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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, 26 Dec 2010 10:28:15 +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/26/t1293359188fd3tnd8am69321t.htm/, Retrieved Mon, 06 May 2024 12:26:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115497, Retrieved Mon, 06 May 2024 12:26:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact152

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] [tijdreeks bevolki...] [2010-12-26 10:28:15] [531024149246456e4f6d79ace2e85c12] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
5140
4749
3635
4305
5805
4260
3869
7325
9280
6222
3272
7598
1345
1900
1480
1472
3823
4454
3357
5393
8329
4152
4042
7747
1451
911
-406
1387
2150
1577
2642
4273
8064
3243
1112
2280
505
744
-1369
-531
1041
2076
577
5080
6584
3761
294
5020
1141
3805
2127
2531
3682
3263
2798
5936
10568
5296
1870
4390
3707
5201
3748
5282
5349
6249
5517
8640
15767
8850
5582
6496
3255
6189
6452
5099
6833
7046
7739
10142
16054
7721
6182
6490
3704
6235
4655
5072
3640
5147
5703
11889
15603
9589

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115497&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]2 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=115497&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115497&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 time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)11008599.2143674Range17423Trim Var.5307892.53815261
V(Y[t],d=1,D=0)8707235.63674614Range15460Trim Var.4879941.87393476
V(Y[t],d=2,D=0)21164496.6119207Range22438Trim Var.11814823.9042457
V(Y[t],d=3,D=0)62330921.5091575Range39087Trim Var.33005528.0114198
V(Y[t],d=0,D=1)4222949.98750376Range10666Trim Var.2667950.34663537
V(Y[t],d=1,D=1)3122348.35493827Range7687Trim Var.2069186.13480885
V(Y[t],d=2,D=1)9429140.66946203Range13039Trim Var.6857263.50156495
V(Y[t],d=3,D=1)32659859.5686465Range21298Trim Var.24425167.9195171
V(Y[t],d=0,D=2)7511654.25279503Range13823Trim Var.4554523.32760444
V(Y[t],d=1,D=2)9314230.0630861Range12720Trim Var.6387864.37213115
V(Y[t],d=2,D=2)28549836.9218613Range23784Trim Var.19147149.6090395
V(Y[t],d=3,D=2)99977920.4549977Range40950Trim Var.66087269.9053185

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 11008599.2143674 & Range & 17423 & Trim Var. & 5307892.53815261 \tabularnewline
V(Y[t],d=1,D=0) & 8707235.63674614 & Range & 15460 & Trim Var. & 4879941.87393476 \tabularnewline
V(Y[t],d=2,D=0) & 21164496.6119207 & Range & 22438 & Trim Var. & 11814823.9042457 \tabularnewline
V(Y[t],d=3,D=0) & 62330921.5091575 & Range & 39087 & Trim Var. & 33005528.0114198 \tabularnewline
V(Y[t],d=0,D=1) & 4222949.98750376 & Range & 10666 & Trim Var. & 2667950.34663537 \tabularnewline
V(Y[t],d=1,D=1) & 3122348.35493827 & Range & 7687 & Trim Var. & 2069186.13480885 \tabularnewline
V(Y[t],d=2,D=1) & 9429140.66946203 & Range & 13039 & Trim Var. & 6857263.50156495 \tabularnewline
V(Y[t],d=3,D=1) & 32659859.5686465 & Range & 21298 & Trim Var. & 24425167.9195171 \tabularnewline
V(Y[t],d=0,D=2) & 7511654.25279503 & Range & 13823 & Trim Var. & 4554523.32760444 \tabularnewline
V(Y[t],d=1,D=2) & 9314230.0630861 & Range & 12720 & Trim Var. & 6387864.37213115 \tabularnewline
V(Y[t],d=2,D=2) & 28549836.9218613 & Range & 23784 & Trim Var. & 19147149.6090395 \tabularnewline
V(Y[t],d=3,D=2) & 99977920.4549977 & Range & 40950 & Trim Var. & 66087269.9053185 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115497&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]11008599.2143674[/C][C]Range[/C][C]17423[/C][C]Trim Var.[/C][C]5307892.53815261[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]8707235.63674614[/C][C]Range[/C][C]15460[/C][C]Trim Var.[/C][C]4879941.87393476[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]21164496.6119207[/C][C]Range[/C][C]22438[/C][C]Trim Var.[/C][C]11814823.9042457[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]62330921.5091575[/C][C]Range[/C][C]39087[/C][C]Trim Var.[/C][C]33005528.0114198[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]4222949.98750376[/C][C]Range[/C][C]10666[/C][C]Trim Var.[/C][C]2667950.34663537[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]3122348.35493827[/C][C]Range[/C][C]7687[/C][C]Trim Var.[/C][C]2069186.13480885[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]9429140.66946203[/C][C]Range[/C][C]13039[/C][C]Trim Var.[/C][C]6857263.50156495[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]32659859.5686465[/C][C]Range[/C][C]21298[/C][C]Trim Var.[/C][C]24425167.9195171[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]7511654.25279503[/C][C]Range[/C][C]13823[/C][C]Trim Var.[/C][C]4554523.32760444[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]9314230.0630861[/C][C]Range[/C][C]12720[/C][C]Trim Var.[/C][C]6387864.37213115[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]28549836.9218613[/C][C]Range[/C][C]23784[/C][C]Trim Var.[/C][C]19147149.6090395[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]99977920.4549977[/C][C]Range[/C][C]40950[/C][C]Trim Var.[/C][C]66087269.9053185[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115497&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115497&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)11008599.2143674Range17423Trim Var.5307892.53815261
V(Y[t],d=1,D=0)8707235.63674614Range15460Trim Var.4879941.87393476
V(Y[t],d=2,D=0)21164496.6119207Range22438Trim Var.11814823.9042457
V(Y[t],d=3,D=0)62330921.5091575Range39087Trim Var.33005528.0114198
V(Y[t],d=0,D=1)4222949.98750376Range10666Trim Var.2667950.34663537
V(Y[t],d=1,D=1)3122348.35493827Range7687Trim Var.2069186.13480885
V(Y[t],d=2,D=1)9429140.66946203Range13039Trim Var.6857263.50156495
V(Y[t],d=3,D=1)32659859.5686465Range21298Trim Var.24425167.9195171
V(Y[t],d=0,D=2)7511654.25279503Range13823Trim Var.4554523.32760444
V(Y[t],d=1,D=2)9314230.0630861Range12720Trim Var.6387864.37213115
V(Y[t],d=2,D=2)28549836.9218613Range23784Trim Var.19147149.6090395
V(Y[t],d=3,D=2)99977920.4549977Range40950Trim Var.66087269.9053185


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 <- 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()