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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_rwalk.wasp
Title produced by softwareLaw of Averages
Date of computationTue, 02 Dec 2008 06:30:16 -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/02/t1228224739kgpxh0dwbz0laid.htm/, Retrieved Sun, 19 May 2024 11:15:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=27756, Retrieved Sun, 19 May 2024 11:15:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact181

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Law of Averages] [Random Walk Simul...] [2008-11-25 18:31:28] [b98453cac15ba1066b407e146608df68]
F R     [Law of Averages] [question 3] [2008-12-01 12:27:05] [379d6c32f73e3218fd773d79e4063d07]
F           [Law of Averages] [variance reductio...] [2008-12-02 13:30:16] [52d1f7c78552cd0e785e1b7a3cade101] [Current]
Feedback Forum
2008-12-08 19:22:30 [94a54c888ac7f7d6874c3108eb0e1808] [reply] 
Het is zeer goed dat de student de uitleg gegeven heeft over de betekenis van de 2 parameters. Maar de conclusie is onvolledig.
In de tweede kolom van de tabel staan de varianties (nadat we de tijdreeks een aantal keer gedifferentieerd hebben). Hoe kleiner de variantie, hoe beter men de gegevens kan verklaren met behulp van deze methode (1ste kolom). De ‘d’ in de eerste kolom is het aantal keer dat je differentieert, de gewone differentiatie. De ‘D’ geeft informatie over de seizoenaliteit, de seizoenale differentiatie. De kleinste variantie vinden we in de tabel bij d=1 en D=0, hier is de variantie 1 en zijn de gegevens 1 keer gedifferentieerd.

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Dataset

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27756&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27756&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'Gwilym Jenkins' @ 72.249.127.135






Variance Reduction Matrix
V(Y[t],d=0,D=0)58.4864769539078Range31Trim Var.40.8278110404063
V(Y[t],d=1,D=0)0.99949296182727Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.51612903225806Range8Trim Var.2.66288936979474
V(Y[t],d=0,D=1)10.8832093445989Range18Trim Var.4.17360877464504
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)3.86802426710789Range8Trim Var.2.41089388150403
V(Y[t],d=3,D=1)11.1404277072506Range16Trim Var.6.88329524602898
V(Y[t],d=0,D=2)28.1494383016364Range30Trim Var.13.2789822283428
V(Y[t],d=1,D=2)6.27840994892294Range8Trim Var.2.75412198117069
V(Y[t],d=2,D=2)11.5940624972123Range16Trim Var.6.60514043771245
V(Y[t],d=3,D=2)33.2961622531981Range32Trim Var.20.5584569045412

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 58.4864769539078 & Range & 31 & Trim Var. & 40.8278110404063 \tabularnewline
V(Y[t],d=1,D=0) & 0.99949296182727 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.90742850678367 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.51612903225806 & Range & 8 & Trim Var. & 2.66288936979474 \tabularnewline
V(Y[t],d=0,D=1) & 10.8832093445989 & Range & 18 & Trim Var. & 4.17360877464504 \tabularnewline
V(Y[t],d=1,D=1) & 2.06582672108568 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.86802426710789 & Range & 8 & Trim Var. & 2.41089388150403 \tabularnewline
V(Y[t],d=3,D=1) & 11.1404277072506 & Range & 16 & Trim Var. & 6.88329524602898 \tabularnewline
V(Y[t],d=0,D=2) & 28.1494383016364 & Range & 30 & Trim Var. & 13.2789822283428 \tabularnewline
V(Y[t],d=1,D=2) & 6.27840994892294 & Range & 8 & Trim Var. & 2.75412198117069 \tabularnewline
V(Y[t],d=2,D=2) & 11.5940624972123 & Range & 16 & Trim Var. & 6.60514043771245 \tabularnewline
V(Y[t],d=3,D=2) & 33.2961622531981 & Range & 32 & Trim Var. & 20.5584569045412 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=27756&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]58.4864769539078[/C][C]Range[/C][C]31[/C][C]Trim Var.[/C][C]40.8278110404063[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]0.99949296182727[/C][C]Range[/C][C]2[/C][C]Trim Var.[/C][C]NA[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=0)[/C][C]1.90742850678367[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=0)[/C][C]5.51612903225806[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.66288936979474[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]10.8832093445989[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]4.17360877464504[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.06582672108568[/C][C]Range[/C][C]4[/C][C]Trim Var.[/C][C]0[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=1)[/C][C]3.86802426710789[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.41089388150403[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.1404277072506[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.88329524602898[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]28.1494383016364[/C][C]Range[/C][C]30[/C][C]Trim Var.[/C][C]13.2789822283428[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.27840994892294[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.75412198117069[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.5940624972123[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.60514043771245[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]33.2961622531981[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]20.5584569045412[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=27756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=27756&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)58.4864769539078Range31Trim Var.40.8278110404063
V(Y[t],d=1,D=0)0.99949296182727Range2Trim Var.NA
V(Y[t],d=2,D=0)1.90742850678367Range4Trim Var.0
V(Y[t],d=3,D=0)5.51612903225806Range8Trim Var.2.66288936979474
V(Y[t],d=0,D=1)10.8832093445989Range18Trim Var.4.17360877464504
V(Y[t],d=1,D=1)2.06582672108568Range4Trim Var.0
V(Y[t],d=2,D=1)3.86802426710789Range8Trim Var.2.41089388150403
V(Y[t],d=3,D=1)11.1404277072506Range16Trim Var.6.88329524602898
V(Y[t],d=0,D=2)28.1494383016364Range30Trim Var.13.2789822283428
V(Y[t],d=1,D=2)6.27840994892294Range8Trim Var.2.75412198117069
V(Y[t],d=2,D=2)11.5940624972123Range16Trim Var.6.60514043771245
V(Y[t],d=3,D=2)33.2961622531981Range32Trim Var.20.5584569045412


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 500 ; par2 = 0.5 ;
Parameters (R input):
par1 = 500 ; par2 = 0.5 ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
R code (references can be found in the software module):
n <- as.numeric(par1)
p <- as.numeric(par2)
heads=rbinom(n-1,1,p)
a=2*(heads)-1
b=diffinv(a,xi=0)
c=1:n
pheads=(diffinv(heads,xi=.5))/c
bitmap(file='test1.png')
op=par(mfrow=c(2,1))
plot(c,b,type='n',main='Law of Averages',xlab='Toss Number',ylab='Excess of Heads',lwd=2,cex.lab=1.5,cex.main=2)
lines(c,b,col='red')
lines(c,rep(0,n),col='black')
plot(c,pheads,type='n',xlab='Toss Number',ylab='Proportion of Heads',lwd=2,cex.lab=1.5)
lines(c,pheads,col='blue')
lines(c,rep(.5,n),col='black')
par(op)
dev.off()
b
par1 <- as.numeric(12)
x <- as.array(b)
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')