Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 16 Dec 2013 05:20:06 -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/16/t1387189243t2zoxw6ik2bmd90.htm/, Retrieved Thu, 28 Mar 2024 12:33:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232381, Retrieved Thu, 28 Mar 2024 12:33:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-16 10:20:06] [15b0219f7c32b8903f806b641c14d708] [Current]
Feedback Forum

Post a new message
Dataseries X:
1,38
1,96
1,36
1,24
1,35
1,23
1,09
1,08
1,33
1,35
1,38
1,5
1,47
2,09
1,52
1,29
1,52
1,27
1,35
1,29
1,41
1,39
1,45
1,53
1,45
2,11
1,53
1,38
1,54
1,35
1,29
1,33
1,47
1,47
1,54
1,59
1,5
2
1,51
1,4
1,62
1,44
1,29
1,28
1,4
1,39
1,46
1,49
1,45
2,05
1,59
1,42
1,73
1,39
1,23
1,37
1,51
1,47
1,5
1,54
1,54
2,15
1,62
1,4
1,65
1,49
1,45
1,45
1,51
1,48
1,56
1,57
1,57
2,28
1,7
1,56
1,8
1,56
1,51
1,46
1,51
1,55
1,57
1,64




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=232381&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=232381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232381&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
alpha0.351422671931043
beta0.0223216540472113
gamma0.707358546735873

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.351422671931043 \tabularnewline
beta & 0.0223216540472113 \tabularnewline
gamma & 0.707358546735873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232381&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]0.351422671931043[/C][/ROW]
[ROW][C]beta[/C][C]0.0223216540472113[/C][/ROW]
[ROW][C]gamma[/C][C]0.707358546735873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232381&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
alpha0.351422671931043
beta0.0223216540472113
gamma0.707358546735873







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131.471.416925747863250.0530742521367522
142.092.046805055776310.0431949442236936
151.521.491051386531790.0289486134682058
161.291.277601649632030.0123983503679681
171.521.518849698536630.0011503014633687
181.271.27657061805821-0.00657061805821479
191.351.211526689280540.138473310719465
201.291.253540716581660.0364592834183364
211.411.51707403401171-0.10707403401171
221.391.50265989822721-0.112659898227214
231.451.49498235443103-0.0449823544310277
241.531.60115204390103-0.0711520439010296
251.451.56816620179532-0.118166201795319
262.112.13176662250706-0.0217666225070583
271.531.54456980786051-0.0145698078605103
281.381.305814169406020.074185830593978
291.541.56168041218046-0.0216804121804599
301.351.305721846851090.0442781531489065
311.291.32337490492451-0.0333749049245056
321.331.255132676093060.0748673239069397
331.471.463551754673450.00644824532654709
341.471.48459781297776-0.0145978129777604
351.541.54132817818006-0.00132817818006292
361.591.65007311638519-0.0600731163851853
371.51.59873879211233-0.0987387921123322
3822.21287185508907-0.212871855089073
391.511.55979849406988-0.0497984940698799
401.41.347085805399430.0529141946005725
411.621.549032739577640.0709672604223641
421.441.354156906938990.0858430930610068
431.291.34938144762011-0.0593814476201107
441.281.32004497567955-0.0400449756795451
451.41.45417680740623-0.0541768074062257
