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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 16:18:52 -0600
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/May/29/t1212013184wtpo7em9597e49n.htm/, Retrieved Wed, 15 May 2024 00:19:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13483, Retrieved Wed, 15 May 2024 00:19:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact209
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Sophie Volckaerts...] [2008-05-24 14:41:00] [4b92e24c7e9c2a828d526c4c975b3e2c]
- RMPD    [Exponential Smoothing] [Robin Van Wijnsbe...] [2008-05-28 22:18:52] [d41d8cd98f00b204e9800998ecf8427e] [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
10698




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 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 & 10 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13483&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]10 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=13483&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13483&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 time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.269020114714124
beta0.000794515688683651
gamma0.647545306842965

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.269020114714124 \tabularnewline
beta & 0.000794515688683651 \tabularnewline
gamma & 0.647545306842965 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13483&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]0.269020114714124[/C][/ROW]
[ROW][C]beta[/C][C]0.000794515688683651[/C][/ROW]
[ROW][C]gamma[/C][C]0.647545306842965[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13483&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13483&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
alpha0.269020114714124
beta0.000794515688683651
gamma0.647545306842965







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770239185.4976388889-1483.49763888890
143036431314.6139080416-950.613908041567
153260933267.3834347123-658.383434712319
163021230598.0864468371-386.086446837056
172996530082.9186368216-117.918636821574
182835228311.201491140340.7985088597452
192581425711.1495038325102.850496167539
202241422088.4793992723325.520600727661
212050619881.531608786624.468391213988
222880627980.1819281687825.818071831342
232222821483.9675393295744.032460670544
241397113659.7018726807311.298127319278
253684537372.9275490270-527.927549027037
263533830011.41931965325326.58068034679
273502233792.61863563721229.38136436279
283477731761.87465608283015.12534391715
292688732291.1799993386-5404.17999933865
302397029173.8934320633-5203.89343206327
312278025192.5782927666-2412.57829276661
321735120998.3614692181-3647.36146921809
332138217863.03902202303518.96097797702
342456126835.1979310001-2274.19793100015
351740919465.1661502368-2056.16615023684
361151410681.0225058542832.97749414576
373151434135.7240364390-2621.72403643896
382707128980.0578886728-1909.05788867276
392946228871.7267237850590.273276215034
402610527510.5626871596-1405.56268715955
412239722860.6975028202-463.697502820152
422384321163.65955446772679.34044553231
432170520622.38150184991082.61849815009
441808916782.75476943471306.24523056534
452076418372.02393104662391.97606895341
462531624298.45759065871017.54240934132
471770417917.4827076874-213.482707687413
481554810997.31538337044550.68461662957
492802933818.3948130442-5789.39481304424
502938328148.71697942481234.28302057521
513643830070.53973028206367.46026971804
523203429321.56793566372712.43206433628
532267926228.9581711308-3549.95817113084
542431925192.3351898077-873.335189807669
551800422941.7075003792-4937.70750037923
561753717589.2453249567-52.2453249567079
572036619327.586778411038.41322159000
582278224239.6284255755-1457.62842557547
591916916609.87874749502559.12125250497
601380712691.06616615521115.93383384485
612974329693.379567072549.6204329274951
622559128920.0192473646-3329.01924736456
632909632043.8970469899-2947.89704698993
642648227056.758868336-574.758868335986
652240520112.80261830632292.19738169368
662704421913.27540155735130.72459844275
671797019353.7820862700-1383.78208626995
681873017270.41634559061459.58365440935
691968419932.5701621988-248.57016219883
701978523317.4742947894-3532.47429478939
711847917030.97430772561448.02569227435
721069812130.0213606686-1432.02136066862

