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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationMon, 08 Dec 2008 11:23:22 -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/t1228760689r7pptv8jj5c6hwa.htm/, Retrieved Thu, 16 May 2024 05:08:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30647, Retrieved Thu, 16 May 2024 05:08:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact182

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Q1 SDMP] [2008-12-08 15:32:12] [547636b63517c1c2916a747d66b36ebf]
F    D    [Standard Deviation-Mean Plot] [SMP Vlaanderen] [2008-12-08 18:23:22] [3817f5e632a8bfeb1be7b5e8c86bd450] [Current]
-           [Standard Deviation-Mean Plot] [] [2008-12-13 20:54:26] [888addc516c3b812dd7be4bd54caa358]
Feedback Forum
2008-12-15 07:52:28 [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.

Voor het bekomen van de correcte lambda waarde maken we gebruik van de Standard Deviation – Mean Plot software. In de taak maakte ik gebruik van mij eigen tijdreeks 'uitvoer van Vlaanderen' en ik bekwam een juiste lambda waarde.
We maken de oefening hier nog eens opnieuw maar dan met 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.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12300.00
12092.80
12380.80
12196.90
9455.00
13168.00
13427.90
11980.50
11884.80
11691.70
12233.80
14341.40
13130.70
12421.10
14285.80
12864.60
11160.20
14316.20
14388.70
14013.90
13419.00
12769.60
13315.50
15332.90
14243.00
13824.40
14962.90
13202.90
12199.00
15508.90
14199.80
15169.60
14058.00
13786.20
14147.90
16541.70
13587.50
15582.40
15802.80
14130.50
12923.20
15612.20
16033.70
16036.60
14037.80
15330.60
15038.30
17401.80
14992.50
16043.70
16929.60
15921.30
14417.20
15961.00
17851.90
16483.90
14215.50
17429.70
17839.50
17629.20

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=30647&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=30647&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30647&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






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
112262.81166.94192423854886.4
213451.51666666671104.608120419624172.7
314320.35833333331123.320070520124342.7
415126.451249.697655435114478.6
516309.58333333331285.379979074693636.4

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 12262.8 & 1166.9419242385 & 4886.4 \tabularnewline
2 & 13451.5166666667 & 1104.60812041962 & 4172.7 \tabularnewline
3 & 14320.3583333333 & 1123.32007052012 & 4342.7 \tabularnewline
4 & 15126.45 & 1249.69765543511 & 4478.6 \tabularnewline
5 & 16309.5833333333 & 1285.37997907469 & 3636.4 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30647&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]12262.8[/C][C]1166.9419242385[/C][C]4886.4[/C][/ROW]
[ROW][C]2[/C][C]13451.5166666667[/C][C]1104.60812041962[/C][C]4172.7[/C][/ROW]
[ROW][C]3[/C][C]14320.3583333333[/C][C]1123.32007052012[/C][C]4342.7[/C][/ROW]
[ROW][C]4[/C][C]15126.45[/C][C]1249.69765543511[/C][C]4478.6[/C][/ROW]
[ROW][C]5[/C][C]16309.5833333333[/C][C]1285.37997907469[/C][C]3636.4[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30647&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30647&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:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
112262.81166.94192423854886.4
213451.51666666671104.608120419624172.7
314320.35833333331123.320070520124342.7
415126.451249.697655435114478.6
516309.58333333331285.379979074693636.4






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha651.045108658677
beta0.0374240338282360
S.D.0.0199184879357296
T-STAT1.87885917590688
p-value0.15687196614732

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 651.045108658677 \tabularnewline
beta & 0.0374240338282360 \tabularnewline
S.D. & 0.0199184879357296 \tabularnewline
T-STAT & 1.87885917590688 \tabularnewline
p-value & 0.15687196614732 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30647&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]651.045108658677[/C][/ROW]
[ROW][C]beta[/C][C]0.0374240338282360[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0199184879357296[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.87885917590688[/C][/ROW]
[ROW][C]p-value[/C][C]0.15687196614732[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30647&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30647&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha651.045108658677
beta0.0374240338282360
S.D.0.0199184879357296
T-STAT1.87885917590688
p-value0.15687196614732






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.01780676398117
beta0.424430695982874
S.D.0.249063513249119
T-STAT1.70410627572875
p-value0.186909408728274
Lambda0.575569304017126

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 3.01780676398117 \tabularnewline
beta & 0.424430695982874 \tabularnewline
S.D. & 0.249063513249119 \tabularnewline
T-STAT & 1.70410627572875 \tabularnewline
p-value & 0.186909408728274 \tabularnewline
Lambda & 0.575569304017126 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30647&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]3.01780676398117[/C][/ROW]
[ROW][C]beta[/C][C]0.424430695982874[/C][/ROW]
[ROW][C]S.D.[/C][C]0.249063513249119[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.70410627572875[/C][/ROW]
[ROW][C]p-value[/C][C]0.186909408728274[/C][/ROW]
[ROW][C]Lambda[/C][C]0.575569304017126[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30647&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30647&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha3.01780676398117
beta0.424430695982874
S.D.0.249063513249119
T-STAT1.70410627572875
p-value0.186909408728274
Lambda0.575569304017126


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))
(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')