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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 2011 17:44:28 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/21/t1324507508n7h43cg57lyszae.htm/, Retrieved Tue, 07 May 2024 12:36:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159113, Retrieved Tue, 07 May 2024 12:36:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact92

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] [VRM] [2011-12-21 22:44:28] [e569a00cc6e8044e6afea1f18dd335a0] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
2582
2624
2566
2645
3167
3051
2503
2574
2988
3086
2632
2604
2377
2258
2266
2601
2843
3018
2493
2647
3015
3101
2496
2342
2271
1969
2196
2294
2706
3001
2691
2554
2961
3226
2960
2749
2379
2254
2592
2780
2833
2911
2494
2643
2902
2880
2657
2609
2394
2492
2414
2621
3055
2940
2582
2430
2781
2904
2474
2254
2244
1972
2408
2523
2634
2798
2418
2551
2741
3011
2558
2167
1944
1836
2292
2576
2653
2900
2438
2439
2717
2872
2157
1541

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'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159113&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159113&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159113&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'Herman Ole Andreas Wold' @ wold.wessa.net






Variance Reduction Matrix
V(Y[t],d=0,D=0)102227.030981067Range1685Trim Var.56879.8646797482
V(Y[t],d=1,D=0)85132.0561269468Range1237Trim Var.57358.3047945205
V(Y[t],d=2,D=0)142945.308039747Range1578Trim Var.96478.8636541471
V(Y[t],d=3,D=0)350996.901234568Range2460Trim Var.242792.896981891
V(Y[t],d=0,D=1)46479.7134194053Range1112Trim Var.24106.3402777778
V(Y[t],d=1,D=1)43252.9806841046Range930Trim Var.30233.1172555044
V(Y[t],d=2,D=1)110439.760662526Range1523Trim Var.73567.251454257
V(Y[t],d=3,D=1)350046.276641091Range2949Trim Var.228843.38852459
V(Y[t],d=0,D=2)124748.077683616Range1560Trim Var.81981.0541579315
V(Y[t],d=1,D=2)140008.050847458Range1634Trim Var.99238.2467343977
V(Y[t],d=2,D=2)374899.444646098Range2564Trim Var.272082.876319759
V(Y[t],d=3,D=2)1198533.79010025Range4730Trim Var.852553.83372549

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 102227.030981067 & Range & 1685 & Trim Var. & 56879.8646797482 \tabularnewline
V(Y[t],d=1,D=0) & 85132.0561269468 & Range & 1237 & Trim Var. & 57358.3047945205 \tabularnewline
V(Y[t],d=2,D=0) & 142945.308039747 & Range & 1578 & Trim Var. & 96478.8636541471 \tabularnewline
V(Y[t],d=3,D=0) & 350996.901234568 & Range & 2460 & Trim Var. & 242792.896981891 \tabularnewline
V(Y[t],d=0,D=1) & 46479.7134194053 & Range & 1112 & Trim Var. & 24106.3402777778 \tabularnewline
V(Y[t],d=1,D=1) & 43252.9806841046 & Range & 930 & Trim Var. & 30233.1172555044 \tabularnewline
V(Y[t],d=2,D=1) & 110439.760662526 & Range & 1523 & Trim Var. & 73567.251454257 \tabularnewline
V(Y[t],d=3,D=1) & 350046.276641091 & Range & 2949 & Trim Var. & 228843.38852459 \tabularnewline
V(Y[t],d=0,D=2) & 124748.077683616 & Range & 1560 & Trim Var. & 81981.0541579315 \tabularnewline
V(Y[t],d=1,D=2) & 140008.050847458 & Range & 1634 & Trim Var. & 99238.2467343977 \tabularnewline
V(Y[t],d=2,D=2) & 374899.444646098 & Range & 2564 & Trim Var. & 272082.876319759 \tabularnewline
V(Y[t],d=3,D=2) & 1198533.79010025 & Range & 4730 & Trim Var. & 852553.83372549 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159113&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]102227.030981067[/C][C]Range[/C][C]1685[/C][C]Trim Var.[/C][C]56879.8646797482[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]85132.0561269468[/C][C]Range[/C][C]1237[/C][C]Trim Var.[/C][C]57358.3047945205[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]142945.308039747[/C][C]Range[/C][C]1578[/C][C]Trim Var.[/C][C]96478.8636541471[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]350996.901234568[/C][C]Range[/C][C]2460[/C][C]Trim Var.[/C][C]242792.896981891[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]46479.7134194053[/C][C]Range[/C][C]1112[/C][C]Trim Var.[/C][C]24106.3402777778[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]43252.9806841046[/C][C]Range[/C][C]930[/C][C]Trim Var.[/C][C]30233.1172555044[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]110439.760662526[/C][C]Range[/C][C]1523[/C][C]Trim Var.[/C][C]73567.251454257[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]350046.276641091[/C][C]Range[/C][C]2949[/C][C]Trim Var.[/C][C]228843.38852459[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]124748.077683616[/C][C]Range[/C][C]1560[/C][C]Trim Var.[/C][C]81981.0541579315[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]140008.050847458[/C][C]Range[/C][C]1634[/C][C]Trim Var.[/C][C]99238.2467343977[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]374899.444646098[/C][C]Range[/C][C]2564[/C][C]Trim Var.[/C][C]272082.876319759[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]1198533.79010025[/C][C]Range[/C][C]4730[/C][C]Trim Var.[/C][C]852553.83372549[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159113&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159113&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)102227.030981067Range1685Trim Var.56879.8646797482
V(Y[t],d=1,D=0)85132.0561269468Range1237Trim Var.57358.3047945205
V(Y[t],d=2,D=0)142945.308039747Range1578Trim Var.96478.8636541471
V(Y[t],d=3,D=0)350996.901234568Range2460Trim Var.242792.896981891
V(Y[t],d=0,D=1)46479.7134194053Range1112Trim Var.24106.3402777778
V(Y[t],d=1,D=1)43252.9806841046Range930Trim Var.30233.1172555044
V(Y[t],d=2,D=1)110439.760662526Range1523Trim Var.73567.251454257
V(Y[t],d=3,D=1)350046.276641091Range2949Trim Var.228843.38852459
V(Y[t],d=0,D=2)124748.077683616Range1560Trim Var.81981.0541579315
V(Y[t],d=1,D=2)140008.050847458Range1634Trim Var.99238.2467343977
V(Y[t],d=2,D=2)374899.444646098Range2564Trim Var.272082.876319759
V(Y[t],d=3,D=2)1198533.79010025Range4730Trim Var.852553.83372549


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()