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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 08:49:30 -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/2013/Dec/12/t1386856216ntuxf2tuoh1c3jy.htm/, Retrieved Tue, 07 Dec 2021 12:17:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232248, Retrieved Tue, 07 Dec 2021 12:17:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 13:49:30] [e13de47ca0b629216b947109e84252a5] [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 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=232248&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=232248&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232248&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
alpha0.298636158737138
beta0
gamma0.619823386020581

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.298636158737138 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.619823386020581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232248&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]0.298636158737138[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.619823386020581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232248&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232248&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
alpha0.298636158737138
beta0
gamma0.619823386020581







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770240443.703792735-2741.70379273504
143036431996.9844969177-1632.9844969177
153260933561.868872721-952.868872720996
163021230629.3186993648-417.318699364834
172996529937.661505924127.3384940759024
182835228050.1283620207301.871637979319
192581421460.41407499194353.58592500806
202241420567.60484560851846.39515439149
212050621231.3911286003-725.391128600277
222880627004.35736827991801.64263172015
232222822474.1539298072-246.153929807246
241397113911.15439232559.8456076750117
253684536937.450884334-92.4508843339863
263533829763.87864981685574.12135018316
273502233776.72645918721245.2735408128
283477731733.4363802133043.56361978704
292688732268.6259243122-5381.62592431222
302397028885.1259417785-4915.12594177854
312278022498.7957044221281.204295577896
321735119299.8958068988-1948.8958068988
332138217712.25964284813669.74035715187
342456125896.3275064264-1335.32750642645
351740919539.0897309733-2130.08973097327
361151410546.5034849996967.496515000363
373151433777.6507658727-2263.65076587269
382707128419.0617157457-1348.06171574573
392946228482.851238213979.148761787044
402610527141.8424173549-1036.84241735494
412239722795.8623629649-398.862362964901
422384321103.19342084042739.8065791596
432170519261.86039823842443.13960176164
441808915739.11962391162349.88037608838
452076417877.79659271422886.20340728579
462531623652.06032641071663.93967358932
471770417845.0117865911-141.011786591058
481554810793.02412994064754.97587005936
492802933750.5998225163-5721.59982251633
502938327757.3685873791625.63141262098
513643829720.89932343796717.10067656211
523203429217.05528682252816.94471317748
532267926299.2991984651-3620.29919846509
542431925009.0402667167-690.040266716715
551800422014.4633810164-4010.46338101641
561753716523.90159175421013.09840824583
572036618496.51839434131869.48160565875
582278223435.8076531827-653.807653182696
591916916151.94436786833017.05563213168
601380712171.46196493981635.53803506023
612974329643.065815351399.9341846487259
622559128582.3560671641-2991.35606716412
632909631380.4596268597-2284.45962685969
642648226492.9417253169-10.9417253169195
652240519932.26680671872472.73319328135
662704421735.45483976225308.54516023778
671797019088.8124465844-1118.81244658439
681873016645.65356074982084.34643925016
691968419310.4721291566373.527870843358
701978522706.0868872248-2921.08688722477
711847916340.93600863142138.06399136864
721069811497.3792250728-799.379225072837

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 40443.703792735 & -2741.70379273504 \tabularnewline
14 & 30364 & 31996.9844969177 & -1632.9844969177 \tabularnewline
15 & 32609 & 33561.868872721 & -952.868872720996 \tabularnewline
16 & 30212 & 30629.3186993648 & -417.318699364834 \tabularnewline
17 & 29965 & 29937.6615059241 & 27.3384940759024 \tabularnewline
18 & 28352 & 28050.1283620207 & 301.871637979319 \tabularnewline
19 & 25814 & 21460.4140749919 & 4353.58592500806 \tabularnewline
20 & 22414 & 20567.6048456085 & 1846.39515439149 \tabularnewline
21 & 20506 & 21231.3911286003 & -725.391128600277 \tabularnewline
22 & 28806 & 27004.3573682799 & 1801.64263172015 \tabularnewline
23 & 22228 & 22474.1539298072 & -246.153929807246 \tabularnewline
24 & 13971 & 13911.154392325 & 59.8456076750117 \tabularnewline
25 & 36845 & 36937.450884334 & -92.4508843339863 \tabularnewline
26 & 35338 & 29763.8786498168 & 5574.12135018316 \tabularnewline
27 & 35022 & 33776.7264591872 & 1245.2735408128 \tabularnewline
28 & 34777 & 31733.436380213 & 3043.56361978704 \tabularnewline
