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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 05:08:31 -0500
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/Dec/17/t1355738958qrer4jvgtci29yr.htm/, Retrieved Thu, 25 Apr 2024 12:34:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200744, Retrieved Thu, 25 Apr 2024 12:34:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 10:08:31] [b5e28e8a989acbea90caf9c77474d9fd] [Current]
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Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200744&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200744&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200744&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.224078933169873
beta0.00356760108917428
gamma0.456394163936053

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.224078933169873 \tabularnewline
beta & 0.00356760108917428 \tabularnewline
gamma & 0.456394163936053 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200744&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]0.224078933169873[/C][/ROW]
[ROW][C]beta[/C][C]0.00356760108917428[/C][/ROW]
[ROW][C]gamma[/C][C]0.456394163936053[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200744&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200744&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
alpha0.224078933169873
beta0.00356760108917428
gamma0.456394163936053







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256582-3785.99612565825
143036432387.3251460408-2023.32514604084
153260934051.6747755966-1442.67477559658
163021230953.5163574249-741.516357424884
172996530164.5326115703-199.532611570339
182835228188.651397837163.348602162972
192581422069.80203738923744.19796261081
202241420790.83787884151623.16212115846
212050621117.6638115926-611.6638115926
222880626744.43246428822061.56753571177
232222822067.7357490893160.264250910706
241397113467.2689781787503.731021821322
253684537013.67860154-168.678601539999
263533829777.99330907955560.00669092053
273502233337.8250157531684.17498424698
283477731166.63951969813610.3604803019
292688731553.7340762912-4666.73407629121
302397028694.0589611525-4724.0589611525
312278022814.6650124887-34.6650124887165
321735120089.8278612945-2738.82786129448
332138218713.43661699012668.5633830099
342456125527.2165146009-966.216514600863
351740920027.4665513452-2618.46655134523
361151411953.9909454801-439.990945480115
373151431792.8447258347-278.844725834664
382707127175.8450752681-104.845075268124
392946227861.7732918361600.22670816396
402610526601.6282610596-496.628261059584
412239723713.7300544687-1316.73005446875
422384321826.18819125082016.81180874916
432170519534.1484828422170.85151715801
441808916744.06436268941344.93563731056
452076418067.26631114682696.7336888532
462531623196.48772017552119.51227982451
471770418076.2165039111-372.216503911113
481554811465.65148963594082.34851036408
492802933577.8526220028-5548.8526220028
502938327762.15738908631620.84261091373
513643829507.69318032186930.30681967818
523203428553.21153442333480.78846557666
532267925956.2430589541-3277.24305895415
542431924795.9479362809-476.947936280892
551800421811.7530556528-3807.75305565284
561753717361.4742232388175.525776761231
572036618866.644778941499.35522106001
582278223418.0739512051-636.073951205133
591916917097.50282103912071.49717896091
601380712592.35923625951214.64076374055
612974329328.3751331316414.624866868413
622559127444.057615925-1853.05761592503
632909629974.3184161578-878.318416157752
642648226404.777553305977.2224466941334
652240521372.78791561241032.21208438762
662704422088.83232192254955.16767807754
671797019302.8868296454-1332.88682964537
681873016885.20409796511844.79590203493
691968419211.5552080175472.444791982474
701978522705.4830677434-2920.48306774341
711847917036.52464795821442.47535204181

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 41487.9961256582 & -3785.99612565825 \tabularnewline
14 & 30364 & 32387.3251460408 & -2023.32514604084 \tabularnewline
15 & 32609 & 34051.6747755966 & -1442.67477559658 \tabularnewline
16 & 30212 & 30953.5163574249 & -741.516357424884 \tabularnewline
17 & 29965 & 30164.5326115703 & -199.532611570339 \tabularnewline
18 & 28352 & 28188.651397837 & 163.348602162972 \tabularnewline
19 & 25814 & 22069.8020373892 & 3744.19796261081 \tabularnewline
20 & 22414 & 20790.8378788415 & 1623.16212115846 \tabularnewline
21 & 20506 & 21117.6638115926 & -611.6638115926 \tabularnewline
22 & 28806 & 26744.4324642882 & 2061.56753571177 \tabularnewline
23 & 22228 & 22067.7357490893 & 160.264250910706 \tabularnewline
24 & 13971 & 13467.2689781787 & 503.731021821322 \tabularnewline
25 & 36845 & 37013.67860154 & -168.678601539999 \tabularnewline
26 & 35338 & 29777.9933090795 & 5560.00669092053 \tabularnewline
27 & 35022 & 33337.825015753 & 1684.17498424698 \tabularnewline
