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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 01 Dec 2009 12:06:01 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/01/t12596943910xgpwghmlm1htuf.htm/, Retrieved Fri, 26 Apr 2024 18:59:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62196, Retrieved Fri, 26 Apr 2024 18:59:16 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2009-12-01 19:06:01] [4563e36d4b7005634fe3557528d9fcab] [Current]
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Dataseries X:
7291
6820
8031
7862
7357
7213
7079
7012
7319
8148
7599
6908
7878
7407
7911
7323
7179
6758
6934
6696
7688
8296
7697
7907
7592
7710
9011
8225
7733
8062
7859
8221
8330
8868
9053
8811
8120
7953
8878
8601
8361
9116
9310
9891
10147
10317
10682
10276
10614
9413
11068
9772
10350
10541
10049
10714
10759
11684
11462
10485
11056
10184
11082
10554
11315
10847
11104
11026
11073
12073
12328
11172




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62196&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62196&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62196&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.327366976611456
beta0.0426741524472546
gamma0.625912584003787

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.327366976611456 \tabularnewline
beta & 0.0426741524472546 \tabularnewline
gamma & 0.625912584003787 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62196&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]0.327366976611456[/C][/ROW]
[ROW][C]beta[/C][C]0.0426741524472546[/C][/ROW]
[ROW][C]gamma[/C][C]0.625912584003787[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62196&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62196&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
alpha0.327366976611456
beta0.0426741524472546
gamma0.625912584003787







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1378787988.59029958755-110.590299587550
1474077488.2790801246-81.279080124601
1579117957.03397465224-46.0339746522377
1673237320.399887306512.60011269348706
1771797157.7759726619221.2240273380803
1867586694.4205162320663.5794837679405
1969347045.18551378264-111.185513782641
2066966887.3713435908-191.371343590807
2176887092.25811729323595.741882706774
2282968137.65718544235158.342814557647
2376977665.8975971135431.102402886464
2479077001.03249965228905.967500347724
2575928313.8716567144-721.8716567144
2677107626.1913356840783.8086643159295
2790118192.96861575676818.03138424324
2882257843.02108207557381.978917924434
2977337827.77997673001-94.7799767300121
3080627330.61346112378731.38653887622
3178597894.26749917752-35.2674991775248
3282217743.35388905604477.646110943964
3383308644.94391775863-314.943917758626
3488689336.47248048307-468.472480483069
3590538570.00870177085482.991298229152
3688118396.0938741835414.906125816506
3781208915.39275819-795.392758189999
3879538554.9567097821-601.956709782096
3988789285.32389313345-407.323893133447
4086018315.66645620527285.333543794732
4183618053.8759117906307.124088209405
4291168022.834096479321093.16590352068
4393108388.98157355441921.01842644559
4498918789.833477755611101.16652224439
45101479640.70611858565506.293881414345
461031710695.2006147717-378.200614771651
