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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

Wed, 06 Dec 2017 19:02:35 +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/06/t1512583724um9s321r4dz8f1d.htm/, Retrieved Mon, 13 May 2024 22:27:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=308631, Retrieved Mon, 13 May 2024 22:27:50 +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] [] [2017-12-06 18:02:35] [834c75312b1a933b06457deba9c9b5e8] [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=308631&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=308631&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308631&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	67.1583333333333	5.51484910093292	18.4
2	72.0916666666667	4.34458039261317	16.3
3	73.9666666666667	3.42433360028789	14.2
4	75.9166666666667	3.59566236996577	13.9
5	80.0416666666667	4.92442120887564	13.9
6	82.25	5.24465095467407	15.9
7	85.9333333333333	5.5102109072543	18.7
8	92.35	5.90277284610608	23.1
9	99.675	4.38864754482828	15.2
10	97.9583333333333	4.61153855874456	13.6
11	100	6.27172587527113	17.7
12	104.925	5.71348086864423	15.9
13	107.791666666667	5.01424485991176	16.7
14	106.116666666667	4.41749277579969	17.9
15	106.491666666667	5.387098786298	19.5
16	109.316666666667	6.00042927757269	18.9
17	113.391666666667	5.3220738154379	16.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 67.1583333333333 & 5.51484910093292 & 18.4 \tabularnewline
2 & 72.0916666666667 & 4.34458039261317 & 16.3 \tabularnewline
3 & 73.9666666666667 & 3.42433360028789 & 14.2 \tabularnewline
4 & 75.9166666666667 & 3.59566236996577 & 13.9 \tabularnewline
5 & 80.0416666666667 & 4.92442120887564 & 13.9 \tabularnewline
6 & 82.25 & 5.24465095467407 & 15.9 \tabularnewline
7 & 85.9333333333333 & 5.5102109072543 & 18.7 \tabularnewline
8 & 92.35 & 5.90277284610608 & 23.1 \tabularnewline
9 & 99.675 & 4.38864754482828 & 15.2 \tabularnewline
10 & 97.9583333333333 & 4.61153855874456 & 13.6 \tabularnewline
11 & 100 & 6.27172587527113 & 17.7 \tabularnewline
12 & 104.925 & 5.71348086864423 & 15.9 \tabularnewline
13 & 107.791666666667 & 5.01424485991176 & 16.7 \tabularnewline
14 & 106.116666666667 & 4.41749277579969 & 17.9 \tabularnewline
15 & 106.491666666667 & 5.387098786298 & 19.5 \tabularnewline
16 & 109.316666666667 & 6.00042927757269 & 18.9 \tabularnewline
17 & 113.391666666667 & 5.3220738154379 & 16.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308631&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]67.1583333333333[/C][C]5.51484910093292[/C][C]18.4[/C][/ROW]
[ROW][C]2[/C][C]72.0916666666667[/C][C]4.34458039261317[/C][C]16.3[/C][/ROW]
[ROW][C]3[/C][C]73.9666666666667[/C][C]3.42433360028789[/C][C]14.2[/C][/ROW]
[ROW][C]4[/C][C]75.9166666666667[/C][C]3.59566236996577[/C][C]13.9[/C][/ROW]
[ROW][C]5[/C][C]80.0416666666667[/C][C]4.92442120887564[/C][C]13.9[/C][/ROW]
[ROW][C]6[/C][C]82.25[/C][C]5.24465095467407[/C][C]15.9[/C][/ROW]
[ROW][C]7[/C][C]85.9333333333333[/C][C]5.5102109072543[/C][C]18.7[/C][/ROW]
[ROW][C]8[/C][C]92.35[/C][C]5.90277284610608[/C][C]23.1[/C][/ROW]
[ROW][C]9[/C][C]99.675[/C][C]4.38864754482828[/C][C]15.2[/C][/ROW]
[ROW][C]10[/C][C]97.9583333333333[/C][C]4.61153855874456[/C][C]13.6[/C][/ROW]
[ROW][C]11[/C][C]100[/C][C]6.27172587527113[/C][C]17.7[/C][/ROW]
[ROW][C]12[/C][C]104.925[/C][C]5.71348086864423[/C][C]15.9[/C][/ROW]
[ROW][C]13[/C][C]107.791666666667[/C][C]5.01424485991176[/C][C]16.7[/C][/ROW]
[ROW][C]14[/C][C]106.116666666667[/C][C]4.41749277579969[/C][C]17.9[/C][/ROW]
[ROW][C]15[/C][C]106.491666666667[/C][C]5.387098786298[/C][C]19.5[/C][/ROW]
[ROW][C]16[/C][C]109.316666666667[/C][C]6.00042927757269[/C][C]18.9[/C][/ROW]
[ROW][C]17[/C][C]113.391666666667[/C][C]5.3220738154379[/C][C]16.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308631&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308631&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	67.1583333333333	5.51484910093292	18.4
2	72.0916666666667	4.34458039261317	16.3
3	73.9666666666667	3.42433360028789	14.2
4	75.9166666666667	3.59566236996577	13.9
5	80.0416666666667	4.92442120887564	13.9
6	82.25	5.24465095467407	15.9
7	85.9333333333333	5.5102109072543	18.7
8	92.35	5.90277284610608	23.1
9	99.675	4.38864754482828	15.2
10	97.9583333333333	4.61153855874456	13.6
11	100	6.27172587527113	17.7
12	104.925	5.71348086864423	15.9
13	107.791666666667	5.01424485991176	16.7
14	106.116666666667	4.41749277579969	17.9
15	106.491666666667	5.387098786298	19.5
16	109.316666666667	6.00042927757269	18.9
17	113.391666666667	5.3220738154379	16.6

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	2.95783269510475
beta	0.0224105739436245
S.D.	0.0126846280488016
T-STAT	1.76675057852735
p-value	0.0976051931923161

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 2.95783269510475 \tabularnewline
beta & 0.0224105739436245 \tabularnewline
S.D. & 0.0126846280488016 \tabularnewline
T-STAT & 1.76675057852735 \tabularnewline
p-value & 0.0976051931923161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308631&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]2.95783269510475[/C][/ROW]
[ROW][C]beta[/C][C]0.0224105739436245[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0126846280488016[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.76675057852735[/C][/ROW]
[ROW][C]p-value[/C][C]0.0976051931923161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308631&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308631&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	2.95783269510475
beta	0.0224105739436245
S.D.	0.0126846280488016
T-STAT	1.76675057852735
p-value	0.0976051931923161

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.372396159809827
beta	0.437437996040776
S.D.	0.237481121345821
T-STAT	1.84199061197702
p-value	0.085334008029138
Lambda	0.562562003959224

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.372396159809827 \tabularnewline
beta & 0.437437996040776 \tabularnewline
S.D. & 0.237481121345821 \tabularnewline
T-STAT & 1.84199061197702 \tabularnewline
p-value & 0.085334008029138 \tabularnewline
Lambda & 0.562562003959224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=308631&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.372396159809827[/C][/ROW]
[ROW][C]beta[/C][C]0.437437996040776[/C][/ROW]
[ROW][C]S.D.[/C][C]0.237481121345821[/C][/ROW]
[ROW][C]T-STAT[/C][C]1.84199061197702[/C][/ROW]
[ROW][C]p-value[/C][C]0.085334008029138[/C][/ROW]
[ROW][C]Lambda[/C][C]0.562562003959224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=308631&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=308631&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	-0.372396159809827
beta	0.437437996040776
S.D.	0.237481121345821
T-STAT	1.84199061197702
p-value	0.085334008029138
Lambda	0.562562003959224

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code