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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, 19 Dec 2010 15:22:31 +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/2010/Dec/19/t1292772050bt5d0a5mib2ttga.htm/, Retrieved Sun, 05 May 2024 05:59:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112493, Retrieved Sun, 05 May 2024 05:59:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact171

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] [Paper: Variance R...] [2010-12-19 15:22:31] [6f3869f9d1e39c73f93153f1f7803f84] [Current]
- R PD    [Variance Reduction Matrix] [Paper: Variance R...] [2010-12-19 20:09:05] [48146708a479232c43a8f6e52fbf83b4]
- RMPD    [ARIMA Backward Selection] [Paper: ARIMA Back...] [2010-12-19 20:13:51] [48146708a479232c43a8f6e52fbf83b4]
-   P       [ARIMA Backward Selection] [Paper: ARIMA Back...] [2010-12-21 12:10:18] [48146708a479232c43a8f6e52fbf83b4]
- RMP       [ARIMA Forecasting] [Paper: ARIMA Fore...] [2010-12-21 13:16:55] [48146708a479232c43a8f6e52fbf83b4]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1.006
789
734
906
532
387
991
841
892
782

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'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112493&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112493&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112493&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)27310.4051805777Range989.994Trim Var.14549.2906330989
V(Y[t],d=1,D=0)54714.3459144837Range1571.988Trim Var.20823.9627092846
V(Y[t],d=2,D=0)148582.273488966Range2414.982Trim Var.70596.3519170579
V(Y[t],d=3,D=0)455303.652539864Range4780.964Trim Var.206028.828925256
V(Y[t],d=0,D=1)12936.8280990916Range942.994Trim Var.3357.01760912698
V(Y[t],d=1,D=1)28637.0835342278Range1669.988Trim Var.6198.84383000512
V(Y[t],d=2,D=1)86608.93915841Range2629.982Trim Var.19129.7580645161
V(Y[t],d=3,D=1)289457.378516130Range5056.964Trim Var.60494.0765027322
V(Y[t],d=0,D=2)21521.7920672667Range963.994Trim Var.9241.52795248078
V(Y[t],d=1,D=2)43912.3181391724Range1628.988Trim Var.14167.2560331825
V(Y[t],d=2,D=2)123474.530692235Range2680.982Trim Var.43092.2877073906
V(Y[t],d=3,D=2)396349.391663233Range4938.964Trim Var.118886.817505020

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 27310.4051805777 & Range & 989.994 & Trim Var. & 14549.2906330989 \tabularnewline
V(Y[t],d=1,D=0) & 54714.3459144837 & Range & 1571.988 & Trim Var. & 20823.9627092846 \tabularnewline
V(Y[t],d=2,D=0) & 148582.273488966 & Range & 2414.982 & Trim Var. & 70596.3519170579 \tabularnewline
V(Y[t],d=3,D=0) & 455303.652539864 & Range & 4780.964 & Trim Var. & 206028.828925256 \tabularnewline
V(Y[t],d=0,D=1) & 12936.8280990916 & Range & 942.994 & Trim Var. & 3357.01760912698 \tabularnewline
V(Y[t],d=1,D=1) & 28637.0835342278 & Range & 1669.988 & Trim Var. & 6198.84383000512 \tabularnewline
V(Y[t],d=2,D=1) & 86608.93915841 & Range & 2629.982 & Trim Var. & 19129.7580645161 \tabularnewline
V(Y[t],d=3,D=1) & 289457.378516130 & Range & 5056.964 & Trim Var. & 60494.0765027322 \tabularnewline
V(Y[t],d=0,D=2) & 21521.7920672667 & Range & 963.994 & Trim Var. & 9241.52795248078 \tabularnewline
V(Y[t],d=1,D=2) & 43912.3181391724 & Range & 1628.988 & Trim Var. & 14167.2560331825 \tabularnewline
V(Y[t],d=2,D=2) & 123474.530692235 & Range & 2680.982 & Trim Var. & 43092.2877073906 \tabularnewline
V(Y[t],d=3,D=2) & 396349.391663233 & Range & 4938.964 & Trim Var. & 118886.817505020 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112493&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]27310.4051805777[/C][C]Range[/C][C]989.994[/C][C]Trim Var.[/C][C]14549.2906330989[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]54714.3459144837[/C][C]Range[/C][C]1571.988[/C][C]Trim Var.[/C][C]20823.9627092846[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]148582.273488966[/C][C]Range[/C][C]2414.982[/C][C]Trim Var.[/C][C]70596.3519170579[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]455303.652539864[/C][C]Range[/C][C]4780.964[/C][C]Trim Var.[/C][C]206028.828925256[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]12936.8280990916[/C][C]Range[/C][C]942.994[/C][C]Trim Var.[/C][C]3357.01760912698[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]28637.0835342278[/C][C]Range[/C][C]1669.988[/C][C]Trim Var.[/C][C]6198.84383000512[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]86608.93915841[/C][C]Range[/C][C]2629.982[/C][C]Trim Var.[/C][C]19129.7580645161[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]289457.378516130[/C][C]Range[/C][C]5056.964[/C][C]Trim Var.[/C][C]60494.0765027322[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]21521.7920672667[/C][C]Range[/C][C]963.994[/C][C]Trim Var.[/C][C]9241.52795248078[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]43912.3181391724[/C][C]Range[/C][C]1628.988[/C][C]Trim Var.[/C][C]14167.2560331825[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]123474.530692235[/C][C]Range[/C][C]2680.982[/C][C]Trim Var.[/C][C]43092.2877073906[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]396349.391663233[/C][C]Range[/C][C]4938.964[/C][C]Trim Var.[/C][C]118886.817505020[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112493&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112493&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)27310.4051805777Range989.994Trim Var.14549.2906330989
V(Y[t],d=1,D=0)54714.3459144837Range1571.988Trim Var.20823.9627092846
V(Y[t],d=2,D=0)148582.273488966Range2414.982Trim Var.70596.3519170579
V(Y[t],d=3,D=0)455303.652539864Range4780.964Trim Var.206028.828925256
V(Y[t],d=0,D=1)12936.8280990916Range942.994Trim Var.3357.01760912698
V(Y[t],d=1,D=1)28637.0835342278Range1669.988Trim Var.6198.84383000512
V(Y[t],d=2,D=1)86608.93915841Range2629.982Trim Var.19129.7580645161
V(Y[t],d=3,D=1)289457.378516130Range5056.964Trim Var.60494.0765027322
V(Y[t],d=0,D=2)21521.7920672667Range963.994Trim Var.9241.52795248078
V(Y[t],d=1,D=2)43912.3181391724Range1628.988Trim Var.14167.2560331825
V(Y[t],d=2,D=2)123474.530692235Range2680.982Trim Var.43092.2877073906
V(Y[t],d=3,D=2)396349.391663233Range4938.964Trim Var.118886.817505020


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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,var(myx))
a<-table.element(a,'Range',header=TRUE)
a<-table.element(a,max(myx)-min(myx))
a<-table.element(a,'Trim Var.',header=TRUE)
smyx <- sort(myx)
sn <- length(smyx)
a<-table.element(a,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()