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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, 17 Dec 2016 12:57:59 +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/17/t1481975932c0rijtz0ovdupt4.htm/, Retrieved Thu, 02 May 2024 02:38:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300738, Retrieved Thu, 02 May 2024 02:38:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56

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] [] [2016-12-17 11:57:59] [349958aef20b862f8399a5ba04d6f6e3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
990
1384
1350
716
2068
1392
734
758
558
1620
3132
1392
918
776
1348
502
1274
1638
912
1250
1614
2840
1150
1652
1526
1412
882
848
820
1226
1212
2110
1178
2548
1568
2088
2178
3016
5514
1358
3604
1962
2036
2246
3434
4316
3032
5296
3850
2098
3992
4860
7336
9614
2988
2756
3540
2710
3730
3508
2640
2788
3502
3700
3250
4866
2836
3498
3468
3924
5738
7028
5608
6030
11976
7774
7906
10940
7626
5930
6286
6788
6932
6660
4910
4182
3550
3184
3872
3226
2504
3648
4448
2954
3842
3982
4864
6796
5844
5656
6118
7068
7696
7016
5820
4904
3860
7222
7738
7142
13804
7964
9716
8462
6884
8072
7320
11700
10792
10930
7112
8196
16818
10524
14878
13696

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=300738&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=300738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300738&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)11279900Range16316Trim Var.6508370
V(Y[t],d=1,D=0)4135630Range15248Trim Var.1111450
V(Y[t],d=2,D=0)11919200Range25564Trim Var.3629210
V(Y[t],d=3,D=0)39128700Range48018Trim Var.11339500
V(Y[t],d=0,D=1)8278110Range16900Trim Var.3960560
V(Y[t],d=1,D=1)5334970Range14314Trim Var.2471120
V(Y[t],d=2,D=1)13698800Range23680Trim Var.6591920
V(Y[t],d=3,D=1)43572400Range43616Trim Var.19617900
V(Y[t],d=0,D=2)25294800Range28456Trim Var.11660300
V(Y[t],d=1,D=2)15148100Range23106Trim Var.8685910
V(Y[t],d=2,D=2)38434600Range33810Trim Var.22561400
V(Y[t],d=3,D=2)122227000Range58740Trim Var.70637200

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 11279900 & Range & 16316 & Trim Var. & 6508370 \tabularnewline
V(Y[t],d=1,D=0) & 4135630 & Range & 15248 & Trim Var. & 1111450 \tabularnewline
V(Y[t],d=2,D=0) & 11919200 & Range & 25564 & Trim Var. & 3629210 \tabularnewline
V(Y[t],d=3,D=0) & 39128700 & Range & 48018 & Trim Var. & 11339500 \tabularnewline
V(Y[t],d=0,D=1) & 8278110 & Range & 16900 & Trim Var. & 3960560 \tabularnewline
V(Y[t],d=1,D=1) & 5334970 & Range & 14314 & Trim Var. & 2471120 \tabularnewline
V(Y[t],d=2,D=1) & 13698800 & Range & 23680 & Trim Var. & 6591920 \tabularnewline
V(Y[t],d=3,D=1) & 43572400 & Range & 43616 & Trim Var. & 19617900 \tabularnewline
V(Y[t],d=0,D=2) & 25294800 & Range & 28456 & Trim Var. & 11660300 \tabularnewline
V(Y[t],d=1,D=2) & 15148100 & Range & 23106 & Trim Var. & 8685910 \tabularnewline
V(Y[t],d=2,D=2) & 38434600 & Range & 33810 & Trim Var. & 22561400 \tabularnewline
V(Y[t],d=3,D=2) & 122227000 & Range & 58740 & Trim Var. & 70637200 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300738&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]11279900[/C][C]Range[/C][C]16316[/C][C]Trim Var.[/C][C]6508370[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]4135630[/C][C]Range[/C][C]15248[/C][C]Trim Var.[/C][C]1111450[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]11919200[/C][C]Range[/C][C]25564[/C][C]Trim Var.[/C][C]3629210[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]39128700[/C][C]Range[/C][C]48018[/C][C]Trim Var.[/C][C]11339500[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]8278110[/C][C]Range[/C][C]16900[/C][C]Trim Var.[/C][C]3960560[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]5334970[/C][C]Range[/C][C]14314[/C][C]Trim Var.[/C][C]2471120[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]13698800[/C][C]Range[/C][C]23680[/C][C]Trim Var.[/C][C]6591920[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]43572400[/C][C]Range[/C][C]43616[/C][C]Trim Var.[/C][C]19617900[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]25294800[/C][C]Range[/C][C]28456[/C][C]Trim Var.[/C][C]11660300[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]15148100[/C][C]Range[/C][C]23106[/C][C]Trim Var.[/C][C]8685910[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]38434600[/C][C]Range[/C][C]33810[/C][C]Trim Var.[/C][C]22561400[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]122227000[/C][C]Range[/C][C]58740[/C][C]Trim Var.[/C][C]70637200[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300738&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)11279900Range16316Trim Var.6508370
V(Y[t],d=1,D=0)4135630Range15248Trim Var.1111450
V(Y[t],d=2,D=0)11919200Range25564Trim Var.3629210
V(Y[t],d=3,D=0)39128700Range48018Trim Var.11339500
V(Y[t],d=0,D=1)8278110Range16900Trim Var.3960560
V(Y[t],d=1,D=1)5334970Range14314Trim Var.2471120
V(Y[t],d=2,D=1)13698800Range23680Trim Var.6591920
V(Y[t],d=3,D=1)43572400Range43616Trim Var.19617900
V(Y[t],d=0,D=2)25294800Range28456Trim Var.11660300
V(Y[t],d=1,D=2)15148100Range23106Trim Var.8685910
V(Y[t],d=2,D=2)38434600Range33810Trim Var.22561400
V(Y[t],d=3,D=2)122227000Range58740Trim Var.70637200


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()