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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 computationSun, 18 Dec 2016 14:20:15 +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/18/t1482067253koouuhzw7470w3f.htm/, Retrieved Wed, 08 May 2024 21:32:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301065, Retrieved Wed, 08 May 2024 21:32:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D    [Variance Reduction Matrix] [] [2016-12-18 13:20:15] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2280
3640
3950
3860
3500
4740
3690
4810
6150
4530
4760
4670
3510
2990
3240
2700
2610
3280
3170
3440
4710
4320
3650
3340
3050
2960
2810
2670
2440
2580
2520
2860
3500
3460
3310
3050
2730
2760
2800
2490
2310
2350
2370
2560
2740
2830
3010
2500
2630
2270
2410
2210
2330
2690
3150
2330
2260
2330
2240
2230
2270
2220
2290
2240
2110
2240
2230
2320
2320
2540
2530
2400
2470
2290
2110
2050
2170
2070
2330
2190
2260
2300
2220
2220
2380
2280
2150
2190
2080
2120
2140
2130
2210
2210
2190
2160
2290
2270
2200
2120
2050
2080
2180
2070
2170
2240
2320
2250

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=301065&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=301065&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301065&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
V(Y[t],d=0,D=0)592891Range4100Trim Var.293237
V(Y[t],d=1,D=0)173965Range2980Trim Var.36611.6
V(Y[t],d=2,D=0)389074Range5130Trim Var.79112.2
V(Y[t],d=3,D=0)1164740Range8700Trim Var.243494
V(Y[t],d=0,D=1)188684Range2690Trim Var.89251.9
V(Y[t],d=1,D=1)160899Range3110Trim Var.52393.3
V(Y[t],d=2,D=1)366258Range3950Trim Var.142431
V(Y[t],d=3,D=1)1101410Range6240Trim Var.471956
V(Y[t],d=0,D=2)235558Range2830Trim Var.93102.1
V(Y[t],d=1,D=2)320400Range3450Trim Var.127659
V(Y[t],d=2,D=2)770518Range5480Trim Var.358454
V(Y[t],d=3,D=2)2382560Range8270Trim Var.1227200

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 592891 & Range & 4100 & Trim Var. & 293237 \tabularnewline
V(Y[t],d=1,D=0) & 173965 & Range & 2980 & Trim Var. & 36611.6 \tabularnewline
V(Y[t],d=2,D=0) & 389074 & Range & 5130 & Trim Var. & 79112.2 \tabularnewline
V(Y[t],d=3,D=0) & 1164740 & Range & 8700 & Trim Var. & 243494 \tabularnewline
V(Y[t],d=0,D=1) & 188684 & Range & 2690 & Trim Var. & 89251.9 \tabularnewline
V(Y[t],d=1,D=1) & 160899 & Range & 3110 & Trim Var. & 52393.3 \tabularnewline
V(Y[t],d=2,D=1) & 366258 & Range & 3950 & Trim Var. & 142431 \tabularnewline
V(Y[t],d=3,D=1) & 1101410 & Range & 6240 & Trim Var. & 471956 \tabularnewline
V(Y[t],d=0,D=2) & 235558 & Range & 2830 & Trim Var. & 93102.1 \tabularnewline
V(Y[t],d=1,D=2) & 320400 & Range & 3450 & Trim Var. & 127659 \tabularnewline
V(Y[t],d=2,D=2) & 770518 & Range & 5480 & Trim Var. & 358454 \tabularnewline
V(Y[t],d=3,D=2) & 2382560 & Range & 8270 & Trim Var. & 1227200 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301065&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]592891[/C][C]Range[/C][C]4100[/C][C]Trim Var.[/C][C]293237[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]173965[/C][C]Range[/C][C]2980[/C][C]Trim Var.[/C][C]36611.6[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]389074[/C][C]Range[/C][C]5130[/C][C]Trim Var.[/C][C]79112.2[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1164740[/C][C]Range[/C][C]8700[/C][C]Trim Var.[/C][C]243494[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]188684[/C][C]Range[/C][C]2690[/C][C]Trim Var.[/C][C]89251.9[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]160899[/C][C]Range[/C][C]3110[/C][C]Trim Var.[/C][C]52393.3[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]366258[/C][C]Range[/C][C]3950[/C][C]Trim Var.[/C][C]142431[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]1101410[/C][C]Range[/C][C]6240[/C][C]Trim Var.[/C][C]471956[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]235558[/C][C]Range[/C][C]2830[/C][C]Trim Var.[/C][C]93102.1[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]320400[/C][C]Range[/C][C]3450[/C][C]Trim Var.[/C][C]127659[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]770518[/C][C]Range[/C][C]5480[/C][C]Trim Var.[/C][C]358454[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]2382560[/C][C]Range[/C][C]8270[/C][C]Trim Var.[/C][C]1227200[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301065&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301065&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)592891Range4100Trim Var.293237
V(Y[t],d=1,D=0)173965Range2980Trim Var.36611.6
V(Y[t],d=2,D=0)389074Range5130Trim Var.79112.2
V(Y[t],d=3,D=0)1164740Range8700Trim Var.243494
V(Y[t],d=0,D=1)188684Range2690Trim Var.89251.9
V(Y[t],d=1,D=1)160899Range3110Trim Var.52393.3
V(Y[t],d=2,D=1)366258Range3950Trim Var.142431
V(Y[t],d=3,D=1)1101410Range6240Trim Var.471956
V(Y[t],d=0,D=2)235558Range2830Trim Var.93102.1
V(Y[t],d=1,D=2)320400Range3450Trim Var.127659
V(Y[t],d=2,D=2)770518Range5480Trim Var.358454
V(Y[t],d=3,D=2)2382560Range8270Trim Var.1227200


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- '12'
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()