461.391.44127146363638-0.051271463636378
471.461.48792305306166-0.0279230530616641
481.491.55688389736425-0.066883897364254
491.451.48187653038407-0.0318765303840667
502.052.06412873806664-0.0141287380666411
511.591.554255304865580.0357446951344185
521.421.417940481326870.00205951867313292
531.731.609113193528950.120886806471053
541.391.43781143031393-0.047811430313929
551.231.31759919600926-0.087599196009263
561.371.285154233778080.0848457662219242
571.511.455608576369430.0543914236305716
581.471.48195754811964-0.0119575481196368
591.51.5532131110561-0.0532131110560976
601.541.59529020884309-0.05529020884309
611.541.54038671795647-0.000386717956473603
622.152.142063476417040.00793652358295605
631.621.66321417652018-0.0432141765201837
641.41.48346719101213-0.083467191012127
651.651.69819792140361-0.0481979214036128
661.491.387853621063770.102146378936233
671.451.301035072442030.148964927557968
681.451.431642340578480.0183576594215205
691.511.56504245721176-0.0550424572117585
701.481.52191902819089-0.0419190281908921
711.561.5629078375786-0.00290783757860047
721.571.6212945178372-0.0512945178372042
731.571.5925990831145-0.0225990831145046
742.282.189729617538870.0902703824611319
751.71.71643460174513-0.0164346017451269
761.561.527928537766570.0320714622334288
771.81.8006463316405-0.000646331640495879
781.561.57756365461067-0.0175636546106728
791.511.470792952662710.0392070473372903
801.461.50268566858473-0.0426856685847299
811.511.58025709588297-0.0702570958829729
821.551.536985857408640.0130141425913564
831.571.61478600443566-0.0447860044356634
841.641.635537708800750.00446229119925223

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1.47 & 1.41692574786325 & 0.0530742521367522 \tabularnewline
14 & 2.09 & 2.04680505577631 & 0.0431949442236936 \tabularnewline
15 & 1.52 & 1.49105138653179 & 0.0289486134682058 \tabularnewline
16 & 1.29 & 1.27760164963203 & 0.0123983503679681 \tabularnewline
17 & 1.52 & 1.51884969853663 & 0.0011503014633687 \tabularnewline
18 & 1.27 & 1.27657061805821 & -0.00657061805821479 \tabularnewline
19 & 1.35 & 1.21152668928054 & 0.138473310719465 \tabularnewline
20 & 1.29 & 1.25354071658166 & 0.0364592834183364 \tabularnewline
21 & 1.41 & 1.51707403401171 & -0.10707403401171 \tabularnewline
22 & 1.39 & 1.50265989822721 & -0.112659898227214 \tabularnewline
23 & 1.45 & 1.49498235443103 & -0.0449823544310277 \tabularnewline
24 & 1.53 & 1.60115204390103 & -0.0711520439010296 \tabularnewline
25 & 1.45 & 1.56816620179532 & -0.118166201795319 \tabularnewline
26 & 2.11 & 2.13176662250706 & -0.0217666225070583 \tabularnewline
27 & 1.53 & 1.54456980786051 & -0.0145698078605103 \tabularnewline
28 & 1.38 & 1.30581416940602 & 0.074185830593978 \tabularnewline
29 & 1.54 & 1.56168041218046 & -0.0216804121804599 \tabularnewline
30 & 1.35 & 1.30572184685109 & 0.0442781531489065 \tabularnewline
31 & 1.29 & 1.32337490492451 & -0.0333749049245056 \tabularnewline
32 & 1.33 & 1.25513267609306 & 0.0748673239069397 \tabularnewline
33 & 1.47 & 1.46355175467345 & 0.00644824532654709 \tabularnewline
34 & 1.47 & 1.48459781297776 & -0.0145978129777604 \tabularnewline
35 & 1.54 & 1.54132817818006 & -0.00132817818006292 \tabularnewline
