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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 computationTue, 07 Dec 2010 00:05:33 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/07/t1291680270ioxk8k8c23t4d78.htm/, Retrieved Sat, 04 May 2024 01:53:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105990, Retrieved Sat, 04 May 2024 01:53:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151

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] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
-   PD      [Standard Deviation-Mean Plot] [SMP 1] [2010-12-07 00:05:33] [278a0539dc236556c5f30b5bc56ff9eb] [Current]
-    D        [Standard Deviation-Mean Plot] [SMP 2] [2010-12-07 00:10:56] [b8e188bcc949964bed729335b3416734]
-    D        [Standard Deviation-Mean Plot] [SMP test] [2010-12-08 17:37:55] [b8e188bcc949964bed729335b3416734]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
300
302
400
392
373
379
303
324
353
392
327
376
329
359
413
338
422
390
370
367
406
418
346
350
330
318
382
337
372
422
428
426
396
458
315
337
386
352
383
439
397
453
363
365
474
373
403
384
364
361
419
352
363
410
361
383
342
369
361
317
386
318
407
393
404
498
438

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 5 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105990&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105990&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105990&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 time5 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1351.7538.4521544496298100
2375.66666666666732.999540859983193
3376.7549.2971048384643143
4397.66666666666738.2891708719398122
5366.83333333333327.4618192250899102

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 351.75 & 38.4521544496298 & 100 \tabularnewline
2 & 375.666666666667 & 32.9995408599831 & 93 \tabularnewline
3 & 376.75 & 49.2971048384643 & 143 \tabularnewline
4 & 397.666666666667 & 38.2891708719398 & 122 \tabularnewline
5 & 366.833333333333 & 27.4618192250899 & 102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105990&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]351.75[/C][C]38.4521544496298[/C][C]100[/C][/ROW]
[ROW][C]2[/C][C]375.666666666667[/C][C]32.9995408599831[/C][C]93[/C][/ROW]
[ROW][C]3[/C][C]376.75[/C][C]49.2971048384643[/C][C]143[/C][/ROW]
[ROW][C]4[/C][C]397.666666666667[/C][C]38.2891708719398[/C][C]122[/C][/ROW]
[ROW][C]5[/C][C]366.833333333333[/C][C]27.4618192250899[/C][C]102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105990&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105990&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
1351.7538.4521544496298100
2375.66666666666732.999540859983193
3376.7549.2971048384643143
4397.66666666666738.2891708719398122
5366.83333333333327.4618192250899102






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha5.79963915546945
beta0.08428554823462
S.D.0.275150876840921
T-STAT0.306324839674597
p-value0.779386178820802

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 5.79963915546945 \tabularnewline
beta & 0.08428554823462 \tabularnewline
S.D. & 0.275150876840921 \tabularnewline
T-STAT & 0.306324839674597 \tabularnewline
p-value & 0.779386178820802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105990&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]5.79963915546945[/C][/ROW]
[ROW][C]beta[/C][C]0.08428554823462[/C][/ROW]
[ROW][C]S.D.[/C][C]0.275150876840921[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.306324839674597[/C][/ROW]
[ROW][C]p-value[/C][C]0.779386178820802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105990&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105990&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)
alpha5.79963915546945
beta0.08428554823462
S.D.0.275150876840921
T-STAT0.306324839674597
p-value0.779386178820802






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-1.62231218013013
beta0.881797108004862
S.D.2.74654830916782
T-STAT0.321056471157443
p-value0.769233906396675
Lambda0.118202891995138

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -1.62231218013013 \tabularnewline
beta & 0.881797108004862 \tabularnewline
S.D. & 2.74654830916782 \tabularnewline
T-STAT & 0.321056471157443 \tabularnewline
p-value & 0.769233906396675 \tabularnewline
Lambda & 0.118202891995138 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105990&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-1.62231218013013[/C][/ROW]
[ROW][C]beta[/C][C]0.881797108004862[/C][/ROW]
[ROW][C]S.D.[/C][C]2.74654830916782[/C][/ROW]
[ROW][C]T-STAT[/C][C]0.321056471157443[/C][/ROW]
[ROW][C]p-value[/C][C]0.769233906396675[/C][/ROW]
[ROW][C]Lambda[/C][C]0.118202891995138[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105990&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105990&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-1.62231218013013
beta0.881797108004862
S.D.2.74654830916782
T-STAT0.321056471157443
p-value0.769233906396675
Lambda0.118202891995138


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')