471068210359.0748719003322.925128099738
481027610075.7969468298200.203053170177
491061410015.1052583161598.894741683946
50941310232.1749382142-819.17493821419
511106811257.6606109571-189.660610957097
52977210570.8562371889-798.856237188917
53103509927.91389587363422.086104126372
541054110324.4336543782216.566345621834
551004910328.6378459917-279.637845991676
561071410421.4859564639292.514043536137
571075910771.2971297291-12.2971297291479
581168411308.5917572169375.40824278306
591146211518.4855746003-56.4855746003213
601048511014.4682379027-529.468237902713
611105610864.7626485383191.237351461694
621018410296.9951938175-112.995193817542
631108211909.7085981216-827.708598121644
641055410689.2533019295-135.253301929491
651131510774.1326579238540.867342076201
661084711125.3832385839-278.383238583918
671110410728.8365580329375.163441967126
681102611299.9780402019-273.978040201899
691107311329.2175760589-256.217576058913
701207311962.4872741234110.512725876644
711232811880.2484368985447.75156310145
721117211292.4070319556-120.407031955603

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7878 & 7988.59029958755 & -110.590299587550 \tabularnewline
14 & 7407 & 7488.2790801246 & -81.279080124601 \tabularnewline
15 & 7911 & 7957.03397465224 & -46.0339746522377 \tabularnewline
16 & 7323 & 7320.39988730651 & 2.60011269348706 \tabularnewline
17 & 7179 & 7157.77597266192 & 21.2240273380803 \tabularnewline
18 & 6758 & 6694.42051623206 & 63.5794837679405 \tabularnewline
19 & 6934 & 7045.18551378264 & -111.185513782641 \tabularnewline
20 & 6696 & 6887.3713435908 & -191.371343590807 \tabularnewline
21 & 7688 & 7092.25811729323 & 595.741882706774 \tabularnewline
22 & 8296 & 8137.65718544235 & 158.342814557647 \tabularnewline
23 & 7697 & 7665.89759711354 & 31.102402886464 \tabularnewline
24 & 7907 & 7001.03249965228 & 905.967500347724 \tabularnewline
25 & 7592 & 8313.8716567144 & -721.8716567144 \tabularnewline
26 & 7710 & 7626.19133568407 & 83.8086643159295 \tabularnewline
27 & 9011 & 8192.96861575676 & 818.03138424324 \tabularnewline
28 & 8225 & 7843.02108207557 & 381.978917924434 \tabularnewline
29 & 7733 & 7827.77997673001 & -94.7799767300121 \tabularnewline
30 & 8062 & 7330.61346112378 & 731.38653887622 \tabularnewline
31 & 7859 & 7894.26749917752 & -35.2674991775248 \tabularnewline
32 & 8221 & 7743.35388905604 & 477.646110943964 \tabularnewline
33 & 8330 & 8644.94391775863 & -314.943917758626 \tabularnewline
34 & 8868 & 9336.47248048307 & -468.472480483069 \tabularnewline
35 & 9053 & 8570.00870177085 & 482.991298229152 \tabularnewline
36 & 8811 & 8396.0938741835 & 414.906125816506 \tabularnewline
37 & 8120 & 8915.39275819 & -795.392758189999 \tabularnewline
38 & 7953 & 8554.9567097821 & -601.956709782096 \tabularnewline
39 & 8878 & 9285.32389313345 & -407.323893133447 \tabularnewline
40 & 8601 & 8315.66645620527 & 285.333543794732 \tabularnewline
41 & 8361 & 8053.8759117906 & 307.124088209405 \tabularnewline
42 & 9116 & 8022.83409647932 & 1093.16590352068 \tabularnewline
43 & 9310 & 8388.98157355441 & 921.01842644559 \tabularnewline
44 & 9891 & 8789.83347775561 & 1101.16652224439 \tabularnewline
45 & 10147 & 9640.70611858565 & 506.293881414345 \tabularnewline
