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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 May 2011 15:27:04 +0000
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/May/18/t1305732190t5z5al47sewovvo.htm/, Retrieved Tue, 14 May 2024 00:12:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121891, Retrieved Tue, 14 May 2024 00:12:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht 10 axel ...] [2011-05-18 15:27:04] [99f56e8d3669c8e32d9c5b2d6e7ae714] [Current]
-   P     [Exponential Smoothing] [opdracht 10 axel ...] [2011-05-19 08:39:13] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
8
8
8.2
8.5
8.7
8.7
8
8
8.3
8.5
8.7
8.6
8.3
7.9
7.9
8.1
8.3
8.1
7.4
7.3
7.7
8
8
7.7
6.9
6.6
6.9
7.5
7.9
7.7
6.5
6.1
6.4
6.8
7.1
7.3
7.2
7
7
7
7.3
7.5
7.2
7.7
8
7.9
8
8
7.9
7.9
8
8.1
8.1
8.2
8
8.3
8.5
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
7.9
8.1
8.2
8.5
8.6
8.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121891&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121891&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121891&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.807498366458812
gamma0.100845034414204

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.807498366458812 \tabularnewline
gamma & 0.100845034414204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121891&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]0.807498366458812[/C][/ROW]
[ROW][C]gamma[/C][C]0.100845034414204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121891&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121891&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
beta0.807498366458812
gamma0.100845034414204







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138.38.49863782051282-0.198637820512822
147.97.751969165537840.148030834462162
157.97.871503822551570.0284961774484316
168.18.086181105958160.0138188940418367
178.38.30150650698988-0.00150650698988208
188.18.11695667172316-0.0169566717231593
197.47.50326418700613-0.103264187006131
207.37.244878524684980.0551214753150164
217.77.514389025958660.185610974041342
2287.976769584293870.0232304157061298
2388.2996947736954-0.299694773695396
247.77.76602506683345-0.0660250668334541
256.97.22104326655344-0.321043266553441
266.66.06596801991560.534031980084398
276.96.597197971470520.302802028529483
287.57.333376781535160.166623218464845
297.98.0720914249263-0.172091424926295
307.77.9497945470834-0.249794547083408
316.57.14808585836324-0.648085858363239
326.15.949757586409870.150242413590134
336.45.996078089956730.403921910043273
346.86.53474437249360.265255627506406
357.17.15310452506569-0.0531045250656899
367.37.118556041156910.181443958843093
377.27.27340507485986-0.0734050748598598
3877.0182972634874-0.0182972634874012
3977.20352225311066-0.203522253110658
4077.23084503285245-0.230845032852449
417.37.048604712585640.251395287414365
427.57.168272663174840.331727336825158
437.27.23614194577089-0.0361419457708916
447.77.431957383600250.268042616399747
4588.4734013584844-0.473401358484393
467.98.30363053482886-0.403630534828864
4787.881866203968330.118133796031674
4887.785592384620810.214407615379185
