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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Dec 2011 10:17:13 -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/t132499909442z9z4u6lybgojf.htm/, Retrieved Wed, 15 May 2024 19:16:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160856, Retrieved Wed, 15 May 2024 19:16:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact124
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 15:17:13] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
49,98
50,12
50,37
50,39
50,34
50,32
50,32
50,32
50,67
50,86
50,95
51,02
51,02
51,06
50,9
51,23
51,29
51,3
51,3
51,3
51,46
51,47
51,77
51,82
51,82
51,84
51,9
51,94
52,22
52,27
52,27
52,28
52,53
52,73
52,72
52,67
52,67
52,65
52,69
52,73
52,84
52,83
52,83
52,84
52,82
53,09
53,4
53,43
53,43
53,42
53,6
53,69
54,05
54,04
54,04
54,08
54,05
54,39
54,38
54,46




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160856&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160856&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160856&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 time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0527186466295645
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0527186466295645 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160856&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0527186466295645[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160856&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160856&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
alpha1
beta0.0527186466295645
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
350.3750.260.109999999999999
450.3950.5157990511292-0.125799051129249
550.3450.5291670954064-0.189167095406432
650.3250.4691944621498-0.149194462149765
750.3250.4413291320206-0.121329132020598
850.3250.4349328243837-0.114932824383736
950.6750.42887372142890.241126278571087
1050.8650.7915855725020.0684144274979985
1150.9550.9851922885296-0.035192288529629
1251.0251.0733369987066-0.0533369987065555
1351.0251.1405251443195-0.120525144319458
1451.0651.1341712218261-0.0741712218261057
1550.951.1702610153926-0.270261015392578
1651.2350.99601322042430.233986779575652
1751.2951.3383486867728-0.0483486867727834
1851.351.3957998094398-0.0957998094398107
1951.351.4007493731388-0.100749373138768
2051.351.3954380025381-0.095438002538117
2151.4651.39040664020730.0695933597927265
2251.4751.55407550795-0.0840755079499544
2351.7751.55964316095610.210356839043868
2451.8251.8707328888198-0.0507328888198089
2551.8251.9180583195816-0.098058319581618
2651.8451.9128888176825-0.0728888176825038
2751.951.9290462178599-0.0290462178598574
2851.9451.9875149405646-0.0475149405645752
2952.2252.02501001720330.194989982796677
3052.2752.3152896252027-0.0452896252026846
3152.2752.3629020174556-0.0929020174556427
3252.2852.3580043488262-0.0780043488262265
3352.5352.36389206512490.166107934875114
3452.7352.62264905064590.107350949354064
3552.7252.8283084474103-0.10830844741028
3652.6752.8125985726443-0.14259857264426
3752.6752.7550809688831-0.0850809688831475
3852.6552.7505956153497-0.100595615349697
3952.6952.7252923506516-0.035292350651595
