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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 25 May 2013 15:17:43 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/25/t1369509485m8tzvpsamrzd9v7.htm/, Retrieved Thu, 02 May 2024 16:32:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210555, Retrieved Thu, 02 May 2024 16:32:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2013-05-25 19:17:43] [3958f9c0a64aeec6b83979b094ee8a96] [Current]
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Dataseries X:
3169889
3051720
3695426
3905501
4296458
4246247
4921849
4821446
4425064
4379099
3472889
3359160
3200944
3153170
3741498
3918719
4403449
4400407
4847473
4716136
4297440
4272253
3271834
3168388
2911748
2720999
3199918
3672623
3892013
3850845
4532467
4484739
4014972
3983758
3158459
3100569
2935404
2855719
3465611
3006985
4095110
4104793
4730788
4642726
4246919
4308117
3508154
3236641
3257275
3045631
3657692
4125747
4472507
4513455
5150896
5057815
4681742
4603682
3580181
3534002
3422762
3295209
3868093
4189245
4544332
4612845
5221595
5137505
4760439
4643697
3692267
3587603




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210555&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210555&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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.47212346037773
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.47212346037773 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210555&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]0.47212346037773[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210555&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
alpha0.47212346037773
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1332009443167204.6994387833739.3005612171
1431531703140498.1000458812671.8999541239
1537414983741453.332560444.6674395971932
1639187193927064.1223945-8345.12239449937
1744034494421241.26383444-17792.2638344411
1844004074426590.06782568-26183.0678256759
1948474734907515.77871157-60042.7787115667
2047161364771496.41039374-55360.4103937391
2142974404347134.76042137-49694.7604213692
2242722534274738.36834083-2485.36834082566
2332718343383859.46242806-112025.462428062
2431683883212094.14024116-43706.1402411629
2529117483037622.05780152-125874.057801517
2627209992938239.65758258-217240.657582576
2731999183371761.03571613-171843.03571613
2836726233453707.53335248218915.466647517
2938920134008571.30229496-116558.302294957
3038508453965714.05185492-114869.051854919
3145324674348410.60911505184056.390884953
3244847394337293.01067192147445.989328079
3340149724036984.40166577-22012.40166577
3439837583980925.242399122832.75760087976
3531584593153128.53798155330.46201849543
3631005693042971.3308169457597.6691830624
3729354042922135.8657640913268.1342359073
3828557192889097.25657061-33378.2565706149
3934656113416560.2707745249050.7292254777
4030069853610240.34483207-603255.344832074
4140951103747445.49874398347664.501256025
4241047933923614.73640148181178.263598524
4347307884457031.25834129273756.741658715
4446427264484978.72151743157747.27848257
4542469194176776.5820872170142.4179127901
4643081174162209.65932592145907.340674081
4735081543350221.14915685157932.850843154
4832366413302591.01499831-65950.0149983079
4932572753113786.1823176143488.817682403
5030456313138915.88075209-93284.8807520871
5136576923680068.73512522-22376.7351252167
5241257473851500.15450347274246.845496533
5344725074486461.8399014-13954.8399014045
5445134554493852.4328551919602.5671448121
5551508965006358.02387848144537.97612152
5650578154962674.1736412395140.8263587737
5746817424587438.3143326394303.6856673677
