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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

Tue, 20 Dec 2016 20:20:05 +0100

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/20/t1482261650k3y43msjzgzcl56.htm/, Retrieved Sat, 27 Apr 2024 21:59:56 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301785, Retrieved Sat, 27 Apr 2024 21:59:56 +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] [] [2016-12-20 19:20:05] [672675941468e072e71d9fb024f2b817] [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=301785&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=301785&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301785&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	1991	132.123679432063	308.8
2	2386.575	237.7978325525	517.4
3	2775.025	280.993824072108	617.2
4	3039.6	214.051816156743	483.4
5	3239.725	371.264545169614	839.7
6	3577.3	306.218930396756	682.9
7	3729.075	284.464870414609	641.3
8	3811.675	339.286077668979	745.900000000001
9	3892.5	408.930499392419	827.7
10	4054.675	469.481787896684	1030.9
11	4200.775	413.389319125043	904.9
12	4389.45	482.859023594534	1031.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 1991 & 132.123679432063 & 308.8 \tabularnewline
2 & 2386.575 & 237.7978325525 & 517.4 \tabularnewline
3 & 2775.025 & 280.993824072108 & 617.2 \tabularnewline
4 & 3039.6 & 214.051816156743 & 483.4 \tabularnewline
5 & 3239.725 & 371.264545169614 & 839.7 \tabularnewline
6 & 3577.3 & 306.218930396756 & 682.9 \tabularnewline
7 & 3729.075 & 284.464870414609 & 641.3 \tabularnewline
8 & 3811.675 & 339.286077668979 & 745.900000000001 \tabularnewline
9 & 3892.5 & 408.930499392419 & 827.7 \tabularnewline
10 & 4054.675 & 469.481787896684 & 1030.9 \tabularnewline
11 & 4200.775 & 413.389319125043 & 904.9 \tabularnewline
12 & 4389.45 & 482.859023594534 & 1031.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301785&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]1991[/C][C]132.123679432063[/C][C]308.8[/C][/ROW]
[ROW][C]2[/C][C]2386.575[/C][C]237.7978325525[/C][C]517.4[/C][/ROW]
[ROW][C]3[/C][C]2775.025[/C][C]280.993824072108[/C][C]617.2[/C][/ROW]
[ROW][C]4[/C][C]3039.6[/C][C]214.051816156743[/C][C]483.4[/C][/ROW]
[ROW][C]5[/C][C]3239.725[/C][C]371.264545169614[/C][C]839.7[/C][/ROW]
[ROW][C]6[/C][C]3577.3[/C][C]306.218930396756[/C][C]682.9[/C][/ROW]
[ROW][C]7[/C][C]3729.075[/C][C]284.464870414609[/C][C]641.3[/C][/ROW]
[ROW][C]8[/C][C]3811.675[/C][C]339.286077668979[/C][C]745.900000000001[/C][/ROW]
[ROW][C]9[/C][C]3892.5[/C][C]408.930499392419[/C][C]827.7[/C][/ROW]
[ROW][C]10[/C][C]4054.675[/C][C]469.481787896684[/C][C]1030.9[/C][/ROW]
[ROW][C]11[/C][C]4200.775[/C][C]413.389319125043[/C][C]904.9[/C][/ROW]
[ROW][C]12[/C][C]4389.45[/C][C]482.859023594534[/C][C]1031.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301785&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301785&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	1991	132.123679432063	308.8
2	2386.575	237.7978325525	517.4
3	2775.025	280.993824072108	617.2
4	3039.6	214.051816156743	483.4
5	3239.725	371.264545169614	839.7
6	3577.3	306.218930396756	682.9
7	3729.075	284.464870414609	641.3
8	3811.675	339.286077668979	745.900000000001
9	3892.5	408.930499392419	827.7
10	4054.675	469.481787896684	1030.9
11	4200.775	413.389319125043	904.9
12	4389.45	482.859023594534	1031.6

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	-100.876458606271
beta	0.125376218586544
S.D.	0.0210252031684441
T-STAT	5.96313945611313
p-value	0.000138777581766812

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -100.876458606271 \tabularnewline
beta & 0.125376218586544 \tabularnewline
S.D. & 0.0210252031684441 \tabularnewline
T-STAT & 5.96313945611313 \tabularnewline
p-value & 0.000138777581766812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301785&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-100.876458606271[/C][/ROW]
[ROW][C]beta[/C][C]0.125376218586544[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0210252031684441[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.96313945611313[/C][/ROW]
[ROW][C]p-value[/C][C]0.000138777581766812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301785&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301785&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	-100.876458606271
beta	0.125376218586544
S.D.	0.0210252031684441
T-STAT	5.96313945611313
p-value	0.000138777581766812

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-5.41161464615888
beta	1.37412442670032
S.D.	0.214765168522358
T-STAT	6.39826484040529
p-value	7.84992004356485e-05
Lambda	-0.374124426700318

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -5.41161464615888 \tabularnewline
beta & 1.37412442670032 \tabularnewline
S.D. & 0.214765168522358 \tabularnewline
T-STAT & 6.39826484040529 \tabularnewline
p-value & 7.84992004356485e-05 \tabularnewline
Lambda & -0.374124426700318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301785&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-5.41161464615888[/C][/ROW]
[ROW][C]beta[/C][C]1.37412442670032[/C][/ROW]
[ROW][C]S.D.[/C][C]0.214765168522358[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.39826484040529[/C][/ROW]
[ROW][C]p-value[/C][C]7.84992004356485e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.374124426700318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301785&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301785&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	-5.41161464615888
beta	1.37412442670032
S.D.	0.214765168522358
T-STAT	6.39826484040529
p-value	7.84992004356485e-05
Lambda	-0.374124426700318

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Single ; par3 = multiplicative ; par4 = 12 ;

Parameters (R input):

par1 = 4 ;

R code (references can be found in the software module):

par1 <- '12'
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code