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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 15:48:06 -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/2012/Dec/21/t1356122918ltry8t569a24ery.htm/, Retrieved Thu, 25 Apr 2024 19:28:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204268, Retrieved Thu, 25 Apr 2024 19:28:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Oef 10 gemiddelde...] [2012-12-21 20:48:06] [3afff8224e6da3a7e2f9dd48a805005a] [Current]
- R PD    [Exponential Smoothing] [Opgave 10 oefenin...] [2013-01-15 02:42:48] [c05f3eadce52e4946a2aac59a0f05a38]
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Dataseries X:
1,01
1,02
1,04
1,06
1,06
1,06
1,06
1,06
1,02
0,98
0,99
0,99
0,94
0,96
0,98
1,01
1,01
1,02
1,04
1,03
1,05
1,08
1,17
1,11
1,11
1,11
1,2
1,21
1,31
1,37
1,37
1,26
1,23
1,17
1,06
0,95
0,92
0,92
0,9
0,93
0,93
0,97
0,96
0,99
0,98
0,96
1
0,99
1,03
1,02
1,07
1,13
1,15
1,16
1,14
1,15
1,15
1,16
1,17
1,22
1,26
1,29
1,36
1,38
1,37
1,37
1,37
1,36
1,38
1,4
1,44
1,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204268&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204268&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204268&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 time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00412567960433317
gamma0.119415377376804

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00412567960433317 \tabularnewline
gamma & 0.119415377376804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204268&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]0.00412567960433317[/C][/ROW]
[ROW][C]gamma[/C][C]0.119415377376804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204268&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204268&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
beta0.00412567960433317
gamma0.119415377376804







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
130.940.961983272056199-0.0219832720561992
140.960.961252375360522-0.00125237536052225
150.980.9792289700265490.000771029973451354
161.011.003764781406360.00623521859363851
171.010.9976477109386820.0123522890613182
181.021.006901307384050.0130986926159471
191.041.06147920510776-0.0214792051077581
201.031.04475306946454-0.0147530694645364
211.050.9952115929248520.0547884070751479
221.081.012842973848470.0671570261515331
231.171.095254562490250.0747454375097498
241.111.17440161588828-0.064401615888277
251.111.056346448393580.0536535516064156
261.111.13597733712784-0.0259773371278378
271.21.133011160475580.0669888395244185
281.211.23023011782245-0.020230117822452
291.311.196185552475390.113814447524614
301.371.307439251061350.0625607489386455
311.371.42745767620478-0.0574576762047809
321.261.37787750518531-0.117877505185307
331.231.218538378091970.0114616219080286
341.171.18728017690399-0.0172801769039943
351.061.18691816194647-0.126918161946471
360.951.06352582676318-0.113525826763181
370.920.9034125652206660.0165874347793343
380.920.940723442483331-0.0207234424833307
390.90.938251570673106-0.0382515706731061
400.930.921447843915130.00855215608486992
410.930.9182668338990540.011733166100946
420.970.9267898042125590.0432101957874407
430.961.00922834331053-0.0492283433105334
440.990.9640279138955110.0259720861044888
