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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 13:34:04 +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/t1482323681um2y2sqs4v0si64.htm/, Retrieved Thu, 20 Feb 2025 19:19:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302229, Retrieved Thu, 20 Feb 2025 19:19:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsN2054
Estimated Impact127

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ML Fitting and QQ Plot- Normal Distribution] [Normal distribution] [2016-12-15 09:27:42] [061bcad4f8cbfaa4a6cadfe6faec1e5a]
- RMPD  [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [Chisquared simula...] [2016-12-15 10:38:18] [061bcad4f8cbfaa4a6cadfe6faec1e5a]
- RMPD      [Variance Reduction Matrix] [VRm] [2016-12-21 12:34:04] [9a9519454d094169f95f881e5b6f16f7] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6675.2
7075.3
8344.1
7328.8
7076.7
7137.1
6018
7248.3
6760.3
7047.7
6368.2
6272.6
6245.4
6039.4
6855.3
6155.2
6291.6
6144.5
5490.4
7289.1
6992.7
7134
6827.2
6335.4
6762.2
7340.8
8123.2
7251.1
8067.6
7609.4
7438.1
9036.5
7853.8
6941.9
6403.9
6347.5
6792.1
6689.7
7734.7
7624.1
7797.9
7273.1
6882.1
7921.2
7359.6
7971.1
6888.1
6959.3
7780.4
7220.9
7707.8
7433.3
7256.8
7207.1
6725.3
7591.2
7440.7
7941.2
6977.4
7320.1
7447.3
7144.7
7560.9
7076.8
7043.6
7678
6942.7
8034.8
8211.8
8563
7891.9
7924.6
7536.4
7677.8
8396.4
7535.1
7397.9
7644.8
6919.8
8820.6
8327.2
8085.3
8297.3
8032.4
8196.9
7504
8898.1
7714.5
8248.6
7854.4
6626.9
9082.4
8461.8
8957.4
8696.5
7255.4
9027.6
8175.6
9129.2
8288
8620
8427.6
7953.5
9151.5
8281.3
9307.8
8646.1
7548.7
8599.1
8277.2
8516.8
7938.3
7994.7
7692.7
7987.6
8898.2
8165.6
9044.5
8187
7952.1
8770.5
8188.6
8559.5
8215.8
7998
7975.4

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=302229&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=302229&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302229&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)643371Range3817.4Trim Var.424702
V(Y[t],d=1,D=0)553842Range3896.6Trim Var.331742
V(Y[t],d=2,D=0)1709420Range6759.1Trim Var.1035710
V(Y[t],d=3,D=0)5935090Range11275.4Trim Var.3843930
V(Y[t],d=0,D=1)385679Range3436.5Trim Var.208565
V(Y[t],d=1,D=1)274684Range2865.2Trim Var.169935
V(Y[t],d=2,D=1)701422Range4852.3Trim Var.444630
V(Y[t],d=3,D=1)2183250Range8037.9Trim Var.1397750
V(Y[t],d=0,D=2)1108220Range5619.4Trim Var.524815
V(Y[t],d=1,D=2)627074Range4906.1Trim Var.330501
V(Y[t],d=2,D=2)1438320Range6868.1Trim Var.811200
V(Y[t],d=3,D=2)4228150Range12165.3Trim Var.2457950

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 643371 & Range & 3817.4 & Trim Var. & 424702 \tabularnewline
V(Y[t],d=1,D=0) & 553842 & Range & 3896.6 & Trim Var. & 331742 \tabularnewline
V(Y[t],d=2,D=0) & 1709420 & Range & 6759.1 & Trim Var. & 1035710 \tabularnewline
V(Y[t],d=3,D=0) & 5935090 & Range & 11275.4 & Trim Var. & 3843930 \tabularnewline
V(Y[t],d=0,D=1) & 385679 & Range & 3436.5 & Trim Var. & 208565 \tabularnewline
V(Y[t],d=1,D=1) & 274684 & Range & 2865.2 & Trim Var. & 169935 \tabularnewline
V(Y[t],d=2,D=1) & 701422 & Range & 4852.3 & Trim Var. & 444630 \tabularnewline
V(Y[t],d=3,D=1) & 2183250 & Range & 8037.9 & Trim Var. & 1397750 \tabularnewline
V(Y[t],d=0,D=2) & 1108220 & Range & 5619.4 & Trim Var. & 524815 \tabularnewline
V(Y[t],d=1,D=2) & 627074 & Range & 4906.1 & Trim Var. & 330501 \tabularnewline
V(Y[t],d=2,D=2) & 1438320 & Range & 6868.1 & Trim Var. & 811200 \tabularnewline
V(Y[t],d=3,D=2) & 4228150 & Range & 12165.3 & Trim Var. & 2457950 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302229&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]643371[/C][C]Range[/C][C]3817.4[/C][C]Trim Var.[/C][C]424702[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]553842[/C][C]Range[/C][C]3896.6[/C][C]Trim Var.[/C][C]331742[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1709420[/C][C]Range[/C][C]6759.1[/C][C]Trim Var.[/C][C]1035710[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]5935090[/C][C]Range[/C][C]11275.4[/C][C]Trim Var.[/C][C]3843930[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]385679[/C][C]Range[/C][C]3436.5[/C][C]Trim Var.[/C][C]208565[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]274684[/C][C]Range[/C][C]2865.2[/C][C]Trim Var.[/C][C]169935[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]701422[/C][C]Range[/C][C]4852.3[/C][C]Trim Var.[/C][C]444630[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]2183250[/C][C]Range[/C][C]8037.9[/C][C]Trim Var.[/C][C]1397750[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]1108220[/C][C]Range[/C][C]5619.4[/C][C]Trim Var.[/C][C]524815[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]627074[/C][C]Range[/C][C]4906.1[/C][C]Trim Var.[/C][C]330501[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]1438320[/C][C]Range[/C][C]6868.1[/C][C]Trim Var.[/C][C]811200[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]4228150[/C][C]Range[/C][C]12165.3[/C][C]Trim Var.[/C][C]2457950[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302229&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302229&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)643371Range3817.4Trim Var.424702
V(Y[t],d=1,D=0)553842Range3896.6Trim Var.331742
V(Y[t],d=2,D=0)1709420Range6759.1Trim Var.1035710
V(Y[t],d=3,D=0)5935090Range11275.4Trim Var.3843930
V(Y[t],d=0,D=1)385679Range3436.5Trim Var.208565
V(Y[t],d=1,D=1)274684Range2865.2Trim Var.169935
V(Y[t],d=2,D=1)701422Range4852.3Trim Var.444630
V(Y[t],d=3,D=1)2183250Range8037.9Trim Var.1397750
V(Y[t],d=0,D=2)1108220Range5619.4Trim Var.524815
V(Y[t],d=1,D=2)627074Range4906.1Trim Var.330501
V(Y[t],d=2,D=2)1438320Range6868.1Trim Var.811200
V(Y[t],d=3,D=2)4228150Range12165.3Trim Var.2457950


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()