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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 computationMon, 08 Dec 2008 05:17:59 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t12287387033gskq08c44myfbn.htm/, Retrieved Thu, 31 Oct 2024 23:40:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30424, Retrieved Thu, 31 Oct 2024 23:40:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact251
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Univariate Data Series] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
- RMPD  [Standard Deviation-Mean Plot] [Q5] [2008-11-30 14:16:42] [a0d819c22534897f04a2f0b92f1eb36a]
F   P     [Standard Deviation-Mean Plot] [Q5 - 12] [2008-11-30 14:21:22] [a0d819c22534897f04a2f0b92f1eb36a]
-           [Standard Deviation-Mean Plot] [] [2008-12-03 20:14:38] [cb714085b233acee8e8acd879ea442b6]
-               [Standard Deviation-Mean Plot] [Q5] [2008-12-08 12:17:59] [b5110a3ab194da7214bdf478e0a05dbd] [Current]
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Dataseries X:
112
118
132
129
121
135
148
148
136
119
104
118
115
126
141
135
125
149
170
170
158
133
114
140
145
150
178
163
172
178
199
199
184
162
146
166
171
180
193
181
183
218
230
242
209
191
172
194
196
196
236
235
229
243
264
272
237
211
180
201
204
188
235
227
234
264
302
293
259
229
203
229
242
233
267
269
270
315
364
347
312
274
237
278
284
277
317
313
318
374
413
405
355
306
271
306
315
301
356
348
355
422
465
467
404
347
305
336
340
318
362
348
363
435
491
505
404
359
310
337
360
342
406
396
420
472
548
559
463
407
362
405
417
391
419
461
472
535
622
606
508
461
390
432




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30424&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]1 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=30424&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30424&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
1126.66666666666713.720146655281244
2139.66666666666719.070840823020156
3170.16666666666718.438267189996454
419722.966378588156871
522528.466886664397292
6238.91666666666734.9244856364370114
728442.1404577789347131
8328.2547.8617801591207142
9368.41666666666757.8908979081166
1038164.5304720126997195
11428.33333333333369.8300968368398217
12476.16666666666777.7371250179771232

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 126.666666666667 & 13.7201466552812 & 44 \tabularnewline
2 & 139.666666666667 & 19.0708408230201 & 56 \tabularnewline
3 & 170.166666666667 & 18.4382671899964 & 54 \tabularnewline
4 & 197 & 22.9663785881568 & 71 \tabularnewline
5 & 225 & 28.4668866643972 & 92 \tabularnewline
6 & 238.916666666667 & 34.9244856364370 & 114 \tabularnewline
7 & 284 & 42.1404577789347 & 131 \tabularnewline
8 & 328.25 & 47.8617801591207 & 142 \tabularnewline
9 & 368.416666666667 & 57.8908979081 & 166 \tabularnewline
10 & 381 & 64.5304720126997 & 195 \tabularnewline
11 & 428.333333333333 & 69.8300968368398 & 217 \tabularnewline
12 & 476.166666666667 & 77.7371250179771 & 232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30424&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]126.666666666667[/C][C]13.7201466552812[/C][C]44[/C][/ROW]
[ROW][C]2[/C][C]139.666666666667[/C][C]19.0708408230201[/C][C]56[/C][/ROW]
[ROW][C]3[/C][C]170.166666666667[/C][C]18.4382671899964[/C][C]54[/C][/ROW]
[ROW][C]4[/C][C]197[/C][C]22.9663785881568[/C][C]71[/C][/ROW]
[ROW][C]5[/C][C]225[/C][C]28.4668866643972[/C][C]92[/C][/ROW]
[ROW][C]6[/C][C]238.916666666667[/C][C]34.9244856364370[/C][C]114[/C][/ROW]
[ROW][C]7[/C][C]284[/C][C]42.1404577789347[/C][C]131[/C][/ROW]
[ROW][C]8[/C][C]328.25[/C][C]47.8617801591207[/C][C]142[/C][/ROW]
[ROW][C]9[/C][C]368.416666666667[/C][C]57.8908979081[/C][C]166[/C][/ROW]
[ROW][C]10[/C][C]381[/C][C]64.5304720126997[/C][C]195[/C][/ROW]
[ROW][C]11[/C][C]428.333333333333[/C][C]69.8300968368398[/C][C]217[/C][/ROW]
[ROW][C]12[/C][C]476.166666666667[/C][C]77.7371250179771[/C][C]232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30424&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30424&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
SectionMeanStandard DeviationRange
1126.66666666666713.720146655281244
2139.66666666666719.070840823020156
3170.16666666666718.438267189996454
419722.966378588156871
522528.466886664397292
6238.91666666666734.9244856364370114
728442.1404577789347131
8328.2547.8617801591207142
9368.41666666666757.8908979081166
1038164.5304720126997195
11428.33333333333369.8300968368398217
12476.16666666666777.7371250179771232







Regression: S.E.(k) = alpha + beta * Mean(k)
alpha-11.4032541425579
beta0.188613398899484
S.D.0.00657733180244678
T-STAT28.6762785525460
p-value6.19171705602778e-11

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & -11.4032541425579 \tabularnewline
beta & 0.188613398899484 \tabularnewline
S.D. & 0.00657733180244678 \tabularnewline
T-STAT & 28.6762785525460 \tabularnewline
p-value & 6.19171705602778e-11 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30424&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-11.4032541425579[/C][/ROW]
[ROW][C]beta[/C][C]0.188613398899484[/C][/ROW]
[ROW][C]S.D.[/C][C]0.00657733180244678[/C][/ROW]
[ROW][C]T-STAT[/C][C]28.6762785525460[/C][/ROW]
[ROW][C]p-value[/C][C]6.19171705602778e-11[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30424&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30424&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-11.4032541425579
beta0.188613398899484
S.D.0.00657733180244678
T-STAT28.6762785525460
p-value6.19171705602778e-11







Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha-3.70703989322048
beta1.31259253972576
S.D.0.0574958902763332
T-STAT22.8293280340083
p-value5.8658934502011e-10
Lambda-0.312592539725757

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & -3.70703989322048 \tabularnewline
beta & 1.31259253972576 \tabularnewline
S.D. & 0.0574958902763332 \tabularnewline
T-STAT & 22.8293280340083 \tabularnewline
p-value & 5.8658934502011e-10 \tabularnewline
Lambda & -0.312592539725757 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30424&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]-3.70703989322048[/C][/ROW]
[ROW][C]beta[/C][C]1.31259253972576[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0574958902763332[/C][/ROW]
[ROW][C]T-STAT[/C][C]22.8293280340083[/C][/ROW]
[ROW][C]p-value[/C][C]5.8658934502011e-10[/C][/ROW]
[ROW][C]Lambda[/C][C]-0.312592539725757[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30424&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30424&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-3.70703989322048
beta1.31259253972576
S.D.0.0574958902763332
T-STAT22.8293280340083
p-value5.8658934502011e-10
Lambda-0.312592539725757



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')