36 & 1.59 & 1.65007311638519 & -0.0600731163851853 \tabularnewline
37 & 1.5 & 1.59873879211233 & -0.0987387921123322 \tabularnewline
38 & 2 & 2.21287185508907 & -0.212871855089073 \tabularnewline
39 & 1.51 & 1.55979849406988 & -0.0497984940698799 \tabularnewline
40 & 1.4 & 1.34708580539943 & 0.0529141946005725 \tabularnewline
41 & 1.62 & 1.54903273957764 & 0.0709672604223641 \tabularnewline
42 & 1.44 & 1.35415690693899 & 0.0858430930610068 \tabularnewline
43 & 1.29 & 1.34938144762011 & -0.0593814476201107 \tabularnewline
44 & 1.28 & 1.32004497567955 & -0.0400449756795451 \tabularnewline
45 & 1.4 & 1.45417680740623 & -0.0541768074062257 \tabularnewline
46 & 1.39 & 1.44127146363638 & -0.051271463636378 \tabularnewline
47 & 1.46 & 1.48792305306166 & -0.0279230530616641 \tabularnewline
48 & 1.49 & 1.55688389736425 & -0.066883897364254 \tabularnewline
49 & 1.45 & 1.48187653038407 & -0.0318765303840667 \tabularnewline
50 & 2.05 & 2.06412873806664 & -0.0141287380666411 \tabularnewline
51 & 1.59 & 1.55425530486558 & 0.0357446951344185 \tabularnewline
52 & 1.42 & 1.41794048132687 & 0.00205951867313292 \tabularnewline
53 & 1.73 & 1.60911319352895 & 0.120886806471053 \tabularnewline
54 & 1.39 & 1.43781143031393 & -0.047811430313929 \tabularnewline
55 & 1.23 & 1.31759919600926 & -0.087599196009263 \tabularnewline
56 & 1.37 & 1.28515423377808 & 0.0848457662219242 \tabularnewline
57 & 1.51 & 1.45560857636943 & 0.0543914236305716 \tabularnewline
58 & 1.47 & 1.48195754811964 & -0.0119575481196368 \tabularnewline
59 & 1.5 & 1.5532131110561 & -0.0532131110560976 \tabularnewline
60 & 1.54 & 1.59529020884309 & -0.05529020884309 \tabularnewline
61 & 1.54 & 1.54038671795647 & -0.000386717956473603 \tabularnewline
62 & 2.15 & 2.14206347641704 & 0.00793652358295605 \tabularnewline
63 & 1.62 & 1.66321417652018 & -0.0432141765201837 \tabularnewline
64 & 1.4 & 1.48346719101213 & -0.083467191012127 \tabularnewline
65 & 1.65 & 1.69819792140361 & -0.0481979214036128 \tabularnewline
66 & 1.49 & 1.38785362106377 & 0.102146378936233 \tabularnewline
67 & 1.45 & 1.30103507244203 & 0.148964927557968 \tabularnewline
68 & 1.45 & 1.43164234057848 & 0.0183576594215205 \tabularnewline
69 & 1.51 & 1.56504245721176 & -0.0550424572117585 \tabularnewline
70 & 1.48 & 1.52191902819089 & -0.0419190281908921 \tabularnewline
71 & 1.56 & 1.5629078375786 & -0.00290783757860047 \tabularnewline
72 & 1.57 & 1.6212945178372 & -0.0512945178372042 \tabularnewline
73 & 1.57 & 1.5925990831145 & -0.0225990831145046 \tabularnewline
74 & 2.28 & 2.18972961753887 & 0.0902703824611319 \tabularnewline
75 & 1.7 & 1.71643460174513 & -0.0164346017451269 \tabularnewline
76 & 1.56 & 1.52792853776657 & 0.0320714622334288 \tabularnewline
77 & 1.8 & 1.8006463316405 & -0.000646331640495879 \tabularnewline
78 & 1.56 & 1.57756365461067 & -0.0175636546106728 \tabularnewline
79 & 1.51 & 1.47079295266271 & 0.0392070473372903 \tabularnewline
80 & 1.46 & 1.50268566858473 & -0.0426856685847299 \tabularnewline
81 & 1.51 & 1.58025709588297 & -0.0702570958829729 \tabularnewline
82 & 1.55 & 1.53698585740864 & 0.0130141425913564 \tabularnewline
