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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Dec 2011 12:21:02 -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/2011/Dec/27/t13250065337bf2gj4sjxapx78.htm/, Retrieved Mon, 20 May 2024 08:48:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160866, Retrieved Mon, 20 May 2024 08:48:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde consum...] [2011-12-27 17:21:02] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
6,19
6,31
6,35
6,38
6,38
6,36
6,34
6,49
6,5
6,5
6,55
6,57
6,65
6,61
6,66
6,73
6,73
6,75
6,75
6,71
6,77
6,83
6,9
6,89
7,14
7,35
7,43
7,42
7,41
7,46
7,47
7,45
7,47
7,44
7,43
7,43
7,44
7,49
7,48
7,43
7,33
7,42
7,98
7,41
7,25
7,04
6,98
6,94
6,9
6,92
6,86
6,86
6,89
6,91
6,9
6,88
6,78
6,79
6,81
6,78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160866&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]2 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=160866&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160866&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.936629683190357
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.936629683190357 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160866&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]0.936629683190357[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160866&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160866&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
alpha0.936629683190357
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26.316.190.119999999999999
36.356.302395561982840.0476044380171574
46.386.346983291681310.0330167083186925
56.386.377907720733830.00209227926616684
66.366.37986741160005-0.0198674116000479
76.346.36125900416728-0.0212590041672831
86.496.341347189829140.148652810170862
96.56.480579824324830.0194201756751715
106.56.498769337314970.00123066268503447
116.556.499922012515760.0500779874842365
126.576.546826542067930.0231734579320655
136.656.568531490629270.0814685093707297
146.616.64483731475117-0.0348373147511678
156.666.612207651672580.0477923483274214
166.736.656971383745410.0730286162545859
176.736.725372153451780.00462784654822279
186.756.729706731898090.0202932681019066
196.756.748714009171280.00128599082872061
206.716.74991850635377-0.0399185063537697
216.776.712529648394210.0574703516057937
226.836.766358085611580.0636419143884215
236.96.825966991722830.0740330082771665
246.896.89530850481111-0.00530850481110612
257.146.890336401631670.249663598368334
267.357.124178738675560.225821261324437
277.437.335689635127520.0943103648724826
287.427.4240235222996-0.00402352229959746
297.417.42025497188282-0.0102549718828158
307.467.410649860817090.0493501391829119
317.477.456872666045380.0131273339546212
327.457.46916811668843-0.0191681166884292
337.477.451214689627190.0187853103728095
347.447.46880956893031-0.0288095689303072
357.437.44182567151026-0.0118256715102634
367.437.43074939655009-0.000749396550092207
377.447.43004748949680.00995251050320523
387.497.439369306256360.0506306937436394
397.487.48679151689717-0.00679151689717372
407.437.48043038057739-0.0504303805773922