497.97.767059517129170.132940482870829
507.97.678575406550280.221424593449724
5188.25737540405474-0.257375404054736
528.18.34121185238052-0.241211852380525
538.18.25060034227942-0.150600342279416
548.27.745657478567310.454342521432686
5587.812538322436990.187461677563014
568.38.288913320842750.0110866791572519
578.58.92286579615168-0.422865796151683
588.68.6939023565279-0.0939023565278934
598.78.72224302369165-0.0222430236916527
608.78.512615151728870.187384848271128
618.58.472261443940270.0277385560597256
628.48.19882694931310.201173050686906
638.58.66127385911831-0.161273859118307
648.78.82271214799443-0.122712147994431
658.78.92778895561094-0.227788955610945
668.68.360516412724410.239483587275588
677.98.05389901824315-0.153899018243147
688.17.754625812412190.345374187587808
698.28.55851490470639-0.358514904706386
708.58.281514704804840.218485295195158
718.68.76210789043687-0.16210789043687
728.58.439539367052350.0604606329476542

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 8.3 & 8.49863782051282 & -0.198637820512822 \tabularnewline
14 & 7.9 & 7.75196916553784 & 0.148030834462162 \tabularnewline
15 & 7.9 & 7.87150382255157 & 0.0284961774484316 \tabularnewline
16 & 8.1 & 8.08618110595816 & 0.0138188940418367 \tabularnewline
17 & 8.3 & 8.30150650698988 & -0.00150650698988208 \tabularnewline
18 & 8.1 & 8.11695667172316 & -0.0169566717231593 \tabularnewline
19 & 7.4 & 7.50326418700613 & -0.103264187006131 \tabularnewline
20 & 7.3 & 7.24487852468498 & 0.0551214753150164 \tabularnewline
21 & 7.7 & 7.51438902595866 & 0.185610974041342 \tabularnewline
22 & 8 & 7.97676958429387 & 0.0232304157061298 \tabularnewline
23 & 8 & 8.2996947736954 & -0.299694773695396 \tabularnewline
24 & 7.7 & 7.76602506683345 & -0.0660250668334541 \tabularnewline
25 & 6.9 & 7.22104326655344 & -0.321043266553441 \tabularnewline
26 & 6.6 & 6.0659680199156 & 0.534031980084398 \tabularnewline
27 & 6.9 & 6.59719797147052 & 0.302802028529483 \tabularnewline
28 & 7.5 & 7.33337678153516 & 0.166623218464845 \tabularnewline
29 & 7.9 & 8.0720914249263 & -0.172091424926295 \tabularnewline
30 & 7.7 & 7.9497945470834 & -0.249794547083408 \tabularnewline
31 & 6.5 & 7.14808585836324 & -0.648085858363239 \tabularnewline
32 & 6.1 & 5.94975758640987 & 0.150242413590134 \tabularnewline
33 & 6.4 & 5.99607808995673 & 0.403921910043273 \tabularnewline
34 & 6.8 & 6.5347443724936 & 0.265255627506406 \tabularnewline
35 & 7.1 & 7.15310452506569 & -0.0531045250656899 \tabularnewline
36 & 7.3 & 7.11855604115691 & 0.181443958843093 \tabularnewline
37 & 7.2 & 7.27340507485986 & -0.0734050748598598 \tabularnewline
38 & 7 & 7.0182972634874 & -0.0182972634874012 \tabularnewline
39 & 7 & 7.20352225311066 & -0.203522253110658 \tabularnewline
40 & 7 & 7.23084503285245 & -0.230845032852449 \tabularnewline
41 & 7.3 & 7.04860471258564 & 0.251395287414365 \tabularnewline
42 & 7.5 & 7.16827266317484 & 0.331727336825158 \tabularnewline
43 & 7.2 & 7.23614194577089 & -0.0361419457708916 \tabularnewline
44 & 7.7 & 7.43195738360025 & 0.268042616399747 \tabularnewline
45 & 8 & 8.4734013584844 & -0.473401358484393 \tabularnewline
46 & 7.9 & 8.30363053482886 & -0.403630534828864 \tabularnewline
