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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Dec 2016 12:48:52 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/23/t1482493744qgxg64ox2kakr5r.htm/, Retrieved Fri, 01 Nov 2024 03:31:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302878, Retrieved Fri, 01 Nov 2024 03:31:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2797] [2016-12-23 11:48:52] [8e56909c70ba580a071e942d9a393c42] [Current]
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Dataseries X:
3560
5360
5720
7360
7400
9120
9400
9680
9600
6920
4560
3840
4160
3760
3840
6120
7080
8840
9320
9600
8400
7040
4320
2520
1160
1680
5040
6360
7280
8880
9920
8800
8400
6760
6040
2400
2560
4680
4440
6400
8120
9080
10320
9960
9240
6000
4960
3320
3640
2880
5040
6000
7560
8960
8760
9040
7640
6720
4520
4640
2880
5640
5160
6920
7760
9680
9280
9320
8960
7280
4400
4600
3720
4680
5480
5920
7480
8720




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302878&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=302878&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302878&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.230011374848214
beta0.0253364109758321
gamma0.33918727294815

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.230011374848214 \tabularnewline
beta & 0.0253364109758321 \tabularnewline
gamma & 0.33918727294815 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302878&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]0.230011374848214[/C][/ROW]
[ROW][C]beta[/C][C]0.0253364109758321[/C][/ROW]
[ROW][C]gamma[/C][C]0.33918727294815[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302878&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302878&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
alpha0.230011374848214
beta0.0253364109758321
gamma0.33918727294815







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1341604555.64102564103-395.641025641026
1437604018.88354348056-258.883543480564
1538404038.73981850353-198.739818503525
1661206262.93831243189-142.938312431892
1770807139.13879121545-59.1387912154505
1888408894.26947215662-54.2694721566186
1993208788.53722102257531.462778977428
2096009178.96056942346421.039430576537
2184009289.77230077083-889.772300770832
2270406478.89713075531561.102869244688
2343204260.0096716026659.9903283973445
2425203526.21023137652-1006.21023137652
2511603467.97897871412-2307.97897871412
2616802507.58935069567-827.589350695672
2750402389.540690224132650.45930977587
2863605277.461374723371082.53862527663
2972806458.36338810967821.636611890328
3088808423.42896386172456.571036138284
3199208597.223550571631322.77644942837
3288009154.48206763862-354.482067638615
3384008753.71373415465-353.713734154646
3467606457.33151420166302.668485798344
3560404058.887222977741981.11277702226
3624003510.46523671953-1110.46523671953
3725603109.62059814066-549.620598140663
3846802971.904223794171708.09577620583
3944404391.8292209511548.1707790488545
4064006302.9083789131197.0916210868891
4181207214.47246871252905.527531287482
4290809129.44446163944-49.4444616394394
43103209436.08285708612883.917142913882
4499609474.79700228061485.202997719385
4592409292.70829344391-52.7082934439059
4660007264.08431818336-1264.08431818336
4749604961.59442365996-1.59442365995801
4833203156.10968602551163.890313974493
4936403208.69476493121431.30523506879
5028803905.80501174427-1025.80501174427