46 & 10317 & 10695.2006147717 & -378.200614771651 \tabularnewline
47 & 10682 & 10359.0748719003 & 322.925128099738 \tabularnewline
48 & 10276 & 10075.7969468298 & 200.203053170177 \tabularnewline
49 & 10614 & 10015.1052583161 & 598.894741683946 \tabularnewline
50 & 9413 & 10232.1749382142 & -819.17493821419 \tabularnewline
51 & 11068 & 11257.6606109571 & -189.660610957097 \tabularnewline
52 & 9772 & 10570.8562371889 & -798.856237188917 \tabularnewline
53 & 10350 & 9927.91389587363 & 422.086104126372 \tabularnewline
54 & 10541 & 10324.4336543782 & 216.566345621834 \tabularnewline
55 & 10049 & 10328.6378459917 & -279.637845991676 \tabularnewline
56 & 10714 & 10421.4859564639 & 292.514043536137 \tabularnewline
57 & 10759 & 10771.2971297291 & -12.2971297291479 \tabularnewline
58 & 11684 & 11308.5917572169 & 375.40824278306 \tabularnewline
59 & 11462 & 11518.4855746003 & -56.4855746003213 \tabularnewline
60 & 10485 & 11014.4682379027 & -529.468237902713 \tabularnewline
61 & 11056 & 10864.7626485383 & 191.237351461694 \tabularnewline
62 & 10184 & 10296.9951938175 & -112.995193817542 \tabularnewline
63 & 11082 & 11909.7085981216 & -827.708598121644 \tabularnewline
64 & 10554 & 10689.2533019295 & -135.253301929491 \tabularnewline
65 & 11315 & 10774.1326579238 & 540.867342076201 \tabularnewline
66 & 10847 & 11125.3832385839 & -278.383238583918 \tabularnewline
67 & 11104 & 10728.8365580329 & 375.163441967126 \tabularnewline
68 & 11026 & 11299.9780402019 & -273.978040201899 \tabularnewline
69 & 11073 & 11329.2175760589 & -256.217576058913 \tabularnewline
70 & 12073 & 11962.4872741234 & 110.512725876644 \tabularnewline
71 & 12328 & 11880.2484368985 & 447.75156310145 \tabularnewline
72 & 11172 & 11292.4070319556 & -120.407031955603 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62196&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]7878[/C][C]7988.59029958755[/C][C]-110.590299587550[/C][/ROW]
[ROW][C]14[/C][C]7407[/C][C]7488.2790801246[/C][C]-81.279080124601[/C][/ROW]
[ROW][C]15[/C][C]7911[/C][C]7957.03397465224[/C][C]-46.0339746522377[/C][/ROW]
[ROW][C]16[/C][C]7323[/C][C]7320.39988730651[/C][C]2.60011269348706[/C][/ROW]
[ROW][C]17[/C][C]7179[/C][C]7157.77597266192[/C][C]21.2240273380803[/C][/ROW]
[ROW][C]18[/C][C]6758[/C][C]6694.42051623206[/C][C]63.5794837679405[/C][/ROW]
[ROW][C]19[/C][C]6934[/C][C]7045.18551378264[/C][C]-111.185513782641[/C][/ROW]
[ROW][C]20[/C][C]6696[/C][C]6887.3713435908[/C][C]-191.371343590807[/C][/ROW]
[ROW][C]21[/C][C]7688[/C][C]7092.25811729323[/C][C]595.741882706774[/C][/ROW]
[ROW][C]22[/C][C]8296[/C][C]8137.65718544235[/C][C]158.342814557647[/C][/ROW]
[ROW][C]23[/C][C]7697[/C][C]7665.89759711354[/C][C]31.102402886464[/C][/ROW]
[ROW][C]24[/C][C]7907[/C][C]7001.03249965228[/C][C]905.967500347724[/C][/ROW]
[ROW][C]25[/C][C]7592[/C][C]8313.8716567144[/C][C]-721.8716567144[/C][/ROW]
[ROW][C]26[/C][C]7710[/C][C]7626.19133568407[/C][C]83.8086643159295[/C][/ROW]
[ROW][C]27[/C][C]9011[/C][C]8192.96861575676[/C][C]818.03138424324[/C][/ROW]
[ROW][C]28[/C][C]8225[/C][C]7843.02108207557[/C][C]381.978917924434[/C][/ROW]
[ROW][C]29[/C][C]7733[/C][C]7827.77997673001[/C][C]-94.7799767300121[/C][/ROW]
