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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationTue, 02 Dec 2008 09:31:50 -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/t1228235565wj00pefv76g2gac.htm/, Retrieved Sat, 18 May 2024 04:25:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=28043, Retrieved Sat, 18 May 2024 04:25:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F       [Standard Deviation-Mean Plot] [] [2008-12-02 16:31:50] [76e580e81b2082744334eb1f6d9ccc3e] [Current]
Feedback Forum
2008-12-06 14:56:00 [Maarten Van Gucht] [reply] 
voor het zoeken van de optimale lambda gaan we inderdaad gebruik maken van de standard deviation mean plot. Voor de eerste tijdreekst vinden we een lambda van 1.5, voor de tweede tijdreeks vinden we een lambda van –0.3. Voor deze waarden vind je de kleinste variantie en dus is daar het risico het laagst.

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
105,3
103
103,8
103,4
105,8
101,4
97
94,3
96,6
97,1
95,7
96,9
97,4
95,3
93,6
91,5
93,1
91,7
94,3
93,9
90,9
88,3
91,3
91,7
92,4
92
95,6
95,8
96,4
99
107
109,7
116,2
115,9
113,8
112,6
113,7
115,9
110,3
111,3
113,4
108,2
104,8
106
110,9
115
118,4
121,4
128,8
131,7
141,7
142,9
139,4
134,7
125
113,6
111,5
108,5
112,3
116,6
115,5
120,1
132,9
128,1
129,3
132,5
131
124,9
120,8
122
122,1
127,4
135,2
137,3
135
136
138,4
134,7
138,4
133,9
133,6
141,2
151,8
155,4
156,6
161,6
160,7
156
159,5
168,7
169,9
169,9
185,9
190,8
195,8
211,9

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=28043&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=28043&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28043&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






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1100.0254.1367806982549311.5
292.752.370078633141269.1
3103.8666666666679.538661363423124.2
4112.4416666666674.8888478533631416.6
5125.55833333333312.694484008514334.4
6125.555.5120529091008617.4
7139.2416666666677.0944867625672921.8
8173.94166666666718.002093733448955.9

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 100.025 & 4.13678069825493 & 11.5 \tabularnewline
2 & 92.75 & 2.37007863314126 & 9.1 \tabularnewline
3 & 103.866666666667 & 9.5386613634231 & 24.2 \tabularnewline
4 & 112.441666666667 & 4.88884785336314 & 16.6 \tabularnewline
5 & 125.558333333333 & 12.6944840085143 & 34.4 \tabularnewline
6 & 125.55 & 5.51205290910086 & 17.4 \tabularnewline
7 & 139.241666666667 & 7.09448676256729 & 21.8 \tabularnewline
8 & 173.941666666667 & 18.0020937334489 & 55.9 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28043&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]100.025[/C][C]4.13678069825493[/C][C]11.5[/C][/ROW]
[ROW][C]2[/C][C]92.75[/C][C]2.37007863314126[/C][C]9.1[/C][/ROW]
[ROW][C]3[/C][C]103.866666666667[/C][C]9.5386613634231[/C][C]24.2[/C][/ROW]
[ROW][C]4[/C][C]112.441666666667[/C][C]4.88884785336314[/C][C]16.6[/C][/ROW]
[ROW][C]5[/C][C]125.558333333333[/C][C]12.6944840085143[/C][C]34.4[/C][/ROW]
[ROW][C]6[/C][C]125.55[/C][C]5.51205290910086[/C][C]17.4[/C][/ROW]
[ROW][C]7[/C][C]139.241666666667[/C][C]7.09448676256729[/C][C]21.8[/C][/ROW]
[ROW][C]8[/C][C]173.941666666667[/C][C]18.0020937334489[/C][C]55.9[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28043&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28043&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
1100.0254.1367806982549311.5
292.752.370078633141269.1
3103.8666666666679.538661363423124.2
4112.4416666666674.8888478533631416.6
5125.55833333333312.694484008514334.4
6125.555.5120529091008617.4
7139.2416666666677.0944867625672921.8
8173.94166666666718.002093733448955.9






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-11.4059274171852
beta0.159737927622238
S.D.0.0479172488598841
T-STAT3.33362059431523
p-value0.0157357977097224

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -11.4059274171852 \tabularnewline
beta & 0.159737927622238 \tabularnewline
S.D. & 0.0479172488598841 \tabularnewline
T-STAT & 3.33362059431523 \tabularnewline
p-value & 0.0157357977097224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28043&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.4059274171852[/C][/ROW]
[ROW][C]beta[/C][C]0.159737927622238[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0479172488598841[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.33362059431523[/C][/ROW]
[ROW][C]p-value[/C][C]0.0157357977097224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28043&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28043&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)
alpha-11.4059274171852
beta0.159737927622238
S.D.0.0479172488598841
T-STAT3.33362059431523
p-value0.0157357977097224






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-10.0454728019443
beta2.49826597355381
S.D.0.81982429744085
T-STAT3.04731877470863
p-value0.0225895364934584
Lambda-1.49826597355381

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -10.0454728019443 \tabularnewline
beta & 2.49826597355381 \tabularnewline
S.D. & 0.81982429744085 \tabularnewline
T-STAT & 3.04731877470863 \tabularnewline
p-value & 0.0225895364934584 \tabularnewline
Lambda & -1.49826597355381 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=28043&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-10.0454728019443[/C][/ROW]
[ROW][C]beta[/C][C]2.49826597355381[/C][/ROW]
[ROW][C]S.D.[/C][C]0.81982429744085[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.04731877470863[/C][/ROW]
[ROW][C]p-value[/C][C]0.0225895364934584[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.49826597355381[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=28043&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=28043&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)
alpha-10.0454728019443
beta2.49826597355381
S.D.0.81982429744085
T-STAT3.04731877470863
p-value0.0225895364934584
Lambda-1.49826597355381


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')