2536920


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()