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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 computationSat, 12 Dec 2009 07:54:21 -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/12/t1260631618oi8idpp6w2r09vl.htm/, Retrieved Mon, 29 Apr 2024 10:07:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=67016, Retrieved Mon, 29 Apr 2024 10:07:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Kernel Density Estimation] [Paper] [2009-12-12 13:34:31] [d31db4f83c6a129f6d3e47077769e868]
-    D  [Bivariate Kernel Density Estimation] [Paper.1] [2009-12-12 13:38:38] [d31db4f83c6a129f6d3e47077769e868]
- RMPD    [Standard Deviation-Mean Plot] [Paper. Mean Plot ...] [2009-12-12 14:46:45] [d31db4f83c6a129f6d3e47077769e868]
-    D        [Standard Deviation-Mean Plot] [Paper] [2009-12-12 14:54:21] [852eae237d08746109043531619a60c9] [Current]
-    D          [Standard Deviation-Mean Plot] [Paper. Ingeschrev...] [2009-12-12 15:28:35] [d31db4f83c6a129f6d3e47077769e868]
-    D            [Standard Deviation-Mean Plot] [Paper. achtergest...] [2009-12-12 15:31:03] [d31db4f83c6a129f6d3e47077769e868]
- RM D              [(Partial) Autocorrelation Function] [Paper, Partiële ...] [2009-12-12 15:59:27] [d31db4f83c6a129f6d3e47077769e868]
- RM D              [Spectral Analysis] [Paper. Spectral A...] [2009-12-12 16:10:11] [d31db4f83c6a129f6d3e47077769e868]
-   P                 [Spectral Analysis] [Paper. Spectral A...] [2009-12-18 15:52:57] [d31db4f83c6a129f6d3e47077769e868]
-   P                   [Spectral Analysis] [Paper. Spectral A...] [2009-12-18 17:24:57] [d31db4f83c6a129f6d3e47077769e868]
-   P                     [Spectral Analysis] [Paper] [2010-01-07 15:25:28] [309ee52d0058ff0a6f7eec15e07b2d9f]
- RM D              [Mean Plot] [Paper. Mean plot] [2009-12-12 16:13:07] [d31db4f83c6a129f6d3e47077769e868]
-    D                [Mean Plot] [Paper. Mean plot ...] [2009-12-12 16:15:50] [d31db4f83c6a129f6d3e47077769e868]
-    D                [Mean Plot] [Paper. Inschrijvi...] [2009-12-12 16:18:27] [d31db4f83c6a129f6d3e47077769e868]
-    D                  [Mean Plot] [Paper. Mean plot ...] [2009-12-12 16:20:40] [d31db4f83c6a129f6d3e47077769e868]
- RM D                  [ARIMA Backward Selection] [Paper. Arima back...] [2009-12-12 17:23:23] [d31db4f83c6a129f6d3e47077769e868]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3922
3759
4138
4634
3996
4308
4143
4429
5219
4929
5761
5592
4163
4962
5208
4755
4491
5732
5731
5040
6102
4904
5369
5578
4619
4731
5011
5299
4146
4625
4736
4219
5116
4205
4121
5103
4300
4578
3809
5526
4248
3830
4428
4834
4406
4565
4104
4798
3935
3792
4387
4006
4078
4724
3157
3558
3899
4118
3790
4278
4035

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'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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67016&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67016&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67016&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
14569.16666666667666.1772673359182002
25169.58333333333562.8604636276661939
34660.91666666667416.2214136148151178
44452.16666666667470.6484565968211717
53976.83333333333401.4333032643121567

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 4569.16666666667 & 666.177267335918 & 2002 \tabularnewline
2 & 5169.58333333333 & 562.860463627666 & 1939 \tabularnewline
3 & 4660.91666666667 & 416.221413614815 & 1178 \tabularnewline
4 & 4452.16666666667 & 470.648456596821 & 1717 \tabularnewline
5 & 3976.83333333333 & 401.433303264312 & 1567 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67016&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]4569.16666666667[/C][C]666.177267335918[/C][C]2002[/C][/ROW]
[ROW][C]2[/C][C]5169.58333333333[/C][C]562.860463627666[/C][C]1939[/C][/ROW]
[ROW][C]3[/C][C]4660.91666666667[/C][C]416.221413614815[/C][C]1178[/C][/ROW]
[ROW][C]4[/C][C]4452.16666666667[/C][C]470.648456596821[/C][C]1717[/C][/ROW]
[ROW][C]5[/C][C]3976.83333333333[/C][C]401.433303264312[/C][C]1567[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67016&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67016&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
14569.16666666667666.1772673359182002
25169.58333333333562.8604636276661939
34660.91666666667416.2214136148151178
44452.16666666667470.6484565968211717
53976.83333333333401.4333032643121567






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-68.8540600154999
beta0.125351657470886
S.D.0.130687182757233
T-STAT0.959173308554225
p-value0.408230802708454

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -68.8540600154999 \tabularnewline
beta & 0.125351657470886 \tabularnewline
S.D. & 0.130687182757233 \tabularnewline
T-STAT & 0.959173308554225 \tabularnewline
p-value & 0.408230802708454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67016&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-68.8540600154999[/C][/ROW]
[ROW][C]beta[/C][C]0.125351657470886[/C][/ROW]
[ROW][C]S.D.[/C][C]0.130687182757233[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.959173308554225[/C][/ROW]
[ROW][C]p-value[/C][C]0.408230802708454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67016&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67016&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-68.8540600154999
beta0.125351657470886
S.D.0.130687182757233
T-STAT0.959173308554225
p-value0.408230802708454






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.9481331354009
beta1.20519631632886
S.D.1.10331384812004
T-STAT1.09234223642024
p-value0.354553097185796
Lambda-0.205196316328861

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.9481331354009 \tabularnewline
beta & 1.20519631632886 \tabularnewline
S.D. & 1.10331384812004 \tabularnewline
T-STAT & 1.09234223642024 \tabularnewline
p-value & 0.354553097185796 \tabularnewline
Lambda & -0.205196316328861 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=67016&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.9481331354009[/C][/ROW]
[ROW][C]beta[/C][C]1.20519631632886[/C][/ROW]
[ROW][C]S.D.[/C][C]1.10331384812004[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.09234223642024[/C][/ROW]
[ROW][C]p-value[/C][C]0.354553097185796[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.205196316328861[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=67016&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=67016&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-3.9481331354009
beta1.20519631632886
S.D.1.10331384812004
T-STAT1.09234223642024
p-value0.354553097185796
Lambda-0.205196316328861


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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')