[ROW][C]30[/C][C]8062[/C][C]7330.61346112378[/C][C]731.38653887622[/C][/ROW]
[ROW][C]31[/C][C]7859[/C][C]7894.26749917752[/C][C]-35.2674991775248[/C][/ROW]
[ROW][C]32[/C][C]8221[/C][C]7743.35388905604[/C][C]477.646110943964[/C][/ROW]
[ROW][C]33[/C][C]8330[/C][C]8644.94391775863[/C][C]-314.943917758626[/C][/ROW]
[ROW][C]34[/C][C]8868[/C][C]9336.47248048307[/C][C]-468.472480483069[/C][/ROW]
[ROW][C]35[/C][C]9053[/C][C]8570.00870177085[/C][C]482.991298229152[/C][/ROW]
[ROW][C]36[/C][C]8811[/C][C]8396.0938741835[/C][C]414.906125816506[/C][/ROW]
[ROW][C]37[/C][C]8120[/C][C]8915.39275819[/C][C]-795.392758189999[/C][/ROW]
[ROW][C]38[/C][C]7953[/C][C]8554.9567097821[/C][C]-601.956709782096[/C][/ROW]
[ROW][C]39[/C][C]8878[/C][C]9285.32389313345[/C][C]-407.323893133447[/C][/ROW]
[ROW][C]40[/C][C]8601[/C][C]8315.66645620527[/C][C]285.333543794732[/C][/ROW]
[ROW][C]41[/C][C]8361[/C][C]8053.8759117906[/C][C]307.124088209405[/C][/ROW]
[ROW][C]42[/C][C]9116[/C][C]8022.83409647932[/C][C]1093.16590352068[/C][/ROW]
[ROW][C]43[/C][C]9310[/C][C]8388.98157355441[/C][C]921.01842644559[/C][/ROW]
[ROW][C]44[/C][C]9891[/C][C]8789.83347775561[/C][C]1101.16652224439[/C][/ROW]
[ROW][C]45[/C][C]10147[/C][C]9640.70611858565[/C][C]506.293881414345[/C][/ROW]
[ROW][C]46[/C][C]10317[/C][C]10695.2006147717[/C][C]-378.200614771651[/C][/ROW]
[ROW][C]47[/C][C]10682[/C][C]10359.0748719003[/C][C]322.925128099738[/C][/ROW]
[ROW][C]48[/C][C]10276[/C][C]10075.7969468298[/C][C]200.203053170177[/C][/ROW]
[ROW][C]49[/C][C]10614[/C][C]10015.1052583161[/C][C]598.894741683946[/C][/ROW]
[ROW][C]50[/C][C]9413[/C][C]10232.1749382142[/C][C]-819.17493821419[/C][/ROW]
[ROW][C]51[/C][C]11068[/C][C]11257.6606109571[/C][C]-189.660610957097[/C][/ROW]
[ROW][C]52[/C][C]9772[/C][C]10570.8562371889[/C][C]-798.856237188917[/C][/ROW]
[ROW][C]53[/C][C]10350[/C][C]9927.91389587363[/C][C]422.086104126372[/C][/ROW]
[ROW][C]54[/C][C]10541[/C][C]10324.4336543782[/C][C]216.566345621834[/C][/ROW]
[ROW][C]55[/C][C]10049[/C][C]10328.6378459917[/C][C]-279.637845991676[/C][/ROW]
[ROW][C]56[/C][C]10714[/C][C]10421.4859564639[/C][C]292.514043536137[/C][/ROW]
[ROW][C]57[/C][C]10759[/C][C]10771.2971297291[/C][C]-12.2971297291479[/C][/ROW]
[ROW][C]58[/C][C]11684[/C][C]11308.5917572169[/C][C]375.40824278306[/C][/ROW]
[ROW][C]59[/C][C]11462[/C][C]11518.4855746003[/C][C]-56.4855746003213[/C][/ROW]
[ROW][C]60[/C][C]10485[/C][C]11014.4682379027[/C][C]-529.468237902713[/C][/ROW]
[ROW][C]61[/C][C]11056[/C][C]10864.7626485383[/C][C]191.237351461694[/C][/ROW]
[ROW][C]62[/C][C]10184[/C][C]10296.9951938175[/C][C]-112.995193817542[/C][/ROW]
[ROW][C]63[/C][C]11082[/C][C]11909.7085981216[/C][C]-827.708598121644[/C][/ROW]
[ROW][C]64[/C][C]10554[/C][C]10689.2533019295[/C][C]-135.253301929491[/C][/ROW]
[ROW][C]65[/C][C]11315[/C][C]10774.1326579238[/C][C]540.867342076201[/C][/ROW]
[ROW][C]66[/C][C]10847[/C][C]11125.3832385839[/C][C]-278.383238583918[/C][/ROW]
[ROW][C]67[/C][C]11104[/C][C]10728.8365580329[/C][C]375.163441967126[/C][/ROW]
[ROW][C]68[/C][C]11026[/C][C]11299.9780402019[/C][C]-273.978040201899[/C][/ROW]
[ROW][C]69[/C][C]11073[/C][C]11329.2175760589[/C][C]-256.217576058913[/C][/ROW]
[ROW][C]70[/C][C]12073[/C][C]11962.4872741234[/C][C]110.512725876644[/C][/ROW]
