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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 22 May 2012 10:57:17 -0400
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/May/22/t1337698782zm606g7oj4wuue2.htm/, Retrieved Fri, 03 May 2024 07:49:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167076, Retrieved Fri, 03 May 2024 07:49:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 Oefening 2] [2012-05-22 14:57:17] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
46,83
45,93
45,93
45,93
45,9
45,91
45,85
45,58
45,56
45,5
45,5
45,5
45,51
45,49
45,4
45,38
45,38
45,38
45,49
45,41
44,99
44,98
44,93
44,93
44,91
44,86
44,76
44,89
44,89
45
45,01
45,11
45,05
44,67
44,48
44,48
44,48
44,58
44,79
44,79
44,41
44,41
44,44
44,43
44,36
44,39
44,39
44,41
44,32
44,43
44,82
44,97
44,91
44,79
44,76
44,8
44,65
44,49
44,56
44,4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167076&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167076&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.918264861346174
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.918264861346174 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167076&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.918264861346174[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167076&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.918264861346174
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1345.5145.7836511752137-0.273651175213672
1445.4945.494102056609-0.00410205660902108
1545.445.39082042202580.0091795779741517
1645.3845.384318179115-0.00431817911496779
1745.3845.3854214201622-0.00542142016217184
1845.3845.3875949270555-0.0075949270554645
1945.4945.33485591227610.155144087723919
2045.4145.24030441633870.169695583661294
2144.9945.376198381134-0.386198381133973
2244.9844.96621778475670.0137822152433245
2344.9344.9831086485863-0.0531086485862815
2444.9344.9377426492827-0.00774264928272572
2544.9144.9150010696239-0.00500106962394398
2644.8644.8941755375624-0.0341755375624473
2744.7644.7643640584056-0.00436405840558507
2844.8944.74432192906510.145678070934856
2944.8944.88307128230680.00692871769317094
304544.89640783493820.103592165061826
3145.0144.95906951582270.0509304841772646
3245.1144.77001169821230.339988301787741
3345.0545.01684341191680.0331565880831874
3444.6745.0246342177063-0.354634217706263
3544.4844.697753882786-0.217753882785985
3644.4844.504907946572-0.0249079465719717
3744.4844.46662816097140.0133718390285509
3844.5844.46028924614410.119710753855848
3944.7944.47422278642190.315777213578052
4044.7944.76041885205630.0295811479436878
4144.4144.7812197827795-0.371219782779455
4244.4144.4552166553295-0.0452166553294759
4344.4444.37692811560150.0630718843985107
4444.4344.22264549998310.207354500016919
4544.3644.32260532143170.0373946785682975
4644.3944.3025916815130.0874083184870429
4744.3944.392811407953-0.00281140795302548
4844.4144.4131018829242-0.00310188292418445
4944.3244.3979746429194-0.0779746429194006
5044.4344.31644708945940.113552910540584
5144.8244.34075161786990.479248382130116
5244.9744.7536652383220.216334761677992
5344.9144.9131959306215-0.00319593062154411
5444.7944.9517820855691-0.161782085569136
5544.7644.7753065860137-0.015306586013665
5644.844.56084473472260.239155265277397
5744.6544.6761143919022-0.0261143919021549
5844.4944.601870475987-0.111870475986976