47 & 8 & 7.88186620396833 & 0.118133796031674 \tabularnewline
48 & 8 & 7.78559238462081 & 0.214407615379185 \tabularnewline
49 & 7.9 & 7.76705951712917 & 0.132940482870829 \tabularnewline
50 & 7.9 & 7.67857540655028 & 0.221424593449724 \tabularnewline
51 & 8 & 8.25737540405474 & -0.257375404054736 \tabularnewline
52 & 8.1 & 8.34121185238052 & -0.241211852380525 \tabularnewline
53 & 8.1 & 8.25060034227942 & -0.150600342279416 \tabularnewline
54 & 8.2 & 7.74565747856731 & 0.454342521432686 \tabularnewline
55 & 8 & 7.81253832243699 & 0.187461677563014 \tabularnewline
56 & 8.3 & 8.28891332084275 & 0.0110866791572519 \tabularnewline
57 & 8.5 & 8.92286579615168 & -0.422865796151683 \tabularnewline
58 & 8.6 & 8.6939023565279 & -0.0939023565278934 \tabularnewline
59 & 8.7 & 8.72224302369165 & -0.0222430236916527 \tabularnewline
60 & 8.7 & 8.51261515172887 & 0.187384848271128 \tabularnewline
61 & 8.5 & 8.47226144394027 & 0.0277385560597256 \tabularnewline
62 & 8.4 & 8.1988269493131 & 0.201173050686906 \tabularnewline
63 & 8.5 & 8.66127385911831 & -0.161273859118307 \tabularnewline
64 & 8.7 & 8.82271214799443 & -0.122712147994431 \tabularnewline
65 & 8.7 & 8.92778895561094 & -0.227788955610945 \tabularnewline
66 & 8.6 & 8.36051641272441 & 0.239483587275588 \tabularnewline
67 & 7.9 & 8.05389901824315 & -0.153899018243147 \tabularnewline
68 & 8.1 & 7.75462581241219 & 0.345374187587808 \tabularnewline
69 & 8.2 & 8.55851490470639 & -0.358514904706386 \tabularnewline
70 & 8.5 & 8.28151470480484 & 0.218485295195158 \tabularnewline
71 & 8.6 & 8.76210789043687 & -0.16210789043687 \tabularnewline
72 & 8.5 & 8.43953936705235 & 0.0604606329476542 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121891&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]8.3[/C][C]8.49863782051282[/C][C]-0.198637820512822[/C][/ROW]
[ROW][C]14[/C][C]7.9[/C][C]7.75196916553784[/C][C]0.148030834462162[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.87150382255157[/C][C]0.0284961774484316[/C][/ROW]
[ROW][C]16[/C][C]8.1[/C][C]8.08618110595816[/C][C]0.0138188940418367[/C][/ROW]
[ROW][C]17[/C][C]8.3[/C][C]8.30150650698988[/C][C]-0.00150650698988208[/C][/ROW]
[ROW][C]18[/C][C]8.1[/C][C]8.11695667172316[/C][C]-0.0169566717231593[/C][/ROW]
[ROW][C]19[/C][C]7.4[/C][C]7.50326418700613[/C][C]-0.103264187006131[/C][/ROW]
[ROW][C]20[/C][C]7.3[/C][C]7.24487852468498[/C][C]0.0551214753150164[/C][/ROW]
[ROW][C]21[/C][C]7.7[/C][C]7.51438902595866[/C][C]0.185610974041342[/C][/ROW]
[ROW][C]22[/C][C]8[/C][C]7.97676958429387[/C][C]0.0232304157061298[/C][/ROW]
[ROW][C]23[/C][C]8[/C][C]8.2996947736954[/C][C]-0.299694773695396[/C][/ROW]
[ROW][C]24[/C][C]7.7[/C][C]7.76602506683345[/C][C]-0.0660250668334541[/C][/ROW]
[ROW][C]25[/C][C]6.9[/C][C]7.22104326655344[/C][C]-0.321043266553441[/C][/ROW]
[ROW][C]26[/C][C]6.6[/C][C]6.0659680199156[/C][C]0.534031980084398[/C][/ROW]
[ROW][C]27[/C][C]6.9[/C][C]6.59719797147052[/C][C]0.302802028529483[/C][/ROW]
[ROW][C]28[/C][C]7.5[/C][C]7.33337678153516[/C][C]0.166623218464845[/C][/ROW]
[ROW][C]29[/C][C]7.9[/C][C]8.0720914249263[/C][C]-0.172091424926295[/C][/ROW]
[ROW][C]30[/C][C]7.7[/C][C]7.9497945470834[/C][C]-0.249794547083408[/C][/ROW]
