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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, 20 Dec 2010 20:07:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t1292875622tgf9c6kj64orh43.htm/, Retrieved Fri, 03 May 2024 21:48:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113106, Retrieved Fri, 03 May 2024 21:48:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact140

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2010-12-13 08:35:23] [21eff0c210342db4afbdafe426a7c254]
-   PD  [(Partial) Autocorrelation Function] [] [2010-12-13 09:29:04] [21eff0c210342db4afbdafe426a7c254]
-    D    [(Partial) Autocorrelation Function] [] [2010-12-13 10:05:17] [21eff0c210342db4afbdafe426a7c254]
- RM D      [ARIMA Forecasting] [] [2010-12-13 10:48:48] [21eff0c210342db4afbdafe426a7c254]
- RMPD        [Univariate Data Series] [] [2010-12-13 20:53:52] [21eff0c210342db4afbdafe426a7c254]
- RMPD          [Histogram] [] [2010-12-14 14:33:39] [21eff0c210342db4afbdafe426a7c254]
- RMPD            [Univariate Explorative Data Analysis] [] [2010-12-16 14:27:05] [de4adef75375d243bafd27c3fb0ddf4c]
- RMPD                [Standard Deviation-Mean Plot] [] [2010-12-20 20:07:24] [13a73be5002723d89d3723d5fe97baf8] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
21.3
21.1
20.6
20.5
20.5
20.8
21.1
21.3
21.3
21.1
20.9
19.9
19.8
19.5
19.6
19.6
19.7
20.2
19.7
19.3
18.9
18.4
18
17.8
17.8
17.7
17.5
17.4
17.1
17.1
17.2
17.8
18.6
18.9
18.9
18.7
18.6
19.1
20.3
21.1
21.6
21.5
21.5
21.7
21.9
22.2
22.6
22.5
23.2
23.6
23.8
23.9
23.8
23.5
23.3
23.2
23.5
23.5
23.5
23.3

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'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113106&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113106&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113106&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'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
120.86666666666670.4271115105265171.40000000000000
219.20833333333330.7633161305458672.4
317.89166666666670.6986458763966621.80000000000000
421.21666666666671.269096552909224
523.50833333333330.2353269807709860.700

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 20.8666666666667 & 0.427111510526517 & 1.40000000000000 \tabularnewline
2 & 19.2083333333333 & 0.763316130545867 & 2.4 \tabularnewline
3 & 17.8916666666667 & 0.698645876396662 & 1.80000000000000 \tabularnewline
4 & 21.2166666666667 & 1.26909655290922 & 4 \tabularnewline
5 & 23.5083333333333 & 0.235326980770986 & 0.700 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113106&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]20.8666666666667[/C][C]0.427111510526517[/C][C]1.40000000000000[/C][/ROW]
[ROW][C]2[/C][C]19.2083333333333[/C][C]0.763316130545867[/C][C]2.4[/C][/ROW]
[ROW][C]3[/C][C]17.8916666666667[/C][C]0.698645876396662[/C][C]1.80000000000000[/C][/ROW]
[ROW][C]4[/C][C]21.2166666666667[/C][C]1.26909655290922[/C][C]4[/C][/ROW]
[ROW][C]5[/C][C]23.5083333333333[/C][C]0.235326980770986[/C][C]0.700[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113106&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113106&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
120.86666666666670.4271115105265171.40000000000000
219.20833333333330.7633161305458672.4
317.89166666666670.6986458763966621.80000000000000
421.21666666666671.269096552909224
523.50833333333330.2353269807709860.700






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha1.99525750937708
beta-0.0641024798740843
S.D.0.0996776043838187
T-STAT-0.643098118883869
p-value0.56593663730289

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 1.99525750937708 \tabularnewline
beta & -0.0641024798740843 \tabularnewline
S.D. & 0.0996776043838187 \tabularnewline
T-STAT & -0.643098118883869 \tabularnewline
p-value & 0.56593663730289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113106&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.99525750937708[/C][/ROW]
[ROW][C]beta[/C][C]-0.0641024798740843[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0996776043838187[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.643098118883869[/C][/ROW]
[ROW][C]p-value[/C][C]0.56593663730289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113106&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113106&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)
alpha1.99525750937708
beta-0.0641024798740843
S.D.0.0996776043838187
T-STAT-0.643098118883869
p-value0.56593663730289






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha9.65682147119226
beta-3.37787096009198
S.D.2.97370200975797
T-STAT-1.13591440870933
p-value0.33852686536998
Lambda4.37787096009198

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 9.65682147119226 \tabularnewline
beta & -3.37787096009198 \tabularnewline
S.D. & 2.97370200975797 \tabularnewline
T-STAT & -1.13591440870933 \tabularnewline
p-value & 0.33852686536998 \tabularnewline
Lambda & 4.37787096009198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113106&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]9.65682147119226[/C][/ROW]
[ROW][C]beta[/C][C]-3.37787096009198[/C][/ROW]
[ROW][C]S.D.[/C][C]2.97370200975797[/C][/ROW]
[ROW][C]T-STAT[/C][C]-1.13591440870933[/C][/ROW]
[ROW][C]p-value[/C][C]0.33852686536998[/C][/ROW]
[ROW][C]Lambda[/C][C]4.37787096009198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113106&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113106&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)
alpha9.65682147119226
beta-3.37787096009198
S.D.2.97370200975797
T-STAT-1.13591440870933
p-value0.33852686536998
Lambda4.37787096009198


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')