83 & 1.57 & 1.61478600443566 & -0.0447860044356634 \tabularnewline
84 & 1.64 & 1.63553770880075 & 0.00446229119925223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232381&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]1.47[/C][C]1.41692574786325[/C][C]0.0530742521367522[/C][/ROW]
[ROW][C]14[/C][C]2.09[/C][C]2.04680505577631[/C][C]0.0431949442236936[/C][/ROW]
[ROW][C]15[/C][C]1.52[/C][C]1.49105138653179[/C][C]0.0289486134682058[/C][/ROW]
[ROW][C]16[/C][C]1.29[/C][C]1.27760164963203[/C][C]0.0123983503679681[/C][/ROW]
[ROW][C]17[/C][C]1.52[/C][C]1.51884969853663[/C][C]0.0011503014633687[/C][/ROW]
[ROW][C]18[/C][C]1.27[/C][C]1.27657061805821[/C][C]-0.00657061805821479[/C][/ROW]
[ROW][C]19[/C][C]1.35[/C][C]1.21152668928054[/C][C]0.138473310719465[/C][/ROW]
[ROW][C]20[/C][C]1.29[/C][C]1.25354071658166[/C][C]0.0364592834183364[/C][/ROW]
[ROW][C]21[/C][C]1.41[/C][C]1.51707403401171[/C][C]-0.10707403401171[/C][/ROW]
[ROW][C]22[/C][C]1.39[/C][C]1.50265989822721[/C][C]-0.112659898227214[/C][/ROW]
[ROW][C]23[/C][C]1.45[/C][C]1.49498235443103[/C][C]-0.0449823544310277[/C][/ROW]
[ROW][C]24[/C][C]1.53[/C][C]1.60115204390103[/C][C]-0.0711520439010296[/C][/ROW]
[ROW][C]25[/C][C]1.45[/C][C]1.56816620179532[/C][C]-0.118166201795319[/C][/ROW]
[ROW][C]26[/C][C]2.11[/C][C]2.13176662250706[/C][C]-0.0217666225070583[/C][/ROW]
[ROW][C]27[/C][C]1.53[/C][C]1.54456980786051[/C][C]-0.0145698078605103[/C][/ROW]
[ROW][C]28[/C][C]1.38[/C][C]1.30581416940602[/C][C]0.074185830593978[/C][/ROW]
[ROW][C]29[/C][C]1.54[/C][C]1.56168041218046[/C][C]-0.0216804121804599[/C][/ROW]
[ROW][C]30[/C][C]1.35[/C][C]1.30572184685109[/C][C]0.0442781531489065[/C][/ROW]
[ROW][C]31[/C][C]1.29[/C][C]1.32337490492451[/C][C]-0.0333749049245056[/C][/ROW]
[ROW][C]32[/C][C]1.33[/C][C]1.25513267609306[/C][C]0.0748673239069397[/C][/ROW]
[ROW][C]33[/C][C]1.47[/C][C]1.46355175467345[/C][C]0.00644824532654709[/C][/ROW]
[ROW][C]34[/C][C]1.47[/C][C]1.48459781297776[/C][C]-0.0145978129777604[/C][/ROW]
[ROW][C]35[/C][C]1.54[/C][C]1.54132817818006[/C][C]-0.00132817818006292[/C][/ROW]
[ROW][C]36[/C][C]1.59[/C][C]1.65007311638519[/C][C]-0.0600731163851853[/C][/ROW]
[ROW][C]37[/C][C]1.5[/C][C]1.59873879211233[/C][C]-0.0987387921123322[/C][/ROW]
[ROW][C]38[/C][C]2[/C][C]2.21287185508907[/C][C]-0.212871855089073[/C][/ROW]
[ROW][C]39[/C][C]1.51[/C][C]1.55979849406988[/C][C]-0.0497984940698799[/C][/ROW]
[ROW][C]40[/C][C]1.4[/C][C]1.34708580539943[/C][C]0.0529141946005725[/C][/ROW]
[ROW][C]41[/C][C]1.62[/C][C]1.54903273957764[/C][C]0.0709672604223641[/C][/ROW]
[ROW][C]42[/C][C]1.44[/C][C]1.35415690693899[/C][C]0.0858430930610068[/C][/ROW]
[ROW][C]43[/C][C]1.29[/C][C]1.34938144762011[/C][C]-0.0593814476201107[/C][/ROW]
[ROW][C]44[/C][C]1.28[/C][C]1.32004497567955[/C][C]-0.0400449756795451[/C][/ROW]
[ROW][C]45[/C][C]1.4[/C][C]1.45417680740623[/C][C]-0.0541768074062257[/C][/ROW]
[ROW][C]46[/C][C]1.39[/C][C]1.44127146363638[/C][C]-0.051271463636378[/C][/ROW]
[ROW][C]47[/C][C]1.46[/C][C]1.48792305306166[/C][C]-0.0279230530616641[/C][/ROW]
[ROW][C]48[/C][C]1.49[/C][C]1.55688389736425[/C][C]-0.066883897364254[/C][/ROW]
[ROW][C]49[/C][C]1.45[/C][C]1.48187653038407[/C][C]-0.0318765303840667[/C][/ROW]