29 & 26887 & 32268.6259243122 & -5381.62592431222 \tabularnewline
30 & 23970 & 28885.1259417785 & -4915.12594177854 \tabularnewline
31 & 22780 & 22498.7957044221 & 281.204295577896 \tabularnewline
32 & 17351 & 19299.8958068988 & -1948.8958068988 \tabularnewline
33 & 21382 & 17712.2596428481 & 3669.74035715187 \tabularnewline
34 & 24561 & 25896.3275064264 & -1335.32750642645 \tabularnewline
35 & 17409 & 19539.0897309733 & -2130.08973097327 \tabularnewline
36 & 11514 & 10546.5034849996 & 967.496515000363 \tabularnewline
37 & 31514 & 33777.6507658727 & -2263.65076587269 \tabularnewline
38 & 27071 & 28419.0617157457 & -1348.06171574573 \tabularnewline
39 & 29462 & 28482.851238213 & 979.148761787044 \tabularnewline
40 & 26105 & 27141.8424173549 & -1036.84241735494 \tabularnewline
41 & 22397 & 22795.8623629649 & -398.862362964901 \tabularnewline
42 & 23843 & 21103.1934208404 & 2739.8065791596 \tabularnewline
43 & 21705 & 19261.8603982384 & 2443.13960176164 \tabularnewline
44 & 18089 & 15739.1196239116 & 2349.88037608838 \tabularnewline
45 & 20764 & 17877.7965927142 & 2886.20340728579 \tabularnewline
46 & 25316 & 23652.0603264107 & 1663.93967358932 \tabularnewline
47 & 17704 & 17845.0117865911 & -141.011786591058 \tabularnewline
48 & 15548 & 10793.0241299406 & 4754.97587005936 \tabularnewline
49 & 28029 & 33750.5998225163 & -5721.59982251633 \tabularnewline
50 & 29383 & 27757.368587379 & 1625.63141262098 \tabularnewline
51 & 36438 & 29720.8993234379 & 6717.10067656211 \tabularnewline
52 & 32034 & 29217.0552868225 & 2816.94471317748 \tabularnewline
53 & 22679 & 26299.2991984651 & -3620.29919846509 \tabularnewline
54 & 24319 & 25009.0402667167 & -690.040266716715 \tabularnewline
55 & 18004 & 22014.4633810164 & -4010.46338101641 \tabularnewline
56 & 17537 & 16523.9015917542 & 1013.09840824583 \tabularnewline
57 & 20366 & 18496.5183943413 & 1869.48160565875 \tabularnewline
58 & 22782 & 23435.8076531827 & -653.807653182696 \tabularnewline
59 & 19169 & 16151.9443678683 & 3017.05563213168 \tabularnewline
60 & 13807 & 12171.4619649398 & 1635.53803506023 \tabularnewline
61 & 29743 & 29643.0658153513 & 99.9341846487259 \tabularnewline
62 & 25591 & 28582.3560671641 & -2991.35606716412 \tabularnewline
63 & 29096 & 31380.4596268597 & -2284.45962685969 \tabularnewline
64 & 26482 & 26492.9417253169 & -10.9417253169195 \tabularnewline
65 & 22405 & 19932.2668067187 & 2472.73319328135 \tabularnewline
66 & 27044 & 21735.4548397622 & 5308.54516023778 \tabularnewline
67 & 17970 & 19088.8124465844 & -1118.81244658439 \tabularnewline
68 & 18730 & 16645.6535607498 & 2084.34643925016 \tabularnewline
69 & 19684 & 19310.4721291566 & 373.527870843358 \tabularnewline
70 & 19785 & 22706.0868872248 & -2921.08688722477 \tabularnewline
71 & 18479 & 16340.9360086314 & 2138.06399136864 \tabularnewline
72 & 10698 & 11497.3792250728 & -799.379225072837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232248&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]40443.703792735[/C][C]-2741.70379273504[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]31996.9844969177[/C][C]-1632.9844969177[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]33561.868872721[/C][C]-952.868872720996[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30629.3186993648[/C][C]-417.318699364834[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]29937.6615059241[/C][C]27.3384940759024[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28050.1283620207[/C][C]301.871637979319[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]21460.4140749919[/C][C]4353.58592500806[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20567.6048456085[/C][C]1846.39515439149[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21231.3911286003[/C][C]-725.391128600277[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]27004.3573682799[/C][C]1801.64263172015[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22474.1539298072[/C][C]-246.153929807246[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13911.154392325[/C][C]59.8456076750117[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]36937.450884334[/C][C]-92.4508843339863[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29763.8786498168[/C][C]5574.12135018316[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33776.7264591872[/C][C]1245.2735408128[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31733.436380213[/C][C]3043.56361978704[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]32268.6259243122[/C][C]-5381.62592431222[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28885.1259417785[/C][C]-4915.12594177854[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22498.7957044221[/C][C]281.204295577896[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]19299.8958068988[/C][C]-1948.8958068988[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]17712.2596428481[/C][C]3669.74035715187[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