5150404267.00026319983772.999736800171
5260006365.42077038498-365.420770384981
5375607386.89163711684173.108362883157
5489608884.8706411624175.1293588375938
5587609465.5368889458-705.536888945797
5690409026.8715025359913.1284974640148
5776408585.30800720585-945.308007205847
5867206019.39287808674700.607121913261
5945204494.3712635243725.6287364756336
6046402734.368498484291905.63150151571
6128803263.56561973137-383.565619731367
6256403394.094437737472245.90556226253
6351604998.08333175615161.916668243847
6469206675.5334670367244.466532963297
6577607998.39476431469-238.394764314686
6696809394.19763239861285.802367601391
6792809838.72540298735-558.725402987347
6893209641.66918616962-321.669186169618
6989608890.9789108081169.0210891918887
7072807012.34208183762267.65791816238
7144005233.03666101914-833.03666101914
7246003783.11181116468816.888188835318
7337203474.25012115829245.749878841712
7446804450.1709184054229.829081594604
7554805048.31655185894431.683448141061
7659206813.10115593432-893.101155934322
7774807745.29599862326-265.29599862326
7887209268.75535334828-548.755353348279

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4160 & 4555.64102564103 & -395.641025641026 \tabularnewline
14 & 3760 & 4018.88354348056 & -258.883543480564 \tabularnewline
15 & 3840 & 4038.73981850353 & -198.739818503525 \tabularnewline
16 & 6120 & 6262.93831243189 & -142.938312431892 \tabularnewline
17 & 7080 & 7139.13879121545 & -59.1387912154505 \tabularnewline
18 & 8840 & 8894.26947215662 & -54.2694721566186 \tabularnewline
19 & 9320 & 8788.53722102257 & 531.462778977428 \tabularnewline
20 & 9600 & 9178.96056942346 & 421.039430576537 \tabularnewline
21 & 8400 & 9289.77230077083 & -889.772300770832 \tabularnewline
22 & 7040 & 6478.89713075531 & 561.102869244688 \tabularnewline
23 & 4320 & 4260.00967160266 & 59.9903283973445 \tabularnewline
24 & 2520 & 3526.21023137652 & -1006.21023137652 \tabularnewline
25 & 1160 & 3467.97897871412 & -2307.97897871412 \tabularnewline
26 & 1680 & 2507.58935069567 & -827.589350695672 \tabularnewline
27 & 5040 & 2389.54069022413 & 2650.45930977587 \tabularnewline
28 & 6360 & 5277.46137472337 & 1082.53862527663 \tabularnewline
29 & 7280 & 6458.36338810967 & 821.636611890328 \tabularnewline
30 & 8880 & 8423.42896386172 & 456.571036138284 \tabularnewline
31 & 9920 & 8597.22355057163 & 1322.77644942837 \tabularnewline
32 & 8800 & 9154.48206763862 & -354.482067638615 \tabularnewline
33 & 8400 & 8753.71373415465 & -353.713734154646 \tabularnewline
34 & 6760 & 6457.33151420166 & 302.668485798344 \tabularnewline
35 & 6040 & 4058.88722297774 & 1981.11277702226 \tabularnewline
36 & 2400 & 3510.46523671953 & -1110.46523671953 \tabularnewline
37 & 2560 & 3109.62059814066 & -549.620598140663 \tabularnewline
38 & 4680 & 2971.90422379417 & 1708.09577620583 \tabularnewline
39 & 4440 & 4391.82922095115 & 48.1707790488545 \tabularnewline
40 & 6400 & 6302.90837891311 & 97.0916210868891 \tabularnewline
41 & 8120 & 7214.47246871252 & 905.527531287482 \tabularnewline
42 & 9080 & 9129.44446163944 & -49.4444616394394 \tabularnewline
43 & 10320 & 9436.08285708612 & 883.917142913882 \tabularnewline
44 & 9960 & 9474.79700228061 & 485.202997719385 \tabularnewline
45 & 9240 & 9292.70829344391 & -52.7082934439059 \tabularnewline
46 & 6000 & 7264.08431818336 & -1264.08431818336 \tabularnewline
47 & 4960 & 4961.59442365996 & -1.59442365995801 \tabularnewline