450.980.9564033041842160.0235966958157843
460.960.9450352507340760.0149647492659243
4710.9730585315678860.0269414684321138
480.991.00309652449507-0.0130965244950734
491.030.9416864491995690.0883135508004311
501.021.05380492759821-0.0338049275982089
511.071.04079709047750.0292029095225019
521.131.09646587457590.0335341254241017
531.151.116822068984490.0331779310155054
541.161.147205754344680.0127942456553161
551.141.20792670710948-0.0679267071094787
561.151.145756504136940.00424349586305572
571.151.111784657464270.0382153425357341
581.161.109805300006220.0501946999937837
591.171.1767891519441-0.0067891519441019
601.221.174449304527180.0455506954728235
611.261.161528973165690.0984710268343123
621.291.2901659614997-0.000165961499696055
631.361.317561571498940.0424384285010646
641.381.39495522493229-0.0149552249322853
651.371.364963053558180.00503694644182473
661.371.367577226116540.00242277388345724
671.371.42749137585656-0.0574913758565589
681.361.37791124387987-0.017911243879867
691.381.315669870222240.064330129777759
701.41.332677932997450.0673220670025465
711.441.421216401581330.0187835984186717
721.421.44654315603357-0.0265431560335687

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 0.94 & 0.961983272056199 & -0.0219832720561992 \tabularnewline
14 & 0.96 & 0.961252375360522 & -0.00125237536052225 \tabularnewline
15 & 0.98 & 0.979228970026549 & 0.000771029973451354 \tabularnewline
16 & 1.01 & 1.00376478140636 & 0.00623521859363851 \tabularnewline
17 & 1.01 & 0.997647710938682 & 0.0123522890613182 \tabularnewline
18 & 1.02 & 1.00690130738405 & 0.0130986926159471 \tabularnewline
19 & 1.04 & 1.06147920510776 & -0.0214792051077581 \tabularnewline
20 & 1.03 & 1.04475306946454 & -0.0147530694645364 \tabularnewline
21 & 1.05 & 0.995211592924852 & 0.0547884070751479 \tabularnewline
22 & 1.08 & 1.01284297384847 & 0.0671570261515331 \tabularnewline
23 & 1.17 & 1.09525456249025 & 0.0747454375097498 \tabularnewline
24 & 1.11 & 1.17440161588828 & -0.064401615888277 \tabularnewline
25 & 1.11 & 1.05634644839358 & 0.0536535516064156 \tabularnewline
26 & 1.11 & 1.13597733712784 & -0.0259773371278378 \tabularnewline
27 & 1.2 & 1.13301116047558 & 0.0669888395244185 \tabularnewline
28 & 1.21 & 1.23023011782245 & -0.020230117822452 \tabularnewline
29 & 1.31 & 1.19618555247539 & 0.113814447524614 \tabularnewline
30 & 1.37 & 1.30743925106135 & 0.0625607489386455 \tabularnewline
31 & 1.37 & 1.42745767620478 & -0.0574576762047809 \tabularnewline
32 & 1.26 & 1.37787750518531 & -0.117877505185307 \tabularnewline
33 & 1.23 & 1.21853837809197 & 0.0114616219080286 \tabularnewline
34 & 1.17 & 1.18728017690399 & -0.0172801769039943 \tabularnewline
35 & 1.06 & 1.18691816194647 & -0.126918161946471 \tabularnewline
36 & 0.95 & 1.06352582676318 & -0.113525826763181 \tabularnewline
37 & 0.92 & 0.903412565220666 & 0.0165874347793343 \tabularnewline
38 & 0.92 & 0.940723442483331 & -0.0207234424833307 \tabularnewline
39 & 0.9 & 0.938251570673106 & -0.0382515706731061 \tabularnewline
40 & 0.93 & 0.92144784391513 & 0.00855215608486992 \tabularnewline
41 & 0.93 & 0.918266833899054 & 0.011733166100946 \tabularnewline
42 & 0.97 & 0.926789804212559 & 0.0432101957874407 \tabularnewline
43 & 0.96 & 1.00922834331053 & -0.0492283433105334 \tabularnewline
