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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 computationWed, 17 Dec 2008 08:42:54 -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/17/t1229528653welsovqrhcsce9f.htm/, Retrieved Sun, 19 May 2024 05:57:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=34414, Retrieved Sun, 19 May 2024 05:57:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact169

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] [Totale Invoer naa...] [2008-12-07 13:03:47] [299afd6311e4c20059ea2f05c8dd029d]
- RMP     [Standard Deviation-Mean Plot] [Totale Invoer - SMP] [2008-12-17 15:42:54] [5e2b1e7aa808f9f0d23fd35605d4968f] [Current]
- RMP       [ARIMA Backward Selection] [Totale Invoer - ABS] [2008-12-17 15:48:37] [299afd6311e4c20059ea2f05c8dd029d]
- RMP       [ARIMA Forecasting] [Totale Invoer - F...] [2008-12-17 15:53:20] [299afd6311e4c20059ea2f05c8dd029d]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
13429.9
13470.1
14785.8
14292
14308.8
14013
13240.9
12153.4
14289.7
15669.2
14169.5
14569.8
14469.1
14264.9
15320.9
14433.5
13691.5
14194.1
13519.2
11857.9
14616
15643.4
14077.2
14887.5
14159.9
14643
17192.5
15386.1
14287.1
17526.6
14497
14398.3
16629.6
16670.7
16614.8
16869.2
15663.9
16359.9
18447.7
16889
16505
18320.9
15052.1
15699.8
18135.3
16768.7
18883
19021
18101.9
17776.1
21489.9
17065.3
18690
18953.1
16398.9
16895.7
18553
19270
19422.1
17579.4
18637.3
18076.7
20438.6
18075.2
19563
19899.2
19227.5
17789.6
19220.8
21968.9
21131.5
19484.6

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34414&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34414&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34414&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114032.675884.2557025544143515.8
214247.9333333333968.2091428211283785.5
315739.56666666671289.155763445303366.7
417145.5251365.020454142453968.9
518349.61666666671379.468943822115091
619459.40833333331267.057804850804179.3

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14032.675 & 884.255702554414 & 3515.8 \tabularnewline
2 & 14247.9333333333 & 968.209142821128 & 3785.5 \tabularnewline
3 & 15739.5666666667 & 1289.15576344530 & 3366.7 \tabularnewline
4 & 17145.525 & 1365.02045414245 & 3968.9 \tabularnewline
5 & 18349.6166666667 & 1379.46894382211 & 5091 \tabularnewline
6 & 19459.4083333333 & 1267.05780485080 & 4179.3 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34414&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]14032.675[/C][C]884.255702554414[/C][C]3515.8[/C][/ROW]
[ROW][C]2[/C][C]14247.9333333333[/C][C]968.209142821128[/C][C]3785.5[/C][/ROW]
[ROW][C]3[/C][C]15739.5666666667[/C][C]1289.15576344530[/C][C]3366.7[/C][/ROW]
[ROW][C]4[/C][C]17145.525[/C][C]1365.02045414245[/C][C]3968.9[/C][/ROW]
[ROW][C]5[/C][C]18349.6166666667[/C][C]1379.46894382211[/C][C]5091[/C][/ROW]
[ROW][C]6[/C][C]19459.4083333333[/C][C]1267.05780485080[/C][C]4179.3[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34414&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34414&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
114032.675884.2557025544143515.8
214247.9333333333968.2091428211283785.5
315739.56666666671289.155763445303366.7
417145.5251365.020454142453968.9
518349.61666666671379.468943822115091
619459.40833333331267.057804850804179.3






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-75.4734769381228
beta0.0768479899617296
S.D.0.0288899384599877
T-STAT2.66002608721938
p-value0.056388826113144

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -75.4734769381228 \tabularnewline
beta & 0.0768479899617296 \tabularnewline
S.D. & 0.0288899384599877 \tabularnewline
T-STAT & 2.66002608721938 \tabularnewline
p-value & 0.056388826113144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34414&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-75.4734769381228[/C][/ROW]
[ROW][C]beta[/C][C]0.0768479899617296[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0288899384599877[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.66002608721938[/C][/ROW]
[ROW][C]p-value[/C][C]0.056388826113144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34414&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34414&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-75.4734769381228
beta0.0768479899617296
S.D.0.0288899384599877
T-STAT2.66002608721938
p-value0.056388826113144






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-4.33512370903504
beta1.17528438315745
S.D.0.398744187000950
T-STAT2.94746461885009
p-value0.0420753278571250
Lambda-0.175284383157446

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -4.33512370903504 \tabularnewline
beta & 1.17528438315745 \tabularnewline
S.D. & 0.398744187000950 \tabularnewline
T-STAT & 2.94746461885009 \tabularnewline
p-value & 0.0420753278571250 \tabularnewline
Lambda & -0.175284383157446 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=34414&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-4.33512370903504[/C][/ROW]
[ROW][C]beta[/C][C]1.17528438315745[/C][/ROW]
[ROW][C]S.D.[/C][C]0.398744187000950[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.94746461885009[/C][/ROW]
[ROW][C]p-value[/C][C]0.0420753278571250[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.175284383157446[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=34414&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=34414&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-4.33512370903504
beta1.17528438315745
S.D.0.398744187000950
T-STAT2.94746461885009
p-value0.0420753278571250
Lambda-0.175284383157446


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')