25896.3275064264[/C][C]-1335.32750642645[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]19539.0897309733[/C][C]-2130.08973097327[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]10546.5034849996[/C][C]967.496515000363[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]33777.6507658727[/C][C]-2263.65076587269[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]28419.0617157457[/C][C]-1348.06171574573[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]28482.851238213[/C][C]979.148761787044[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27141.8424173549[/C][C]-1036.84241735494[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]22795.8623629649[/C][C]-398.862362964901[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21103.1934208404[/C][C]2739.8065791596[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19261.8603982384[/C][C]2443.13960176164[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]15739.1196239116[/C][C]2349.88037608838[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]17877.7965927142[/C][C]2886.20340728579[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23652.0603264107[/C][C]1663.93967358932[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]17845.0117865911[/C][C]-141.011786591058[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]10793.0241299406[/C][C]4754.97587005936[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33750.5998225163[/C][C]-5721.59982251633[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27757.368587379[/C][C]1625.63141262098[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29720.8993234379[/C][C]6717.10067656211[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]29217.0552868225[/C][C]2816.94471317748[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]26299.2991984651[/C][C]-3620.29919846509[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25009.0402667167[/C][C]-690.040266716715[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]22014.4633810164[/C][C]-4010.46338101641[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]16523.9015917542[/C][C]1013.09840824583[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18496.5183943413[/C][C]1869.48160565875[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23435.8076531827[/C][C]-653.807653182696[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]16151.9443678683[/C][C]3017.05563213168[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12171.4619649398[/C][C]1635.53803506023[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29643.0658153513[/C][C]99.9341846487259[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]28582.3560671641[/C][C]-2991.35606716412[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]31380.4596268597[/C][C]-2284.45962685969[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26492.9417253169[/C][C]-10.9417253169195[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]19932.2668067187[/C][C]2472.73319328135[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]21735.4548397622[/C][C]5308.54516023778[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19088.8124465844[/C][C]-1118.81244658439[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16645.6535607498[/C][C]2084.34643925016[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19310.4721291566[/C][C]373.527870843358[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22706.0868872248[/C][C]-2921.08688722477[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]16340.9360086314[/C][C]2138.06399136864[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]11497.3792250728[/C][C]-799.379225072837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232248&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232248&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
133770240443.703792735-2741.70379273504
143036431996.9844969177-1632.9844969177
153260933561.868872721-952.868872720996
163021230629.3186993648-417.318699364834
172996529937.661505924127.3384940759024
182835228050.1283620207301.871637979319
192581421460.41407499194353.58592500806
202241420567.60484560851846.39515439149
212050621231.3911286003-725.391128600277
222880627004.35736827991801.64263172015
232222822474.1539298072-246.153929807246
241397113911.15439232559.8456076750117
253684536937.450884334-92.4508843339863
263533829763.87864981685574.12135018316
273502233776.72645918721245.2735408128
283477731733.4363802133043.56361978704
292688732268.6259243122-5381.62592431222
302397028885.1259417785-4915.12594177854
312278022498.7957044221281.204295577896
321735119299.8958068988-1948.8958068988
332138217712.25964284813669.74035715187
342456125896.3275064264-1335.32750642645
351740919539.0897309733-2130.08973097327
361151410546.5034849996967.496515000363
373151433777.6507658727-2263.65076587269
382707128419.0617157457-1348.06171574573
392946228482.851238213979.148761787044
402610527141.8424173549-1036.84241735494