44 & 0.99 & 0.964027913895511 & 0.0259720861044888 \tabularnewline
45 & 0.98 & 0.956403304184216 & 0.0235966958157843 \tabularnewline
46 & 0.96 & 0.945035250734076 & 0.0149647492659243 \tabularnewline
47 & 1 & 0.973058531567886 & 0.0269414684321138 \tabularnewline
48 & 0.99 & 1.00309652449507 & -0.0130965244950734 \tabularnewline
49 & 1.03 & 0.941686449199569 & 0.0883135508004311 \tabularnewline
50 & 1.02 & 1.05380492759821 & -0.0338049275982089 \tabularnewline
51 & 1.07 & 1.0407970904775 & 0.0292029095225019 \tabularnewline
52 & 1.13 & 1.0964658745759 & 0.0335341254241017 \tabularnewline
53 & 1.15 & 1.11682206898449 & 0.0331779310155054 \tabularnewline
54 & 1.16 & 1.14720575434468 & 0.0127942456553161 \tabularnewline
55 & 1.14 & 1.20792670710948 & -0.0679267071094787 \tabularnewline
56 & 1.15 & 1.14575650413694 & 0.00424349586305572 \tabularnewline
57 & 1.15 & 1.11178465746427 & 0.0382153425357341 \tabularnewline
58 & 1.16 & 1.10980530000622 & 0.0501946999937837 \tabularnewline
59 & 1.17 & 1.1767891519441 & -0.0067891519441019 \tabularnewline
60 & 1.22 & 1.17444930452718 & 0.0455506954728235 \tabularnewline
61 & 1.26 & 1.16152897316569 & 0.0984710268343123 \tabularnewline
62 & 1.29 & 1.2901659614997 & -0.000165961499696055 \tabularnewline
63 & 1.36 & 1.31756157149894 & 0.0424384285010646 \tabularnewline
64 & 1.38 & 1.39495522493229 & -0.0149552249322853 \tabularnewline
65 & 1.37 & 1.36496305355818 & 0.00503694644182473 \tabularnewline
66 & 1.37 & 1.36757722611654 & 0.00242277388345724 \tabularnewline
67 & 1.37 & 1.42749137585656 & -0.0574913758565589 \tabularnewline
68 & 1.36 & 1.37791124387987 & -0.017911243879867 \tabularnewline
69 & 1.38 & 1.31566987022224 & 0.064330129777759 \tabularnewline
70 & 1.4 & 1.33267793299745 & 0.0673220670025465 \tabularnewline
71 & 1.44 & 1.42121640158133 & 0.0187835984186717 \tabularnewline
72 & 1.42 & 1.44654315603357 & -0.0265431560335687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204268&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]0.94[/C][C]0.961983272056199[/C][C]-0.0219832720561992[/C][/ROW]
[ROW][C]14[/C][C]0.96[/C][C]0.961252375360522[/C][C]-0.00125237536052225[/C][/ROW]
[ROW][C]15[/C][C]0.98[/C][C]0.979228970026549[/C][C]0.000771029973451354[/C][/ROW]
[ROW][C]16[/C][C]1.01[/C][C]1.00376478140636[/C][C]0.00623521859363851[/C][/ROW]
[ROW][C]17[/C][C]1.01[/C][C]0.997647710938682[/C][C]0.0123522890613182[/C][/ROW]
[ROW][C]18[/C][C]1.02[/C][C]1.00690130738405[/C][C]0.0130986926159471[/C][/ROW]
[ROW][C]19[/C][C]1.04[/C][C]1.06147920510776[/C][C]-0.0214792051077581[/C][/ROW]
[ROW][C]20[/C][C]1.03[/C][C]1.04475306946454[/C][C]-0.0147530694645364[/C][/ROW]
[ROW][C]21[/C][C]1.05[/C][C]0.995211592924852[/C][C]0.0547884070751479[/C][/ROW]
[ROW][C]22[/C][C]1.08[/C][C]1.01284297384847[/C][C]0.0671570261515331[/C][/ROW]
[ROW][C]23[/C][C]1.17[/C][C]1.09525456249025[/C][C]0.0747454375097498[/C][/ROW]
[ROW][C]24[/C][C]1.11[/C][C]1.17440161588828[/C][C]-0.064401615888277[/C][/ROW]
[ROW][C]25[/C][C]1.11[/C][C]1.05634644839358[/C][C]0.0536535516064156[/C][/ROW]
[ROW][C]26[/C][C]1.11[/C][C]1.13597733712784[/C][C]-0.0259773371278378[/C][/ROW]
[ROW][C]27[/C][C]1.2[/C][C]1.13301116047558[/C][C]0.0669888395244185[/C][/ROW]
[ROW][C]28[/C][C]1.21[/C][C]1.23023011782245[/C][C]-0.020230117822452[/C][/ROW]