[ROW][C]50[/C][C]2.05[/C][C]2.06412873806664[/C][C]-0.0141287380666411[/C][/ROW]
[ROW][C]51[/C][C]1.59[/C][C]1.55425530486558[/C][C]0.0357446951344185[/C][/ROW]
[ROW][C]52[/C][C]1.42[/C][C]1.41794048132687[/C][C]0.00205951867313292[/C][/ROW]
[ROW][C]53[/C][C]1.73[/C][C]1.60911319352895[/C][C]0.120886806471053[/C][/ROW]
[ROW][C]54[/C][C]1.39[/C][C]1.43781143031393[/C][C]-0.047811430313929[/C][/ROW]
[ROW][C]55[/C][C]1.23[/C][C]1.31759919600926[/C][C]-0.087599196009263[/C][/ROW]
[ROW][C]56[/C][C]1.37[/C][C]1.28515423377808[/C][C]0.0848457662219242[/C][/ROW]
[ROW][C]57[/C][C]1.51[/C][C]1.45560857636943[/C][C]0.0543914236305716[/C][/ROW]
[ROW][C]58[/C][C]1.47[/C][C]1.48195754811964[/C][C]-0.0119575481196368[/C][/ROW]
[ROW][C]59[/C][C]1.5[/C][C]1.5532131110561[/C][C]-0.0532131110560976[/C][/ROW]
[ROW][C]60[/C][C]1.54[/C][C]1.59529020884309[/C][C]-0.05529020884309[/C][/ROW]
[ROW][C]61[/C][C]1.54[/C][C]1.54038671795647[/C][C]-0.000386717956473603[/C][/ROW]
[ROW][C]62[/C][C]2.15[/C][C]2.14206347641704[/C][C]0.00793652358295605[/C][/ROW]
[ROW][C]63[/C][C]1.62[/C][C]1.66321417652018[/C][C]-0.0432141765201837[/C][/ROW]
[ROW][C]64[/C][C]1.4[/C][C]1.48346719101213[/C][C]-0.083467191012127[/C][/ROW]
[ROW][C]65[/C][C]1.65[/C][C]1.69819792140361[/C][C]-0.0481979214036128[/C][/ROW]
[ROW][C]66[/C][C]1.49[/C][C]1.38785362106377[/C][C]0.102146378936233[/C][/ROW]
[ROW][C]67[/C][C]1.45[/C][C]1.30103507244203[/C][C]0.148964927557968[/C][/ROW]
[ROW][C]68[/C][C]1.45[/C][C]1.43164234057848[/C][C]0.0183576594215205[/C][/ROW]
[ROW][C]69[/C][C]1.51[/C][C]1.56504245721176[/C][C]-0.0550424572117585[/C][/ROW]
[ROW][C]70[/C][C]1.48[/C][C]1.52191902819089[/C][C]-0.0419190281908921[/C][/ROW]
[ROW][C]71[/C][C]1.56[/C][C]1.5629078375786[/C][C]-0.00290783757860047[/C][/ROW]
[ROW][C]72[/C][C]1.57[/C][C]1.6212945178372[/C][C]-0.0512945178372042[/C][/ROW]
[ROW][C]73[/C][C]1.57[/C][C]1.5925990831145[/C][C]-0.0225990831145046[/C][/ROW]
[ROW][C]74[/C][C]2.28[/C][C]2.18972961753887[/C][C]0.0902703824611319[/C][/ROW]
[ROW][C]75[/C][C]1.7[/C][C]1.71643460174513[/C][C]-0.0164346017451269[/C][/ROW]
[ROW][C]76[/C][C]1.56[/C][C]1.52792853776657[/C][C]0.0320714622334288[/C][/ROW]
[ROW][C]77[/C][C]1.8[/C][C]1.8006463316405[/C][C]-0.000646331640495879[/C][/ROW]
[ROW][C]78[/C][C]1.56[/C][C]1.57756365461067[/C][C]-0.0175636546106728[/C][/ROW]
[ROW][C]79[/C][C]1.51[/C][C]1.47079295266271[/C][C]0.0392070473372903[/C][/ROW]
[ROW][C]80[/C][C]1.46[/C][C]1.50268566858473[/C][C]-0.0426856685847299[/C][/ROW]
[ROW][C]81[/C][C]1.51[/C][C]1.58025709588297[/C][C]-0.0702570958829729[/C][/ROW]
[ROW][C]82[/C][C]1.55[/C][C]1.53698585740864[/C][C]0.0130141425913564[/C][/ROW]
[ROW][C]83[/C][C]1.57[/C][C]1.61478600443566[/C][C]-0.0447860044356634[/C][/ROW]
[ROW][C]84[/C][C]1.64[/C][C]1.63553770880075[/C][C]0.00446229119925223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232381&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
131.471.416925747863250.0530742521367522
142.092.046805055776310.0431949442236936
151.521.491051386531790.0289486134682058
161.291.277601649632030.0123983503679681
171.521.518849698536630.0011503014633687
