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*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

Sat, 23 Dec 2017 16:24:13 +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/23/t1514042672cywrkv1g45oupm3.htm/, Retrieved Wed, 15 May 2024 11:25:38 +0200

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Wed, 15 May 2024 11:25:38 +0200

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Estimated Impact

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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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	180.016666666667	31.9428988646739	91.6
2	188.4	35.8872476717642	108.1
3	186.008333333333	35.9921571844184	99.9
4	176.175	39.4769696958067	109.6
5	146.208333333333	34.7320250000783	101.3
6	146.808333333333	37.8908350236291	116.1
7	142.15	39.3714132565518	114.9
8	134.025	41.0234550426505	120.9
9	122.966666666667	35.0066314064099	115.2
10	103.608333333333	25.736866318159	81.2
11	100	20.7289871699248	76.2
12	95.825	17.3661177427353	54.6
13	86.9916666666667	21.3750261385628	63
14	79.6333333333333	15.745841201775	47.1
15	75.5833333333333	20.0458036113358	60.7
16	75.675	21.2983193959267	72.7
17	69.6083333333333	21.0904311923391	74.8

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 180.016666666667 & 31.9428988646739 & 91.6 \tabularnewline
2 & 188.4 & 35.8872476717642 & 108.1 \tabularnewline
3 & 186.008333333333 & 35.9921571844184 & 99.9 \tabularnewline
4 & 176.175 & 39.4769696958067 & 109.6 \tabularnewline
5 & 146.208333333333 & 34.7320250000783 & 101.3 \tabularnewline
6 & 146.808333333333 & 37.8908350236291 & 116.1 \tabularnewline
7 & 142.15 & 39.3714132565518 & 114.9 \tabularnewline
8 & 134.025 & 41.0234550426505 & 120.9 \tabularnewline
9 & 122.966666666667 & 35.0066314064099 & 115.2 \tabularnewline
10 & 103.608333333333 & 25.736866318159 & 81.2 \tabularnewline
11 & 100 & 20.7289871699248 & 76.2 \tabularnewline
12 & 95.825 & 17.3661177427353 & 54.6 \tabularnewline
13 & 86.9916666666667 & 21.3750261385628 & 63 \tabularnewline
14 & 79.6333333333333 & 15.745841201775 & 47.1 \tabularnewline
15 & 75.5833333333333 & 20.0458036113358 & 60.7 \tabularnewline
16 & 75.675 & 21.2983193959267 & 72.7 \tabularnewline
17 & 69.6083333333333 & 21.0904311923391 & 74.8 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]180.016666666667[/C][C]31.9428988646739[/C][C]91.6[/C][/ROW]
[ROW][C]2[/C][C]188.4[/C][C]35.8872476717642[/C][C]108.1[/C][/ROW]
[ROW][C]3[/C][C]186.008333333333[/C][C]35.9921571844184[/C][C]99.9[/C][/ROW]
[ROW][C]4[/C][C]176.175[/C][C]39.4769696958067[/C][C]109.6[/C][/ROW]
[ROW][C]5[/C][C]146.208333333333[/C][C]34.7320250000783[/C][C]101.3[/C][/ROW]
[ROW][C]6[/C][C]146.808333333333[/C][C]37.8908350236291[/C][C]116.1[/C][/ROW]
[ROW][C]7[/C][C]142.15[/C][C]39.3714132565518[/C][C]114.9[/C][/ROW]
[ROW][C]8[/C][C]134.025[/C][C]41.0234550426505[/C][C]120.9[/C][/ROW]
[ROW][C]9[/C][C]122.966666666667[/C][C]35.0066314064099[/C][C]115.2[/C][/ROW]
[ROW][C]10[/C][C]103.608333333333[/C][C]25.736866318159[/C][C]81.2[/C][/ROW]
[ROW][C]11[/C][C]100[/C][C]20.7289871699248[/C][C]76.2[/C][/ROW]
[ROW][C]12[/C][C]95.825[/C][C]17.3661177427353[/C][C]54.6[/C][/ROW]
[ROW][C]13[/C][C]86.9916666666667[/C][C]21.3750261385628[/C][C]63[/C][/ROW]
[ROW][C]14[/C][C]79.6333333333333[/C][C]15.745841201775[/C][C]47.1[/C][/ROW]
[ROW][C]15[/C][C]75.5833333333333[/C][C]20.0458036113358[/C][C]60.7[/C][/ROW]
[ROW][C]16[/C][C]75.675[/C][C]21.2983193959267[/C][C]72.7[/C][/ROW]
[ROW][C]17[/C][C]69.6083333333333[/C][C]21.0904311923391[/C][C]74.8[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	180.016666666667	31.9428988646739	91.6
2	188.4	35.8872476717642	108.1
3	186.008333333333	35.9921571844184	99.9
4	176.175	39.4769696958067	109.6
5	146.208333333333	34.7320250000783	101.3
6	146.808333333333	37.8908350236291	116.1
7	142.15	39.3714132565518	114.9
8	134.025	41.0234550426505	120.9
9	122.966666666667	35.0066314064099	115.2
10	103.608333333333	25.736866318159	81.2
11	100	20.7289871699248	76.2
12	95.825	17.3661177427353	54.6
13	86.9916666666667	21.3750261385628	63
14	79.6333333333333	15.745841201775	47.1
15	75.5833333333333	20.0458036113358	60.7
16	75.675	21.2983193959267	72.7
17	69.6083333333333	21.0904311923391	74.8