[ROW][C]29[/C][C]1.31[/C][C]1.19618555247539[/C][C]0.113814447524614[/C][/ROW]
[ROW][C]30[/C][C]1.37[/C][C]1.30743925106135[/C][C]0.0625607489386455[/C][/ROW]
[ROW][C]31[/C][C]1.37[/C][C]1.42745767620478[/C][C]-0.0574576762047809[/C][/ROW]
[ROW][C]32[/C][C]1.26[/C][C]1.37787750518531[/C][C]-0.117877505185307[/C][/ROW]
[ROW][C]33[/C][C]1.23[/C][C]1.21853837809197[/C][C]0.0114616219080286[/C][/ROW]
[ROW][C]34[/C][C]1.17[/C][C]1.18728017690399[/C][C]-0.0172801769039943[/C][/ROW]
[ROW][C]35[/C][C]1.06[/C][C]1.18691816194647[/C][C]-0.126918161946471[/C][/ROW]
[ROW][C]36[/C][C]0.95[/C][C]1.06352582676318[/C][C]-0.113525826763181[/C][/ROW]
[ROW][C]37[/C][C]0.92[/C][C]0.903412565220666[/C][C]0.0165874347793343[/C][/ROW]
[ROW][C]38[/C][C]0.92[/C][C]0.940723442483331[/C][C]-0.0207234424833307[/C][/ROW]
[ROW][C]39[/C][C]0.9[/C][C]0.938251570673106[/C][C]-0.0382515706731061[/C][/ROW]
[ROW][C]40[/C][C]0.93[/C][C]0.92144784391513[/C][C]0.00855215608486992[/C][/ROW]
[ROW][C]41[/C][C]0.93[/C][C]0.918266833899054[/C][C]0.011733166100946[/C][/ROW]
[ROW][C]42[/C][C]0.97[/C][C]0.926789804212559[/C][C]0.0432101957874407[/C][/ROW]
[ROW][C]43[/C][C]0.96[/C][C]1.00922834331053[/C][C]-0.0492283433105334[/C][/ROW]
[ROW][C]44[/C][C]0.99[/C][C]0.964027913895511[/C][C]0.0259720861044888[/C][/ROW]
[ROW][C]45[/C][C]0.98[/C][C]0.956403304184216[/C][C]0.0235966958157843[/C][/ROW]
[ROW][C]46[/C][C]0.96[/C][C]0.945035250734076[/C][C]0.0149647492659243[/C][/ROW]
[ROW][C]47[/C][C]1[/C][C]0.973058531567886[/C][C]0.0269414684321138[/C][/ROW]
[ROW][C]48[/C][C]0.99[/C][C]1.00309652449507[/C][C]-0.0130965244950734[/C][/ROW]
[ROW][C]49[/C][C]1.03[/C][C]0.941686449199569[/C][C]0.0883135508004311[/C][/ROW]
[ROW][C]50[/C][C]1.02[/C][C]1.05380492759821[/C][C]-0.0338049275982089[/C][/ROW]
[ROW][C]51[/C][C]1.07[/C][C]1.0407970904775[/C][C]0.0292029095225019[/C][/ROW]
[ROW][C]52[/C][C]1.13[/C][C]1.0964658745759[/C][C]0.0335341254241017[/C][/ROW]
[ROW][C]53[/C][C]1.15[/C][C]1.11682206898449[/C][C]0.0331779310155054[/C][/ROW]
[ROW][C]54[/C][C]1.16[/C][C]1.14720575434468[/C][C]0.0127942456553161[/C][/ROW]
[ROW][C]55[/C][C]1.14[/C][C]1.20792670710948[/C][C]-0.0679267071094787[/C][/ROW]
[ROW][C]56[/C][C]1.15[/C][C]1.14575650413694[/C][C]0.00424349586305572[/C][/ROW]
[ROW][C]57[/C][C]1.15[/C][C]1.11178465746427[/C][C]0.0382153425357341[/C][/ROW]
[ROW][C]58[/C][C]1.16[/C][C]1.10980530000622[/C][C]0.0501946999937837[/C][/ROW]
[ROW][C]59[/C][C]1.17[/C][C]1.1767891519441[/C][C]-0.0067891519441019[/C][/ROW]
[ROW][C]60[/C][C]1.22[/C][C]1.17444930452718[/C][C]0.0455506954728235[/C][/ROW]
[ROW][C]61[/C][C]1.26[/C][C]1.16152897316569[/C][C]0.0984710268343123[/C][/ROW]
[ROW][C]62[/C][C]1.29[/C][C]1.2901659614997[/C][C]-0.000165961499696055[/C][/ROW]
[ROW][C]63[/C][C]1.36[/C][C]1.31756157149894[/C][C]0.0424384285010646[/C][/ROW]
[ROW][C]64[/C][C]1.38[/C][C]1.39495522493229[/C][C]-0.0149552249322853[/C][/ROW]
[ROW][C]65[/C][C]1.37[/C][C]1.36496305355818[/C][C]0.00503694644182473[/C][/ROW]
[ROW][C]66[/C][C]1.37[/C][C]1.36757722611654[/C][C]0.00242277388345724[/C][/ROW]
[ROW][C]67[/C][C]1.37[/C][C]1.42749137585656[/C][C]-0.0574913758565589[/C][/ROW]
[ROW][C]68[/C][C]1.36[/C][C]1.37791124387987[/C][C]-0.017911243879867[/C][/ROW]
[ROW][C]69[/C][C]1.38[/C][C]1.31566987022224[/C][C]0.064330129777759[/C][/ROW]
