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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Tue, 09 Dec 2008 01:33:18 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/09/t1228811630e7recnhmy6ci98s.htm/, Retrieved Fri, 17 May 2024 05:14:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31202, Retrieved Fri, 17 May 2024 05:14:47 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

182

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [ARIMA Backward Selection] [] [2008-12-07 14:04:55] [74be16979710d4c4e7c6647856088456]
F RMPD  [Standard Deviation-Mean Plot] [] [2008-12-08 19:35:41] [a4ee3bef49b119f4bd2e925060c84f5e]
F   P       [Standard Deviation-Mean Plot] [] [2008-12-09 08:33:18] [428345b1a3979ee2ad6751f9aac15fbb] [Current]

Feedback Forum

2008-12-16 07:42:15 [Glenn De Maeyer] [reply] 
Bij de eerste stap wordt gevraagd om de correcte lambda waarde te berekenen. De student lost deze vraag correct op. Hij maakt gebruik van  van de Standard Deviation – Mean Plot software. 
 
Uit de tabel Regression: ln S.E.(k) = alpha + beta * ln Mean(k) kunnen we een lamba waarde van 0.376909377571558 afleiden. 
 
Als we 1 in vermindering hadden gebracht met de Beta waarde had dit ook geresulteerd in de optimale Lamba Coëfficiënt. Nl, (1 - 0.623090622428442) is gelijk aan 0.376909377571558. 
 
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.

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31202&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31202&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31202&T=0

As an alternative you can also use a 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 Output	view raw output of R engine
Computing time	3 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	22949.0833333333	5573.5134741893	20000
2	24334	6241.0159283711	20890
3	22668.8333333333	5025.71975547842	15936
4	23242.1666666667	6893.00831321569	23808
5	22208.0833333333	6395.88827377449	21757
6	24429.0833333333	6043.18402617713	19196

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 22949.0833333333 & 5573.5134741893 & 20000 \tabularnewline
2 & 24334 & 6241.0159283711 & 20890 \tabularnewline
3 & 22668.8333333333 & 5025.71975547842 & 15936 \tabularnewline
4 & 23242.1666666667 & 6893.00831321569 & 23808 \tabularnewline
5 & 22208.0833333333 & 6395.88827377449 & 21757 \tabularnewline
6 & 24429.0833333333 & 6043.18402617713 & 19196 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31202&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]22949.0833333333[/C][C]5573.5134741893[/C][C]20000[/C][/ROW]
[ROW][C]2[/C][C]24334[/C][C]6241.0159283711[/C][C]20890[/C][/ROW]
[ROW][C]3[/C][C]22668.8333333333[/C][C]5025.71975547842[/C][C]15936[/C][/ROW]
[ROW][C]4[/C][C]23242.1666666667[/C][C]6893.00831321569[/C][C]23808[/C][/ROW]
[ROW][C]5[/C][C]22208.0833333333[/C][C]6395.88827377449[/C][C]21757[/C][/ROW]
[ROW][C]6[/C][C]24429.0833333333[/C][C]6043.18402617713[/C][C]19196[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31202&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31202&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	22949.0833333333	5573.5134741893	20000
2	24334	6241.0159283711	20890
3	22668.8333333333	5025.71975547842	15936
4	23242.1666666667	6893.00831321569	23808
5	22208.0833333333	6395.88827377449	21757
6	24429.0833333333	6043.18402617713	19196

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2713.14775985543
beta	0.142267506098054
S.D.	0.355950988081976
T-STAT	0.399682852025937
p-value	0.709812923097311

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2713.14775985543 \tabularnewline
beta & 0.142267506098054 \tabularnewline
S.D. & 0.355950988081976 \tabularnewline
T-STAT & 0.399682852025937 \tabularnewline
p-value & 0.709812923097311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31202&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2713.14775985543[/C][/ROW]
[ROW][C]beta[/C][C]0.142267506098054[/C][/ROW]
[ROW][C]S.D.[/C][C]0.355950988081976[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.399682852025937[/C][/ROW]
[ROW][C]p-value[/C][C]0.709812923097311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31202&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31202&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2713.14775985543
beta	0.142267506098054
S.D.	0.355950988081976
T-STAT	0.399682852025937
p-value	0.709812923097311

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.43354478273853
beta	0.623090622428442
S.D.	1.4087718377737
T-STAT	0.442293496875349
p-value	0.681139439478788
Lambda	0.376909377571558

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 2.43354478273853 \tabularnewline
beta & 0.623090622428442 \tabularnewline
S.D. & 1.4087718377737 \tabularnewline
T-STAT & 0.442293496875349 \tabularnewline
p-value & 0.681139439478788 \tabularnewline
Lambda & 0.376909377571558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31202&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.43354478273853[/C][/ROW]
[ROW][C]beta[/C][C]0.623090622428442[/C][/ROW]
[ROW][C]S.D.[/C][C]1.4087718377737[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.442293496875349[/C][/ROW]
[ROW][C]p-value[/C][C]0.681139439478788[/C][/ROW]
[ROW][C]Lambda[/C][C]0.376909377571558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31202&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31202&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	2.43354478273853
beta	0.623090622428442
S.D.	1.4087718377737
T-STAT	0.442293496875349
p-value	0.681139439478788
Lambda	0.376909377571558

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 1 ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code