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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, 12 Dec 2010 13:55:03 +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/12/t1292162025t78dbnzzfyoycci.htm/, Retrieved Tue, 07 May 2024 23:49:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108448, Retrieved Tue, 07 May 2024 23:49:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact155

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Spectral Analysis] [Unemployment] [2010-11-29 09:27:34] [b98453cac15ba1066b407e146608df68]
-   PD    [Spectral Analysis] [Workshop 9 CP (1)] [2010-12-07 15:31:19] [a9e130f95bad0a0597234e75c6380c5a]
-           [Spectral Analysis] [] [2010-12-07 22:07:26] [afdb2fc47981b6a655b732edc8065db9]
- RMPD          [Standard Deviation-Mean Plot] [] [2010-12-12 13:55:03] [297722d8c88c4886be8e106c47d8f3cc] [Current]
- RMP             [ARIMA Backward Selection] [] [2010-12-13 14:20:03] [afdb2fc47981b6a655b732edc8065db9]
- RMPD            [Central Tendency] [] [2010-12-13 14:57:03] [afdb2fc47981b6a655b732edc8065db9]
- RMPD            [Univariate Explorative Data Analysis] [] [2010-12-13 15:34:16] [afdb2fc47981b6a655b732edc8065db9]
- RMP             [ARIMA Forecasting] [] [2010-12-13 16:23:13] [afdb2fc47981b6a655b732edc8065db9]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
100918
105017
108666
116083
117359
102191
102617
106640
108783
112534
113149
117125
107597
108745
111311
115669
114585
101628
97493
99180
100247
97657
95378
89406
82880
82662
83469
86371
86822
73899
71415
76335
76844
78192
80651
81485
78872
81632
84822
92175
92844
77443
77550
80367
83117
86622
90999
90276
91982
96279
106810
109483
110159
98305
99450
101536
99925
102850
101993
108928
107605

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'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108448&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108448&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108448&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'RServer@AstonUniversity' @ vre.aston.ac.uk






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1109256.8333333335946.6233326658616441
2103241.3333333338218.865497172126263
380085.41666666674811.6454841510815407
484726.58333333335761.2779588991315401
5102308.3333333335649.1848218583818177

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 109256.833333333 & 5946.62333266586 & 16441 \tabularnewline
2 & 103241.333333333 & 8218.8654971721 & 26263 \tabularnewline
3 & 80085.4166666667 & 4811.64548415108 & 15407 \tabularnewline
4 & 84726.5833333333 & 5761.27795889913 & 15401 \tabularnewline
5 & 102308.333333333 & 5649.18482185838 & 18177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108448&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]109256.833333333[/C][C]5946.62333266586[/C][C]16441[/C][/ROW]
[ROW][C]2[/C][C]103241.333333333[/C][C]8218.8654971721[/C][C]26263[/C][/ROW]
[ROW][C]3[/C][C]80085.4166666667[/C][C]4811.64548415108[/C][C]15407[/C][/ROW]
[ROW][C]4[/C][C]84726.5833333333[/C][C]5761.27795889913[/C][C]15401[/C][/ROW]
[ROW][C]5[/C][C]102308.333333333[/C][C]5649.18482185838[/C][C]18177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108448&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108448&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
1109256.8333333335946.6233326658616441
2103241.3333333338218.865497172126263
380085.41666666674811.6454841510815407
484726.58333333335761.2779588991315401
5102308.3333333335649.1848218583818177






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha931.511569051526
beta0.0536468865347958
S.D.0.0487517537761818
T-STAT1.10040936744732
p-value0.351530421371623

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 931.511569051526 \tabularnewline
beta & 0.0536468865347958 \tabularnewline
S.D. & 0.0487517537761818 \tabularnewline
T-STAT & 1.10040936744732 \tabularnewline
p-value & 0.351530421371623 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108448&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]931.511569051526[/C][/ROW]
[ROW][C]beta[/C][C]0.0536468865347958[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0487517537761818[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.10040936744732[/C][/ROW]
[ROW][C]p-value[/C][C]0.351530421371623[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108448&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108448&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)
alpha931.511569051526
beta0.0536468865347958
S.D.0.0487517537761818
T-STAT1.10040936744732
p-value0.351530421371623






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.01282378041529
beta0.846926181929549
S.D.0.669642873021623
T-STAT1.26474306835817
p-value0.295281467476585
Lambda0.153073818070451

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.01282378041529 \tabularnewline
beta & 0.846926181929549 \tabularnewline
S.D. & 0.669642873021623 \tabularnewline
T-STAT & 1.26474306835817 \tabularnewline
p-value & 0.295281467476585 \tabularnewline
Lambda & 0.153073818070451 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108448&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.01282378041529[/C][/ROW]
[ROW][C]beta[/C][C]0.846926181929549[/C][/ROW]
[ROW][C]S.D.[/C][C]0.669642873021623[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.26474306835817[/C][/ROW]
[ROW][C]p-value[/C][C]0.295281467476585[/C][/ROW]
[ROW][C]Lambda[/C][C]0.153073818070451[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108448&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108448&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-1.01282378041529
beta0.846926181929549
S.D.0.669642873021623
T-STAT1.26474306835817
p-value0.295281467476585
Lambda0.153073818070451


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')