48 & 3320 & 3156.10968602551 & 163.890313974493 \tabularnewline
49 & 3640 & 3208.69476493121 & 431.30523506879 \tabularnewline
50 & 2880 & 3905.80501174427 & -1025.80501174427 \tabularnewline
51 & 5040 & 4267.00026319983 & 772.999736800171 \tabularnewline
52 & 6000 & 6365.42077038498 & -365.420770384981 \tabularnewline
53 & 7560 & 7386.89163711684 & 173.108362883157 \tabularnewline
54 & 8960 & 8884.87064116241 & 75.1293588375938 \tabularnewline
55 & 8760 & 9465.5368889458 & -705.536888945797 \tabularnewline
56 & 9040 & 9026.87150253599 & 13.1284974640148 \tabularnewline
57 & 7640 & 8585.30800720585 & -945.308007205847 \tabularnewline
58 & 6720 & 6019.39287808674 & 700.607121913261 \tabularnewline
59 & 4520 & 4494.37126352437 & 25.6287364756336 \tabularnewline
60 & 4640 & 2734.36849848429 & 1905.63150151571 \tabularnewline
61 & 2880 & 3263.56561973137 & -383.565619731367 \tabularnewline
62 & 5640 & 3394.09443773747 & 2245.90556226253 \tabularnewline
63 & 5160 & 4998.08333175615 & 161.916668243847 \tabularnewline
64 & 6920 & 6675.5334670367 & 244.466532963297 \tabularnewline
65 & 7760 & 7998.39476431469 & -238.394764314686 \tabularnewline
66 & 9680 & 9394.19763239861 & 285.802367601391 \tabularnewline
67 & 9280 & 9838.72540298735 & -558.725402987347 \tabularnewline
68 & 9320 & 9641.66918616962 & -321.669186169618 \tabularnewline
69 & 8960 & 8890.97891080811 & 69.0210891918887 \tabularnewline
70 & 7280 & 7012.34208183762 & 267.65791816238 \tabularnewline
71 & 4400 & 5233.03666101914 & -833.03666101914 \tabularnewline
72 & 4600 & 3783.11181116468 & 816.888188835318 \tabularnewline
73 & 3720 & 3474.25012115829 & 245.749878841712 \tabularnewline
74 & 4680 & 4450.1709184054 & 229.829081594604 \tabularnewline
75 & 5480 & 5048.31655185894 & 431.683448141061 \tabularnewline
76 & 5920 & 6813.10115593432 & -893.101155934322 \tabularnewline
77 & 7480 & 7745.29599862326 & -265.29599862326 \tabularnewline
78 & 8720 & 9268.75535334828 & -548.755353348279 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302878&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]4160[/C][C]4555.64102564103[/C][C]-395.641025641026[/C][/ROW]
[ROW][C]14[/C][C]3760[/C][C]4018.88354348056[/C][C]-258.883543480564[/C][/ROW]
[ROW][C]15[/C][C]3840[/C][C]4038.73981850353[/C][C]-198.739818503525[/C][/ROW]
[ROW][C]16[/C][C]6120[/C][C]6262.93831243189[/C][C]-142.938312431892[/C][/ROW]
[ROW][C]17[/C][C]7080[/C][C]7139.13879121545[/C][C]-59.1387912154505[/C][/ROW]
[ROW][C]18[/C][C]8840[/C][C]8894.26947215662[/C][C]-54.2694721566186[/C][/ROW]
[ROW][C]19[/C][C]9320[/C][C]8788.53722102257[/C][C]531.462778977428[/C][/ROW]
[ROW][C]20[/C][C]9600[/C][C]9178.96056942346[/C][C]421.039430576537[/C][/ROW]
[ROW][C]21[/C][C]8400[/C][C]9289.77230077083[/C][C]-889.772300770832[/C][/ROW]
[ROW][C]22[/C][C]7040[/C][C]6478.89713075531[/C][C]561.102869244688[/C][/ROW]
[ROW][C]23[/C][C]4320[/C][C]4260.00967160266[/C][C]59.9903283973445[/C][/ROW]
[ROW][C]24[/C][C]2520[/C][C]3526.21023137652[/C][C]-1006.21023137652[/C][/ROW]
[ROW][C]25[/C][C]1160[/C][C]3467.97897871412[/C][C]-2307.97897871412[/C][/ROW]
[ROW][C]26[/C][C]1680[/C][C]2507.58935069567[/C][C]-827.589350695672[/C][/ROW]
[ROW][C]27[/C][C]5040[/C][C]2389.54069022413[/C][C]2650.45930977587[/C][/ROW]
[ROW][C]28[/C][C]6360[/C][C]5277.46137472337[/C][C]1082.53862527663[/C][/ROW]
[ROW][C]29[/C][C]7280[/C][C]6458.36338810967[/C][C]821.636611890328[/C][/ROW]