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 39185.4976388889 & -1483.49763888890 \tabularnewline
14 & 30364 & 31314.6139080416 & -950.613908041567 \tabularnewline
15 & 32609 & 33267.3834347123 & -658.383434712319 \tabularnewline
16 & 30212 & 30598.0864468371 & -386.086446837056 \tabularnewline
17 & 29965 & 30082.9186368216 & -117.918636821574 \tabularnewline
18 & 28352 & 28311.2014911403 & 40.7985088597452 \tabularnewline
19 & 25814 & 25711.1495038325 & 102.850496167539 \tabularnewline
20 & 22414 & 22088.4793992723 & 325.520600727661 \tabularnewline
21 & 20506 & 19881.531608786 & 624.468391213988 \tabularnewline
22 & 28806 & 27980.1819281687 & 825.818071831342 \tabularnewline
23 & 22228 & 21483.9675393295 & 744.032460670544 \tabularnewline
24 & 13971 & 13659.7018726807 & 311.298127319278 \tabularnewline
25 & 36845 & 37372.9275490270 & -527.927549027037 \tabularnewline
26 & 35338 & 30011.4193196532 & 5326.58068034679 \tabularnewline
27 & 35022 & 33792.6186356372 & 1229.38136436279 \tabularnewline
28 & 34777 & 31761.8746560828 & 3015.12534391715 \tabularnewline
29 & 26887 & 32291.1799993386 & -5404.17999933865 \tabularnewline
30 & 23970 & 29173.8934320633 & -5203.89343206327 \tabularnewline
31 & 22780 & 25192.5782927666 & -2412.57829276661 \tabularnewline
32 & 17351 & 20998.3614692181 & -3647.36146921809 \tabularnewline
33 & 21382 & 17863.0390220230 & 3518.96097797702 \tabularnewline
34 & 24561 & 26835.1979310001 & -2274.19793100015 \tabularnewline
35 & 17409 & 19465.1661502368 & -2056.16615023684 \tabularnewline
36 & 11514 & 10681.0225058542 & 832.97749414576 \tabularnewline
37 & 31514 & 34135.7240364390 & -2621.72403643896 \tabularnewline
38 & 27071 & 28980.0578886728 & -1909.05788867276 \tabularnewline
39 & 29462 & 28871.7267237850 & 590.273276215034 \tabularnewline
40 & 26105 & 27510.5626871596 & -1405.56268715955 \tabularnewline
41 & 22397 & 22860.6975028202 & -463.697502820152 \tabularnewline
42 & 23843 & 21163.6595544677 & 2679.34044553231 \tabularnewline
43 & 21705 & 20622.3815018499 & 1082.61849815009 \tabularnewline
44 & 18089 & 16782.7547694347 & 1306.24523056534 \tabularnewline
45 & 20764 & 18372.0239310466 & 2391.97606895341 \tabularnewline
46 & 25316 & 24298.4575906587 & 1017.54240934132 \tabularnewline
47 & 17704 & 17917.4827076874 & -213.482707687413 \tabularnewline
48 & 15548 & 10997.3153833704 & 4550.68461662957 \tabularnewline
49 & 28029 & 33818.3948130442 & -5789.39481304424 \tabularnewline
50 & 29383 & 28148.7169794248 & 1234.28302057521 \tabularnewline
51 & 36438 & 30070.5397302820 & 6367.46026971804 \tabularnewline
52 & 32034 & 29321.5679356637 & 2712.43206433628 \tabularnewline
53 & 22679 & 26228.9581711308 & -3549.95817113084 \tabularnewline
54 & 24319 & 25192.3351898077 & -873.335189807669 \tabularnewline
55 & 18004 & 22941.7075003792 & -4937.70750037923 \tabularnewline
56 & 17537 & 17589.2453249567 & -52.2453249567079 \tabularnewline
57 & 20366 & 19327.58677841 & 1038.41322159000 \tabularnewline
58 & 22782 & 24239.6284255755 & -1457.62842557547 \tabularnewline
59 & 19169 & 16609.8787474950 & 2559.12125250497 \tabularnewline
60 & 13807 & 12691.0661661552 & 1115.93383384485 \tabularnewline
61 & 29743 & 29693.3795670725 & 49.6204329274951 \tabularnewline
62 & 25591 & 28920.0192473646 & -3329.01924736456 \tabularnewline
63 & 29096 & 32043.8970469899 & -2947.89704698993 \tabularnewline
64 & 26482 & 27056.758868336 & -574.758868335986 \tabularnewline
65 & 22405 & 20112.8026183063 & 2292.19738169368 \tabularnewline
66 & 27044 & 21913.2754015573 & 5130.72459844275 \tabularnewline
67 & 17970 & 19353.7820862700 & -1383.78208626995 \tabularnewline
68 & 18730 & 17270.4163455906 & 1459.58365440935 \tabularnewline
69 & 19684 & 19932.5701621988 & -248.57016219883 \tabularnewline
70 & 19785 & 23317.4742947894 & -3532.47429478939 \tabularnewline
71 & 18479 & 17030.9743077256 & 1448.02569227435 \tabularnewline
72 & 10698 & 12130.0213606686 & -1432.02136066862 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13483&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]39185.4976388889[/C][C]-1483.49763888890[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]31314.6139080416[/C][C]-950.613908041567[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]33267.3834347123[/C][C]-658.383434712319[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30598.0864468371[/C][C]-386.086446837056[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30082.9186368216[/C][C]-117.918636821574[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28311.2014911403[/C][C]40.7985088597452[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]25711.1495038325[/C][C]102.850496167539[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]22088.4793992723[/C][C]325.520600727661[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]19881.531608786[/C][C]624.468391213988[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]27980.1819281687[/C][C]825.818071831342[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]21483.9675393295[/C][C]744.032460670544[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13659.7018726807[/C][C]311.298127319278[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]37372.9275490270[/C][C]-527.927549027037[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]30011.4193196532[/C][C]5326.58068034679[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33792.6186356372[/C][C]1229.38136436279[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31761.8746560828[/C][C]3015.12534391715[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]32291.1799993386[/C][C]-5404.17999933865[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]29173.8934320633[/C][C]-5203.89343206327[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]25192.5782927666[/C][C]-2412.57829276661[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]20998.3614692181[/C][C]-3647.36146921809[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]17863.0390220230[/C][C]3518.96097797702[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]26835.1979310001[/C][C]-2274.19793100015[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