4052.7352.7634317856889-0.0334317856888617
4152.8452.80166930719290.0383306928070724
4252.8352.9136900494421-0.0836900494421045
4352.8352.8992780232991-0.0692780232991481
4452.8452.8956257796696-0.05562577966964
4552.8252.9026932638478-0.0826932638477516
4653.0952.87833378689230.211666213107691
4753.453.15949254318460.240507456815436
4853.4353.4821717708122-0.0521717708121869
4953.4353.5094213456627-0.079421345662702
5053.4253.5052343598059-0.0852343598058596
5153.653.49074091971060.109259080289441
5253.6953.67650091055540.0134990894445863
5354.0553.76721256428170.28278743571834
5454.0454.1421207351766-0.102120735176577
5554.0454.1267370682253-0.0867370682252542
5654.0854.1221644073758-0.0421644073758003
5754.0554.159941556883-0.109941556883008
5854.3954.12414558679580.265854413204217
5954.3854.4781610716604-0.0981610716604138
6054.4654.4629861528108-0.00298615281077019

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 50.37 & 50.26 & 0.109999999999999 \tabularnewline
4 & 50.39 & 50.5157990511292 & -0.125799051129249 \tabularnewline
5 & 50.34 & 50.5291670954064 & -0.189167095406432 \tabularnewline
6 & 50.32 & 50.4691944621498 & -0.149194462149765 \tabularnewline
7 & 50.32 & 50.4413291320206 & -0.121329132020598 \tabularnewline
8 & 50.32 & 50.4349328243837 & -0.114932824383736 \tabularnewline
9 & 50.67 & 50.4288737214289 & 0.241126278571087 \tabularnewline
10 & 50.86 & 50.791585572502 & 0.0684144274979985 \tabularnewline
11 & 50.95 & 50.9851922885296 & -0.035192288529629 \tabularnewline
12 & 51.02 & 51.0733369987066 & -0.0533369987065555 \tabularnewline
13 & 51.02 & 51.1405251443195 & -0.120525144319458 \tabularnewline
14 & 51.06 & 51.1341712218261 & -0.0741712218261057 \tabularnewline
15 & 50.9 & 51.1702610153926 & -0.270261015392578 \tabularnewline
16 & 51.23 & 50.9960132204243 & 0.233986779575652 \tabularnewline
17 & 51.29 & 51.3383486867728 & -0.0483486867727834 \tabularnewline
18 & 51.3 & 51.3957998094398 & -0.0957998094398107 \tabularnewline
19 & 51.3 & 51.4007493731388 & -0.100749373138768 \tabularnewline
20 & 51.3 & 51.3954380025381 & -0.095438002538117 \tabularnewline
21 & 51.46 & 51.3904066402073 & 0.0695933597927265 \tabularnewline
22 & 51.47 & 51.55407550795 & -0.0840755079499544 \tabularnewline
23 & 51.77 & 51.5596431609561 & 0.210356839043868 \tabularnewline
24 & 51.82 & 51.8707328888198 & -0.0507328888198089 \tabularnewline
25 & 51.82 & 51.9180583195816 & -0.098058319581618 \tabularnewline
26 & 51.84 & 51.9128888176825 & -0.0728888176825038 \tabularnewline
27 & 51.9 & 51.9290462178599 & -0.0290462178598574 \tabularnewline
28 & 51.94 & 51.9875149405646 & -0.0475149405645752 \tabularnewline
29 & 52.22 & 52.0250100172033 & 0.194989982796677 \tabularnewline
30 & 52.27 & 52.3152896252027 & -0.0452896252026846 \tabularnewline
31 & 52.27 & 52.3629020174556 & -0.0929020174556427 \tabularnewline
32 & 52.28 & 52.3580043488262 & -0.0780043488262265 \tabularnewline
33 & 52.53 & 52.3638920651249 & 0.166107934875114 \tabularnewline
34 & 52.73 & 52.6226490506459 & 0.107350949354064 \tabularnewline
35 & 52.72 & 52.8283084474103 & -0.10830844741028 \tabularnewline
