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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 computationWed, 17 Dec 2014 14:45:12 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418827528la2dvby1pzey6mi.htm/, Retrieved Thu, 16 May 2024 04:26:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270350, Retrieved Thu, 16 May 2024 04:26:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68

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] [variantie] [2014-12-17 14:45:12] [a9ee49ff8435be51911716bad99dd485] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-6.399530
1.957360
2.478650
1.589720
0.184681
0.918505
-1.995250
1.586390
-0.140506
1.356850
1.727480
5.067280
-2.558530
-0.947617
1.134260
0.264652
2.593240
0.743810
0.743969
-1.112320
1.219600
1.306220
0.553112
0.291992
2.656690
-0.855357
1.923590
1.744140
0.735418
1.048160
0.426579
3.418350
-0.513488
0.833442
-1.064710
-0.237221
-0.759509
1.165110
-7.109370
1.726660
1.589090
-1.344360
1.481350
-0.236383
1.388380
1.018800
-1.946000
-2.255320
1.808120
2.125650
-1.159330
7.908360
0.926642
0.590183
2.058870
0.760719
-0.455908
-2.371740
1.112290
2.440940
-2.108970
-1.545510
-1.471520
3.059330
-0.878558
2.184800
-1.854340
-2.484340
-1.072920
-2.315740
2.722060
-0.029346
-3.150900
0.404606
1.887430
-2.627560
-3.574700
0.754203
-2.192110
1.409100
-3.193550
2.848590
-0.385986
1.743400
-2.023100
0.413897
1.122490
0.182360
-0.302073
0.411861
-2.430770
-0.489293
-0.852392
1.413970
0.056108
1.001380
3.783360
3.091870
-0.146159
-0.833078
-1.827790
0.067725
-0.429261
-0.310928
1.809600
0.624170
-0.700127
-0.723910
1.868270
-3.616350
-1.970360
1.675560
1.876060
3.632780
1.012410
2.040960
3.995540
2.484770
1.588610
2.972830
-0.499202
-3.911090
-2.829110
-6.120530
0.339289
-0.944523
0.035212
-1.042880
-1.323190
-1.133120
0.183183
1.967530
-2.511840
-0.287708
-0.369008
0.685670
0.758509
-1.400430
-3.497010
-0.776372
0.760543
2.310800
-2.673360
0.700963
-4.503390
-5.186020
-1.880700
-7.006000
-0.421422
-2.080020
-3.165650
0.737049
1.532660
0.811355
-0.429889
0.602124
1.069580
-1.168290
-0.541346
-0.852089
1.349240
1.763480
0.356035
-0.821847
0.901744
-1.230250

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270350&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270350&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270350&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)4.73015Range15.0177Trim Var.2.32805
V(Y[t],d=1,D=0)8.31471Range17.3422Trim Var.4.25932
V(Y[t],d=2,D=0)24.5459Range33.1599Trim Var.13.9413
V(Y[t],d=3,D=0)82.3087Range55.7117Trim Var.44.914
V(Y[t],d=0,D=1)8.47129Range15.8392Trim Var.4.85618
V(Y[t],d=1,D=1)14.0929Range21.0439Trim Var.8.69167
V(Y[t],d=2,D=1)42.7021Range36.559Trim Var.26.8509
V(Y[t],d=3,D=1)145.885Range65.4154Trim Var.92.5216
V(Y[t],d=0,D=2)24.7315Range29.4809Trim Var.13.6433
V(Y[t],d=1,D=2)38.5308Range29.242Trim Var.24.9116
V(Y[t],d=2,D=2)117.7Range48.2639Trim Var.77.7028
V(Y[t],d=3,D=2)409.322Range90.4376Trim Var.276.304

