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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, 07 Dec 2016 19:56:18 +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/07/t1481137036vwbyga0vtkkm69l.htm/, Retrieved Tue, 07 May 2024 10:11:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298305, Retrieved Tue, 07 May 2024 10:11:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact42

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] [N2596] [2016-12-07 18:56:18] [85f5800284aab30c091766186b093bb4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1819.6
1312.4
2584
1479.6
1742
2639.2
1706
1408
1951.6
1690.4
2288.4
2912
1460.8
1009.6
2410
1603.2
2115.2
2330
1690
1358
1806.8
1973.6
1402
1857.6
1974.4
1438
1923.2
1996.8
2238.8
2540.4
1704.4
1856
2214.8
1948
1802
1431.6
2857.6
1784
2770.8
2313.6
3707.6
4322.4
3297.6
2223.6
2136.4
2459.2
1650.4
2921.2
1979.6
1403.2
2374
2876.4
2500
3888
1508.8
1011.2
1590.8
2076.4
3736
2125.6
982.8
2034.8
2260
1726
2270.4
1951.6
2104.4
2972.8
2834.4
4227.6
3392.4
3069.2
3138.8
3570
4800.4
4769.2
5124.8
3476.8
2866.8
2549.2
2728
2448.8
3286.8
2830
3251.2
4188.8
2747.6
2269.2
2493.2
2147.6
2689.2
3557.2
2840
3979.6
2683.2
2852
3012.8
2950.8
3065.2
3942.4
4272
4564
5222.8
5164.4
3883.6
4103.2
5244
8071.6
5441.6
7496
10100.4
9616
5645.6
10490
5582
7579.2
4023.6
8146.4
8534.4
10113.6
8504.4
9782.4
13110
8192.8
8708.8
9528.8

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=298305&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=298305&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298305&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)5774940Range12127.2Trim Var.2994760
V(Y[t],d=1,D=0)1877840Range9761.6Trim Var.599490
V(Y[t],d=2,D=0)5631210Range18567.2Trim Var.1647990
V(Y[t],d=3,D=0)19190900Range35224.8Trim Var.4943210
V(Y[t],d=0,D=1)2922010Range9666.8Trim Var.1403990
V(Y[t],d=1,D=1)2668400Range10119.2Trim Var.1216060
V(Y[t],d=2,D=1)8002200Range19038.4Trim Var.3135750
V(Y[t],d=3,D=1)26815400Range36713.2Trim Var.10090200
V(Y[t],d=0,D=2)6567470Range13814.4Trim Var.3424990
V(Y[t],d=1,D=2)6855170Range17363.2Trim Var.3704940
V(Y[t],d=2,D=2)19510500Range29220.8Trim Var.10563100
V(Y[t],d=3,D=2)61710700Range47485.6Trim Var.36493300

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 5774940 & Range & 12127.2 & Trim Var. & 2994760 \tabularnewline
V(Y[t],d=1,D=0) & 1877840 & Range & 9761.6 & Trim Var. & 599490 \tabularnewline
V(Y[t],d=2,D=0) & 5631210 & Range & 18567.2 & Trim Var. & 1647990 \tabularnewline
V(Y[t],d=3,D=0) & 19190900 & Range & 35224.8 & Trim Var. & 4943210 \tabularnewline
V(Y[t],d=0,D=1) & 2922010 & Range & 9666.8 & Trim Var. & 1403990 \tabularnewline
V(Y[t],d=1,D=1) & 2668400 & Range & 10119.2 & Trim Var. & 1216060 \tabularnewline
V(Y[t],d=2,D=1) & 8002200 & Range & 19038.4 & Trim Var. & 3135750 \tabularnewline
V(Y[t],d=3,D=1) & 26815400 & Range & 36713.2 & Trim Var. & 10090200 \tabularnewline
V(Y[t],d=0,D=2) & 6567470 & Range & 13814.4 & Trim Var. & 3424990 \tabularnewline
V(Y[t],d=1,D=2) & 6855170 & Range & 17363.2 & Trim Var. & 3704940 \tabularnewline
V(Y[t],d=2,D=2) & 19510500 & Range & 29220.8 & Trim Var. & 10563100 \tabularnewline
V(Y[t],d=3,D=2) & 61710700 & Range & 47485.6 & Trim Var. & 36493300 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298305&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]5774940[/C][C]Range[/C][C]12127.2[/C][C]Trim Var.[/C][C]2994760[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1877840[/C][C]Range[/C][C]9761.6[/C][C]Trim Var.[/C][C]599490[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]5631210[/C][C]Range[/C][C]18567.2[/C][C]Trim Var.[/C][C]1647990[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]19190900[/C][C]Range[/C][C]35224.8[/C][C]Trim Var.[/C][C]4943210[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]2922010[/C][C]Range[/C][C]9666.8[/C][C]Trim Var.[/C][C]1403990[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2668400[/C][C]Range[/C][C]10119.2[/C][C]Trim Var.[/C][C]1216060[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]8002200[/C][C]Range[/C][C]19038.4[/C][C]Trim Var.[/C][C]3135750[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]26815400[/C][C]Range[/C][C]36713.2[/C][C]Trim Var.[/C][C]10090200[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]6567470[/C][C]Range[/C][C]13814.4[/C][C]Trim Var.[/C][C]3424990[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6855170[/C][C]Range[/C][C]17363.2[/C][C]Trim Var.[/C][C]3704940[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]19510500[/C][C]Range[/C][C]29220.8[/C][C]Trim Var.[/C][C]10563100[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]61710700[/C][C]Range[/C][C]47485.6[/C][C]Trim Var.[/C][C]36493300[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298305&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298305&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)5774940Range12127.2Trim Var.2994760
V(Y[t],d=1,D=0)1877840Range9761.6Trim Var.599490
V(Y[t],d=2,D=0)5631210Range18567.2Trim Var.1647990
V(Y[t],d=3,D=0)19190900Range35224.8Trim Var.4943210
V(Y[t],d=0,D=1)2922010Range9666.8Trim Var.1403990
V(Y[t],d=1,D=1)2668400Range10119.2Trim Var.1216060
V(Y[t],d=2,D=1)8002200Range19038.4Trim Var.3135750
V(Y[t],d=3,D=1)26815400Range36713.2Trim Var.10090200
V(Y[t],d=0,D=2)6567470Range13814.4Trim Var.3424990
V(Y[t],d=1,D=2)6855170Range17363.2Trim Var.3704940
V(Y[t],d=2,D=2)19510500Range29220.8Trim Var.10563100
V(Y[t],d=3,D=2)61710700Range47485.6Trim Var.36493300


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = -1.0 ; par2 = 1 ; par3 = 0 ; par4 = 1 ;
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()