5846036824579635.9456363424046.0543636642
5935801813635280.26013979-55099.2601397862
6035340023480547.1269018553454.8730981476
6134227623336894.2757731285867.7242268813
6232952093332256.52033048-37047.520330478
6338680933941622.09423663-73529.0942366323
6441892454100757.5647492888487.4352507219
6545443324668587.83935144-124255.839351444
6646128454624349.06804308-11504.0680430802
6752215955135150.9570422786444.0429577315
6851375055061834.2457035275670.7542964779
6947604394669882.5019108190556.4980891896
7046436974659423.61259163-15726.612591628
7136922673683604.308267778662.69173222873
7235876033556200.5246125431402.4753874578

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3200944 & 3167204.69943878 & 33739.3005612171 \tabularnewline
14 & 3153170 & 3140498.10004588 & 12671.8999541239 \tabularnewline
15 & 3741498 & 3741453.3325604 & 44.6674395971932 \tabularnewline
16 & 3918719 & 3927064.1223945 & -8345.12239449937 \tabularnewline
17 & 4403449 & 4421241.26383444 & -17792.2638344411 \tabularnewline
18 & 4400407 & 4426590.06782568 & -26183.0678256759 \tabularnewline
19 & 4847473 & 4907515.77871157 & -60042.7787115667 \tabularnewline
20 & 4716136 & 4771496.41039374 & -55360.4103937391 \tabularnewline
21 & 4297440 & 4347134.76042137 & -49694.7604213692 \tabularnewline
22 & 4272253 & 4274738.36834083 & -2485.36834082566 \tabularnewline
23 & 3271834 & 3383859.46242806 & -112025.462428062 \tabularnewline
24 & 3168388 & 3212094.14024116 & -43706.1402411629 \tabularnewline
25 & 2911748 & 3037622.05780152 & -125874.057801517 \tabularnewline
26 & 2720999 & 2938239.65758258 & -217240.657582576 \tabularnewline
27 & 3199918 & 3371761.03571613 & -171843.03571613 \tabularnewline
28 & 3672623 & 3453707.53335248 & 218915.466647517 \tabularnewline
29 & 3892013 & 4008571.30229496 & -116558.302294957 \tabularnewline
30 & 3850845 & 3965714.05185492 & -114869.051854919 \tabularnewline
31 & 4532467 & 4348410.60911505 & 184056.390884953 \tabularnewline
32 & 4484739 & 4337293.01067192 & 147445.989328079 \tabularnewline
33 & 4014972 & 4036984.40166577 & -22012.40166577 \tabularnewline
34 & 3983758 & 3980925.24239912 & 2832.75760087976 \tabularnewline
35 & 3158459 & 3153128.5379815 & 5330.46201849543 \tabularnewline
36 & 3100569 & 3042971.33081694 & 57597.6691830624 \tabularnewline
37 & 2935404 & 2922135.86576409 & 13268.1342359073 \tabularnewline
38 & 2855719 & 2889097.25657061 & -33378.2565706149 \tabularnewline
39 & 3465611 & 3416560.27077452 & 49050.7292254777 \tabularnewline
40 & 3006985 & 3610240.34483207 & -603255.344832074 \tabularnewline
41 & 4095110 & 3747445.49874398 & 347664.501256025 \tabularnewline
42 & 4104793 & 3923614.73640148 & 181178.263598524 \tabularnewline
43 & 4730788 & 4457031.25834129 & 273756.741658715 \tabularnewline
44 & 4642726 & 4484978.72151743 & 157747.27848257 \tabularnewline
45 & 4246919 & 4176776.58208721 & 70142.4179127901 \tabularnewline
46 & 4308117 & 4162209.65932592 & 145907.340674081 \tabularnewline
47 & 3508154 & 3350221.14915685 & 157932.850843154 \tabularnewline
48 & 3236641 & 3302591.01499831 & -65950.0149983079 \tabularnewline
49 & 3257275 & 3113786.1823176 & 143488.817682403 \tabularnewline
50 & 3045631 & 3138915.88075209 & -93284.8807520871 \tabularnewline
51 & 3657692 & 3680068.73512522 & -22376.7351252167 \tabularnewline
52 & 4125747 & 3851500.15450347 & 274246.845496533 \tabularnewline
53 & 4472507 & 4486461.8399014 & -13954.8399014045 \tabularnewline
54 & 4513455 & 4493852.43285519 & 19602.5671448121 \tabularnewline
55 & 5150896 & 5006358.02387848 & 144537.97612152 \tabularnewline
56 & 5057815 & 4962674.17364123 & 95140.8263587737 \tabularnewline