28 & 34777 & 31166.6395196981 & 3610.3604803019 \tabularnewline
29 & 26887 & 31553.7340762912 & -4666.73407629121 \tabularnewline
30 & 23970 & 28694.0589611525 & -4724.0589611525 \tabularnewline
31 & 22780 & 22814.6650124887 & -34.6650124887165 \tabularnewline
32 & 17351 & 20089.8278612945 & -2738.82786129448 \tabularnewline
33 & 21382 & 18713.4366169901 & 2668.5633830099 \tabularnewline
34 & 24561 & 25527.2165146009 & -966.216514600863 \tabularnewline
35 & 17409 & 20027.4665513452 & -2618.46655134523 \tabularnewline
36 & 11514 & 11953.9909454801 & -439.990945480115 \tabularnewline
37 & 31514 & 31792.8447258347 & -278.844725834664 \tabularnewline
38 & 27071 & 27175.8450752681 & -104.845075268124 \tabularnewline
39 & 29462 & 27861.773291836 & 1600.22670816396 \tabularnewline
40 & 26105 & 26601.6282610596 & -496.628261059584 \tabularnewline
41 & 22397 & 23713.7300544687 & -1316.73005446875 \tabularnewline
42 & 23843 & 21826.1881912508 & 2016.81180874916 \tabularnewline
43 & 21705 & 19534.148482842 & 2170.85151715801 \tabularnewline
44 & 18089 & 16744.0643626894 & 1344.93563731056 \tabularnewline
45 & 20764 & 18067.2663111468 & 2696.7336888532 \tabularnewline
46 & 25316 & 23196.4877201755 & 2119.51227982451 \tabularnewline
47 & 17704 & 18076.2165039111 & -372.216503911113 \tabularnewline
48 & 15548 & 11465.6514896359 & 4082.34851036408 \tabularnewline
49 & 28029 & 33577.8526220028 & -5548.8526220028 \tabularnewline
50 & 29383 & 27762.1573890863 & 1620.84261091373 \tabularnewline
51 & 36438 & 29507.6931803218 & 6930.30681967818 \tabularnewline
52 & 32034 & 28553.2115344233 & 3480.78846557666 \tabularnewline
53 & 22679 & 25956.2430589541 & -3277.24305895415 \tabularnewline
54 & 24319 & 24795.9479362809 & -476.947936280892 \tabularnewline
55 & 18004 & 21811.7530556528 & -3807.75305565284 \tabularnewline
56 & 17537 & 17361.4742232388 & 175.525776761231 \tabularnewline
57 & 20366 & 18866.64477894 & 1499.35522106001 \tabularnewline
58 & 22782 & 23418.0739512051 & -636.073951205133 \tabularnewline
59 & 19169 & 17097.5028210391 & 2071.49717896091 \tabularnewline
60 & 13807 & 12592.3592362595 & 1214.64076374055 \tabularnewline
61 & 29743 & 29328.3751331316 & 414.624866868413 \tabularnewline
62 & 25591 & 27444.057615925 & -1853.05761592503 \tabularnewline
63 & 29096 & 29974.3184161578 & -878.318416157752 \tabularnewline
64 & 26482 & 26404.7775533059 & 77.2224466941334 \tabularnewline
65 & 22405 & 21372.7879156124 & 1032.21208438762 \tabularnewline
66 & 27044 & 22088.8323219225 & 4955.16767807754 \tabularnewline
67 & 17970 & 19302.8868296454 & -1332.88682964537 \tabularnewline
68 & 18730 & 16885.2040979651 & 1844.79590203493 \tabularnewline
69 & 19684 & 19211.5552080175 & 472.444791982474 \tabularnewline
70 & 19785 & 22705.4830677434 & -2920.48306774341 \tabularnewline
71 & 18479 & 17036.5246479582 & 1442.47535204181 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200744&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]37702[/C][C]41487.9961256582[/C][C]-3785.99612565825[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]32387.3251460408[/C][C]-2023.32514604084[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]34051.6747755966[/C][C]-1442.67477559658[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30953.5163574249[/C][C]-741.516357424884[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30164.5326115703[/C][C]-199.532611570339[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28188.651397837[/C][C]163.348602162972[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]22069.8020373892[/C][C]3744.19796261081[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20790.8378788415[/C][C]1623.16212115846[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21117.6638115926[/C][C]-611.6638115926[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]26744.4324642882[/C][C]2061.56753571177[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22067.7357490893[/C][C]160.264250910706[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13467.2689781787[/C][C]503.731021821322[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]37013.67860154[/C][C]-168.678601539999[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29777.9933090795[/C][C]5560.00669092053[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33337.825015753[/C][C]1684.17498424698[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31166.6395196981[/C][C]3610.3604803019[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]31553.7340762912[/C][C]-4666.73407629121[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28694.0589611525[/C][C]-4724.0589611525[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22814.6650124887[/C][C]-34.6650124887165[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]20089.8278612945[/C][C]-2738.82786129448[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18713.4366169901[/C][C]2668.5633