[ROW][C]30[/C][C]8880[/C][C]8423.42896386172[/C][C]456.571036138284[/C][/ROW]
[ROW][C]31[/C][C]9920[/C][C]8597.22355057163[/C][C]1322.77644942837[/C][/ROW]
[ROW][C]32[/C][C]8800[/C][C]9154.48206763862[/C][C]-354.482067638615[/C][/ROW]
[ROW][C]33[/C][C]8400[/C][C]8753.71373415465[/C][C]-353.713734154646[/C][/ROW]
[ROW][C]34[/C][C]6760[/C][C]6457.33151420166[/C][C]302.668485798344[/C][/ROW]
[ROW][C]35[/C][C]6040[/C][C]4058.88722297774[/C][C]1981.11277702226[/C][/ROW]
[ROW][C]36[/C][C]2400[/C][C]3510.46523671953[/C][C]-1110.46523671953[/C][/ROW]
[ROW][C]37[/C][C]2560[/C][C]3109.62059814066[/C][C]-549.620598140663[/C][/ROW]
[ROW][C]38[/C][C]4680[/C][C]2971.90422379417[/C][C]1708.09577620583[/C][/ROW]
[ROW][C]39[/C][C]4440[/C][C]4391.82922095115[/C][C]48.1707790488545[/C][/ROW]
[ROW][C]40[/C][C]6400[/C][C]6302.90837891311[/C][C]97.0916210868891[/C][/ROW]
[ROW][C]41[/C][C]8120[/C][C]7214.47246871252[/C][C]905.527531287482[/C][/ROW]
[ROW][C]42[/C][C]9080[/C][C]9129.44446163944[/C][C]-49.4444616394394[/C][/ROW]
[ROW][C]43[/C][C]10320[/C][C]9436.08285708612[/C][C]883.917142913882[/C][/ROW]
[ROW][C]44[/C][C]9960[/C][C]9474.79700228061[/C][C]485.202997719385[/C][/ROW]
[ROW][C]45[/C][C]9240[/C][C]9292.70829344391[/C][C]-52.7082934439059[/C][/ROW]
[ROW][C]46[/C][C]6000[/C][C]7264.08431818336[/C][C]-1264.08431818336[/C][/ROW]
[ROW][C]47[/C][C]4960[/C][C]4961.59442365996[/C][C]-1.59442365995801[/C][/ROW]
[ROW][C]48[/C][C]3320[/C][C]3156.10968602551[/C][C]163.890313974493[/C][/ROW]
[ROW][C]49[/C][C]3640[/C][C]3208.69476493121[/C][C]431.30523506879[/C][/ROW]
[ROW][C]50[/C][C]2880[/C][C]3905.80501174427[/C][C]-1025.80501174427[/C][/ROW]
[ROW][C]51[/C][C]5040[/C][C]4267.00026319983[/C][C]772.999736800171[/C][/ROW]
[ROW][C]52[/C][C]6000[/C][C]6365.42077038498[/C][C]-365.420770384981[/C][/ROW]
[ROW][C]53[/C][C]7560[/C][C]7386.89163711684[/C][C]173.108362883157[/C][/ROW]
[ROW][C]54[/C][C]8960[/C][C]8884.87064116241[/C][C]75.1293588375938[/C][/ROW]
[ROW][C]55[/C][C]8760[/C][C]9465.5368889458[/C][C]-705.536888945797[/C][/ROW]
[ROW][C]56[/C][C]9040[/C][C]9026.87150253599[/C][C]13.1284974640148[/C][/ROW]
[ROW][C]57[/C][C]7640[/C][C]8585.30800720585[/C][C]-945.308007205847[/C][/ROW]
[ROW][C]58[/C][C]6720[/C][C]6019.39287808674[/C][C]700.607121913261[/C][/ROW]
[ROW][C]59[/C][C]4520[/C][C]4494.37126352437[/C][C]25.6287364756336[/C][/ROW]
[ROW][C]60[/C][C]4640[/C][C]2734.36849848429[/C][C]1905.63150151571[/C][/ROW]
[ROW][C]61[/C][C]2880[/C][C]3263.56561973137[/C][C]-383.565619731367[/C][/ROW]
[ROW][C]62[/C][C]5640[/C][C]3394.09443773747[/C][C]2245.90556226253[/C][/ROW]
[ROW][C]63[/C][C]5160[/C][C]4998.08333175615[/C][C]161.916668243847[/C][/ROW]
[ROW][C]64[/C][C]6920[/C][C]6675.5334670367[/C][C]244.466532963297[/C][/ROW]
[ROW][C]65[/C][C]7760[/C][C]7998.39476431469[/C][C]-238.394764314686[/C][/ROW]
[ROW][C]66[/C][C]9680[/C][C]9394.19763239861[/C][C]285.802367601391[/C][/ROW]
[ROW][C]67[/C][C]9280[/C][C]9838.72540298735[/C][C]-558.725402987347[/C][/ROW]
[ROW][C]68[/C][C]9320[/C][C]9641.66918616962[/C][C]-321.669186169618[/C][/ROW]
[ROW][C]69[/C][C]8960[/C][C]8890.97891080811[/C][C]69.0210891918887[/C][/ROW]
[ROW][C]70[/C][C]7280[/C][C]7012.34208183762[/C][C]267.65791816238[/C][/ROW]
[ROW][C]71[/C][C]4400[/C][C]5233.03666101914[/C][C]-833.03666101914[/C][/ROW]
[ROW][C]72[/C][C]4600[/C][C]3783.11181116468[/C][C]816.888188835318[/C][/ROW]
[ROW][C]73[/C][C]3720[/C][C]3474.25012115829[/C][C]245.749878841712[/C][/ROW]