181.271.27657061805821-0.00657061805821479
191.351.211526689280540.138473310719465
201.291.253540716581660.0364592834183364
211.411.51707403401171-0.10707403401171
221.391.50265989822721-0.112659898227214
231.451.49498235443103-0.0449823544310277
241.531.60115204390103-0.0711520439010296
251.451.56816620179532-0.118166201795319
262.112.13176662250706-0.0217666225070583
271.531.54456980786051-0.0145698078605103
281.381.305814169406020.074185830593978
291.541.56168041218046-0.0216804121804599
301.351.305721846851090.0442781531489065
311.291.32337490492451-0.0333749049245056
321.331.255132676093060.0748673239069397
331.471.463551754673450.00644824532654709
341.471.48459781297776-0.0145978129777604
351.541.54132817818006-0.00132817818006292
361.591.65007311638519-0.0600731163851853
371.51.59873879211233-0.0987387921123322
3822.21287185508907-0.212871855089073
391.511.55979849406988-0.0497984940698799
401.41.347085805399430.0529141946005725
411.621.549032739577640.0709672604223641
421.441.354156906938990.0858430930610068
431.291.34938144762011-0.0593814476201107
441.281.32004497567955-0.0400449756795451
451.41.45417680740623-0.0541768074062257
461.391.44127146363638-0.051271463636378
471.461.48792305306166-0.0279230530616641
481.491.55688389736425-0.066883897364254
491.451.48187653038407-0.0318765303840667
502.052.06412873806664-0.0141287380666411
511.591.554255304865580.0357446951344185
521.421.417940481326870.00205951867313292
531.731.609113193528950.120886806471053
541.391.43781143031393-0.047811430313929
551.231.31759919600926-0.087599196009263
561.371.285154233778080.0848457662219242
571.511.455608576369430.0543914236305716
581.471.48195754811964-0.0119575481196368
591.51.5532131110561-0.0532131110560976
601.541.59529020884309-0.05529020884309
611.541.54038671795647-0.000386717956473603
622.152.142063476417040.00793652358295605
631.621.66321417652018-0.0432141765201837
641.41.48346719101213-0.083467191012127
651.651.69819792140361-0.0481979214036128
661.491.387853621063770.102146378936233
671.451.301035072442030.148964927557968
681.451.431642340578480.0183576594215205
691.511.56504245721176-0.0550424572117585
701.481.52191902819089-0.0419190281908921
711.561.5629078375786-0.00290783757860047
721.571.6212945178372-0.0512945178372042
731.571.5925990831145-0.0225990831145046
742.282.189729617538870.0902703824611319
751.71.71643460174513-0.0164346017451269
761.561.527928537766570.0320714622334288
771.81.8006463316405-0.000646331640495879
781.561.57756365461067-0.0175636546106728
791.511.470792952662710.0392070473372903
801.461.50268566858473-0.0426856685847299
811.511.58025709588297-0.0702570958829729
821.551.536985857408640.0130141425913564
831.571.61478600443566-0.0447860044356634
841.641.635537708800750.00446229119925223







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851.639319296983781.514273879483441.76436471448412
862.296068837927252.163198282606412.42893939324809
871.74128418329361.600707130524321.88186123606289
881.580123164668641.431933250563751.72831307877353
891.825624679199411.669895627879151.98135373051968
901.59407745556751.430866878594441.75728803254056
911.518731463150861.348083755878791.68937917042293
