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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, 21 Dec 2016 18:41:21 +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/21/t14823420927a4lrkfi6j3jtyr.htm/, Retrieved Mon, 06 May 2024 13:24:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302443, Retrieved Mon, 06 May 2024 13:24:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact50

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] [] [2016-12-21 17:41:21] [037fdaa34a77b5f63489b3bcd360a80c] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3455
3585
3675
3680
3735
3860
3765
3905
4110
4170
4110
4025
4145
4285
4370
4355
4385
4525
4375
4525
4610
4595
4500
4370
4390
4530
4590
4580
4595
4685
4490
4635
4710
4655
4665
4550
4590
4675
4645
4665
4635
4720
4565
4720
4830
4830
4765
4705
4675
4900
4945
4905
4955
5120
4860
5040
5140
5240
5145
5070
5085
5215
5255
5275
5315
5450
5205
5370
5500
5490
5440
5360
5380
5460
5450
5520
5475
5600
5250
5465
5515
5425
5325
5275
5160
5360
5435
5285
5415
5575
5265
5480
5565
5500
5280
5135
5050
5100
5070
5115
5140
5330
5080
5285
5405
5385
5255
5100
5040
5235
5310
5265
5380
5465
5225
5445

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=302443&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=302443&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302443&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)266319Range2145Trim Var.178370
V(Y[t],d=1,D=0)15431.7Range575Trim Var.9781.63
V(Y[t],d=2,D=0)38021.1Range1040Trim Var.18315.7
V(Y[t],d=3,D=0)114249Range1770Trim Var.55965.2
V(Y[t],d=0,D=1)54135.4Range1065Trim Var.31391.5
V(Y[t],d=1,D=1)5238.95Range415Trim Var.2882.13
V(Y[t],d=2,D=1)12963.1Range700Trim Var.6216.62
V(Y[t],d=3,D=1)41925.5Range1300Trim Var.22037.8
V(Y[t],d=0,D=2)65600.6Range1120Trim Var.44880.5
V(Y[t],d=1,D=2)16315.7Range700Trim Var.8660.07
V(Y[t],d=2,D=2)43920.4Range1300Trim Var.20775.3
V(Y[t],d=3,D=2)143427Range2275Trim Var.71541

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 266319 & Range & 2145 & Trim Var. & 178370 \tabularnewline
V(Y[t],d=1,D=0) & 15431.7 & Range & 575 & Trim Var. & 9781.63 \tabularnewline
V(Y[t],d=2,D=0) & 38021.1 & Range & 1040 & Trim Var. & 18315.7 \tabularnewline
V(Y[t],d=3,D=0) & 114249 & Range & 1770 & Trim Var. & 55965.2 \tabularnewline
V(Y[t],d=0,D=1) & 54135.4 & Range & 1065 & Trim Var. & 31391.5 \tabularnewline
V(Y[t],d=1,D=1) & 5238.95 & Range & 415 & Trim Var. & 2882.13 \tabularnewline
V(Y[t],d=2,D=1) & 12963.1 & Range & 700 & Trim Var. & 6216.62 \tabularnewline
V(Y[t],d=3,D=1) & 41925.5 & Range & 1300 & Trim Var. & 22037.8 \tabularnewline
V(Y[t],d=0,D=2) & 65600.6 & Range & 1120 & Trim Var. & 44880.5 \tabularnewline
V(Y[t],d=1,D=2) & 16315.7 & Range & 700 & Trim Var. & 8660.07 \tabularnewline
V(Y[t],d=2,D=2) & 43920.4 & Range & 1300 & Trim Var. & 20775.3 \tabularnewline
V(Y[t],d=3,D=2) & 143427 & Range & 2275 & Trim Var. & 71541 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302443&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]266319[/C][C]Range[/C][C]2145[/C][C]Trim Var.[/C][C]178370[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]15431.7[/C][C]Range[/C][C]575[/C][C]Trim Var.[/C][C]9781.63[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]38021.1[/C][C]Range[/C][C]1040[/C][C]Trim Var.[/C][C]18315.7[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]114249[/C][C]Range[/C][C]1770[/C][C]Trim Var.[/C][C]55965.2[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]54135.4[/C][C]Range[/C][C]1065[/C][C]Trim Var.[/C][C]31391.5[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]5238.95[/C][C]Range[/C][C]415[/C][C]Trim Var.[/C][C]2882.13[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]12963.1[/C][C]Range[/C][C]700[/C][C]Trim Var.[/C][C]6216.62[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]41925.5[/C][C]Range[/C][C]1300[/C][C]Trim Var.[/C][C]22037.8[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]65600.6[/C][C]Range[/C][C]1120[/C][C]Trim Var.[/C][C]44880.5[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]16315.7[/C][C]Range[/C][C]700[/C][C]Trim Var.[/C][C]8660.07[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]43920.4[/C][C]Range[/C][C]1300[/C][C]Trim Var.[/C][C]20775.3[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]143427[/C][C]Range[/C][C]2275[/C][C]Trim Var.[/C][C]71541[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302443&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302443&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)266319Range2145Trim Var.178370
V(Y[t],d=1,D=0)15431.7Range575Trim Var.9781.63
V(Y[t],d=2,D=0)38021.1Range1040Trim Var.18315.7
V(Y[t],d=3,D=0)114249Range1770Trim Var.55965.2
V(Y[t],d=0,D=1)54135.4Range1065Trim Var.31391.5
V(Y[t],d=1,D=1)5238.95Range415Trim Var.2882.13
V(Y[t],d=2,D=1)12963.1Range700Trim Var.6216.62
V(Y[t],d=3,D=1)41925.5Range1300Trim Var.22037.8
V(Y[t],d=0,D=2)65600.6Range1120Trim Var.44880.5
V(Y[t],d=1,D=2)16315.7Range700Trim Var.8660.07
V(Y[t],d=2,D=2)43920.4Range1300Trim Var.20775.3
V(Y[t],d=3,D=2)143427Range2275Trim Var.71541


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()