417.337.43319578919402-0.10319578919402
427.427.336539549854650.0834604501453535
437.987.414711084833210.565288915166787
447.417.9441774623569-0.534177462356902
457.257.44385099502213-0.193850995022128
467.047.26228439896842-0.222284398968417
476.987.05408623278447-0.0740862327844694
486.946.98469486804279-0.044694868042785
496.96.94283232794764-0.0428323279476368
506.926.902714298191740.0172857018082633
516.866.91890459960013-0.0589045996001332
526.866.86373280313821-0.00373280313820601
536.896.860236548917460.0297634510825429
546.916.888113880675550.0218861193244493
556.96.90861306968468-0.00861306968467535
566.886.90054581295462-0.0205458129546221
576.786.88130199467605-0.101301994676046
586.796.786419539496070.00358046050392957
596.816.789773105083540.0202268949164583
606.786.80871821526107-0.0287182152610681

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.31 & 6.19 & 0.119999999999999 \tabularnewline
3 & 6.35 & 6.30239556198284 & 0.0476044380171574 \tabularnewline
4 & 6.38 & 6.34698329168131 & 0.0330167083186925 \tabularnewline
5 & 6.38 & 6.37790772073383 & 0.00209227926616684 \tabularnewline
6 & 6.36 & 6.37986741160005 & -0.0198674116000479 \tabularnewline
7 & 6.34 & 6.36125900416728 & -0.0212590041672831 \tabularnewline
8 & 6.49 & 6.34134718982914 & 0.148652810170862 \tabularnewline
9 & 6.5 & 6.48057982432483 & 0.0194201756751715 \tabularnewline
10 & 6.5 & 6.49876933731497 & 0.00123066268503447 \tabularnewline
11 & 6.55 & 6.49992201251576 & 0.0500779874842365 \tabularnewline
12 & 6.57 & 6.54682654206793 & 0.0231734579320655 \tabularnewline
13 & 6.65 & 6.56853149062927 & 0.0814685093707297 \tabularnewline
14 & 6.61 & 6.64483731475117 & -0.0348373147511678 \tabularnewline
15 & 6.66 & 6.61220765167258 & 0.0477923483274214 \tabularnewline
16 & 6.73 & 6.65697138374541 & 0.0730286162545859 \tabularnewline
17 & 6.73 & 6.72537215345178 & 0.00462784654822279 \tabularnewline
18 & 6.75 & 6.72970673189809 & 0.0202932681019066 \tabularnewline
19 & 6.75 & 6.74871400917128 & 0.00128599082872061 \tabularnewline
20 & 6.71 & 6.74991850635377 & -0.0399185063537697 \tabularnewline
21 & 6.77 & 6.71252964839421 & 0.0574703516057937 \tabularnewline
22 & 6.83 & 6.76635808561158 & 0.0636419143884215 \tabularnewline
23 & 6.9 & 6.82596699172283 & 0.0740330082771665 \tabularnewline
24 & 6.89 & 6.89530850481111 & -0.00530850481110612 \tabularnewline
25 & 7.14 & 6.89033640163167 & 0.249663598368334 \tabularnewline
26 & 7.35 & 7.12417873867556 & 0.225821261324437 \tabularnewline
27 & 7.43 & 7.33568963512752 & 0.0943103648724826 \tabularnewline
28 & 7.42 & 7.4240235222996 & -0.00402352229959746 \tabularnewline
29 & 7.41 & 7.42025497188282 & -0.0102549718828158 \tabularnewline
30 & 7.46 & 7.41064986081709 & 0.0493501391829119 \tabularnewline
31 & 7.47 & 7.45687266604538 & 0.0131273339546212 \tabularnewline
32 & 7.45 & 7.46916811668843 & -0.0191681166884292 \tabularnewline
33 & 7.47 & 7.45121468962719 & 0.0187853103728095 \tabularnewline
34 & 7.44 & 7.46880956893031 & -0.0288095689303072 \tabularnewline
35 & 7.43 & 7.44182567151026 & -0.0118256715102634 \tabularnewline
36 & 7.43 & 7.43074939655009 & -0.000749396550092207 \tabularnewline