830099[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25527.2165146009[/C][C]-966.216514600863[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]20027.4665513452[/C][C]-2618.46655134523[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]11953.9909454801[/C][C]-439.990945480115[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]31792.8447258347[/C][C]-278.844725834664[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]27175.8450752681[/C][C]-104.845075268124[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]27861.773291836[/C][C]1600.22670816396[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]26601.6282610596[/C][C]-496.628261059584[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]23713.7300544687[/C][C]-1316.73005446875[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21826.1881912508[/C][C]2016.81180874916[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19534.148482842[/C][C]2170.85151715801[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]16744.0643626894[/C][C]1344.93563731056[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18067.2663111468[/C][C]2696.7336888532[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23196.4877201755[/C][C]2119.51227982451[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]18076.2165039111[/C][C]-372.216503911113[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]11465.6514896359[/C][C]4082.34851036408[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33577.8526220028[/C][C]-5548.8526220028[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27762.1573890863[/C][C]1620.84261091373[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29507.6931803218[/C][C]6930.30681967818[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]28553.2115344233[/C][C]3480.78846557666[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]25956.2430589541[/C][C]-3277.24305895415[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]24795.9479362809[/C][C]-476.947936280892[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]21811.7530556528[/C][C]-3807.75305565284[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]17361.4742232388[/C][C]175.525776761231[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18866.64477894[/C][C]1499.35522106001[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23418.0739512051[/C][C]-636.073951205133[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]17097.5028210391[/C][C]2071.49717896091[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12592.3592362595[/C][C]1214.64076374055[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29328.3751331316[/C][C]414.624866868413[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]27444.057615925[/C][C]-1853.05761592503[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]29974.3184161578[/C][C]-878.318416157752[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26404.7775533059[/C][C]77.2224466941334[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]21372.7879156124[/C][C]1032.21208438762[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]22088.8323219225[/C][C]4955.16767807754[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19302.8868296454[/C][C]-1332.88682964537[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16885.2040979651[/C][C]1844.79590203493[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19211.5552080175[/C][C]472.444791982474[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22705.4830677434[/C][C]-2920.48306774341[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]17036.5246479582[/C][C]1442.47535204181[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200744&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200744&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
133770241487.9961256582-3785.99612565825
143036432387.3251460408-2023.32514604084
153260934051.6747755966-1442.67477559658
163021230953.5163574249-741.516357424884
172996530164.5326115703-199.532611570339
182835228188.651397837163.348602162972
192581422069.80203738923744.19796261081
202241420790.83787884151623.16212115846
212050621117.6638115926-611.6638115926
222880626744.43246428822061.56753571177
232222822067.7357490893160.264250910706
241397113467.2689781787503.731021821322
253684537013.67860154-168.678601539999
263533829777.99330907955560.00669092053
273502233337.8250157531684.17498424698
283477731166.63951969813610.3604803019
292688731553.7340762912-4666.73407629121
302397028694.0589611525-4724.0589611525
312278022814.6650124887-34.6650124887165
321735120089.8278612945-2738.82786129448
332138218713.43661699012668.5633830099
342456125527.2165146009-966.216514600863
351740920027.4665513452-2618.46655134523
361151411953.9909454801-439.990945480115
373151431792.8447258347-278.844725834664
382707127175.8450752681-104.845075268124
392946227861.7732918361600.22670816396
402610526601.6282610596-496.628261059584