36 & 52.67 & 52.8125985726443 & -0.14259857264426 \tabularnewline
37 & 52.67 & 52.7550809688831 & -0.0850809688831475 \tabularnewline
38 & 52.65 & 52.7505956153497 & -0.100595615349697 \tabularnewline
39 & 52.69 & 52.7252923506516 & -0.035292350651595 \tabularnewline
40 & 52.73 & 52.7634317856889 & -0.0334317856888617 \tabularnewline
41 & 52.84 & 52.8016693071929 & 0.0383306928070724 \tabularnewline
42 & 52.83 & 52.9136900494421 & -0.0836900494421045 \tabularnewline
43 & 52.83 & 52.8992780232991 & -0.0692780232991481 \tabularnewline
44 & 52.84 & 52.8956257796696 & -0.05562577966964 \tabularnewline
45 & 52.82 & 52.9026932638478 & -0.0826932638477516 \tabularnewline
46 & 53.09 & 52.8783337868923 & 0.211666213107691 \tabularnewline
47 & 53.4 & 53.1594925431846 & 0.240507456815436 \tabularnewline
48 & 53.43 & 53.4821717708122 & -0.0521717708121869 \tabularnewline
49 & 53.43 & 53.5094213456627 & -0.079421345662702 \tabularnewline
50 & 53.42 & 53.5052343598059 & -0.0852343598058596 \tabularnewline
51 & 53.6 & 53.4907409197106 & 0.109259080289441 \tabularnewline
52 & 53.69 & 53.6765009105554 & 0.0134990894445863 \tabularnewline
53 & 54.05 & 53.7672125642817 & 0.28278743571834 \tabularnewline
54 & 54.04 & 54.1421207351766 & -0.102120735176577 \tabularnewline
55 & 54.04 & 54.1267370682253 & -0.0867370682252542 \tabularnewline
56 & 54.08 & 54.1221644073758 & -0.0421644073758003 \tabularnewline
57 & 54.05 & 54.159941556883 & -0.109941556883008 \tabularnewline
58 & 54.39 & 54.1241455867958 & 0.265854413204217 \tabularnewline
59 & 54.38 & 54.4781610716604 & -0.0981610716604138 \tabularnewline
60 & 54.46 & 54.4629861528108 & -0.00298615281077019 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160856&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]3[/C][C]50.37[/C][C]50.26[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]4[/C][C]50.39[/C][C]50.5157990511292[/C][C]-0.125799051129249[/C][/ROW]
[ROW][C]5[/C][C]50.34[/C][C]50.5291670954064[/C][C]-0.189167095406432[/C][/ROW]
[ROW][C]6[/C][C]50.32[/C][C]50.4691944621498[/C][C]-0.149194462149765[/C][/ROW]
[ROW][C]7[/C][C]50.32[/C][C]50.4413291320206[/C][C]-0.121329132020598[/C][/ROW]
[ROW][C]8[/C][C]50.32[/C][C]50.4349328243837[/C][C]-0.114932824383736[/C][/ROW]
[ROW][C]9[/C][C]50.67[/C][C]50.4288737214289[/C][C]0.241126278571087[/C][/ROW]
[ROW][C]10[/C][C]50.86[/C][C]50.791585572502[/C][C]0.0684144274979985[/C][/ROW]
[ROW][C]11[/C][C]50.95[/C][C]50.9851922885296[/C][C]-0.035192288529629[/C][/ROW]
[ROW][C]12[/C][C]51.02[/C][C]51.0733369987066[/C][C]-0.0533369987065555[/C][/ROW]
[ROW][C]13[/C][C]51.02[/C][C]51.1405251443195[/C][C]-0.120525144319458[/C][/ROW]
[ROW][C]14[/C][C]51.06[/C][C]51.1341712218261[/C][C]-0.0741712218261057[/C][/ROW]
[ROW][C]15[/C][C]50.9[/C][C]51.1702610153926[/C][C]-0.270261015392578[/C][/ROW]
[ROW][C]16[/C][C]51.23[/C][C]50.9960132204243[/C][C]0.233986779575652[/C][/ROW]
[ROW][C]17[/C][C]51.29[/C][C]51.3383486867728[/C][C]-0.0483486867727834[/C][/ROW]
[ROW][C]18[/C][C]51.3[/C][C]51.3957998094398[/C][C]-0.0957998094398107[/C][/ROW]
[ROW][C]19[/C][C]51.3[/C][C]51.4007493731388[/C][C]-0.100749373138768[/C][/ROW]
[ROW][C]20[/C][C]51.3[/C][C]51.3954380025381[/C][C]-0.095438002538117[/C][/ROW]