[ROW][C]31[/C][C]6.5[/C][C]7.14808585836324[/C][C]-0.648085858363239[/C][/ROW]
[ROW][C]32[/C][C]6.1[/C][C]5.94975758640987[/C][C]0.150242413590134[/C][/ROW]
[ROW][C]33[/C][C]6.4[/C][C]5.99607808995673[/C][C]0.403921910043273[/C][/ROW]
[ROW][C]34[/C][C]6.8[/C][C]6.5347443724936[/C][C]0.265255627506406[/C][/ROW]
[ROW][C]35[/C][C]7.1[/C][C]7.15310452506569[/C][C]-0.0531045250656899[/C][/ROW]
[ROW][C]36[/C][C]7.3[/C][C]7.11855604115691[/C][C]0.181443958843093[/C][/ROW]
[ROW][C]37[/C][C]7.2[/C][C]7.27340507485986[/C][C]-0.0734050748598598[/C][/ROW]
[ROW][C]38[/C][C]7[/C][C]7.0182972634874[/C][C]-0.0182972634874012[/C][/ROW]
[ROW][C]39[/C][C]7[/C][C]7.20352225311066[/C][C]-0.203522253110658[/C][/ROW]
[ROW][C]40[/C][C]7[/C][C]7.23084503285245[/C][C]-0.230845032852449[/C][/ROW]
[ROW][C]41[/C][C]7.3[/C][C]7.04860471258564[/C][C]0.251395287414365[/C][/ROW]
[ROW][C]42[/C][C]7.5[/C][C]7.16827266317484[/C][C]0.331727336825158[/C][/ROW]
[ROW][C]43[/C][C]7.2[/C][C]7.23614194577089[/C][C]-0.0361419457708916[/C][/ROW]
[ROW][C]44[/C][C]7.7[/C][C]7.43195738360025[/C][C]0.268042616399747[/C][/ROW]
[ROW][C]45[/C][C]8[/C][C]8.4734013584844[/C][C]-0.473401358484393[/C][/ROW]
[ROW][C]46[/C][C]7.9[/C][C]8.30363053482886[/C][C]-0.403630534828864[/C][/ROW]
[ROW][C]47[/C][C]8[/C][C]7.88186620396833[/C][C]0.118133796031674[/C][/ROW]
[ROW][C]48[/C][C]8[/C][C]7.78559238462081[/C][C]0.214407615379185[/C][/ROW]
[ROW][C]49[/C][C]7.9[/C][C]7.76705951712917[/C][C]0.132940482870829[/C][/ROW]
[ROW][C]50[/C][C]7.9[/C][C]7.67857540655028[/C][C]0.221424593449724[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8.25737540405474[/C][C]-0.257375404054736[/C][/ROW]
[ROW][C]52[/C][C]8.1[/C][C]8.34121185238052[/C][C]-0.241211852380525[/C][/ROW]
[ROW][C]53[/C][C]8.1[/C][C]8.25060034227942[/C][C]-0.150600342279416[/C][/ROW]
[ROW][C]54[/C][C]8.2[/C][C]7.74565747856731[/C][C]0.454342521432686[/C][/ROW]
[ROW][C]55[/C][C]8[/C][C]7.81253832243699[/C][C]0.187461677563014[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]8.28891332084275[/C][C]0.0110866791572519[/C][/ROW]
[ROW][C]57[/C][C]8.5[/C][C]8.92286579615168[/C][C]-0.422865796151683[/C][/ROW]
[ROW][C]58[/C][C]8.6[/C][C]8.6939023565279[/C][C]-0.0939023565278934[/C][/ROW]
[ROW][C]59[/C][C]8.7[/C][C]8.72224302369165[/C][C]-0.0222430236916527[/C][/ROW]
[ROW][C]60[/C][C]8.7[/C][C]8.51261515172887[/C][C]0.187384848271128[/C][/ROW]
[ROW][C]61[/C][C]8.5[/C][C]8.47226144394027[/C][C]0.0277385560597256[/C][/ROW]
[ROW][C]62[/C][C]8.4[/C][C]8.1988269493131[/C][C]0.201173050686906[/C][/ROW]
[ROW][C]63[/C][C]8.5[/C][C]8.66127385911831[/C][C]-0.161273859118307[/C][/ROW]
[ROW][C]64[/C][C]8.7[/C][C]8.82271214799443[/C][C]-0.122712147994431[/C][/ROW]
[ROW][C]65[/C][C]8.7[/C][C]8.92778895561094[/C][C]-0.227788955610945[/C][/ROW]
[ROW][C]66[/C][C]8.6[/C][C]8.36051641272441[/C][C]0.239483587275588[/C][/ROW]
[ROW][C]67[/C][C]7.9[/C][C]8.05389901824315[/C][C]-0.153899018243147[/C][/ROW]
[ROW][C]68[/C][C]8.1[/C][C]7.75462581241219[/C][C]0.345374187587808[/C][/ROW]
[ROW][C]69[/C][C]8.2[/C][C]8.55851490470639[/C][C]-0.358514904706386[/C][/ROW]
[ROW][C]70[/C][C]8.5[/C][C]8.28151470480484[/C][C]0.218485295195158[/C][/ROW]