37 & 7.44 & 7.4300474894968 & 0.00995251050320523 \tabularnewline
38 & 7.49 & 7.43936930625636 & 0.0506306937436394 \tabularnewline
39 & 7.48 & 7.48679151689717 & -0.00679151689717372 \tabularnewline
40 & 7.43 & 7.48043038057739 & -0.0504303805773922 \tabularnewline
41 & 7.33 & 7.43319578919402 & -0.10319578919402 \tabularnewline
42 & 7.42 & 7.33653954985465 & 0.0834604501453535 \tabularnewline
43 & 7.98 & 7.41471108483321 & 0.565288915166787 \tabularnewline
44 & 7.41 & 7.9441774623569 & -0.534177462356902 \tabularnewline
45 & 7.25 & 7.44385099502213 & -0.193850995022128 \tabularnewline
46 & 7.04 & 7.26228439896842 & -0.222284398968417 \tabularnewline
47 & 6.98 & 7.05408623278447 & -0.0740862327844694 \tabularnewline
48 & 6.94 & 6.98469486804279 & -0.044694868042785 \tabularnewline
49 & 6.9 & 6.94283232794764 & -0.0428323279476368 \tabularnewline
50 & 6.92 & 6.90271429819174 & 0.0172857018082633 \tabularnewline
51 & 6.86 & 6.91890459960013 & -0.0589045996001332 \tabularnewline
52 & 6.86 & 6.86373280313821 & -0.00373280313820601 \tabularnewline
53 & 6.89 & 6.86023654891746 & 0.0297634510825429 \tabularnewline
54 & 6.91 & 6.88811388067555 & 0.0218861193244493 \tabularnewline
55 & 6.9 & 6.90861306968468 & -0.00861306968467535 \tabularnewline
56 & 6.88 & 6.90054581295462 & -0.0205458129546221 \tabularnewline
57 & 6.78 & 6.88130199467605 & -0.101301994676046 \tabularnewline
58 & 6.79 & 6.78641953949607 & 0.00358046050392957 \tabularnewline
59 & 6.81 & 6.78977310508354 & 0.0202268949164583 \tabularnewline
60 & 6.78 & 6.80871821526107 & -0.0287182152610681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160866&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]2[/C][C]6.31[/C][C]6.19[/C][C]0.119999999999999[/C][/ROW]
[ROW][C]3[/C][C]6.35[/C][C]6.30239556198284[/C][C]0.0476044380171574[/C][/ROW]
[ROW][C]4[/C][C]6.38[/C][C]6.34698329168131[/C][C]0.0330167083186925[/C][/ROW]
[ROW][C]5[/C][C]6.38[/C][C]6.37790772073383[/C][C]0.00209227926616684[/C][/ROW]
[ROW][C]6[/C][C]6.36[/C][C]6.37986741160005[/C][C]-0.0198674116000479[/C][/ROW]
[ROW][C]7[/C][C]6.34[/C][C]6.36125900416728[/C][C]-0.0212590041672831[/C][/ROW]
[ROW][C]8[/C][C]6.49[/C][C]6.34134718982914[/C][C]0.148652810170862[/C][/ROW]
[ROW][C]9[/C][C]6.5[/C][C]6.48057982432483[/C][C]0.0194201756751715[/C][/ROW]
[ROW][C]10[/C][C]6.5[/C][C]6.49876933731497[/C][C]0.00123066268503447[/C][/ROW]
[ROW][C]11[/C][C]6.55[/C][C]6.49992201251576[/C][C]0.0500779874842365[/C][/ROW]
[ROW][C]12[/C][C]6.57[/C][C]6.54682654206793[/C][C]0.0231734579320655[/C][/ROW]
[ROW][C]13[/C][C]6.65[/C][C]6.56853149062927[/C][C]0.0814685093707297[/C][/ROW]
[ROW][C]14[/C][C]6.61[/C][C]6.64483731475117[/C][C]-0.0348373147511678[/C][/ROW]
[ROW][C]15[/C][C]6.66[/C][C]6.61220765167258[/C][C]0.0477923483274214[/C][/ROW]
[ROW][C]16[/C][C]6.73[/C][C]6.65697138374541[/C][C]0.0730286162545859[/C][/ROW]
[ROW][C]17[/C][C]6.73[/C][C]6.72537215345178[/C][C]0.00462784654822279[/C][/ROW]
[ROW][C]18[/C][C]6.75[/C][C]6.72970673189809[/C][C]0.0202932681019066[/C][/ROW]
[ROW][C]19[/C][C]6.75[/C][C]6.74871400917128[/C][C]0.00128599082872061[/C][/ROW]