[ROW][C]21[/C][C]51.46[/C][C]51.3904066402073[/C][C]0.0695933597927265[/C][/ROW]
[ROW][C]22[/C][C]51.47[/C][C]51.55407550795[/C][C]-0.0840755079499544[/C][/ROW]
[ROW][C]23[/C][C]51.77[/C][C]51.5596431609561[/C][C]0.210356839043868[/C][/ROW]
[ROW][C]24[/C][C]51.82[/C][C]51.8707328888198[/C][C]-0.0507328888198089[/C][/ROW]
[ROW][C]25[/C][C]51.82[/C][C]51.9180583195816[/C][C]-0.098058319581618[/C][/ROW]
[ROW][C]26[/C][C]51.84[/C][C]51.9128888176825[/C][C]-0.0728888176825038[/C][/ROW]
[ROW][C]27[/C][C]51.9[/C][C]51.9290462178599[/C][C]-0.0290462178598574[/C][/ROW]
[ROW][C]28[/C][C]51.94[/C][C]51.9875149405646[/C][C]-0.0475149405645752[/C][/ROW]
[ROW][C]29[/C][C]52.22[/C][C]52.0250100172033[/C][C]0.194989982796677[/C][/ROW]
[ROW][C]30[/C][C]52.27[/C][C]52.3152896252027[/C][C]-0.0452896252026846[/C][/ROW]
[ROW][C]31[/C][C]52.27[/C][C]52.3629020174556[/C][C]-0.0929020174556427[/C][/ROW]
[ROW][C]32[/C][C]52.28[/C][C]52.3580043488262[/C][C]-0.0780043488262265[/C][/ROW]
[ROW][C]33[/C][C]52.53[/C][C]52.3638920651249[/C][C]0.166107934875114[/C][/ROW]
[ROW][C]34[/C][C]52.73[/C][C]52.6226490506459[/C][C]0.107350949354064[/C][/ROW]
[ROW][C]35[/C][C]52.72[/C][C]52.8283084474103[/C][C]-0.10830844741028[/C][/ROW]
[ROW][C]36[/C][C]52.67[/C][C]52.8125985726443[/C][C]-0.14259857264426[/C][/ROW]
[ROW][C]37[/C][C]52.67[/C][C]52.7550809688831[/C][C]-0.0850809688831475[/C][/ROW]
[ROW][C]38[/C][C]52.65[/C][C]52.7505956153497[/C][C]-0.100595615349697[/C][/ROW]
[ROW][C]39[/C][C]52.69[/C][C]52.7252923506516[/C][C]-0.035292350651595[/C][/ROW]
[ROW][C]40[/C][C]52.73[/C][C]52.7634317856889[/C][C]-0.0334317856888617[/C][/ROW]
[ROW][C]41[/C][C]52.84[/C][C]52.8016693071929[/C][C]0.0383306928070724[/C][/ROW]
[ROW][C]42[/C][C]52.83[/C][C]52.9136900494421[/C][C]-0.0836900494421045[/C][/ROW]
[ROW][C]43[/C][C]52.83[/C][C]52.8992780232991[/C][C]-0.0692780232991481[/C][/ROW]
[ROW][C]44[/C][C]52.84[/C][C]52.8956257796696[/C][C]-0.05562577966964[/C][/ROW]
[ROW][C]45[/C][C]52.82[/C][C]52.9026932638478[/C][C]-0.0826932638477516[/C][/ROW]
[ROW][C]46[/C][C]53.09[/C][C]52.8783337868923[/C][C]0.211666213107691[/C][/ROW]
[ROW][C]47[/C][C]53.4[/C][C]53.1594925431846[/C][C]0.240507456815436[/C][/ROW]
[ROW][C]48[/C][C]53.43[/C][C]53.4821717708122[/C][C]-0.0521717708121869[/C][/ROW]
[ROW][C]49[/C][C]53.43[/C][C]53.5094213456627[/C][C]-0.079421345662702[/C][/ROW]
[ROW][C]50[/C][C]53.42[/C][C]53.5052343598059[/C][C]-0.0852343598058596[/C][/ROW]
[ROW][C]51[/C][C]53.6[/C][C]53.4907409197106[/C][C]0.109259080289441[/C][/ROW]
[ROW][C]52[/C][C]53.69[/C][C]53.6765009105554[/C][C]0.0134990894445863[/C][/ROW]
[ROW][C]53[/C][C]54.05[/C][C]53.7672125642817[/C][C]0.28278743571834[/C][/ROW]
[ROW][C]54[/C][C]54.04[/C][C]54.1421207351766[/C][C]-0.102120735176577[/C][/ROW]
[ROW][C]55[/C][C]54.04[/C][C]54.1267370682253[/C][C]-0.0867370682252542[/C][/ROW]
[ROW][C]56[/C][C]54.08[/C][C]54.1221644073758[/C][C]-0.0421644073758003[/C][/ROW]
[ROW][C]57[/C][C]54.05[/C][C]54.159941556883[/C][C]-0.109941556883008[/C][/ROW]
[ROW][C]58[/C][C]54.39[/C][C]54.1241455867958[/C][C]0.265854413204217[/C][/ROW]
[ROW][C]59[/C][C]54.38[/C][C]54.4781610716604[/C][C]-0.0981610716604138[/C][/ROW]