[ROW][C]74[/C][C]4680[/C][C]4450.1709184054[/C][C]229.829081594604[/C][/ROW]
[ROW][C]75[/C][C]5480[/C][C]5048.31655185894[/C][C]431.683448141061[/C][/ROW]
[ROW][C]76[/C][C]5920[/C][C]6813.10115593432[/C][C]-893.101155934322[/C][/ROW]
[ROW][C]77[/C][C]7480[/C][C]7745.29599862326[/C][C]-265.29599862326[/C][/ROW]
[ROW][C]78[/C][C]8720[/C][C]9268.75535334828[/C][C]-548.755353348279[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302878&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302878&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
1341604555.64102564103-395.641025641026
1437604018.88354348056-258.883543480564
1538404038.73981850353-198.739818503525
1661206262.93831243189-142.938312431892
1770807139.13879121545-59.1387912154505
1888408894.26947215662-54.2694721566186
1993208788.53722102257531.462778977428
2096009178.96056942346421.039430576537
2184009289.77230077083-889.772300770832
2270406478.89713075531561.102869244688
2343204260.0096716026659.9903283973445
2425203526.21023137652-1006.21023137652
2511603467.97897871412-2307.97897871412
2616802507.58935069567-827.589350695672
2750402389.540690224132650.45930977587
2863605277.461374723371082.53862527663
2972806458.36338810967821.636611890328
3088808423.42896386172456.571036138284
3199208597.223550571631322.77644942837
3288009154.48206763862-354.482067638615
3384008753.71373415465-353.713734154646
3467606457.33151420166302.668485798344
3560404058.887222977741981.11277702226
3624003510.46523671953-1110.46523671953
3725603109.62059814066-549.620598140663
3846802971.904223794171708.09577620583
3944404391.8292209511548.1707790488545
4064006302.9083789131197.0916210868891
4181207214.47246871252905.527531287482
4290809129.44446163944-49.4444616394394
43103209436.08285708612883.917142913882
4499609474.79700228061485.202997719385
4592409292.70829344391-52.7082934439059
4660007264.08431818336-1264.08431818336
4749604961.59442365996-1.59442365995801
4833203156.10968602551163.890313974493
4936403208.69476493121431.30523506879
5028803905.80501174427-1025.80501174427
5150404267.00026319983772.999736800171
5260006365.42077038498-365.420770384981
5375607386.89163711684173.108362883157
5489608884.8706411624175.1293588375938
5587609465.5368889458-705.536888945797
5690409026.8715025359913.1284974640148
5776408585.30800720585-945.308007205847
5867206019.39287808674700.607121913261
5945204494.3712635243725.6287364756336
6046402734.368498484291905.63150151571
6128803263.56561973137-383.565619731367
6256403394.094437737472245.90556226253
6351604998.08333175615161.916668243847
6469206675.5334670367244.466532963297
6577607998.39476431469-238.394764314686
6696809394.19763239861285.802367601391
6792809838.72540298735-558.725402987347
6893209641.66918616962-321.669186169618
6989608890.9789108081169.0210891918887
7072807012.34208183762267.65791816238
7144005233.03666101914-833.03666101914
7246003783.11181116468816.888188835318
7337203474.25012115829245.749878841712
7446804450.1709184054229.829081594604
7554805048.31655185894431.683448141061
7659206813.10115593432-893.101155934322
7774807745.29599862326-265.29599862326
7887209268.75535334828-548.755353348279







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
799292.835559915747617.2520857835210968.419034048
809281.536469025547559.9855048671811003.0874331839
818704.076932377696935.5441400836410472.6097246717
826858.246738846845041.743993301878674.7494843918