[ROW][C]20[/C][C]6.71[/C][C]6.74991850635377[/C][C]-0.0399185063537697[/C][/ROW]
[ROW][C]21[/C][C]6.77[/C][C]6.71252964839421[/C][C]0.0574703516057937[/C][/ROW]
[ROW][C]22[/C][C]6.83[/C][C]6.76635808561158[/C][C]0.0636419143884215[/C][/ROW]
[ROW][C]23[/C][C]6.9[/C][C]6.82596699172283[/C][C]0.0740330082771665[/C][/ROW]
[ROW][C]24[/C][C]6.89[/C][C]6.89530850481111[/C][C]-0.00530850481110612[/C][/ROW]
[ROW][C]25[/C][C]7.14[/C][C]6.89033640163167[/C][C]0.249663598368334[/C][/ROW]
[ROW][C]26[/C][C]7.35[/C][C]7.12417873867556[/C][C]0.225821261324437[/C][/ROW]
[ROW][C]27[/C][C]7.43[/C][C]7.33568963512752[/C][C]0.0943103648724826[/C][/ROW]
[ROW][C]28[/C][C]7.42[/C][C]7.4240235222996[/C][C]-0.00402352229959746[/C][/ROW]
[ROW][C]29[/C][C]7.41[/C][C]7.42025497188282[/C][C]-0.0102549718828158[/C][/ROW]
[ROW][C]30[/C][C]7.46[/C][C]7.41064986081709[/C][C]0.0493501391829119[/C][/ROW]
[ROW][C]31[/C][C]7.47[/C][C]7.45687266604538[/C][C]0.0131273339546212[/C][/ROW]
[ROW][C]32[/C][C]7.45[/C][C]7.46916811668843[/C][C]-0.0191681166884292[/C][/ROW]
[ROW][C]33[/C][C]7.47[/C][C]7.45121468962719[/C][C]0.0187853103728095[/C][/ROW]
[ROW][C]34[/C][C]7.44[/C][C]7.46880956893031[/C][C]-0.0288095689303072[/C][/ROW]
[ROW][C]35[/C][C]7.43[/C][C]7.44182567151026[/C][C]-0.0118256715102634[/C][/ROW]
[ROW][C]36[/C][C]7.43[/C][C]7.43074939655009[/C][C]-0.000749396550092207[/C][/ROW]
[ROW][C]37[/C][C]7.44[/C][C]7.4300474894968[/C][C]0.00995251050320523[/C][/ROW]
[ROW][C]38[/C][C]7.49[/C][C]7.43936930625636[/C][C]0.0506306937436394[/C][/ROW]
[ROW][C]39[/C][C]7.48[/C][C]7.48679151689717[/C][C]-0.00679151689717372[/C][/ROW]
[ROW][C]40[/C][C]7.43[/C][C]7.48043038057739[/C][C]-0.0504303805773922[/C][/ROW]
[ROW][C]41[/C][C]7.33[/C][C]7.43319578919402[/C][C]-0.10319578919402[/C][/ROW]
[ROW][C]42[/C][C]7.42[/C][C]7.33653954985465[/C][C]0.0834604501453535[/C][/ROW]
[ROW][C]43[/C][C]7.98[/C][C]7.41471108483321[/C][C]0.565288915166787[/C][/ROW]
[ROW][C]44[/C][C]7.41[/C][C]7.9441774623569[/C][C]-0.534177462356902[/C][/ROW]
[ROW][C]45[/C][C]7.25[/C][C]7.44385099502213[/C][C]-0.193850995022128[/C][/ROW]
[ROW][C]46[/C][C]7.04[/C][C]7.26228439896842[/C][C]-0.222284398968417[/C][/ROW]
[ROW][C]47[/C][C]6.98[/C][C]7.05408623278447[/C][C]-0.0740862327844694[/C][/ROW]
[ROW][C]48[/C][C]6.94[/C][C]6.98469486804279[/C][C]-0.044694868042785[/C][/ROW]
[ROW][C]49[/C][C]6.9[/C][C]6.94283232794764[/C][C]-0.0428323279476368[/C][/ROW]
[ROW][C]50[/C][C]6.92[/C][C]6.90271429819174[/C][C]0.0172857018082633[/C][/ROW]
[ROW][C]51[/C][C]6.86[/C][C]6.91890459960013[/C][C]-0.0589045996001332[/C][/ROW]
[ROW][C]52[/C][C]6.86[/C][C]6.86373280313821[/C][C]-0.00373280313820601[/C][/ROW]
[ROW][C]53[/C][C]6.89[/C][C]6.86023654891746[/C][C]0.0297634510825429[/C][/ROW]
[ROW][C]54[/C][C]6.91[/C][C]6.88811388067555[/C][C]0.0218861193244493[/C][/ROW]
[ROW][C]55[/C][C]6.9[/C][C]6.90861306968468[/C][C]-0.00861306968467535[/C][/ROW]
[ROW][C]56[/C][C]6.88[/C][C]6.90054581295462[/C][C]-0.0205458129546221[/C][/ROW]
[ROW][C]57[/C][C]6.78[/C][C]6.88130199467605[/C][C]-0.101301994676046[/C][/ROW]
[ROW][C]58[/C][C]6.79[/C][C]6.78641953949607[/C][C]0.00358046050392957[/C][/ROW]
