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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, 21 Dec 2010 17:38:10 +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/21/t1292953085f2k2md9l3rqwp2w.htm/, Retrieved Sun, 19 May 2024 19:51:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113777, Retrieved Sun, 19 May 2024 19:51:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109

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] [paper - SMP] [2010-12-21 17:38:10] [5398da98f4f83c6a353e4d3806d4bcaa] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
631 923
654 294
671 833
586 840
600 969
625 568
558 110
630 577
628 654
603 184
656 255
600 730
670 326
678 423
641 502
625 311
628 177
589 767
582 471
636 248
599 885
621 694
637 406
595 994
696 308
674 201
648 861
649 605
672 392
598 396
613 177
638 104
615 632
634 465
638 686
604 243
706 669
677 185
644 328
644 825
605 707
600 136
612 166
599 659
634 210
618 234
613 576
627 200
668 973
651 479
619 661
644 260
579 936
601 752
595 376
588 902
634 341
594 305
606 200
610 926
633 685
639 696
659 451
593 248
606 677
599 434
569 578
629 873
613 438
604 172
658 328
612 633
707 372
739 770
777 535
685 030
730 234
714 154
630 872
719 492
677 023
679 272
718 317
645 672

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113777&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113777&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113777&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'Gwilym Jenkins' @ 72.249.127.135






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1620744.7532300.6897396803113723
2625600.33333333330151.423642955495952
3640339.16666666730026.685285632697912
4631991.2532524.7289000651107010
5616342.58333333327745.007237857989037
6618351.08333333326751.118975604989873
7702061.91666666740830.5187896111146663

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 620744.75 & 32300.6897396803 & 113723 \tabularnewline
2 & 625600.333333333 & 30151.4236429554 & 95952 \tabularnewline
3 & 640339.166666667 & 30026.6852856326 & 97912 \tabularnewline
4 & 631991.25 & 32524.7289000651 & 107010 \tabularnewline
5 & 616342.583333333 & 27745.0072378579 & 89037 \tabularnewline
6 & 618351.083333333 & 26751.1189756049 & 89873 \tabularnewline
7 & 702061.916666667 & 40830.5187896111 & 146663 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113777&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]620744.75[/C][C]32300.6897396803[/C][C]113723[/C][/ROW]
[ROW][C]2[/C][C]625600.333333333[/C][C]30151.4236429554[/C][C]95952[/C][/ROW]
[ROW][C]3[/C][C]640339.166666667[/C][C]30026.6852856326[/C][C]97912[/C][/ROW]
[ROW][C]4[/C][C]631991.25[/C][C]32524.7289000651[/C][C]107010[/C][/ROW]
[ROW][C]5[/C][C]616342.583333333[/C][C]27745.0072378579[/C][C]89037[/C][/ROW]
[ROW][C]6[/C][C]618351.083333333[/C][C]26751.1189756049[/C][C]89873[/C][/ROW]
[ROW][C]7[/C][C]702061.916666667[/C][C]40830.5187896111[/C][C]146663[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113777&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113777&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
1620744.7532300.6897396803113723
2625600.33333333330151.423642955495952
3640339.16666666730026.685285632697912
4631991.2532524.7289000651107010
5616342.58333333327745.007237857989037
6618351.08333333326751.118975604989873
7702061.91666666740830.5187896111146663






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-58141.8470194089
beta0.140799642048988
S.D.0.0282012945739423
T-STAT4.99266591041836
p-value0.00413058919420224

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -58141.8470194089 \tabularnewline
beta & 0.140799642048988 \tabularnewline
S.D. & 0.0282012945739423 \tabularnewline
T-STAT & 4.99266591041836 \tabularnewline
p-value & 0.00413058919420224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113777&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-58141.8470194089[/C][/ROW]
[ROW][C]beta[/C][C]0.140799642048988[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0282012945739423[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.99266591041836[/C][/ROW]
[ROW][C]p-value[/C][C]0.00413058919420224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113777&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113777&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-58141.8470194089
beta0.140799642048988
S.D.0.0282012945739423
T-STAT4.99266591041836
p-value0.00413058919420224






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-25.8076850274140
beta2.70572414502969
S.D.0.619014557228938
T-STAT4.37101860276445
p-value0.00721515956925357
Lambda-1.70572414502969

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -25.8076850274140 \tabularnewline
beta & 2.70572414502969 \tabularnewline
S.D. & 0.619014557228938 \tabularnewline
T-STAT & 4.37101860276445 \tabularnewline
p-value & 0.00721515956925357 \tabularnewline
Lambda & -1.70572414502969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113777&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-25.8076850274140[/C][/ROW]
[ROW][C]beta[/C][C]2.70572414502969[/C][/ROW]
[ROW][C]S.D.[/C][C]0.619014557228938[/C][/ROW]
[ROW][C]T-STAT[/C][C]4.37101860276445[/C][/ROW]
[ROW][C]p-value[/C][C]0.00721515956925357[/C][/ROW]
[ROW][C]Lambda[/C][C]-1.70572414502969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113777&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113777&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-25.8076850274140
beta2.70572414502969
S.D.0.619014557228938
T-STAT4.37101860276445
p-value0.00721515956925357
Lambda-1.70572414502969


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')