5944.5644.50172536600020.0582746339997584
6044.444.5780852648033-0.178085264803315

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 45.51 & 45.7836511752137 & -0.273651175213672 \tabularnewline
14 & 45.49 & 45.494102056609 & -0.00410205660902108 \tabularnewline
15 & 45.4 & 45.3908204220258 & 0.0091795779741517 \tabularnewline
16 & 45.38 & 45.384318179115 & -0.00431817911496779 \tabularnewline
17 & 45.38 & 45.3854214201622 & -0.00542142016217184 \tabularnewline
18 & 45.38 & 45.3875949270555 & -0.0075949270554645 \tabularnewline
19 & 45.49 & 45.3348559122761 & 0.155144087723919 \tabularnewline
20 & 45.41 & 45.2403044163387 & 0.169695583661294 \tabularnewline
21 & 44.99 & 45.376198381134 & -0.386198381133973 \tabularnewline
22 & 44.98 & 44.9662177847567 & 0.0137822152433245 \tabularnewline
23 & 44.93 & 44.9831086485863 & -0.0531086485862815 \tabularnewline
24 & 44.93 & 44.9377426492827 & -0.00774264928272572 \tabularnewline
25 & 44.91 & 44.9150010696239 & -0.00500106962394398 \tabularnewline
26 & 44.86 & 44.8941755375624 & -0.0341755375624473 \tabularnewline
27 & 44.76 & 44.7643640584056 & -0.00436405840558507 \tabularnewline
28 & 44.89 & 44.7443219290651 & 0.145678070934856 \tabularnewline
29 & 44.89 & 44.8830712823068 & 0.00692871769317094 \tabularnewline
30 & 45 & 44.8964078349382 & 0.103592165061826 \tabularnewline
31 & 45.01 & 44.9590695158227 & 0.0509304841772646 \tabularnewline
32 & 45.11 & 44.7700116982123 & 0.339988301787741 \tabularnewline
33 & 45.05 & 45.0168434119168 & 0.0331565880831874 \tabularnewline
34 & 44.67 & 45.0246342177063 & -0.354634217706263 \tabularnewline
35 & 44.48 & 44.697753882786 & -0.217753882785985 \tabularnewline
36 & 44.48 & 44.504907946572 & -0.0249079465719717 \tabularnewline
37 & 44.48 & 44.4666281609714 & 0.0133718390285509 \tabularnewline
38 & 44.58 & 44.4602892461441 & 0.119710753855848 \tabularnewline
39 & 44.79 & 44.4742227864219 & 0.315777213578052 \tabularnewline
40 & 44.79 & 44.7604188520563 & 0.0295811479436878 \tabularnewline
41 & 44.41 & 44.7812197827795 & -0.371219782779455 \tabularnewline
42 & 44.41 & 44.4552166553295 & -0.0452166553294759 \tabularnewline
43 & 44.44 & 44.3769281156015 & 0.0630718843985107 \tabularnewline
44 & 44.43 & 44.2226454999831 & 0.207354500016919 \tabularnewline
45 & 44.36 & 44.3226053214317 & 0.0373946785682975 \tabularnewline
46 & 44.39 & 44.302591681513 & 0.0874083184870429 \tabularnewline
47 & 44.39 & 44.392811407953 & -0.00281140795302548 \tabularnewline
48 & 44.41 & 44.4131018829242 & -0.00310188292418445 \tabularnewline
49 & 44.32 & 44.3979746429194 & -0.0779746429194006 \tabularnewline
50 & 44.43 & 44.3164470894594 & 0.113552910540584 \tabularnewline
51 & 44.82 & 44.3407516178699 & 0.479248382130116 \tabularnewline
52 & 44.97 & 44.753665238322 & 0.216334761677992 \tabularnewline
53 & 44.91 & 44.9131959306215 & -0.00319593062154411 \tabularnewline
54 & 44.79 & 44.9517820855691 & -0.161782085569136 \tabularnewline
55 & 44.76 & 44.7753065860137 & -0.015306586013665 \tabularnewline
56 & 44.8 & 44.5608447347226 & 0.239155265277397 \tabularnewline
57 & 44.65 & 44.6761143919022 & -0.0261143919021549 \tabularnewline
58 & 44.49 & 44.601870475987 & -0.111870475986976 \tabularnewline
59 & 44.56 & 44.5017253660002 & 0.0582746339997584 \tabularnewline