[ROW][C]59[/C][C]6.81[/C][C]6.78977310508354[/C][C]0.0202268949164583[/C][/ROW]
[ROW][C]60[/C][C]6.78[/C][C]6.80871821526107[/C][C]-0.0287182152610681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160866&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160866&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
26.316.190.119999999999999
36.356.302395561982840.0476044380171574
46.386.346983291681310.0330167083186925
56.386.377907720733830.00209227926616684
66.366.37986741160005-0.0198674116000479
76.346.36125900416728-0.0212590041672831
86.496.341347189829140.148652810170862
96.56.480579824324830.0194201756751715
106.56.498769337314970.00123066268503447
116.556.499922012515760.0500779874842365
126.576.546826542067930.0231734579320655
136.656.568531490629270.0814685093707297
146.616.64483731475117-0.0348373147511678
156.666.612207651672580.0477923483274214
166.736.656971383745410.0730286162545859
176.736.725372153451780.00462784654822279
186.756.729706731898090.0202932681019066
196.756.748714009171280.00128599082872061
206.716.74991850635377-0.0399185063537697
216.776.712529648394210.0574703516057937
226.836.766358085611580.0636419143884215
236.96.825966991722830.0740330082771665
246.896.89530850481111-0.00530850481110612
257.146.890336401631670.249663598368334
267.357.124178738675560.225821261324437
277.437.335689635127520.0943103648724826
287.427.4240235222996-0.00402352229959746
297.417.42025497188282-0.0102549718828158
307.467.410649860817090.0493501391829119
317.477.456872666045380.0131273339546212
327.457.46916811668843-0.0191681166884292
337.477.451214689627190.0187853103728095
347.447.46880956893031-0.0288095689303072
357.437.44182567151026-0.0118256715102634
367.437.43074939655009-0.000749396550092207
377.447.43004748949680.00995251050320523
387.497.439369306256360.0506306937436394
397.487.48679151689717-0.00679151689717372
407.437.48043038057739-0.0504303805773922
417.337.43319578919402-0.10319578919402
427.427.336539549854650.0834604501453535
437.987.414711084833210.565288915166787
447.417.9441774623569-0.534177462356902
457.257.44385099502213-0.193850995022128
467.047.26228439896842-0.222284398968417
476.987.05408623278447-0.0740862327844694
486.946.98469486804279-0.044694868042785
496.96.94283232794764-0.0428323279476368
506.926.902714298191740.0172857018082633
516.866.91890459960013-0.0589045996001332
526.866.86373280313821-0.00373280313820601
536.896.860236548917460.0297634510825429
546.916.888113880675550.0218861193244493
556.96.90861306968468-0.00861306968467535
566.886.90054581295462-0.0205458129546221
576.786.88130199467605-0.101301994676046
586.796.786419539496070.00358046050392957
596.816.789773105083540.0202268949164583
606.786.80871821526107-0.0287182152610681







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
616.78181988239936.532890409900627.03074935489798
626.78181988239936.440752423116537.12288734168207
636.78181988239936.368675668734477.19496409606414
646.78181988239936.30742630024647.25621346455221
656.78181988239936.253227033137237.31041273166138
666.78181988239936.204090248579017.3595495162196
676.78181988239936.158816945570547.40482281922806