[ROW][C]70[/C][C]1.4[/C][C]1.33267793299745[/C][C]0.0673220670025465[/C][/ROW]
[ROW][C]71[/C][C]1.44[/C][C]1.42121640158133[/C][C]0.0187835984186717[/C][/ROW]
[ROW][C]72[/C][C]1.42[/C][C]1.44654315603357[/C][C]-0.0265431560335687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204268&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204268&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
130.940.961983272056199-0.0219832720561992
140.960.961252375360522-0.00125237536052225
150.980.9792289700265490.000771029973451354
161.011.003764781406360.00623521859363851
171.010.9976477109386820.0123522890613182
181.021.006901307384050.0130986926159471
191.041.06147920510776-0.0214792051077581
201.031.04475306946454-0.0147530694645364
211.050.9952115929248520.0547884070751479
221.081.012842973848470.0671570261515331
231.171.095254562490250.0747454375097498
241.111.17440161588828-0.064401615888277
251.111.056346448393580.0536535516064156
261.111.13597733712784-0.0259773371278378
271.21.133011160475580.0669888395244185
281.211.23023011782245-0.020230117822452
291.311.196185552475390.113814447524614
301.371.307439251061350.0625607489386455
311.371.42745767620478-0.0574576762047809
321.261.37787750518531-0.117877505185307
331.231.218538378091970.0114616219080286
341.171.18728017690399-0.0172801769039943
351.061.18691816194647-0.126918161946471
360.951.06352582676318-0.113525826763181
370.920.9034125652206660.0165874347793343
380.920.940723442483331-0.0207234424833307
390.90.938251570673106-0.0382515706731061
400.930.921447843915130.00855215608486992
410.930.9182668338990540.011733166100946
420.970.9267898042125590.0432101957874407
430.961.00922834331053-0.0492283433105334
440.990.9640279138955110.0259720861044888
450.980.9564033041842160.0235966958157843
460.960.9450352507340760.0149647492659243
4710.9730585315678860.0269414684321138
480.991.00309652449507-0.0130965244950734
491.030.9416864491995690.0883135508004311
501.021.05380492759821-0.0338049275982089
511.071.04079709047750.0292029095225019
521.131.09646587457590.0335341254241017
531.151.116822068984490.0331779310155054
541.161.147205754344680.0127942456553161
551.141.20792670710948-0.0679267071094787
561.151.145756504136940.00424349586305572
571.151.111784657464270.0382153425357341
581.161.109805300006220.0501946999937837
591.171.1767891519441-0.0067891519441019
601.221.174449304527180.0455506954728235
611.261.161528973165690.0984710268343123
621.291.2901659614997-0.000165961499696055
631.361.317561571498940.0424384285010646
641.381.39495522493229-0.0149552249322853
651.371.364963053558180.00503694644182473
661.371.367577226116540.00242277388345724
671.371.42749137585656-0.0574913758565589
681.361.37791124387987-0.017911243879867
691.381.315669870222240.064330129777759
701.41.332677932997450.0673220670025465
711.441.421216401581330.0187835984186717
721.421.44654315603357-0.0265431560335687







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731.35265170007111.255426288675041.44987711146716
741.385337508752541.245927601881851.52474741562322
751.41524444949281.242405671424131.58808322756147
761.451772405136241.249040981315491.65450382895699
771.436158685612571.212676877683611.65964049354152
781.433804988912291.189740536407611.67786944141698
