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Author

*The author of this computation has been verified*

R Software Module

rwasp_smp.wasp

Title produced by software

Standard Deviation-Mean Plot

Date of computation

Sun, 24 Dec 2017 11:09:51 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Dec/24/t1514110227hvvel2xwoepq1r0.htm/, Retrieved Tue, 14 May 2024 15:31:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=310892, Retrieved Tue, 14 May 2024 15:31:57 +0000

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Estimated Impact

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [Standard Deviation-Mean Plot] [] [2017-12-24 10:09:51] [ec772448347bb766a411d58621b503be] [Current]

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310892&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=310892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310892&T=0

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	Big Analytics Cloud Computing Center

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	76.1	10.7643350510335	36
2	80.425	12.3527048933348	33.5
3	81.2	7.92590688817374	24.3
4	88.0333333333333	11.4959544926452	37.9
5	91.0333333333333	11.2139793710053	38
6	94.525	11.7816594756426	39.7
7	96.8416666666667	11.6213329178661	39.7
8	100.483333333333	10.9143636247531	35.9
9	101.183333333333	9.67018222384792	35
10	102.325	12.0388103459376	43.8
11	100.008333333333	14.010739928117	54.2
12	107.983333333333	12.4676186640238	45.7
13	112.066666666667	10.264531458406	38.6
14	111.825	13.0322066086641	48.2
15	114.425	13.4987625695503	45.9
16	112.283333333333	12.8124820768537	43
17	123.808333333333	14.2419009413857	49.7

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 76.1 & 10.7643350510335 & 36 \tabularnewline
2 & 80.425 & 12.3527048933348 & 33.5 \tabularnewline
3 & 81.2 & 7.92590688817374 & 24.3 \tabularnewline
4 & 88.0333333333333 & 11.4959544926452 & 37.9 \tabularnewline
5 & 91.0333333333333 & 11.2139793710053 & 38 \tabularnewline
6 & 94.525 & 11.7816594756426 & 39.7 \tabularnewline
7 & 96.8416666666667 & 11.6213329178661 & 39.7 \tabularnewline
8 & 100.483333333333 & 10.9143636247531 & 35.9 \tabularnewline
9 & 101.183333333333 & 9.67018222384792 & 35 \tabularnewline
10 & 102.325 & 12.0388103459376 & 43.8 \tabularnewline
11 & 100.008333333333 & 14.010739928117 & 54.2 \tabularnewline
12 & 107.983333333333 & 12.4676186640238 & 45.7 \tabularnewline
13 & 112.066666666667 & 10.264531458406 & 38.6 \tabularnewline
14 & 111.825 & 13.0322066086641 & 48.2 \tabularnewline
15 & 114.425 & 13.4987625695503 & 45.9 \tabularnewline
16 & 112.283333333333 & 12.8124820768537 & 43 \tabularnewline
17 & 123.808333333333 & 14.2419009413857 & 49.7 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310892&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]76.1[/C][C]10.7643350510335[/C][C]36[/C][/ROW]
[ROW][C]2[/C][C]80.425[/C][C]12.3527048933348[/C][C]33.5[/C][/ROW]
[ROW][C]3[/C][C]81.2[/C][C]7.92590688817374[/C][C]24.3[/C][/ROW]
[ROW][C]4[/C][C]88.0333333333333[/C][C]11.4959544926452[/C][C]37.9[/C][/ROW]
[ROW][C]5[/C][C]91.0333333333333[/C][C]11.2139793710053[/C][C]38[/C][/ROW]
[ROW][C]6[/C][C]94.525[/C][C]11.7816594756426[/C][C]39.7[/C][/ROW]
[ROW][C]7[/C][C]96.8416666666667[/C][C]11.6213329178661[/C][C]39.7[/C][/ROW]
[ROW][C]8[/C][C]100.483333333333[/C][C]10.9143636247531[/C][C]35.9[/C][/ROW]
[ROW][C]9[/C][C]101.183333333333[/C][C]9.67018222384792[/C][C]35[/C][/ROW]
[ROW][C]10[/C][C]102.325[/C][C]12.0388103459376[/C][C]43.8[/C][/ROW]
[ROW][C]11[/C][C]100.008333333333[/C][C]14.010739928117[/C][C]54.2[/C][/ROW]
[ROW][C]12[/C][C]107.983333333333[/C][C]12.4676186640238[/C][C]45.7[/C][/ROW]
[ROW][C]13[/C][C]112.066666666667[/C][C]10.264531458406[/C][C]38.6[/C][/ROW]
[ROW][C]14[/C][C]111.825[/C][C]13.0322066086641[/C][C]48.2[/C][/ROW]
[ROW][C]15[/C][C]114.425[/C][C]13.4987625695503[/C][C]45.9[/C][/ROW]
[ROW][C]16[/C][C]112.283333333333[/C][C]12.8124820768537[/C][C]43[/C][/ROW]
[ROW][C]17[/C][C]123.808333333333[/C][C]14.2419009413857[/C][C]49.7[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310892&T=1

