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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 computationSun, 07 Dec 2008 06:12:10 -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/07/t1228655562qqe8dtu75dsvch0.htm/, Retrieved Sun, 19 May 2024 10:08:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29928, Retrieved Sun, 19 May 2024 10:08:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact256

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] [Airline data] [2007-10-18 09:58:47] [42daae401fd3def69a25014f2252b4c2]
F RMPD  [Variance Reduction Matrix] [] [2008-11-30 18:13:06] [b745fd448f60064800b631a75a630267]
F RM D      [Standard Deviation-Mean Plot] [SMP Q1] [2008-12-07 13:12:10] [55ca0ca4a201c9689dcf5fae352c92eb] [Current]
F RM          [Variance Reduction Matrix] [VRM Q1] [2008-12-07 13:13:31] [e5d91604aae608e98a8ea24759233f66]
F RMP           [(Partial) Autocorrelation Function] [ACF Q2] [2008-12-07 13:20:49] [e5d91604aae608e98a8ea24759233f66]
- RMP             [Spectral Analysis] [Spectral Q2] [2008-12-07 13:23:21] [e5d91604aae608e98a8ea24759233f66]
F   P               [Spectral Analysis] [Spectral Q3] [2008-12-07 13:28:29] [e5d91604aae608e98a8ea24759233f66]
-   P                 [Spectral Analysis] [spectrum aangepast] [2008-12-18 14:46:11] [e5d91604aae608e98a8ea24759233f66]
-                   [Spectral Analysis] [spectrum] [2008-12-18 14:39:41] [e5d91604aae608e98a8ea24759233f66]
-    D                [Spectral Analysis] [spectrum zonder d...] [2008-12-18 15:10:35] [e5d91604aae608e98a8ea24759233f66]
-    D                  [Spectral Analysis] [spectrum aangepast] [2008-12-18 15:14:31] [e5d91604aae608e98a8ea24759233f66]
F   P             [(Partial) Autocorrelation Function] [ACF Q3] [2008-12-07 13:30:19] [e5d91604aae608e98a8ea24759233f66]
F RMP             [ARIMA Backward Selection] [ARMA Q5] [2008-12-07 13:46:58] [e5d91604aae608e98a8ea24759233f66]
-   P               [ARIMA Backward Selection] [ARIMA] [2008-12-10 17:52:14] [e5d91604aae608e98a8ea24759233f66]
- RMPD              [Histogram] [Histogram inflatie] [2008-12-10 18:06:14] [e5d91604aae608e98a8ea24759233f66]
- RMPD              [Variance Reduction Matrix] [VRM werkloosheid] [2008-12-10 18:11:05] [e5d91604aae608e98a8ea24759233f66]
- RMPD              [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-10 18:14:21] [e5d91604aae608e98a8ea24759233f66]
-   PD              [ARIMA Backward Selection] [ARIMA Inflatie op...] [2008-12-10 18:24:04] [e5d91604aae608e98a8ea24759233f66]
-   PD              [ARIMA Backward Selection] [ARIMA Inflatie op...] [2008-12-10 18:32:43] [e5d91604aae608e98a8ea24759233f66]
-   P                 [ARIMA Backward Selection] [Arima backward 1] [2008-12-18 15:19:24] [e5d91604aae608e98a8ea24759233f66]
F RMPD              [ARIMA Forecasting] [Forecasting Infla...] [2008-12-10 18:36:07] [e5d91604aae608e98a8ea24759233f66]
-   P                 [ARIMA Forecasting] [Forecasting] [2008-12-18 16:01:41] [e5d91604aae608e98a8ea24759233f66]
-   P             [(Partial) Autocorrelation Function] [Verbetering works...] [2008-12-15 09:55:17] [cf9c64468d04c2c4dd548cc66b4e3677]
-   PD          [Variance Reduction Matrix] [vrm] [2008-12-18 15:08:52] [e5d91604aae608e98a8ea24759233f66]
-   PD        [Standard Deviation-Mean Plot] [SMP] [2008-12-18 15:00:29] [e5d91604aae608e98a8ea24759233f66]
Feedback Forum
2008-12-14 14:18:45 [Dana Molenberghs] [reply] 
Ik mag de lambda niet toepassen omdat de p-value groter is dan beta. Beta verschilt dus niet significant van nul. En dit moet
2008-12-15 09:49:11 [Jan Van Riet] [reply] 
Volgens mij mag je deze lambda-waarde wel aflezen. Je model voldoet immers aan de 2 vooropgestelde voorwaarden:

-er zijn geen grote outliers: dit is wél het geval, maar die éne grote outlier ligt pal in het midden van de scatterplot, dus levert dit geen problemen op voor de verdere berekening;
-de B-waarde is significant verschillend van 0.

Aan deze voorwaarden wordt voldaan, dus je mag de lambda waarde instellen op 1,30.
2008-12-15 20:02:20 [Jeroen Aerts] [reply] 
De p-value duidt aan of er een significant verschil is ten opzichte van 0, de p-value hoort dus zo laag mogelijk te liggen. Dit is hier echter niet het geval ( bij de berekening bij de werkloosheid ligt deze ongeveer op 0.003, is dus wel significant verschillend van 0). Ik zou de lambda-waarde alsnog gebruiken, aangezien je geen uitzonderlijke lambdawaarde bekomt.