[ROW][C]71[/C][C]8.6[/C][C]8.76210789043687[/C][C]-0.16210789043687[/C][/ROW]
[ROW][C]72[/C][C]8.5[/C][C]8.43953936705235[/C][C]0.0604606329476542[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121891&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121891&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
138.38.49863782051282-0.198637820512822
147.97.751969165537840.148030834462162
157.97.871503822551570.0284961774484316
168.18.086181105958160.0138188940418367
178.38.30150650698988-0.00150650698988208
188.18.11695667172316-0.0169566717231593
197.47.50326418700613-0.103264187006131
207.37.244878524684980.0551214753150164
217.77.514389025958660.185610974041342
2287.976769584293870.0232304157061298
2388.2996947736954-0.299694773695396
247.77.76602506683345-0.0660250668334541
256.97.22104326655344-0.321043266553441
266.66.06596801991560.534031980084398
276.96.597197971470520.302802028529483
287.57.333376781535160.166623218464845
297.98.0720914249263-0.172091424926295
307.77.9497945470834-0.249794547083408
316.57.14808585836324-0.648085858363239
326.15.949757586409870.150242413590134
336.45.996078089956730.403921910043273
346.86.53474437249360.265255627506406
357.17.15310452506569-0.0531045250656899
367.37.118556041156910.181443958843093
377.27.27340507485986-0.0734050748598598
3877.0182972634874-0.0182972634874012
3977.20352225311066-0.203522253110658
4077.23084503285245-0.230845032852449
417.37.048604712585640.251395287414365
427.57.168272663174840.331727336825158
437.27.23614194577089-0.0361419457708916
447.77.431957383600250.268042616399747
4588.4734013584844-0.473401358484393
467.98.30363053482886-0.403630534828864
4787.881866203968330.118133796031674
4887.785592384620810.214407615379185
497.97.767059517129170.132940482870829
507.97.678575406550280.221424593449724
5188.25737540405474-0.257375404054736
528.18.34121185238052-0.241211852380525
538.18.25060034227942-0.150600342279416
548.27.745657478567310.454342521432686
5587.812538322436990.187461677563014
568.38.288913320842750.0110866791572519
578.58.92286579615168-0.422865796151683
588.68.6939023565279-0.0939023565278934
598.78.72224302369165-0.0222430236916527
608.78.512615151728870.187384848271128
618.58.472261443940270.0277385560597256
628.48.19882694931310.201173050686906
638.58.66127385911831-0.161273859118307
648.78.82271214799443-0.122712147994431
658.78.92778895561094-0.227788955610945
668.68.360516412724410.239483587275588
677.98.05389901824315-0.153899018243147
688.17.754625812412190.345374187587808
698.28.55851490470639-0.358514904706386
708.58.281514704804840.218485295195158
718.68.76210789043687-0.16210789043687
728.58.439539367052350.0604606329476542







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.196694562725987.717258992303088.67613013314888
747.797555792118626.807193410267378.78791817396987
757.798417021511266.200719418779999.39611462424254
767.990944917570575.7007312813515710.2811585537896
778.187639480296555.1285709385976511.2467080219955
788.001000709689194.1034549119064811.8985465074719
797.414361939081842.6139736949182312.2147501832454
807.352723168474481.5893688868379313.116077450111
