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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Module--
Title produced by softwareStandard Deviation-Mean Plot
Date of computationThu, 20 Dec 2012 14:40:31 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/20/t1356032446d4qk3j6l9d8hg4q.htm/, Retrieved Fri, 26 Apr 2024 08:45:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203061, Retrieved Fri, 26 Apr 2024 08:45:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [HPC Retail Sales] [2008-03-02 15:42:48] [74be16979710d4c4e7c6647856088456]
- RMPD  [(Partial) Autocorrelation Function] [Autocorrelatiefun...] [2012-11-10 16:56:48] [391561951b5d7f721cfaa4f5575ab127]
- R P     [(Partial) Autocorrelation Function] [] [2012-11-24 00:03:24] [74be16979710d4c4e7c6647856088456]
-   P       [(Partial) Autocorrelation Function] [Langetermijntrend...] [2012-11-24 09:07:33] [74be16979710d4c4e7c6647856088456]
- RMP         [Standard Deviation-Mean Plot] [] [2012-11-24 10:58:52] [391561951b5d7f721cfaa4f5575ab127]
- RM              [Standard Deviation-Mean Plot] [] [2012-12-20 19:40:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
617
614
647
580
614
636
388
356
639
753
611
639
630
586
695
552
619
681
421
307
754
690
644
643
608
651
691
627
634
731
475
337
803
722
590
724
627
696
825
677
656
785
412
352
839
729
696
641
695
638
762
635
721
854
418
367
824
687
601
676
740
691
683
594
729
731
386
331
706
715
657
653
642
643
718
654
632
731
392
344
792
852
649
629
685
617
715
715
629
916
531
357
917
828
708
858
775
785
1006
789
734
906
532
387
991
841
892
782
811
792
978
773
796
946
594
438
1023
868
791
760
779
852
1001
734
996
869
599
426
1138
1091
830
909

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203061&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203061&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203061&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1591.166666666667110.659866530762397
2601.833333333333125.335066074418447
3632.75125.583818442288466
4661.25147.816916856938487
5656.5144.512660659574487
6634.666666666667135.801548614368409
7639.833333333333145.229494458275508
8706.333333333333163.343104222277560
9785177.262517188491619
10797.5160.501770027057585
11852202.397897940935712

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 591.166666666667 & 110.659866530762 & 397 \tabularnewline
2 & 601.833333333333 & 125.335066074418 & 447 \tabularnewline
3 & 632.75 & 125.583818442288 & 466 \tabularnewline
4 & 661.25 & 147.816916856938 & 487 \tabularnewline
5 & 656.5 & 144.512660659574 & 487 \tabularnewline
6 & 634.666666666667 & 135.801548614368 & 409 \tabularnewline
7 & 639.833333333333 & 145.229494458275 & 508 \tabularnewline
8 & 706.333333333333 & 163.343104222277 & 560 \tabularnewline
9 & 785 & 177.262517188491 & 619 \tabularnewline
10 & 797.5 & 160.501770027057 & 585 \tabularnewline
11 & 852 & 202.397897940935 & 712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203061&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]591.166666666667[/C][C]110.659866530762[/C][C]397[/C][/ROW]
[ROW][C]2[/C][C]601.833333333333[/C][C]125.335066074418[/C][C]447[/C][/ROW]
[ROW][C]3[/C][C]632.75[/C][C]125.583818442288[/C][C]466[/C][/ROW]
[ROW][C]4[/C][C]661.25[/C][C]147.816916856938[/C][C]487[/C][/ROW]
[ROW][C]5[/C][C]656.5[/C][C]144.512660659574[/C][C]487[/C][/ROW]
[ROW][C]6[/C][C]634.666666666667[/C][C]135.801548614368[/C][C]409[/C][/ROW]
[ROW][C]7[/C][C]639.833333333333[/C][C]145.229494458275[/C][C]508[/C][/ROW]
[ROW][C]8[/C][C]706.333333333333[/C][C]163.343104222277[/C][C]560[/C][/ROW]
[ROW][C]9[/C][C]785[/C][C]177.262517188491[/C][C]619[/C][/ROW]
[ROW][C]10[/C][C]797.5[/C][C]160.501770027057[/C][C]585[/C][/ROW]
[ROW][C]11[/C][C]852[/C][C]202.397897940935[/C][C]712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203061&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203061&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
1591.166666666667110.659866530762397
2601.833333333333125.335066074418447
3632.75125.583818442288466
4661.25147.816916856938487
5656.5144.512660659574487
6634.666666666667135.801548614368409
7639.833333333333145.229494458275508
8706.333333333333163.343104222277560
9785177.262517188491619
10797.5160.501770027057585
11852202.397897940935712






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-43.7004030094409
beta0.280353991240169
S.D.0.0354861999114489
T-STAT7.90036667605309
p-value2.44624017990008e-05

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -43.7004030094409 \tabularnewline
beta & 0.280353991240169 \tabularnewline
S.D. & 0.0354861999114489 \tabularnewline
T-STAT & 7.90036667605309 \tabularnewline
p-value & 2.44624017990008e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203061&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-43.7004030094409[/C][/ROW]
[ROW][C]beta[/C][C]0.280353991240169[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0354861999114489[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.90036667605309[/C][/ROW]
[ROW][C]p-value[/C][C]2.44624017990008e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203061&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203061&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)
alpha-43.7004030094409
beta0.280353991240169
S.D.0.0354861999114489
T-STAT7.90036667605309
p-value2.44624017990008e-05






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.55345992431631
beta1.3092264850053
S.D.0.171913522810738
T-STAT7.61561082339431
p-value3.27319840874157e-05
Lambda-0.309226485005303

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.55345992431631 \tabularnewline
beta & 1.3092264850053 \tabularnewline
S.D. & 0.171913522810738 \tabularnewline
T-STAT & 7.61561082339431 \tabularnewline
p-value & 3.27319840874157e-05 \tabularnewline
Lambda & -0.309226485005303 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203061&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.55345992431631[/C][/ROW]
[ROW][C]beta[/C][C]1.3092264850053[/C][/ROW]
[ROW][C]S.D.[/C][C]0.171913522810738[/C][/ROW]
[ROW][C]T-STAT[/C][C]7.61561082339431[/C][/ROW]
[ROW][C]p-value[/C][C]3.27319840874157e-05[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.309226485005303[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203061&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203061&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-3.55345992431631
beta1.3092264850053
S.D.0.171913522810738
T-STAT7.61561082339431
p-value3.27319840874157e-05
Lambda-0.309226485005303


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = ; par3 = ; par4 = ; par5 = ; par6 = ; par7 = ; par8 = ; par9 = ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')