921.498175276101091.320123866582361.67622668561981
931.577332940581861.391902063806851.76276381735687
941.596740318379161.403946435671391.78953420108692
951.643133326265781.442986274830951.84328037770061
961.702252823034411.494756757169041.90974888889979

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.63931929698378 & 1.51427387948344 & 1.76436471448412 \tabularnewline
86 & 2.29606883792725 & 2.16319828260641 & 2.42893939324809 \tabularnewline
87 & 1.7412841832936 & 1.60070713052432 & 1.88186123606289 \tabularnewline
88 & 1.58012316466864 & 1.43193325056375 & 1.72831307877353 \tabularnewline
89 & 1.82562467919941 & 1.66989562787915 & 1.98135373051968 \tabularnewline
90 & 1.5940774555675 & 1.43086687859444 & 1.75728803254056 \tabularnewline
91 & 1.51873146315086 & 1.34808375587879 & 1.68937917042293 \tabularnewline
92 & 1.49817527610109 & 1.32012386658236 & 1.67622668561981 \tabularnewline
93 & 1.57733294058186 & 1.39190206380685 & 1.76276381735687 \tabularnewline
94 & 1.59674031837916 & 1.40394643567139 & 1.78953420108692 \tabularnewline
95 & 1.64313332626578 & 1.44298627483095 & 1.84328037770061 \tabularnewline
96 & 1.70225282303441 & 1.49475675716904 & 1.90974888889979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232381&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]85[/C][C]1.63931929698378[/C][C]1.51427387948344[/C][C]1.76436471448412[/C][/ROW]
[ROW][C]86[/C][C]2.29606883792725[/C][C]2.16319828260641[/C][C]2.42893939324809[/C][/ROW]
[ROW][C]87[/C][C]1.7412841832936[/C][C]1.60070713052432[/C][C]1.88186123606289[/C][/ROW]
[ROW][C]88[/C][C]1.58012316466864[/C][C]1.43193325056375[/C][C]1.72831307877353[/C][/ROW]
[ROW][C]89[/C][C]1.82562467919941[/C][C]1.66989562787915[/C][C]1.98135373051968[/C][/ROW]
[ROW][C]90[/C][C]1.5940774555675[/C][C]1.43086687859444[/C][C]1.75728803254056[/C][/ROW]
[ROW][C]91[/C][C]1.51873146315086[/C][C]1.34808375587879[/C][C]1.68937917042293[/C][/ROW]
[ROW][C]92[/C][C]1.49817527610109[/C][C]1.32012386658236[/C][C]1.67622668561981[/C][/ROW]
[ROW][C]93[/C][C]1.57733294058186[/C][C]1.39190206380685[/C][C]1.76276381735687[/C][/ROW]
[ROW][C]94[/C][C]1.59674031837916[/C][C]1.40394643567139[/C][C]1.78953420108692[/C][/ROW]
[ROW][C]95[/C][C]1.64313332626578[/C][C]1.44298627483095[/C][C]1.84328037770061[/C][/ROW]
[ROW][C]96[/C][C]1.70225282303441[/C][C]1.49475675716904[/C][C]1.90974888889979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232381&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
851.639319296983781.514273879483441.76436471448412
862.296068837927252.163198282606412.42893939324809
871.74128418329361.600707130524321.88186123606289
881.580123164668641.431933250563751.72831307877353
891.825624679199411.669895627879151.98135373051968
901.59407745556751.430866878594441.75728803254056
911.518731463150861.348083755878791.68937917042293
921.498175276101091.320123866582361.67622668561981
931.577332940581861.391902063806851.76276381735687
941.596740318379161.403946435671391.78953420108692
951.643133326265781.442986274830951.84328037770061
961.702252823034411.494756757169041.90974888889979



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')