817.616084397867120.83314999048474714.3990188052495
827.79194562725976-0.064219288171886815.6481105426914
837.97197352331907-1.0085273910317616.9524744376699
847.86033475271172-2.2933920381576218.014061543581

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.19669456272598 & 7.71725899230308 & 8.67613013314888 \tabularnewline
74 & 7.79755579211862 & 6.80719341026737 & 8.78791817396987 \tabularnewline
75 & 7.79841702151126 & 6.20071941877999 & 9.39611462424254 \tabularnewline
76 & 7.99094491757057 & 5.70073128135157 & 10.2811585537896 \tabularnewline
77 & 8.18763948029655 & 5.12857093859765 & 11.2467080219955 \tabularnewline
78 & 8.00100070968919 & 4.10345491190648 & 11.8985465074719 \tabularnewline
79 & 7.41436193908184 & 2.61397369491823 & 12.2147501832454 \tabularnewline
80 & 7.35272316847448 & 1.58936888683793 & 13.116077450111 \tabularnewline
81 & 7.61608439786712 & 0.833149990484747 & 14.3990188052495 \tabularnewline
82 & 7.79194562725976 & -0.0642192881718868 & 15.6481105426914 \tabularnewline
83 & 7.97197352331907 & -1.00852739103176 & 16.9524744376699 \tabularnewline
84 & 7.86033475271172 & -2.29339203815762 & 18.014061543581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121891&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]8.19669456272598[/C][C]7.71725899230308[/C][C]8.67613013314888[/C][/ROW]
[ROW][C]74[/C][C]7.79755579211862[/C][C]6.80719341026737[/C][C]8.78791817396987[/C][/ROW]
[ROW][C]75[/C][C]7.79841702151126[/C][C]6.20071941877999[/C][C]9.39611462424254[/C][/ROW]
[ROW][C]76[/C][C]7.99094491757057[/C][C]5.70073128135157[/C][C]10.2811585537896[/C][/ROW]
[ROW][C]77[/C][C]8.18763948029655[/C][C]5.12857093859765[/C][C]11.2467080219955[/C][/ROW]
[ROW][C]78[/C][C]8.00100070968919[/C][C]4.10345491190648[/C][C]11.8985465074719[/C][/ROW]
[ROW][C]79[/C][C]7.41436193908184[/C][C]2.61397369491823[/C][C]12.2147501832454[/C][/ROW]
[ROW][C]80[/C][C]7.35272316847448[/C][C]1.58936888683793[/C][C]13.116077450111[/C][/ROW]
[ROW][C]81[/C][C]7.61608439786712[/C][C]0.833149990484747[/C][C]14.3990188052495[/C][/ROW]
[ROW][C]82[/C][C]7.79194562725976[/C][C]-0.0642192881718868[/C][C]15.6481105426914[/C][/ROW]
[ROW][C]83[/C][C]7.97197352331907[/C][C]-1.00852739103176[/C][C]16.9524744376699[/C][/ROW]
[ROW][C]84[/C][C]7.86033475271172[/C][C]-2.29339203815762[/C][C]18.014061543581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121891&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121891&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
738.196694562725987.717258992303088.67613013314888
747.797555792118626.807193410267378.78791817396987
757.798417021511266.200719418779999.39611462424254
767.990944917570575.7007312813515710.2811585537896
778.187639480296555.1285709385976511.2467080219955
788.001000709689194.1034549119064811.8985465074719
797.414361939081842.6139736949182312.2147501832454
807.352723168474481.5893688868379313.116077450111
817.616084397867120.83314999048474714.3990188052495
827.79194562725976-0.064219288171886815.6481105426914
837.97197352331907-1.0085273910317616.9524744376699
847.86033475271172-2.2933920381576218.014061543581



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')