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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 computationMon, 08 Dec 2008 10:18:29 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t1228756755et7h59kxtbs7bw7.htm/, Retrieved Thu, 16 May 2024 22:03:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30607, Retrieved Thu, 16 May 2024 22:03:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact230

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Variance Reduction Matrix] [Unemployment - St...] [2008-12-08 17:18:29] [0831954c833179c36e9320daee0825b5] [Current]
F         [Variance Reduction Matrix] [STEP 1 1] [2008-12-08 18:47:26] [547636b63517c1c2916a747d66b36ebf]
- RM        [Standard Deviation-Mean Plot] [SD mean plot step 1] [2008-12-13 18:45:31] [7d3039e6253bb5fb3b26df1537d500b4]
-         [Variance Reduction Matrix] [Step1] [2008-12-08 20:26:47] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
-           [Variance Reduction Matrix] [step 1] [2008-12-08 23:47:41] [73d6180dc45497329efd1b6934a84aba]
F    D    [Variance Reduction Matrix] [] [2008-12-08 21:16:26] [4c8dfb519edec2da3492d7e6be9a5685]
Feedback Forum
2008-12-12 12:55:27 [Wim Golsteyn] [reply] 
Je had hier de Lambda waarde moeten berekenen, en die in de volgende stap in de VRM/ACF/Spectrum analyse moeten invullen. Doordat je dit niet hebt gedaan, klopt het model niet dat je uiteindelijk uitkomt in stap 5.
2008-12-14 23:45:46 [Bob Leysen] [reply] 
2008-12-14 23:51:56 [Bob Leysen] [reply] 
We zoeken in de tabel van VRM naar de laagste waarde omdat hoe kleiner de variantie, hoe beter. De variantie is het kleinst bij d=1 en D=1

De bedoeling van stap 1 is om de lambda waarde te berekenen en deze dan te gebruiken in stap 5. De waarde vinden we door een SMP analyse uit te voeren en dan te kijken naar de tabel 'Regression'.
2008-12-15 09:05:06 [Glenn De Maeyer] [reply] 
Bij step 1 wordt eigelijk gevraagd om een correcte lambda waarde te berekenen. We dienden dit te doen op de eigen tijdreeksen of op de tijdreeks unemployment data. De student maakte hier gebruik van zijn eigen tijdreeks. Hij maakte hier terecht gebruik van de VRM en kwam tot het juiste resultaat.

Dezelfde stap diende ook uitgevoerd te worden op de tijdreeks unemployment data.

Voor het bekomen van de correcte lambda waarde maken we gebruik van de Standard Deviation – Mean Plot software. Hier maken we gebruik van de unemployment data.

LINK:
http://www.freestatistics.org/blog/index.php?v=date/2008/Dec/14/t1229240118n4b6am5ynn7a5bl.htm


Uit de tabel Regression: ln S.E.(k) = alpha + beta * ln Mean(k) kunnen we een lamba waarde van 0.467057973925013 afleiden.

Als we 1 in vermindering hadden gebracht met de Beta waarde had dit ook geresulteerd in de optimale Lamba Coëfficiënt. Nl, (1 - 0.532942026074987) is gelijk aan 0.467057973925013.

Op de grafische weergave van de Standard Deviation – Mean Plot noteren we op de x as het gemiddelde en op y as de standaard fout.
2008-12-15 09:10:51 [Glenn De Maeyer] [reply] 
Kleine rechtzetting. De student diende de VRM pas te gebruiken in stap 2. Hier diende hij gebruik te maken van de Standard Deviation – Mean Plot software om de correcte lambda waarde te berekenen. Het gebruik van de VRM in deze stap is dus niet correct.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
569323
579714
577992
565464
547344
554788
562325
560854
555332
543599
536662
542722
593530
610763
612613
611324
594167
595454
590865
589379
584428
573100
567456
569028
620735
628884
628232
612117
595404
597141
593408
590072
579799
574205
572775
572942
619567
625809
619916
587625
565742
557274
560576
548854
531673
525919
511038
498662
555362
564591
541657
527070
509846
514258
516922
507561
492622
490243
469357
477580
528379

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'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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30607&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30607&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30607&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24






Variance Reduction Matrix
V(Y[t],d=0,D=0)1557347239.34317Range159527Trim Var.980667684.840348
V(Y[t],d=1,D=0)342831078.752542Range88991Trim Var.178435383.86478
V(Y[t],d=2,D=0)483881802.864991Range116547Trim Var.247445494.785196
V(Y[t],d=3,D=0)1115812618.92226Range183118Trim Var.476944900.785822
V(Y[t],d=0,D=1)1262942043.32568Range125082Trim Var.952911855.24917
V(Y[t],d=1,D=1)66151084.2109929Range37640Trim Var.34582914.0069686
V(Y[t],d=2,D=1)137648897.287697Range61245Trim Var.63452326.795122
V(Y[t],d=3,D=1)420870926Range107877Trim Var.198007537.053846
V(Y[t],d=0,D=2)803525106.471471Range131392Trim Var.437060272.142045
V(Y[t],d=1,D=2)168006953.714286Range59945Trim Var.86172946.3709677
V(Y[t],d=2,D=2)323552080.310924Range94798Trim Var.162068685.331183
V(Y[t],d=3,D=2)922803748.916221Range137188Trim Var.474612757.748276