60 & 44.4 & 44.5780852648033 & -0.178085264803315 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167076&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]45.51[/C][C]45.7836511752137[/C][C]-0.273651175213672[/C][/ROW]
[ROW][C]14[/C][C]45.49[/C][C]45.494102056609[/C][C]-0.00410205660902108[/C][/ROW]
[ROW][C]15[/C][C]45.4[/C][C]45.3908204220258[/C][C]0.0091795779741517[/C][/ROW]
[ROW][C]16[/C][C]45.38[/C][C]45.384318179115[/C][C]-0.00431817911496779[/C][/ROW]
[ROW][C]17[/C][C]45.38[/C][C]45.3854214201622[/C][C]-0.00542142016217184[/C][/ROW]
[ROW][C]18[/C][C]45.38[/C][C]45.3875949270555[/C][C]-0.0075949270554645[/C][/ROW]
[ROW][C]19[/C][C]45.49[/C][C]45.3348559122761[/C][C]0.155144087723919[/C][/ROW]
[ROW][C]20[/C][C]45.41[/C][C]45.2403044163387[/C][C]0.169695583661294[/C][/ROW]
[ROW][C]21[/C][C]44.99[/C][C]45.376198381134[/C][C]-0.386198381133973[/C][/ROW]
[ROW][C]22[/C][C]44.98[/C][C]44.9662177847567[/C][C]0.0137822152433245[/C][/ROW]
[ROW][C]23[/C][C]44.93[/C][C]44.9831086485863[/C][C]-0.0531086485862815[/C][/ROW]
[ROW][C]24[/C][C]44.93[/C][C]44.9377426492827[/C][C]-0.00774264928272572[/C][/ROW]
[ROW][C]25[/C][C]44.91[/C][C]44.9150010696239[/C][C]-0.00500106962394398[/C][/ROW]
[ROW][C]26[/C][C]44.86[/C][C]44.8941755375624[/C][C]-0.0341755375624473[/C][/ROW]
[ROW][C]27[/C][C]44.76[/C][C]44.7643640584056[/C][C]-0.00436405840558507[/C][/ROW]
[ROW][C]28[/C][C]44.89[/C][C]44.7443219290651[/C][C]0.145678070934856[/C][/ROW]
[ROW][C]29[/C][C]44.89[/C][C]44.8830712823068[/C][C]0.00692871769317094[/C][/ROW]
[ROW][C]30[/C][C]45[/C][C]44.8964078349382[/C][C]0.103592165061826[/C][/ROW]
[ROW][C]31[/C][C]45.01[/C][C]44.9590695158227[/C][C]0.0509304841772646[/C][/ROW]
[ROW][C]32[/C][C]45.11[/C][C]44.7700116982123[/C][C]0.339988301787741[/C][/ROW]
[ROW][C]33[/C][C]45.05[/C][C]45.0168434119168[/C][C]0.0331565880831874[/C][/ROW]
[ROW][C]34[/C][C]44.67[/C][C]45.0246342177063[/C][C]-0.354634217706263[/C][/ROW]
[ROW][C]35[/C][C]44.48[/C][C]44.697753882786[/C][C]-0.217753882785985[/C][/ROW]
[ROW][C]36[/C][C]44.48[/C][C]44.504907946572[/C][C]-0.0249079465719717[/C][/ROW]
[ROW][C]37[/C][C]44.48[/C][C]44.4666281609714[/C][C]0.0133718390285509[/C][/ROW]
[ROW][C]38[/C][C]44.58[/C][C]44.4602892461441[/C][C]0.119710753855848[/C][/ROW]
[ROW][C]39[/C][C]44.79[/C][C]44.4742227864219[/C][C]0.315777213578052[/C][/ROW]
[ROW][C]40[/C][C]44.79[/C][C]44.7604188520563[/C][C]0.0295811479436878[/C][/ROW]
[ROW][C]41[/C][C]44.41[/C][C]44.7812197827795[/C][C]-0.371219782779455[/C][/ROW]
[ROW][C]42[/C][C]44.41[/C][C]44.4552166553295[/C][C]-0.0452166553294759[/C][/ROW]
[ROW][C]43[/C][C]44.44[/C][C]44.3769281156015[/C][C]0.0630718843985107[/C][/ROW]
[ROW][C]44[/C][C]44.43[/C][C]44.2226454999831[/C][C]0.207354500016919[/C][/ROW]
[ROW][C]45[/C][C]44.36[/C][C]44.3226053214317[/C][C]0.0373946785682975[/C][/ROW]
[ROW][C]46[/C][C]44.39[/C][C]44.302591681513[/C][C]0.0874083184870429[/C][/ROW]
[ROW][C]47[/C][C]44.39[/C][C]44.392811407953[/C][C]-0.00281140795302548[/C][/ROW]
[ROW][C]48[/C][C]44.41[/C][C]44.4131018829242[/C][C]-0.00310188292418445[/C][/ROW]
[ROW][C]49[/C][C]44.32[/C][C]44.3979746429194[/C][C]-0.0779746429194006[/C][/ROW]
[ROW][C]50[/C][C]44.43[/C][C]44.3164470894594[/C][C]0.113552910540584[/C][/ROW]
[ROW][C]51[/C][C]44.82[/C][C]44.3407516178699[/C][C]0.479248382130116[/C][/ROW]
[ROW][C]52[/C][C]44.97[/C][C]44.753665238322[/C][C]0.216334761677992[/C][/ROW]