412239722795.8623629649-398.862362964901
422384321103.19342084042739.8065791596
432170519261.86039823842443.13960176164
441808915739.11962391162349.88037608838
452076417877.79659271422886.20340728579
462531623652.06032641071663.93967358932
471770417845.0117865911-141.011786591058
481554810793.02412994064754.97587005936
492802933750.5998225163-5721.59982251633
502938327757.3685873791625.63141262098
513643829720.89932343796717.10067656211
523203429217.05528682252816.94471317748
532267926299.2991984651-3620.29919846509
542431925009.0402667167-690.040266716715
551800422014.4633810164-4010.46338101641
561753716523.90159175421013.09840824583
572036618496.51839434131869.48160565875
582278223435.8076531827-653.807653182696
591916916151.94436786833017.05563213168
601380712171.46196493981635.53803506023
612974329643.065815351399.9341846487259
622559128582.3560671641-2991.35606716412
632909631380.4596268597-2284.45962685969
642648226492.9417253169-10.9417253169195
652240519932.26680671872472.73319328135
662704421735.45483976225308.54516023778
671797019088.8124465844-1118.81244658439
681873016645.65356074982084.34643925016
691968419310.4721291566373.527870843358
701978522706.0868872248-2921.08688722477
711847916340.93600863142138.06399136864
721069811497.3792250728-799.379225072837







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327574.268404923222373.729637356432774.8071724899
7425139.863708475419712.375657262330567.3517596884
7529138.597583459123493.276545718534783.9186211996
7625921.649521646620066.594210870231776.7048324231
7720443.949607858914386.417456450426501.4817592674
7822741.47912861316488.022577357328994.9356798688
7915715.40130474149271.9750491271422158.8275603556
8014998.84298151338370.889678672821626.7962843539
8116297.47036068689489.9900590090423104.9506623645
8218149.295625762311166.902688464525131.6885630601
8314855.80964027167702.7799182642222008.8393622791
848096.77929840321777.08960026592215416.4689965405

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27574.2684049232 & 22373.7296373564 & 32774.8071724899 \tabularnewline
74 & 25139.8637084754 & 19712.3756572623 & 30567.3517596884 \tabularnewline
75 & 29138.5975834591 & 23493.2765457185 & 34783.9186211996 \tabularnewline
76 & 25921.6495216466 & 20066.5942108702 & 31776.7048324231 \tabularnewline
77 & 20443.9496078589 & 14386.4174564504 & 26501.4817592674 \tabularnewline
78 & 22741.479128613 & 16488.0225773573 & 28994.9356798688 \tabularnewline
79 & 15715.4013047414 & 9271.97504912714 & 22158.8275603556 \tabularnewline
80 & 14998.8429815133 & 8370.8896786728 & 21626.7962843539 \tabularnewline
81 & 16297.4703606868 & 9489.99005900904 & 23104.9506623645 \tabularnewline
82 & 18149.2956257623 & 11166.9026884645 & 25131.6885630601 \tabularnewline
83 & 14855.8096402716 & 7702.77991826422 & 22008.8393622791 \tabularnewline
84 & 8096.77929840321 & 777.089600265922 & 15416.4689965405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232248&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]27574.2684049232[/C][C]22373.7296373564[/C][C]32774.8071724899[/C][/ROW]
[ROW][C]74[/C][C]25139.8637084754[/C][C]19712.3756572623[/C][C]30567.3517596884[/C][/ROW]
[ROW][C]75[/C][C]29138.5975834591[/C][C]23493.2765457185[/C][C]34783.9186211996[/C][/ROW]
[ROW][C]76[/C][C]25921.6495216466[/C][C]20066.5942108702[/C][C]31776.7048324231[/C][/ROW]
[ROW][C]77[/C][C]20443.9496078589[/C][C]14386.4174564504[/C][C]26501.4817592674[/C][/ROW]
[ROW][C]78[/C][C]22741.479128613[/C][C]16488.0225773573[/C][C]28994.9356798688[/C][/ROW]
[ROW][C]79[/C][C]15715.4013047414[/C][C]9271.97504912714[/C][C]22158.8275603556[/C][/ROW]
[ROW][C]80[/C][C]14998.8429815133[/C][C]8370.8896786728[/C][C]21626.7962843539[/C][/ROW]
[ROW][C]81[/C][C]16297.4703606868[/C][C]9489.99005900904[/C][C]23104.9506623645[/C][/ROW]
[ROW][C]82[/C][C]18149.2956257623[/C][C]11166.9026884645[/C][C]25131.6885630601[/C][/ROW]
[ROW][C]83[/C][C]14855.8096402716[/C][C]7702.77991826422[/C][C]22008.8393622791[/C][/ROW]
[ROW][C]84[/C][C]8096.77929840321[/C][C]777.089600265922[/C][C]15416.4689965405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232248&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232248&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
7327574.268404923222373.729637356432774.8071724899
7425139.863708475419712.375657262330567.3517596884
7529138.597583459123493.276545718534783.9186211996
7625921.649521646620066.594210870231776.7048324231
7720443.949607858914386.417456450426501.4817592674
7822741.47912861316488.022577357328994.9356798688
7915715.40130474149271.9750491271422158.8275603556
8014998.84298151338370.889678672821626.7962843539
8116297.47036068689489.9900590090423104.9506623645
8218149.295625762311166.902688464525131.6885630601
8314855.80964027167702.7799182642222008.8393622791
848096.77929840321777.08960026592215416.4689965405



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')