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 1557347239.34317 & Range & 159527 & Trim Var. & 980667684.840348 \tabularnewline
V(Y[t],d=1,D=0) & 342831078.752542 & Range & 88991 & Trim Var. & 178435383.86478 \tabularnewline
V(Y[t],d=2,D=0) & 483881802.864991 & Range & 116547 & Trim Var. & 247445494.785196 \tabularnewline
V(Y[t],d=3,D=0) & 1115812618.92226 & Range & 183118 & Trim Var. & 476944900.785822 \tabularnewline
V(Y[t],d=0,D=1) & 1262942043.32568 & Range & 125082 & Trim Var. & 952911855.24917 \tabularnewline
V(Y[t],d=1,D=1) & 66151084.2109929 & Range & 37640 & Trim Var. & 34582914.0069686 \tabularnewline
V(Y[t],d=2,D=1) & 137648897.287697 & Range & 61245 & Trim Var. & 63452326.795122 \tabularnewline
V(Y[t],d=3,D=1) & 420870926 & Range & 107877 & Trim Var. & 198007537.053846 \tabularnewline
V(Y[t],d=0,D=2) & 803525106.471471 & Range & 131392 & Trim Var. & 437060272.142045 \tabularnewline
V(Y[t],d=1,D=2) & 168006953.714286 & Range & 59945 & Trim Var. & 86172946.3709677 \tabularnewline
V(Y[t],d=2,D=2) & 323552080.310924 & Range & 94798 & Trim Var. & 162068685.331183 \tabularnewline
V(Y[t],d=3,D=2) & 922803748.916221 & Range & 137188 & Trim Var. & 474612757.748276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30607&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]1557347239.34317[/C][C]Range[/C][C]159527[/C][C]Trim Var.[/C][C]980667684.840348[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]342831078.752542[/C][C]Range[/C][C]88991[/C][C]Trim Var.[/C][C]178435383.86478[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]483881802.864991[/C][C]Range[/C][C]116547[/C][C]Trim Var.[/C][C]247445494.785196[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]1115812618.92226[/C][C]Range[/C][C]183118[/C][C]Trim Var.[/C][C]476944900.785822[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]1262942043.32568[/C][C]Range[/C][C]125082[/C][C]Trim Var.[/C][C]952911855.24917[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]66151084.2109929[/C][C]Range[/C][C]37640[/C][C]Trim Var.[/C][C]34582914.0069686[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]137648897.287697[/C][C]Range[/C][C]61245[/C][C]Trim Var.[/C][C]63452326.795122[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]420870926[/C][C]Range[/C][C]107877[/C][C]Trim Var.[/C][C]198007537.053846[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]803525106.471471[/C][C]Range[/C][C]131392[/C][C]Trim Var.[/C][C]437060272.142045[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]168006953.714286[/C][C]Range[/C][C]59945[/C][C]Trim Var.[/C][C]86172946.3709677[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]323552080.310924[/C][C]Range[/C][C]94798[/C][C]Trim Var.[/C][C]162068685.331183[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]922803748.916221[/C][C]Range[/C][C]137188[/C][C]Trim Var.[/C][C]474612757.748276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30607&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30607&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)1557347239.34317Range159527Trim Var.980667684.840348
V(Y[t],d=1,D=0)342831078.752542Range88991Trim Var.178435383.86478
V(Y[t],d=2,D=0)483881802.864991Range116547Trim Var.247445494.785196
V(Y[t],d=3,D=0)1115812618.92226Range183118Trim Var.476944900.785822
V(Y[t],d=0,D=1)1262942043.32568Range125082Trim Var.952911855.24917
V(Y[t],d=1,D=1)66151084.2109929Range37640Trim Var.34582914.0069686
V(Y[t],d=2,D=1)137648897.287697Range61245Trim Var.63452326.795122
V(Y[t],d=3,D=1)420870926Range107877Trim Var.198007537.053846
V(Y[t],d=0,D=2)803525106.471471Range131392Trim Var.437060272.142045
V(Y[t],d=1,D=2)168006953.714286Range59945Trim Var.86172946.3709677
V(Y[t],d=2,D=2)323552080.310924Range94798Trim Var.162068685.331183
V(Y[t],d=3,D=2)922803748.916221Range137188Trim Var.474612757.748276


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(x,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')