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 4.73015 & Range & 15.0177 & Trim Var. & 2.32805 \tabularnewline
V(Y[t],d=1,D=0) & 8.31471 & Range & 17.3422 & Trim Var. & 4.25932 \tabularnewline
V(Y[t],d=2,D=0) & 24.5459 & Range & 33.1599 & Trim Var. & 13.9413 \tabularnewline
V(Y[t],d=3,D=0) & 82.3087 & Range & 55.7117 & Trim Var. & 44.914 \tabularnewline
V(Y[t],d=0,D=1) & 8.47129 & Range & 15.8392 & Trim Var. & 4.85618 \tabularnewline
V(Y[t],d=1,D=1) & 14.0929 & Range & 21.0439 & Trim Var. & 8.69167 \tabularnewline
V(Y[t],d=2,D=1) & 42.7021 & Range & 36.559 & Trim Var. & 26.8509 \tabularnewline
V(Y[t],d=3,D=1) & 145.885 & Range & 65.4154 & Trim Var. & 92.5216 \tabularnewline
V(Y[t],d=0,D=2) & 24.7315 & Range & 29.4809 & Trim Var. & 13.6433 \tabularnewline
V(Y[t],d=1,D=2) & 38.5308 & Range & 29.242 & Trim Var. & 24.9116 \tabularnewline
V(Y[t],d=2,D=2) & 117.7 & Range & 48.2639 & Trim Var. & 77.7028 \tabularnewline
V(Y[t],d=3,D=2) & 409.322 & Range & 90.4376 & Trim Var. & 276.304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270350&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]4.73015[/C][C]Range[/C][C]15.0177[/C][C]Trim Var.[/C][C]2.32805[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]8.31471[/C][C]Range[/C][C]17.3422[/C][C]Trim Var.[/C][C]4.25932[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]24.5459[/C][C]Range[/C][C]33.1599[/C][C]Trim Var.[/C][C]13.9413[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]82.3087[/C][C]Range[/C][C]55.7117[/C][C]Trim Var.[/C][C]44.914[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]8.47129[/C][C]Range[/C][C]15.8392[/C][C]Trim Var.[/C][C]4.85618[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]14.0929[/C][C]Range[/C][C]21.0439[/C][C]Trim Var.[/C][C]8.69167[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]42.7021[/C][C]Range[/C][C]36.559[/C][C]Trim Var.[/C][C]26.8509[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]145.885[/C][C]Range[/C][C]65.4154[/C][C]Trim Var.[/C][C]92.5216[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]24.7315[/C][C]Range[/C][C]29.4809[/C][C]Trim Var.[/C][C]13.6433[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]38.5308[/C][C]Range[/C][C]29.242[/C][C]Trim Var.[/C][C]24.9116[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]117.7[/C][C]Range[/C][C]48.2639[/C][C]Trim Var.[/C][C]77.7028[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]409.322[/C][C]Range[/C][C]90.4376[/C][C]Trim Var.[/C][C]276.304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270350&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270350&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)4.73015Range15.0177Trim Var.2.32805
V(Y[t],d=1,D=0)8.31471Range17.3422Trim Var.4.25932
V(Y[t],d=2,D=0)24.5459Range33.1599Trim Var.13.9413
V(Y[t],d=3,D=0)82.3087Range55.7117Trim Var.44.914
V(Y[t],d=0,D=1)8.47129Range15.8392Trim Var.4.85618
V(Y[t],d=1,D=1)14.0929Range21.0439Trim Var.8.69167
V(Y[t],d=2,D=1)42.7021Range36.559Trim Var.26.8509
V(Y[t],d=3,D=1)145.885Range65.4154Trim Var.92.5216
V(Y[t],d=0,D=2)24.7315Range29.4809Trim Var.13.6433
V(Y[t],d=1,D=2)38.5308Range29.242Trim Var.24.9116
V(Y[t],d=2,D=2)117.7Range48.2639Trim Var.77.7028
V(Y[t],d=3,D=2)409.322Range90.4376Trim Var.276.304


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 <- 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)
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()