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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 computationSun, 20 Dec 2009 12:53:16 -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/2009/Dec/20/t1261339742dvuxx8bunizqgcf.htm/, Retrieved Sat, 27 Apr 2024 11:49:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70013, Retrieved Sat, 27 Apr 2024 11:49:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact153

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Standard Deviation-Mean Plot] [Identifying Integ...] [2009-11-22 12:50:05] [b98453cac15ba1066b407e146608df68]
-   PD        [Standard Deviation-Mean Plot] [Identifying integ...] [2009-11-23 19:29:32] [d46757a0a8c9b00540ab7e7e0c34bfc4]
-   PD            [Standard Deviation-Mean Plot] [Heteroskedasticit...] [2009-12-20 19:53:16] [8cd69d0f4298074aa572ca2f9b39b6ae] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
-1,2
-2,4
0,8
-0,1
-1,5
-4,4
-4,2
3,5
10
8,6
9,5
9,9
10,4
16
12,7
10,2
8,9
12,6
13,6
14,8
9,5
13,7
17
14,7
17,4
9
9,1
12,2
15,9
12,9
10,9
10,6
13,2
9,6
6,4
5,8
-1
-0,2
2,7
3,6
-0,9
0,3
-1,1
-2,5
-3,4
-3,5
-3,9
-4,6
-0,1
4,3
10,2
8,7
13,3
15
20,7
20,7
26,4
31,2
31,4
26,6
26,6
19,2
6,5
3,1
-0,2
-4
-12,6
-13
-17,6
-21,7
-23,2
-16,8
-19,8

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=70013&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=70013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70013&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
12.3755.6719605396755314.4
212.84166666666672.621400851499528.1
311.08333333333333.4734926968616911.6
4-1.208333333333332.563895591879798.2
517.366666666666710.452518907667731.5
6-4.47516.047323481163249.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 2.375 & 5.67196053967553 & 14.4 \tabularnewline
2 & 12.8416666666667 & 2.62140085149952 & 8.1 \tabularnewline
3 & 11.0833333333333 & 3.47349269686169 & 11.6 \tabularnewline
4 & -1.20833333333333 & 2.56389559187979 & 8.2 \tabularnewline
5 & 17.3666666666667 & 10.4525189076677 & 31.5 \tabularnewline
6 & -4.475 & 16.0473234811632 & 49.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70013&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]2.375[/C][C]5.67196053967553[/C][C]14.4[/C][/ROW]
[ROW][C]2[/C][C]12.8416666666667[/C][C]2.62140085149952[/C][C]8.1[/C][/ROW]
[ROW][C]3[/C][C]11.0833333333333[/C][C]3.47349269686169[/C][C]11.6[/C][/ROW]
[ROW][C]4[/C][C]-1.20833333333333[/C][C]2.56389559187979[/C][C]8.2[/C][/ROW]
[ROW][C]5[/C][C]17.3666666666667[/C][C]10.4525189076677[/C][C]31.5[/C][/ROW]
[ROW][C]6[/C][C]-4.475[/C][C]16.0473234811632[/C][C]49.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70013&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
12.3755.6719605396755314.4
212.84166666666672.621400851499528.1
311.08333333333333.4734926968616911.6
4-1.208333333333332.563895591879798.2
517.366666666666710.452518907667731.5
6-4.47516.047323481163249.8






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha7.92017183737186
beta-0.176141438055735
S.D.0.299515817447643
T-STAT-0.588087265496506
p-value0.588073479474427

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 7.92017183737186 \tabularnewline
beta & -0.176141438055735 \tabularnewline
S.D. & 0.299515817447643 \tabularnewline
T-STAT & -0.588087265496506 \tabularnewline
p-value & 0.588073479474427 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70013&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.92017183737186[/C][/ROW]
[ROW][C]beta[/C][C]-0.176141438055735[/C][/ROW]
[ROW][C]S.D.[/C][C]0.299515817447643[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.588087265496506[/C][/ROW]
[ROW][C]p-value[/C][C]0.588073479474427[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70013&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)
alpha7.92017183737186
beta-0.176141438055735
S.D.0.299515817447643
T-STAT-0.588087265496506
p-value0.588073479474427






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.56616935614210
beta0.00306186180254478
S.D.0.482237236287878
T-STAT0.00634928531465985
p-value0.995510422545648
Lambda0.996938138197455

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.56616935614210 \tabularnewline
beta & 0.00306186180254478 \tabularnewline
S.D. & 0.482237236287878 \tabularnewline
T-STAT & 0.00634928531465985 \tabularnewline
p-value & 0.995510422545648 \tabularnewline
Lambda & 0.996938138197455 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70013&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.56616935614210[/C][/ROW]
[ROW][C]beta[/C][C]0.00306186180254478[/C][/ROW]
[ROW][C]S.D.[/C][C]0.482237236287878[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.00634928531465985[/C][/ROW]
[ROW][C]p-value[/C][C]0.995510422545648[/C][/ROW]
[ROW][C]Lambda[/C][C]0.996938138197455[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70013&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)
alpha1.56616935614210
beta0.00306186180254478
S.D.0.482237236287878
T-STAT0.00634928531465985
p-value0.995510422545648
Lambda0.996938138197455


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
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')