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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 12:47:19 -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/t1228247491hld9x8cmvk60gtt.htm/, Retrieved Fri, 17 May 2024 04:19:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28288, Retrieved Fri, 17 May 2024 04:19:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

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         [Law of Averages] [q3] [2008-12-02 19:47:19] [c4248bbb85fa4e400deddbf50234dcae] [Current]
Feedback Forum
2008-12-07 13:41:40 [Katrijn Truyman] [reply] 
We moeten de waarde zoeken die de kleinste variantie aangeeft (deze waarde vinden we terug in de tweede kolom van de tabel), hier is dat als d=1 en D=0. De gegevens worden 1 keer gedifferentieerd om de LT-trend weg te werken, er wordt niet seizonaal gezuiverd omdat er geen seizonaliteit aanwezig is.
2008-12-08 10:36:30 [Jessica Alves Pires] [reply] 
De conclusie is juist. De student heeft de juiste waarden voor d en D gevonden. Hoe kleiner de variantie, hoe kleiner het risico, hoe meer je kan verklaren en hoe beter het model. De student had wel nog kunnen zeggen dat indien er veel outliers aanwezig zijn in een tijdreeks, men best kijkt naar de getrimde variantie.

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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 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=28288&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=28288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28288&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)51.7382605210421Range33Trim Var.32.9277394889698
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97987927565392Range4Trim Var.0
V(Y[t],d=3,D=0)5.85483870967742Range8Trim Var.2.70417997500347
V(Y[t],d=0,D=1)13.1239101895176Range18Trim Var.6.3949578789345
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)3.92570531585423Range8Trim Var.2.37828737926941
V(Y[t],d=3,D=1)11.7355371900826Range16Trim Var.6.33978231740285
V(Y[t],d=0,D=2)27.5933657673596Range28Trim Var.12.9683094348717
V(Y[t],d=1,D=2)6.12629802353986Range8Trim Var.2.65099715099715
V(Y[t],d=2,D=2)11.7547568710359Range16Trim Var.6.6414401264976
V(Y[t],d=3,D=2)35.3728096893253Range32Trim Var.18.9390216937326

\begin{tabular}{lllllllll}
\hline
Variance Reduction Matrix \tabularnewline
V(Y[t],d=0,D=0) & 51.7382605210421 & Range & 33 & Trim Var. & 32.9277394889698 \tabularnewline
V(Y[t],d=1,D=0) & 1.00132795711906 & Range & 2 & Trim Var. & NA \tabularnewline
V(Y[t],d=2,D=0) & 1.97987927565392 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=3,D=0) & 5.85483870967742 & Range & 8 & Trim Var. & 2.70417997500347 \tabularnewline
V(Y[t],d=0,D=1) & 13.1239101895176 & Range & 18 & Trim Var. & 6.3949578789345 \tabularnewline
V(Y[t],d=1,D=1) & 2.02462375677069 & Range & 4 & Trim Var. & 0 \tabularnewline
V(Y[t],d=2,D=1) & 3.92570531585423 & Range & 8 & Trim Var. & 2.37828737926941 \tabularnewline
V(Y[t],d=3,D=1) & 11.7355371900826 & Range & 16 & Trim Var. & 6.33978231740285 \tabularnewline
V(Y[t],d=0,D=2) & 27.5933657673596 & Range & 28 & Trim Var. & 12.9683094348717 \tabularnewline
V(Y[t],d=1,D=2) & 6.12629802353986 & Range & 8 & Trim Var. & 2.65099715099715 \tabularnewline
V(Y[t],d=2,D=2) & 11.7547568710359 & Range & 16 & Trim Var. & 6.6414401264976 \tabularnewline
V(Y[t],d=3,D=2) & 35.3728096893253 & Range & 32 & Trim Var. & 18.9390216937326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28288&T=1

[TABLE]
[ROW][C]Variance Reduction Matrix[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=0)[/C][C]51.7382605210421[/C][C]Range[/C][C]33[/C][C]Trim Var.[/C][C]32.9277394889698[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=0)[/C][C]1.00132795711906[/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]1.97987927565392[/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]5.85483870967742[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.70417997500347[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=1)[/C][C]13.1239101895176[/C][C]Range[/C][C]18[/C][C]Trim Var.[/C][C]6.3949578789345[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=1)[/C][C]2.02462375677069[/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]3.92570531585423[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.37828737926941[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=1)[/C][C]11.7355371900826[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.33978231740285[/C][/ROW]
[ROW][C]V(Y[t],d=0,D=2)[/C][C]27.5933657673596[/C][C]Range[/C][C]28[/C][C]Trim Var.[/C][C]12.9683094348717[/C][/ROW]
[ROW][C]V(Y[t],d=1,D=2)[/C][C]6.12629802353986[/C][C]Range[/C][C]8[/C][C]Trim Var.[/C][C]2.65099715099715[/C][/ROW]
[ROW][C]V(Y[t],d=2,D=2)[/C][C]11.7547568710359[/C][C]Range[/C][C]16[/C][C]Trim Var.[/C][C]6.6414401264976[/C][/ROW]
[ROW][C]V(Y[t],d=3,D=2)[/C][C]35.3728096893253[/C][C]Range[/C][C]32[/C][C]Trim Var.[/C][C]18.9390216937326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28288&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)51.7382605210421Range33Trim Var.32.9277394889698
V(Y[t],d=1,D=0)1.00132795711906Range2Trim Var.NA
V(Y[t],d=2,D=0)1.97987927565392Range4Trim Var.0
V(Y[t],d=3,D=0)5.85483870967742Range8Trim Var.2.70417997500347
V(Y[t],d=0,D=1)13.1239101895176Range18Trim Var.6.3949578789345
V(Y[t],d=1,D=1)2.02462375677069Range4Trim Var.0
V(Y[t],d=2,D=1)3.92570531585423Range8Trim Var.2.37828737926941
V(Y[t],d=3,D=1)11.7355371900826Range16Trim Var.6.33978231740285
V(Y[t],d=0,D=2)27.5933657673596Range28Trim Var.12.9683094348717
V(Y[t],d=1,D=2)6.12629802353986Range8Trim Var.2.65099715099715
V(Y[t],d=2,D=2)11.7547568710359Range16Trim Var.6.6414401264976
V(Y[t],d=3,D=2)35.3728096893253Range32Trim Var.18.9390216937326


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')