791.494158267846281.2210764191281.76724011656456
801.503193095064151.210900092394681.79548609773361
811.454658566080731.154670076529631.75464705563183
821.404980412530611.098447978348411.71151284671281
831.426236844992381.099247852285321.75322583769943
841.43261905210506-90.289868630037693.1551067342477

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1.3526517000711 & 1.25542628867504 & 1.44987711146716 \tabularnewline
74 & 1.38533750875254 & 1.24592760188185 & 1.52474741562322 \tabularnewline
75 & 1.4152444494928 & 1.24240567142413 & 1.58808322756147 \tabularnewline
76 & 1.45177240513624 & 1.24904098131549 & 1.65450382895699 \tabularnewline
77 & 1.43615868561257 & 1.21267687768361 & 1.65964049354152 \tabularnewline
78 & 1.43380498891229 & 1.18974053640761 & 1.67786944141698 \tabularnewline
79 & 1.49415826784628 & 1.221076419128 & 1.76724011656456 \tabularnewline
80 & 1.50319309506415 & 1.21090009239468 & 1.79548609773361 \tabularnewline
81 & 1.45465856608073 & 1.15467007652963 & 1.75464705563183 \tabularnewline
82 & 1.40498041253061 & 1.09844797834841 & 1.71151284671281 \tabularnewline
83 & 1.42623684499238 & 1.09924785228532 & 1.75322583769943 \tabularnewline
84 & 1.43261905210506 & -90.2898686300376 & 93.1551067342477 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204268&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]1.3526517000711[/C][C]1.25542628867504[/C][C]1.44987711146716[/C][/ROW]
[ROW][C]74[/C][C]1.38533750875254[/C][C]1.24592760188185[/C][C]1.52474741562322[/C][/ROW]
[ROW][C]75[/C][C]1.4152444494928[/C][C]1.24240567142413[/C][C]1.58808322756147[/C][/ROW]
[ROW][C]76[/C][C]1.45177240513624[/C][C]1.24904098131549[/C][C]1.65450382895699[/C][/ROW]
[ROW][C]77[/C][C]1.43615868561257[/C][C]1.21267687768361[/C][C]1.65964049354152[/C][/ROW]
[ROW][C]78[/C][C]1.43380498891229[/C][C]1.18974053640761[/C][C]1.67786944141698[/C][/ROW]
[ROW][C]79[/C][C]1.49415826784628[/C][C]1.221076419128[/C][C]1.76724011656456[/C][/ROW]
[ROW][C]80[/C][C]1.50319309506415[/C][C]1.21090009239468[/C][C]1.79548609773361[/C][/ROW]
[ROW][C]81[/C][C]1.45465856608073[/C][C]1.15467007652963[/C][C]1.75464705563183[/C][/ROW]
[ROW][C]82[/C][C]1.40498041253061[/C][C]1.09844797834841[/C][C]1.71151284671281[/C][/ROW]
[ROW][C]83[/C][C]1.42623684499238[/C][C]1.09924785228532[/C][C]1.75322583769943[/C][/ROW]
[ROW][C]84[/C][C]1.43261905210506[/C][C]-90.2898686300376[/C][C]93.1551067342477[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204268&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204268&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
731.35265170007111.255426288675041.44987711146716
741.385337508752541.245927601881851.52474741562322
751.41524444949281.242405671424131.58808322756147
761.451772405136241.249040981315491.65450382895699
771.436158685612571.212676877683611.65964049354152
781.433804988912291.189740536407611.67786944141698
791.494158267846281.2210764191281.76724011656456
801.503193095064151.210900092394681.79548609773361
811.454658566080731.154670076529631.75464705563183
821.404980412530611.098447978348411.71151284671281
831.426236844992381.099247852285321.75322583769943
841.43261905210506-90.289868630037693.1551067342477



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')