[ROW][C]60[/C][C]54.46[/C][C]54.4629861528108[/C][C]-0.00298615281077019[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160856&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160856&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
350.3750.260.109999999999999
450.3950.5157990511292-0.125799051129249
550.3450.5291670954064-0.189167095406432
650.3250.4691944621498-0.149194462149765
750.3250.4413291320206-0.121329132020598
850.3250.4349328243837-0.114932824383736
950.6750.42887372142890.241126278571087
1050.8650.7915855725020.0684144274979985
1150.9550.9851922885296-0.035192288529629
1251.0251.0733369987066-0.0533369987065555
1351.0251.1405251443195-0.120525144319458
1451.0651.1341712218261-0.0741712218261057
1550.951.1702610153926-0.270261015392578
1651.2350.99601322042430.233986779575652
1751.2951.3383486867728-0.0483486867727834
1851.351.3957998094398-0.0957998094398107
1951.351.4007493731388-0.100749373138768
2051.351.3954380025381-0.095438002538117
2151.4651.39040664020730.0695933597927265
2251.4751.55407550795-0.0840755079499544
2351.7751.55964316095610.210356839043868
2451.8251.8707328888198-0.0507328888198089
2551.8251.9180583195816-0.098058319581618
2651.8451.9128888176825-0.0728888176825038
2751.951.9290462178599-0.0290462178598574
2851.9451.9875149405646-0.0475149405645752
2952.2252.02501001720330.194989982796677
3052.2752.3152896252027-0.0452896252026846
3152.2752.3629020174556-0.0929020174556427
3252.2852.3580043488262-0.0780043488262265
3352.5352.36389206512490.166107934875114
3452.7352.62264905064590.107350949354064
3552.7252.8283084474103-0.10830844741028
3652.6752.8125985726443-0.14259857264426
3752.6752.7550809688831-0.0850809688831475
3852.6552.7505956153497-0.100595615349697
3952.6952.7252923506516-0.035292350651595
4052.7352.7634317856889-0.0334317856888617
4152.8452.80166930719290.0383306928070724
4252.8352.9136900494421-0.0836900494421045
4352.8352.8992780232991-0.0692780232991481
4452.8452.8956257796696-0.05562577966964
4552.8252.9026932638478-0.0826932638477516
4653.0952.87833378689230.211666213107691
4753.453.15949254318460.240507456815436
4853.4353.4821717708122-0.0521717708121869
4953.4353.5094213456627-0.079421345662702
5053.4253.5052343598059-0.0852343598058596
5153.653.49074091971060.109259080289441
5253.6953.67650091055540.0134990894445863
5354.0553.76721256428170.28278743571834
5454.0454.1421207351766-0.102120735176577
5554.0454.1267370682253-0.0867370682252542
5654.0854.1221644073758-0.0421644073758003
5754.0554.159941556883-0.109941556883008
5854.3954.12414558679580.265854413204217
5954.3854.4781610716604-0.0981610716604138
6054.4654.4629861528108-0.00298615281077019







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6154.54282872687654.295461710827954.790195742924
6254.625657453751954.266487995736254.9848269117676
6354.708486180627954.257069627330955.1599027339248
6454.791314907503854.25666251253355.3259673024747
6554.874143634379854.261304614810855.4869826539488
6654.956972361255754.269024344522555.6449203779889
6755.039801088131754.278686286887655.8009158893758
6855.122629815007654.289574239127355.955685390888