]19465.1661502368[/C][C]-2056.16615023684[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]10681.0225058542[/C][C]832.97749414576[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]34135.7240364390[/C][C]-2621.72403643896[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]28980.0578886728[/C][C]-1909.05788867276[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]28871.7267237850[/C][C]590.273276215034[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27510.5626871596[/C][C]-1405.56268715955[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]22860.6975028202[/C][C]-463.697502820152[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21163.6595544677[/C][C]2679.34044553231[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]20622.3815018499[/C][C]1082.61849815009[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]16782.7547694347[/C][C]1306.24523056534[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18372.0239310466[/C][C]2391.97606895341[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]24298.4575906587[/C][C]1017.54240934132[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]17917.4827076874[/C][C]-213.482707687413[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]10997.3153833704[/C][C]4550.68461662957[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33818.3948130442[/C][C]-5789.39481304424[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]28148.7169794248[/C][C]1234.28302057521[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]30070.5397302820[/C][C]6367.46026971804[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]29321.5679356637[/C][C]2712.43206433628[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]26228.9581711308[/C][C]-3549.95817113084[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25192.3351898077[/C][C]-873.335189807669[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]22941.7075003792[/C][C]-4937.70750037923[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]17589.2453249567[/C][C]-52.2453249567079[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]19327.58677841[/C][C]1038.41322159000[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]24239.6284255755[/C][C]-1457.62842557547[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]16609.8787474950[/C][C]2559.12125250497[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12691.0661661552[/C][C]1115.93383384485[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29693.3795670725[/C][C]49.6204329274951[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]28920.0192473646[/C][C]-3329.01924736456[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]32043.8970469899[/C][C]-2947.89704698993[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]27056.758868336[/C][C]-574.758868335986[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]20112.8026183063[/C][C]2292.19738169368[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]21913.2754015573[/C][C]5130.72459844275[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19353.7820862700[/C][C]-1383.78208626995[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]17270.4163455906[/C][C]1459.58365440935[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19932.5701621988[/C][C]-248.57016219883[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]23317.4742947894[/C][C]-3532.47429478939[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]17030.9743077256[/C][C]1448.02569227435[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]12130.0213606686[/C][C]-1432.02136066862[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13483&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13483&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
133770239185.4976388889-1483.49763888890
143036431314.6139080416-950.613908041567
153260933267.3834347123-658.383434712319
163021230598.0864468371-386.086446837056
172996530082.9186368216-117.918636821574
182835228311.201491140340.7985088597452
192581425711.1495038325102.850496167539
202241422088.4793992723325.520600727661
212050619881.531608786624.468391213988
222880627980.1819281687825.818071831342
232222821483.9675393295744.032460670544
241397113659.7018726807311.298127319278
253684537372.9275490270-527.927549027037
263533830011.41931965325326.58068034679
273502233792.61863563721229.38136436279
283477731761.87465608283015.12534391715
292688732291.1799993386-5404.17999933865
302397029173.8934320633-5203.89343206327
312278025192.5782927666-2412.57829276661
321735120998.3614692181-3647.36146921809
332138217863.03902202303518.96097797702
342456126835.1979310001-2274.19793100015
351740919465.1661502368-2056.16615023684
361151410681.0225058542832.97749414576
373151434135.7240364390-2621.72403643896
382707128980.0578886728-1909.05788867276
392946228871.7267237850590.273276215034
402610527510.5626871596-1405.56268715955
412239722860.6975028202-463.697502820152
422384321163.65955446772679.34044553231
432170520622.38150184991082.61849815009
441808916782.75476943471306.24523056534
452076418372.02393104662391.97606895341
462531624298.45759065871017.54240934132
471770417917.4827076874-213.482707687413
481554810997.31538337044550.68461662957
492802933818.3948130442-5789.39481304424
502938328148.71697942481234.28302057521
513643830070.53973028206367.46026971804
523203429321.56793566372712.43206433628
532267926228.9581711308-3549.95817113084
542431925192.3351898077-873.335189807669
551800422941.7075003792-4937.70750037923
561753717589.2453249567-52.2453249567079
572036619327.586778411038.41322159000
582278224239.6284255755-1457.62842557547
591916916609.87874749502559.12125250497
601380712691.06616615521115.93383384485
612974329693.379567072549.6204329274951
622559128920.0192473646-3329.01924736456
632909632043.8970469899-2947.89704698993
642648227056.758868336-574.758868335986
652240520112.80261830632292.19738169368
662704421913.27540155735130.72459844275
671797019353.7820862700-1383.78208626995
681873017270.41634559061459.58365440935
691968419932.5701621988-248.57016219883
701978523317.4742947894-3532.47429478939
711847917030.97430772561448.02569227435
721069812130.0213606686-1432.02136066862