412239723713.7300544687-1316.73005446875
422384321826.18819125082016.81180874916
432170519534.1484828422170.85151715801
441808916744.06436268941344.93563731056
452076418067.26631114682696.7336888532
462531623196.48772017552119.51227982451
471770418076.2165039111-372.216503911113
481554811465.65148963594082.34851036408
492802933577.8526220028-5548.8526220028
502938327762.15738908631620.84261091373
513643829507.69318032186930.30681967818
523203428553.21153442333480.78846557666
532267925956.2430589541-3277.24305895415
542431924795.9479362809-476.947936280892
551800421811.7530556528-3807.75305565284
561753717361.4742232388175.525776761231
572036618866.644778941499.35522106001
582278223418.0739512051-636.073951205133
591916917097.50282103912071.49717896091
601380712592.35923625951214.64076374055
612974329328.3751331316414.624866868413
622559127444.057615925-1853.05761592503
632909629974.3184161578-878.318416157752
642648226404.777553305977.2224466941334
652240521372.78791561241032.21208438762
662704422088.83232192254955.16767807754
671797019302.8868296454-1332.88682964537
681873016885.20409796511844.79590203493
691968419211.5552080175472.444791982474
701978522705.4830677434-2920.48306774341
711847917036.52464795821442.47535204181







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7212344.44454446199486.6995540319515202.1895348918
7327352.216187842423563.179550427131141.2528252576
7424755.305342965320958.881311458228551.7293744724
7527830.017229569823601.705720854932058.3287382847
7624955.244542769920806.36903549129104.1200500488
7720498.912383528916587.679763614524410.1450034433
7822157.264850582117889.440165220726425.0895359435
7916693.576825029112852.577821381720534.5758286765
8015768.169156417211851.160383181519685.177929653
8116997.324157310212728.760204413121265.8881102073
8218850.009609300714111.245372139923588.7738464615
8315712.202143585812379.660233632119044.7440535396

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 12344.4445444619 & 9486.69955403195 & 15202.1895348918 \tabularnewline
73 & 27352.2161878424 & 23563.1795504271 & 31141.2528252576 \tabularnewline
74 & 24755.3053429653 & 20958.8813114582 & 28551.7293744724 \tabularnewline
75 & 27830.0172295698 & 23601.7057208549 & 32058.3287382847 \tabularnewline
76 & 24955.2445427699 & 20806.369035491 & 29104.1200500488 \tabularnewline
77 & 20498.9123835289 & 16587.6797636145 & 24410.1450034433 \tabularnewline
78 & 22157.2648505821 & 17889.4401652207 & 26425.0895359435 \tabularnewline
79 & 16693.5768250291 & 12852.5778213817 & 20534.5758286765 \tabularnewline
80 & 15768.1691564172 & 11851.1603831815 & 19685.177929653 \tabularnewline
81 & 16997.3241573102 & 12728.7602044131 & 21265.8881102073 \tabularnewline
82 & 18850.0096093007 & 14111.2453721399 & 23588.7738464615 \tabularnewline
83 & 15712.2021435858 & 12379.6602336321 & 19044.7440535396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200744&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]72[/C][C]12344.4445444619[/C][C]9486.69955403195[/C][C]15202.1895348918[/C][/ROW]
[ROW][C]73[/C][C]27352.2161878424[/C][C]23563.1795504271[/C][C]31141.2528252576[/C][/ROW]
[ROW][C]74[/C][C]24755.3053429653[/C][C]20958.8813114582[/C][C]28551.7293744724[/C][/ROW]
[ROW][C]75[/C][C]27830.0172295698[/C][C]23601.7057208549[/C][C]32058.3287382847[/C][/ROW]
[ROW][C]76[/C][C]24955.2445427699[/C][C]20806.369035491[/C][C]29104.1200500488[/C][/ROW]
[ROW][C]77[/C][C]20498.9123835289[/C][C]16587.6797636145[/C][C]24410.1450034433[/C][/ROW]
[ROW][C]78[/C][C]22157.2648505821[/C][C]17889.4401652207[/C][C]26425.0895359435[/C][/ROW]
[ROW][C]79[/C][C]16693.5768250291[/C][C]12852.5778213817[/C][C]20534.5758286765[/C][/ROW]
[ROW][C]80[/C][C]15768.1691564172[/C][C]11851.1603831815[/C][C]19685.177929653[/C][/ROW]
[ROW][C]81[/C][C]16997.3241573102[/C][C]12728.7602044131[/C][C]21265.8881102073[/C][/ROW]
[ROW][C]82[/C][C]18850.0096093007[/C][C]14111.2453721399[/C][C]23588.7738464615[/C][/ROW]
[ROW][C]83[/C][C]15712.2021435858[/C][C]12379.6602336321[/C][C]19044.7440535396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200744&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200744&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
7212344.44454446199486.6995540319515202.1895348918
7327352.216187842423563.179550427131141.2528252576
7424755.305342965320958.881311458228551.7293744724
7527830.017229569823601.705720854932058.3287382847
7624955.244542769920806.36903549129104.1200500488
7720498.912383528916587.679763614524410.1450034433
7822157.264850582117889.440165220726425.0895359435
7916693.576825029112852.577821381720534.5758286765
8015768.169156417211851.160383181519685.177929653
8116997.324157310212728.760204413121265.8881102073
8218850.009609300714111.245372139923588.7738464615
8315712.202143585812379.660233632119044.7440535396



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')