686.78181988239936.116617816256697.44702194854191
696.78181988239936.07694051803727.48669924676141
706.78181988239936.039380627101837.52425913769677
716.78181988239936.003631487915177.56000827688343
726.78181988239935.969454012354957.59418575244366

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 6.7818198823993 & 6.53289040990062 & 7.03074935489798 \tabularnewline
62 & 6.7818198823993 & 6.44075242311653 & 7.12288734168207 \tabularnewline
63 & 6.7818198823993 & 6.36867566873447 & 7.19496409606414 \tabularnewline
64 & 6.7818198823993 & 6.3074263002464 & 7.25621346455221 \tabularnewline
65 & 6.7818198823993 & 6.25322703313723 & 7.31041273166138 \tabularnewline
66 & 6.7818198823993 & 6.20409024857901 & 7.3595495162196 \tabularnewline
67 & 6.7818198823993 & 6.15881694557054 & 7.40482281922806 \tabularnewline
68 & 6.7818198823993 & 6.11661781625669 & 7.44702194854191 \tabularnewline
69 & 6.7818198823993 & 6.0769405180372 & 7.48669924676141 \tabularnewline
70 & 6.7818198823993 & 6.03938062710183 & 7.52425913769677 \tabularnewline
71 & 6.7818198823993 & 6.00363148791517 & 7.56000827688343 \tabularnewline
72 & 6.7818198823993 & 5.96945401235495 & 7.59418575244366 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160866&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]61[/C][C]6.7818198823993[/C][C]6.53289040990062[/C][C]7.03074935489798[/C][/ROW]
[ROW][C]62[/C][C]6.7818198823993[/C][C]6.44075242311653[/C][C]7.12288734168207[/C][/ROW]
[ROW][C]63[/C][C]6.7818198823993[/C][C]6.36867566873447[/C][C]7.19496409606414[/C][/ROW]
[ROW][C]64[/C][C]6.7818198823993[/C][C]6.3074263002464[/C][C]7.25621346455221[/C][/ROW]
[ROW][C]65[/C][C]6.7818198823993[/C][C]6.25322703313723[/C][C]7.31041273166138[/C][/ROW]
[ROW][C]66[/C][C]6.7818198823993[/C][C]6.20409024857901[/C][C]7.3595495162196[/C][/ROW]
[ROW][C]67[/C][C]6.7818198823993[/C][C]6.15881694557054[/C][C]7.40482281922806[/C][/ROW]
[ROW][C]68[/C][C]6.7818198823993[/C][C]6.11661781625669[/C][C]7.44702194854191[/C][/ROW]
[ROW][C]69[/C][C]6.7818198823993[/C][C]6.0769405180372[/C][C]7.48669924676141[/C][/ROW]
[ROW][C]70[/C][C]6.7818198823993[/C][C]6.03938062710183[/C][C]7.52425913769677[/C][/ROW]
[ROW][C]71[/C][C]6.7818198823993[/C][C]6.00363148791517[/C][C]7.56000827688343[/C][/ROW]
[ROW][C]72[/C][C]6.7818198823993[/C][C]5.96945401235495[/C][C]7.59418575244366[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160866&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160866&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
616.78181988239936.532890409900627.03074935489798
626.78181988239936.440752423116537.12288734168207
636.78181988239936.368675668734477.19496409606414
646.78181988239936.30742630024647.25621346455221
656.78181988239936.253227033137237.31041273166138
666.78181988239936.204090248579017.3595495162196
676.78181988239936.158816945570547.40482281922806
686.78181988239936.116617816256697.44702194854191
696.78181988239936.07694051803727.48669924676141
706.78181988239936.039380627101837.52425913769677
716.78181988239936.003631487915177.56000827688343
726.78181988239935.969454012354957.59418575244366



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')