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha	7.33970139912024
beta	0.175351483460407
S.D.	0.0309141031642902
T-STAT	5.67221641619419
p-value	4.43004309510547e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 7.33970139912024 \tabularnewline
beta & 0.175351483460407 \tabularnewline
S.D. & 0.0309141031642902 \tabularnewline
T-STAT & 5.67221641619419 \tabularnewline
p-value & 4.43004309510547e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]7.33970139912024[/C][/ROW]
[ROW][C]beta[/C][C]0.175351483460407[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0309141031642902[/C][/ROW]
[ROW][C]T-STAT[/C][C]5.67221641619419[/C][/ROW]
[ROW][C]p-value[/C][C]4.43004309510547e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	7.33970139912024
beta	0.175351483460407
S.D.	0.0309141031642902
T-STAT	5.67221641619419
p-value	4.43004309510547e-05

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha	-0.511885612412434
beta	0.804640434247871
S.D.	0.126598587280395
T-STAT	6.35584054714388
p-value	1.29037858688826e-05
Lambda	0.195359565752129

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -0.511885612412434 \tabularnewline
beta & 0.804640434247871 \tabularnewline
S.D. & 0.126598587280395 \tabularnewline
T-STAT & 6.35584054714388 \tabularnewline
p-value & 1.29037858688826e-05 \tabularnewline
Lambda & 0.195359565752129 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-0.511885612412434[/C][/ROW]
[ROW][C]beta[/C][C]0.804640434247871[/C][/ROW]
[ROW][C]S.D.[/C][C]0.126598587280395[/C][/ROW]
[ROW][C]T-STAT[/C][C]6.35584054714388[/C][/ROW]
[ROW][C]p-value[/C][C]1.29037858688826e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]0.195359565752129[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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	-0.511885612412434
beta	0.804640434247871
S.D.	0.126598587280395
T-STAT	6.35584054714388
p-value	1.29037858688826e-05
Lambda	0.195359565752129

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSEFALSEFALSEFALSEFALSEFALSEFALSEadditiveFALSEFALSEFALSEadditivemultiplicativeadditivemultiplicativemultiplicativeadditivemultiplicative12additiveFALSEFALSEFALSEFALSEFALSEFALSEFALSEFALSEFALSE12additive12additivemultiplicativeadditive12additiveFALSEFALSEFALSEFALSEadditiveFALSEadditive1212121212additiveadditive1212 ; par2 = 0.20.20.20.20.20.20.2120.2121212121212121212120.20.10.20.20.20.20.20.20.20.212periodic12121212120.20.21212120.21212SingleDoubleTripleTriple1212 ; par3 = 000000000000100000BFGSBFGSadditiveadditiveadditiveadditive ; par4 = 1111111111111111112121212 ; par5 = 12121212121212121212121212121212121 ; par6 = 22233233322233221 ; par7 = 111111111111111111 ; par8 = 12121101112122211FALSE ; par9 = 11111111111111111 ; par10 = FALSE ;

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

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code