834725.152575074362859.716866247466590.58828390126
843897.846129307681982.538473834375813.15378478099
853247.264986445141281.169358371625213.36061451865
864156.408839007982138.631127087066174.18655092889
874746.976539869182676.643536892946817.30954284541
886056.525883428773932.784311507628180.26745534991
897353.364221777955175.379796186659531.34864736924
908860.615536164596627.5720693323911093.6590029968

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
79 & 9292.83555991574 & 7617.25208578352 & 10968.419034048 \tabularnewline
80 & 9281.53646902554 & 7559.98550486718 & 11003.0874331839 \tabularnewline
81 & 8704.07693237769 & 6935.54414008364 & 10472.6097246717 \tabularnewline
82 & 6858.24673884684 & 5041.74399330187 & 8674.7494843918 \tabularnewline
83 & 4725.15257507436 & 2859.71686624746 & 6590.58828390126 \tabularnewline
84 & 3897.84612930768 & 1982.53847383437 & 5813.15378478099 \tabularnewline
85 & 3247.26498644514 & 1281.16935837162 & 5213.36061451865 \tabularnewline
86 & 4156.40883900798 & 2138.63112708706 & 6174.18655092889 \tabularnewline
87 & 4746.97653986918 & 2676.64353689294 & 6817.30954284541 \tabularnewline
88 & 6056.52588342877 & 3932.78431150762 & 8180.26745534991 \tabularnewline
89 & 7353.36422177795 & 5175.37979618665 & 9531.34864736924 \tabularnewline
90 & 8860.61553616459 & 6627.57206933239 & 11093.6590029968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302878&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]79[/C][C]9292.83555991574[/C][C]7617.25208578352[/C][C]10968.419034048[/C][/ROW]
[ROW][C]80[/C][C]9281.53646902554[/C][C]7559.98550486718[/C][C]11003.0874331839[/C][/ROW]
[ROW][C]81[/C][C]8704.07693237769[/C][C]6935.54414008364[/C][C]10472.6097246717[/C][/ROW]
[ROW][C]82[/C][C]6858.24673884684[/C][C]5041.74399330187[/C][C]8674.7494843918[/C][/ROW]
[ROW][C]83[/C][C]4725.15257507436[/C][C]2859.71686624746[/C][C]6590.58828390126[/C][/ROW]
[ROW][C]84[/C][C]3897.84612930768[/C][C]1982.53847383437[/C][C]5813.15378478099[/C][/ROW]
[ROW][C]85[/C][C]3247.26498644514[/C][C]1281.16935837162[/C][C]5213.36061451865[/C][/ROW]
[ROW][C]86[/C][C]4156.40883900798[/C][C]2138.63112708706[/C][C]6174.18655092889[/C][/ROW]
[ROW][C]87[/C][C]4746.97653986918[/C][C]2676.64353689294[/C][C]6817.30954284541[/C][/ROW]
[ROW][C]88[/C][C]6056.52588342877[/C][C]3932.78431150762[/C][C]8180.26745534991[/C][/ROW]
[ROW][C]89[/C][C]7353.36422177795[/C][C]5175.37979618665[/C][C]9531.34864736924[/C][/ROW]
[ROW][C]90[/C][C]8860.61553616459[/C][C]6627.57206933239[/C][C]11093.6590029968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302878&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302878&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
799292.835559915747617.2520857835210968.419034048
809281.536469025547559.9855048671811003.0874331839
818704.076932377696935.5441400836410472.6097246717
826858.246738846845041.743993301878674.7494843918
834725.152575074362859.716866247466590.58828390126
843897.846129307681982.538473834375813.15378478099
853247.264986445141281.169358371625213.36061451865
864156.408839007982138.631127087066174.18655092889
874746.976539869182676.643536892946817.30954284541
886056.525883428773932.784311507628180.26745534991
897353.364221777955175.379796186659531.34864736924
908860.615536164596627.5720693323911093.6590029968



Parameters (Session):
par1 = additive ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')