[ROW][C]71[/C][C]12328[/C][C]11880.2484368985[/C][C]447.75156310145[/C][/ROW]
[ROW][C]72[/C][C]11172[/C][C]11292.4070319556[/C][C]-120.407031955603[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62196&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62196&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
1378787988.59029958755-110.590299587550
1474077488.2790801246-81.279080124601
1579117957.03397465224-46.0339746522377
1673237320.399887306512.60011269348706
1771797157.7759726619221.2240273380803
1867586694.4205162320663.5794837679405
1969347045.18551378264-111.185513782641
2066966887.3713435908-191.371343590807
2176887092.25811729323595.741882706774
2282968137.65718544235158.342814557647
2376977665.8975971135431.102402886464
2479077001.03249965228905.967500347724
2575928313.8716567144-721.8716567144
2677107626.1913356840783.8086643159295
2790118192.96861575676818.03138424324
2882257843.02108207557381.978917924434
2977337827.77997673001-94.7799767300121
3080627330.61346112378731.38653887622
3178597894.26749917752-35.2674991775248
3282217743.35388905604477.646110943964
3383308644.94391775863-314.943917758626
3488689336.47248048307-468.472480483069
3590538570.00870177085482.991298229152
3688118396.0938741835414.906125816506
3781208915.39275819-795.392758189999
3879538554.9567097821-601.956709782096
3988789285.32389313345-407.323893133447
4086018315.66645620527285.333543794732
4183618053.8759117906307.124088209405
4291168022.834096479321093.16590352068
4393108388.98157355441921.01842644559
4498918789.833477755611101.16652224439
45101479640.70611858565506.293881414345
461031710695.2006147717-378.200614771651
471068210359.0748719003322.925128099738
481027610075.7969468298200.203053170177
491061410015.1052583161598.894741683946
50941310232.1749382142-819.17493821419
511106811257.6606109571-189.660610957097
52977210570.8562371889-798.856237188917
53103509927.91389587363422.086104126372
541054110324.4336543782216.566345621834
551004910328.6378459917-279.637845991676
561071410421.4859564639292.514043536137
571075910771.2971297291-12.2971297291479
581168411308.5917572169375.40824278306
591146211518.4855746003-56.4855746003213
601048511014.4682379027-529.468237902713
611105610864.7626485383191.237351461694
621018410296.9951938175-112.995193817542
631108211909.7085981216-827.708598121644
641055410689.2533019295-135.253301929491
651131510774.1326579238540.867342076201
661084711125.3832385839-278.383238583918
671110410728.8365580329375.163441967126
681102611299.9780402019-273.978040201899
691107311329.2175760589-256.217576058913
701207311962.4872741234110.512725876644
711232811880.2484368985447.75156310145
721117211292.4070319556-120.407031955603







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7311590.857521610610900.361912724612281.3531304966
7410782.228833901910032.772166291811531.6855015120
7512188.336314568711340.722016824413035.9506123130
7611478.752358496610588.111636993612369.3930799996
7711926.223752326510952.705748821512899.7417558315
7811738.727411654210709.796857129512767.6579661790
7911703.554591801510612.393266278412794.7159173246
8011882.929531390210716.325521214913049.5335415656
8112015.279355769810775.227427997913255.3312835417