[ROW][C]53[/C][C]44.91[/C][C]44.9131959306215[/C][C]-0.00319593062154411[/C][/ROW]
[ROW][C]54[/C][C]44.79[/C][C]44.9517820855691[/C][C]-0.161782085569136[/C][/ROW]
[ROW][C]55[/C][C]44.76[/C][C]44.7753065860137[/C][C]-0.015306586013665[/C][/ROW]
[ROW][C]56[/C][C]44.8[/C][C]44.5608447347226[/C][C]0.239155265277397[/C][/ROW]
[ROW][C]57[/C][C]44.65[/C][C]44.6761143919022[/C][C]-0.0261143919021549[/C][/ROW]
[ROW][C]58[/C][C]44.49[/C][C]44.601870475987[/C][C]-0.111870475986976[/C][/ROW]
[ROW][C]59[/C][C]44.56[/C][C]44.5017253660002[/C][C]0.0582746339997584[/C][/ROW]
[ROW][C]60[/C][C]44.4[/C][C]44.5780852648033[/C][C]-0.178085264803315[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167076&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167076&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1345.5145.7836511752137-0.273651175213672
1445.4945.494102056609-0.00410205660902108
1545.445.39082042202580.0091795779741517
1645.3845.384318179115-0.00431817911496779
1745.3845.3854214201622-0.00542142016217184
1845.3845.3875949270555-0.0075949270554645
1945.4945.33485591227610.155144087723919
2045.4145.24030441633870.169695583661294
2144.9945.376198381134-0.386198381133973
2244.9844.96621778475670.0137822152433245
2344.9344.9831086485863-0.0531086485862815
2444.9344.9377426492827-0.00774264928272572
2544.9144.9150010696239-0.00500106962394398
2644.8644.8941755375624-0.0341755375624473
2744.7644.7643640584056-0.00436405840558507
2844.8944.74432192906510.145678070934856
2944.8944.88307128230680.00692871769317094
304544.89640783493820.103592165061826
3145.0144.95906951582270.0509304841772646
3245.1144.77001169821230.339988301787741
3345.0545.01684341191680.0331565880831874
3444.6745.0246342177063-0.354634217706263
3544.4844.697753882786-0.217753882785985
3644.4844.504907946572-0.0249079465719717
3744.4844.46662816097140.0133718390285509
3844.5844.46028924614410.119710753855848
3944.7944.47422278642190.315777213578052
4044.7944.76041885205630.0295811479436878
4144.4144.7812197827795-0.371219782779455
4244.4144.4552166553295-0.0452166553294759
4344.4444.37692811560150.0630718843985107
4444.4344.22264549998310.207354500016919
4544.3644.32260532143170.0373946785682975
4644.3944.3025916815130.0874083184870429
4744.3944.392811407953-0.00281140795302548
4844.4144.4131018829242-0.00310188292418445
4944.3244.3979746429194-0.0779746429194006
5044.4344.31644708945940.113552910540584
5144.8244.34075161786990.479248382130116
5244.9744.7536652383220.216334761677992
5344.9144.9131959306215-0.00319593062154411
5444.7944.9517820855691-0.161782085569136
5544.7644.7753065860137-0.015306586013665
5644.844.56084473472260.239155265277397
5744.6544.6761143919022-0.0261143919021549
5844.4944.601870475987-0.111870475986976
5944.5644.50172536600020.0582746339997584
6044.444.5780852648033-0.178085264803315







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6144.396157198479844.06563575612544.7266786408346
6244.401885550826843.953153500108844.8506176015449
6344.351808601659743.810073903835244.8935432994842
6444.303155991723143.682195032956544.9241169504897
6544.246090702512243.554926075380844.9372553296435
6644.274649506885643.519782252805245.0295167609661
6744.258705006969143.445107685950745.0723023279875
6844.07909713045943.210732788576144.9474614723418
6943.953077058918143.033200621705544.8729534961307