6955.205458541883654.301207383749556.1097097000177
7055.288287268759654.313248007047856.2633265304714
7155.371115995635554.325450688309456.4167813029616
7255.453944722511554.337632309274756.5702571357482

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 54.542828726876 & 54.2954617108279 & 54.790195742924 \tabularnewline
62 & 54.6256574537519 & 54.2664879957362 & 54.9848269117676 \tabularnewline
63 & 54.7084861806279 & 54.2570696273309 & 55.1599027339248 \tabularnewline
64 & 54.7913149075038 & 54.256662512533 & 55.3259673024747 \tabularnewline
65 & 54.8741436343798 & 54.2613046148108 & 55.4869826539488 \tabularnewline
66 & 54.9569723612557 & 54.2690243445225 & 55.6449203779889 \tabularnewline
67 & 55.0398010881317 & 54.2786862868876 & 55.8009158893758 \tabularnewline
68 & 55.1226298150076 & 54.2895742391273 & 55.955685390888 \tabularnewline
69 & 55.2054585418836 & 54.3012073837495 & 56.1097097000177 \tabularnewline
70 & 55.2882872687596 & 54.3132480070478 & 56.2633265304714 \tabularnewline
71 & 55.3711159956355 & 54.3254506883094 & 56.4167813029616 \tabularnewline
72 & 55.4539447225115 & 54.3376323092747 & 56.5702571357482 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160856&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]54.542828726876[/C][C]54.2954617108279[/C][C]54.790195742924[/C][/ROW]
[ROW][C]62[/C][C]54.6256574537519[/C][C]54.2664879957362[/C][C]54.9848269117676[/C][/ROW]
[ROW][C]63[/C][C]54.7084861806279[/C][C]54.2570696273309[/C][C]55.1599027339248[/C][/ROW]
[ROW][C]64[/C][C]54.7913149075038[/C][C]54.256662512533[/C][C]55.3259673024747[/C][/ROW]
[ROW][C]65[/C][C]54.8741436343798[/C][C]54.2613046148108[/C][C]55.4869826539488[/C][/ROW]
[ROW][C]66[/C][C]54.9569723612557[/C][C]54.2690243445225[/C][C]55.6449203779889[/C][/ROW]
[ROW][C]67[/C][C]55.0398010881317[/C][C]54.2786862868876[/C][C]55.8009158893758[/C][/ROW]
[ROW][C]68[/C][C]55.1226298150076[/C][C]54.2895742391273[/C][C]55.955685390888[/C][/ROW]
[ROW][C]69[/C][C]55.2054585418836[/C][C]54.3012073837495[/C][C]56.1097097000177[/C][/ROW]
[ROW][C]70[/C][C]55.2882872687596[/C][C]54.3132480070478[/C][C]56.2633265304714[/C][/ROW]
[ROW][C]71[/C][C]55.3711159956355[/C][C]54.3254506883094[/C][C]56.4167813029616[/C][/ROW]
[ROW][C]72[/C][C]55.4539447225115[/C][C]54.3376323092747[/C][C]56.5702571357482[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160856&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160856&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
6154.54282872687654.295461710827954.790195742924
6254.625657453751954.266487995736254.9848269117676
6354.708486180627954.257069627330955.1599027339248
6454.791314907503854.25666251253355.3259673024747
6554.874143634379854.261304614810855.4869826539488
6654.956972361255754.269024344522555.6449203779889
6755.039801088131754.278686286887655.8009158893758
6855.122629815007654.289574239127355.955685390888
6955.205458541883654.301207383749556.1097097000177
7055.288287268759654.313248007047856.2633265304714
7155.371115995635554.325450688309456.4167813029616
7255.453944722511554.337632309274756.5702571357482



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')