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
Section	Mean	Standard Deviation	Range
1	76.1	10.7643350510335	36
2	80.425	12.3527048933348	33.5
3	81.2	7.92590688817374	24.3
4	88.0333333333333	11.4959544926452	37.9
5	91.0333333333333	11.2139793710053	38
6	94.525	11.7816594756426	39.7
7	96.8416666666667	11.6213329178661	39.7
8	100.483333333333	10.9143636247531	35.9
9	101.183333333333	9.67018222384792	35
10	102.325	12.0388103459376	43.8
11	100.008333333333	14.010739928117	54.2
12	107.983333333333	12.4676186640238	45.7
13	112.066666666667	10.264531458406	38.6
14	111.825	13.0322066086641	48.2
15	114.425	13.4987625695503	45.9
16	112.283333333333	12.8124820768537	43
17	123.808333333333	14.2419009413857	49.7

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	5.12106989799529
beta	0.0667134538758495
S.D.	0.0258618373264932
T-STAT	2.57960998801533
p-value	0.0209308935207077

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.12106989799529 \tabularnewline
beta & 0.0667134538758495 \tabularnewline
S.D. & 0.0258618373264932 \tabularnewline
T-STAT & 2.57960998801533 \tabularnewline
p-value & 0.0209308935207077 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310892&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.12106989799529[/C][/ROW]
[ROW][C]beta[/C][C]0.0667134538758495[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0258618373264932[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.57960998801533[/C][/ROW]
[ROW][C]p-value[/C][C]0.0209308935207077[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310892&T=2

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	5.12106989799529
beta	0.0667134538758495
S.D.	0.0258618373264932
T-STAT	2.57960998801533
p-value	0.0209308935207077

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.122778378250206
beta	0.561458208211935
S.D.	0.231842026757836
T-STAT	2.42172748428563
p-value	0.0285835101188613
Lambda	0.438541791788065

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.122778378250206 \tabularnewline
beta & 0.561458208211935 \tabularnewline
S.D. & 0.231842026757836 \tabularnewline
T-STAT & 2.42172748428563 \tabularnewline
p-value & 0.0285835101188613 \tabularnewline
Lambda & 0.438541791788065 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=310892&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.122778378250206[/C][/ROW]
[ROW][C]beta[/C][C]0.561458208211935[/C][/ROW]
[ROW][C]S.D.[/C][C]0.231842026757836[/C][/ROW]
[ROW][C]T-STAT[/C][C]2.42172748428563[/C][/ROW]
[ROW][C]p-value[/C][C]0.0285835101188613[/C][/ROW]
[ROW][C]Lambda[/C][C]0.438541791788065[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=310892&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=310892&T=3

As an alternative you can also use a QR Code:

The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.122778378250206
beta	0.561458208211935
S.D.	0.231842026757836
T-STAT	2.42172748428563
p-value	0.0285835101188613
Lambda	0.438541791788065

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 2 ; par2 = Do not include Seasonal Dummies ; par3 = First and Seasonal Differences (s) ; par4 = 2 ; par5 = 1 ; par6 = 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code