7043.89580378603942.927150757744444.8644568143336
7143.912292237329342.897203709805944.9273807648527
7243.915821678321742.856330881667544.9753124749759

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 44.3961571984798 & 44.065635756125 & 44.7266786408346 \tabularnewline
62 & 44.4018855508268 & 43.9531535001088 & 44.8506176015449 \tabularnewline
63 & 44.3518086016597 & 43.8100739038352 & 44.8935432994842 \tabularnewline
64 & 44.3031559917231 & 43.6821950329565 & 44.9241169504897 \tabularnewline
65 & 44.2460907025122 & 43.5549260753808 & 44.9372553296435 \tabularnewline
66 & 44.2746495068856 & 43.5197822528052 & 45.0295167609661 \tabularnewline
67 & 44.2587050069691 & 43.4451076859507 & 45.0723023279875 \tabularnewline
68 & 44.079097130459 & 43.2107327885761 & 44.9474614723418 \tabularnewline
69 & 43.9530770589181 & 43.0332006217055 & 44.8729534961307 \tabularnewline
70 & 43.895803786039 & 42.9271507577444 & 44.8644568143336 \tabularnewline
71 & 43.9122922373293 & 42.8972037098059 & 44.9273807648527 \tabularnewline
72 & 43.9158216783217 & 42.8563308816675 & 44.9753124749759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167076&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]61[/C][C]44.3961571984798[/C][C]44.065635756125[/C][C]44.7266786408346[/C][/ROW]
[ROW][C]62[/C][C]44.4018855508268[/C][C]43.9531535001088[/C][C]44.8506176015449[/C][/ROW]
[ROW][C]63[/C][C]44.3518086016597[/C][C]43.8100739038352[/C][C]44.8935432994842[/C][/ROW]
[ROW][C]64[/C][C]44.3031559917231[/C][C]43.6821950329565[/C][C]44.9241169504897[/C][/ROW]
[ROW][C]65[/C][C]44.2460907025122[/C][C]43.5549260753808[/C][C]44.9372553296435[/C][/ROW]
[ROW][C]66[/C][C]44.2746495068856[/C][C]43.5197822528052[/C][C]45.0295167609661[/C][/ROW]
[ROW][C]67[/C][C]44.2587050069691[/C][C]43.4451076859507[/C][C]45.0723023279875[/C][/ROW]
[ROW][C]68[/C][C]44.079097130459[/C][C]43.2107327885761[/C][C]44.9474614723418[/C][/ROW]
[ROW][C]69[/C][C]43.9530770589181[/C][C]43.0332006217055[/C][C]44.8729534961307[/C][/ROW]
[ROW][C]70[/C][C]43.895803786039[/C][C]42.9271507577444[/C][C]44.8644568143336[/C][/ROW]
[ROW][C]71[/C][C]43.9122922373293[/C][C]42.8972037098059[/C][C]44.9273807648527[/C][/ROW]
[ROW][C]72[/C][C]43.9158216783217[/C][C]42.8563308816675[/C][C]44.9753124749759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167076&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167076&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6144.396157198479844.06563575612544.7266786408346
6244.401885550826843.953153500108844.8506176015449
6344.351808601659743.810073903835244.8935432994842
6444.303155991723143.682195032956544.9241169504897
6544.246090702512243.554926075380844.9372553296435
6644.274649506885643.519782252805245.0295167609661
6744.258705006969143.445107685950745.0723023279875
6844.07909713045943.210732788576144.9474614723418
6943.953077058918143.033200621705544.8729534961307
7043.89580378603942.927150757744444.8644568143336
7143.912292237329342.897203709805944.9273807648527
7243.915821678321742.856330881667544.9753124749759



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
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,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
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,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')