8212956.626458598411578.155386294514335.0975309023
8312979.291369216611533.870792949714424.7119454835
8411938.972502685910703.131431788413174.8135735835

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 11590.8575216106 & 10900.3619127246 & 12281.3531304966 \tabularnewline
74 & 10782.2288339019 & 10032.7721662918 & 11531.6855015120 \tabularnewline
75 & 12188.3363145687 & 11340.7220168244 & 13035.9506123130 \tabularnewline
76 & 11478.7523584966 & 10588.1116369936 & 12369.3930799996 \tabularnewline
77 & 11926.2237523265 & 10952.7057488215 & 12899.7417558315 \tabularnewline
78 & 11738.7274116542 & 10709.7968571295 & 12767.6579661790 \tabularnewline
79 & 11703.5545918015 & 10612.3932662784 & 12794.7159173246 \tabularnewline
80 & 11882.9295313902 & 10716.3255212149 & 13049.5335415656 \tabularnewline
81 & 12015.2793557698 & 10775.2274279979 & 13255.3312835417 \tabularnewline
82 & 12956.6264585984 & 11578.1553862945 & 14335.0975309023 \tabularnewline
83 & 12979.2913692166 & 11533.8707929497 & 14424.7119454835 \tabularnewline
84 & 11938.9725026859 & 10703.1314317884 & 13174.8135735835 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62196&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]11590.8575216106[/C][C]10900.3619127246[/C][C]12281.3531304966[/C][/ROW]
[ROW][C]74[/C][C]10782.2288339019[/C][C]10032.7721662918[/C][C]11531.6855015120[/C][/ROW]
[ROW][C]75[/C][C]12188.3363145687[/C][C]11340.7220168244[/C][C]13035.9506123130[/C][/ROW]
[ROW][C]76[/C][C]11478.7523584966[/C][C]10588.1116369936[/C][C]12369.3930799996[/C][/ROW]
[ROW][C]77[/C][C]11926.2237523265[/C][C]10952.7057488215[/C][C]12899.7417558315[/C][/ROW]
[ROW][C]78[/C][C]11738.7274116542[/C][C]10709.7968571295[/C][C]12767.6579661790[/C][/ROW]
[ROW][C]79[/C][C]11703.5545918015[/C][C]10612.3932662784[/C][C]12794.7159173246[/C][/ROW]
[ROW][C]80[/C][C]11882.9295313902[/C][C]10716.3255212149[/C][C]13049.5335415656[/C][/ROW]
[ROW][C]81[/C][C]12015.2793557698[/C][C]10775.2274279979[/C][C]13255.3312835417[/C][/ROW]
[ROW][C]82[/C][C]12956.6264585984[/C][C]11578.1553862945[/C][C]14335.0975309023[/C][/ROW]
[ROW][C]83[/C][C]12979.2913692166[/C][C]11533.8707929497[/C][C]14424.7119454835[/C][/ROW]
[ROW][C]84[/C][C]11938.9725026859[/C][C]10703.1314317884[/C][C]13174.8135735835[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62196&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62196&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
7311590.857521610610900.361912724612281.3531304966
7410782.228833901910032.772166291811531.6855015120
7512188.336314568711340.722016824413035.9506123130
7611478.752358496610588.111636993612369.3930799996
7711926.223752326510952.705748821512899.7417558315
7811738.727411654210709.796857129512767.6579661790
7911703.554591801510612.393266278412794.7159173246
8011882.929531390210716.325521214913049.5335415656
8112015.279355769810775.227427997913255.3312835417
8212956.626458598411578.155386294514335.0975309023
8312979.291369216611533.870792949714424.7119454835
8411938.972502685910703.131431788413174.8135735835



Parameters (Session):
par1 = 12 ; par2 = periodic ; par3 = 0 ; par5 = 1 ; par7 = 1 ; par8 = FALSE ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')