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
19
23
22
23
25
25
23
22
21
16
21
21
26
23
22
22
22
12
20
18
23
25
28
28
29
31
33
32
33
35
33
36
30
34
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35
33
28
27
23
23
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24
20
16
6
2
12
19
21
22
20
21
20
19
17
17
17
16
12
11
7
2
9
11
10
7
9
15
5
14
14
17
19
17
16
14
20
16
18
18
14
13
14
14
17
18
15
9
9
9
10
6
12
11
15
19
18
15
16
14
18
18
18
18
22
21
12
19
21
19
22
22
21
19
18
18
19
12
16

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29928&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29928&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29928&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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
121.752.490892501603689
222.41666666666674.4406865426076816
332.91666666666672.108783937953277
419.83333333333339.2030956583624531
518.41666666666672.7784342658585610
69.53.8729833462074213
716.33333333333332.229281716090857
812.08333333333333.7040109300185612
917.41666666666672.8109633849474410
1018.83333333333332.7906771199618910

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 21.75 & 2.49089250160368 & 9 \tabularnewline
2 & 22.4166666666667 & 4.44068654260768 & 16 \tabularnewline
3 & 32.9166666666667 & 2.10878393795327 & 7 \tabularnewline
4 & 19.8333333333333 & 9.20309565836245 & 31 \tabularnewline
5 & 18.4166666666667 & 2.77843426585856 & 10 \tabularnewline
6 & 9.5 & 3.87298334620742 & 13 \tabularnewline
7 & 16.3333333333333 & 2.22928171609085 & 7 \tabularnewline
8 & 12.0833333333333 & 3.70401093001856 & 12 \tabularnewline
9 & 17.4166666666667 & 2.81096338494744 & 10 \tabularnewline
10 & 18.8333333333333 & 2.79067711996189 & 10 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29928&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]21.75[/C][C]2.49089250160368[/C][C]9[/C][/ROW]
[ROW][C]2[/C][C]22.4166666666667[/C][C]4.44068654260768[/C][C]16[/C][/ROW]
[ROW][C]3[/C][C]32.9166666666667[/C][C]2.10878393795327[/C][C]7[/C][/ROW]
[ROW][C]4[/C][C]19.8333333333333[/C][C]9.20309565836245[/C][C]31[/C][/ROW]
[ROW][C]5[/C][C]18.4166666666667[/C][C]2.77843426585856[/C][C]10[/C][/ROW]
[ROW][C]6[/C][C]9.5[/C][C]3.87298334620742[/C][C]13[/C][/ROW]
[ROW][C]7[/C][C]16.3333333333333[/C][C]2.22928171609085[/C][C]7[/C][/ROW]
[ROW][C]8[/C][C]12.0833333333333[/C][C]3.70401093001856[/C][C]12[/C][/ROW]
[ROW][C]9[/C][C]17.4166666666667[/C][C]2.81096338494744[/C][C]10[/C][/ROW]
[ROW][C]10[/C][C]18.8333333333333[/C][C]2.79067711996189[/C][C]10[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29928&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29928&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
121.752.490892501603689
222.41666666666674.4406865426076816
332.91666666666672.108783937953277
419.83333333333339.2030956583624531
518.41666666666672.7784342658585610
69.53.8729833462074213
716.33333333333332.229281716090857
812.08333333333333.7040109300185612
917.41666666666672.8109633849474410
1018.83333333333332.7906771199618910






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha4.37832187182896
beta-0.0388042707898563
S.D.0.115966471013810
T-STAT-0.334616294266947
p-value0.746518681991706

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 4.37832187182896 \tabularnewline
beta & -0.0388042707898563 \tabularnewline
S.D. & 0.115966471013810 \tabularnewline
T-STAT & -0.334616294266947 \tabularnewline
p-value & 0.746518681991706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29928&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]4.37832187182896[/C][/ROW]
[ROW][C]beta[/C][C]-0.0388042707898563[/C][/ROW]
[ROW][C]S.D.[/C][C]0.115966471013810[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.334616294266947[/C][/ROW]
[ROW][C]p-value[/C][C]0.746518681991706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29928&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29928&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)
alpha4.37832187182896
beta-0.0388042707898563
S.D.0.115966471013810
T-STAT-0.334616294266947
p-value0.746518681991706






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.95856350980925
beta-0.265265020379939
S.D.0.442059925596924
T-STAT-0.600065749053696
p-value0.565068345967237
Lambda1.26526502037994

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.95856350980925 \tabularnewline
beta & -0.265265020379939 \tabularnewline
S.D. & 0.442059925596924 \tabularnewline
T-STAT & -0.600065749053696 \tabularnewline
p-value & 0.565068345967237 \tabularnewline
Lambda & 1.26526502037994 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29928&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.95856350980925[/C][/ROW]
[ROW][C]beta[/C][C]-0.265265020379939[/C][/ROW]
[ROW][C]S.D.[/C][C]0.442059925596924[/C][/ROW]
[ROW][C]T-STAT[/C][C]-0.600065749053696[/C][/ROW]
[ROW][C]p-value[/C][C]0.565068345967237[/C][/ROW]
[ROW][C]Lambda[/C][C]1.26526502037994[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29928&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29928&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)
alpha1.95856350980925
beta-0.265265020379939
S.D.0.442059925596924
T-STAT-0.600065749053696
p-value0.565068345967237
Lambda1.26526502037994


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')