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327941.496175707122858.463400967333024.5289504469
7425554.866448854320290.829829804930818.9030679036
7529754.763864458324315.470186570735194.0575423458
7626684.651859975721075.309018548132293.9947014034
7721253.167855352415478.523443568527027.8122671364
7823780.897376508417845.302125425629716.4926275912
7916756.753907231910664.213535612522849.2942788513
8016391.04672796310145.264789029522636.8286668964
8117851.196481410611455.610121106124246.7828417151
8219747.807673852513205.617739986326289.9976077187
8316769.100531433710083.297131283323454.903931584
8410115.04452207263288.428876168116941.6601679771

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27941.4961757071 & 22858.4634009673 & 33024.5289504469 \tabularnewline
74 & 25554.8664488543 & 20290.8298298049 & 30818.9030679036 \tabularnewline
75 & 29754.7638644583 & 24315.4701865707 & 35194.0575423458 \tabularnewline
76 & 26684.6518599757 & 21075.3090185481 & 32293.9947014034 \tabularnewline
77 & 21253.1678553524 & 15478.5234435685 & 27027.8122671364 \tabularnewline
78 & 23780.8973765084 & 17845.3021254256 & 29716.4926275912 \tabularnewline
79 & 16756.7539072319 & 10664.2135356125 & 22849.2942788513 \tabularnewline
80 & 16391.046727963 & 10145.2647890295 & 22636.8286668964 \tabularnewline
81 & 17851.1964814106 & 11455.6101211061 & 24246.7828417151 \tabularnewline
82 & 19747.8076738525 & 13205.6177399863 & 26289.9976077187 \tabularnewline
83 & 16769.1005314337 & 10083.2971312833 & 23454.903931584 \tabularnewline
84 & 10115.0445220726 & 3288.4288761681 & 16941.6601679771 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13483&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]73[/C][C]27941.4961757071[/C][C]22858.4634009673[/C][C]33024.5289504469[/C][/ROW]
[ROW][C]74[/C][C]25554.8664488543[/C][C]20290.8298298049[/C][C]30818.9030679036[/C][/ROW]
[ROW][C]75[/C][C]29754.7638644583[/C][C]24315.4701865707[/C][C]35194.0575423458[/C][/ROW]
[ROW][C]76[/C][C]26684.6518599757[/C][C]21075.3090185481[/C][C]32293.9947014034[/C][/ROW]
[ROW][C]77[/C][C]21253.1678553524[/C][C]15478.5234435685[/C][C]27027.8122671364[/C][/ROW]
[ROW][C]78[/C][C]23780.8973765084[/C][C]17845.3021254256[/C][C]29716.4926275912[/C][/ROW]
[ROW][C]79[/C][C]16756.7539072319[/C][C]10664.2135356125[/C][C]22849.2942788513[/C][/ROW]
[ROW][C]80[/C][C]16391.046727963[/C][C]10145.2647890295[/C][C]22636.8286668964[/C][/ROW]
[ROW][C]81[/C][C]17851.1964814106[/C][C]11455.6101211061[/C][C]24246.7828417151[/C][/ROW]
[ROW][C]82[/C][C]19747.8076738525[/C][C]13205.6177399863[/C][C]26289.9976077187[/C][/ROW]
[ROW][C]83[/C][C]16769.1005314337[/C][C]10083.2971312833[/C][C]23454.903931584[/C][/ROW]
[ROW][C]84[/C][C]10115.0445220726[/C][C]3288.4288761681[/C][C]16941.6601679771[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13483&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13483&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
7327941.496175707122858.463400967333024.5289504469
7425554.866448854320290.829829804930818.9030679036
7529754.763864458324315.470186570735194.0575423458
7626684.651859975721075.309018548132293.9947014034
7721253.167855352415478.523443568527027.8122671364
7823780.897376508417845.302125425629716.4926275912
7916756.753907231910664.213535612522849.2942788513
8016391.04672796310145.264789029522636.8286668964
8117851.196481410611455.610121106124246.7828417151
8219747.807673852513205.617739986326289.9976077187
8316769.100531433710083.297131283323454.903931584
8410115.04452207263288.428876168116941.6601679771



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')