57 & 4681742 & 4587438.31433263 & 94303.6856673677 \tabularnewline
58 & 4603682 & 4579635.94563634 & 24046.0543636642 \tabularnewline
59 & 3580181 & 3635280.26013979 & -55099.2601397862 \tabularnewline
60 & 3534002 & 3480547.12690185 & 53454.8730981476 \tabularnewline
61 & 3422762 & 3336894.27577312 & 85867.7242268813 \tabularnewline
62 & 3295209 & 3332256.52033048 & -37047.520330478 \tabularnewline
63 & 3868093 & 3941622.09423663 & -73529.0942366323 \tabularnewline
64 & 4189245 & 4100757.56474928 & 88487.4352507219 \tabularnewline
65 & 4544332 & 4668587.83935144 & -124255.839351444 \tabularnewline
66 & 4612845 & 4624349.06804308 & -11504.0680430802 \tabularnewline
67 & 5221595 & 5135150.95704227 & 86444.0429577315 \tabularnewline
68 & 5137505 & 5061834.24570352 & 75670.7542964779 \tabularnewline
69 & 4760439 & 4669882.50191081 & 90556.4980891896 \tabularnewline
70 & 4643697 & 4659423.61259163 & -15726.612591628 \tabularnewline
71 & 3692267 & 3683604.30826777 & 8662.69173222873 \tabularnewline
72 & 3587603 & 3556200.52461254 & 31402.4753874578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210555&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]3200944[/C][C]3167204.69943878[/C][C]33739.3005612171[/C][/ROW]
[ROW][C]14[/C][C]3153170[/C][C]3140498.10004588[/C][C]12671.8999541239[/C][/ROW]
[ROW][C]15[/C][C]3741498[/C][C]3741453.3325604[/C][C]44.6674395971932[/C][/ROW]
[ROW][C]16[/C][C]3918719[/C][C]3927064.1223945[/C][C]-8345.12239449937[/C][/ROW]
[ROW][C]17[/C][C]4403449[/C][C]4421241.26383444[/C][C]-17792.2638344411[/C][/ROW]
[ROW][C]18[/C][C]4400407[/C][C]4426590.06782568[/C][C]-26183.0678256759[/C][/ROW]
[ROW][C]19[/C][C]4847473[/C][C]4907515.77871157[/C][C]-60042.7787115667[/C][/ROW]
[ROW][C]20[/C][C]4716136[/C][C]4771496.41039374[/C][C]-55360.4103937391[/C][/ROW]
[ROW][C]21[/C][C]4297440[/C][C]4347134.76042137[/C][C]-49694.7604213692[/C][/ROW]
[ROW][C]22[/C][C]4272253[/C][C]4274738.36834083[/C][C]-2485.36834082566[/C][/ROW]
[ROW][C]23[/C][C]3271834[/C][C]3383859.46242806[/C][C]-112025.462428062[/C][/ROW]
[ROW][C]24[/C][C]3168388[/C][C]3212094.14024116[/C][C]-43706.1402411629[/C][/ROW]
[ROW][C]25[/C][C]2911748[/C][C]3037622.05780152[/C][C]-125874.057801517[/C][/ROW]
[ROW][C]26[/C][C]2720999[/C][C]2938239.65758258[/C][C]-217240.657582576[/C][/ROW]
[ROW][C]27[/C][C]3199918[/C][C]3371761.03571613[/C][C]-171843.03571613[/C][/ROW]
[ROW][C]28[/C][C]3672623[/C][C]3453707.53335248[/C][C]218915.466647517[/C][/ROW]
[ROW][C]29[/C][C]3892013[/C][C]4008571.30229496[/C][C]-116558.302294957[/C][/ROW]
[ROW][C]30[/C][C]3850845[/C][C]3965714.05185492[/C][C]-114869.051854919[/C][/ROW]
[ROW][C]31[/C][C]4532467[/C][C]4348410.60911505[/C][C]184056.390884953[/C][/ROW]
[ROW][C]32[/C][C]4484739[/C][C]4337293.01067192[/C][C]147445.989328079[/C][/ROW]
[ROW][C]33[/C][C]4014972[/C][C]4036984.40166577[/C][C]-22012.40166577[/C][/ROW]
[ROW][C]34[/C][C]3983758[/C][C]3980925.24239912[/C][C]2832.75760087976[/C][/ROW]
[ROW][C]35[/C][C]3158459[/C][C]3153128.5379815[/C][C]5330.46201849543[/C][/ROW]
[ROW][C]36[/C][C]3100569[/C][C]3042971.33081694[/C][C]57597.6691830624[/C][/ROW]
[ROW][C]37[/C][C]2935404[/C][C]2922135.86576409[/C][C]13268.1342359073[/C][/ROW]
[ROW][C]38[/C][C]2855719[/C][C]2889097.25657061[/C][C]-33378.2565706149[/C][/ROW]
[ROW][C]39[/C][C]3465611[/C][C]3416560.27077452[/C][C]49050.7292254777[/C][/ROW]
[ROW][C]40[/C][C]3006985[/C][C]3610240.34483207[/C][C]-603255.344832074[/C][/ROW]
[ROW][C]41[/C][C]4095110[/C][C]3747445.49874398[/C][C]347664.501256025[/C][/ROW]
[ROW][C]42[/C][C]4104793[/C][C]3923614.73640148[/C][C]181178.263598524[/C][/ROW]
[ROW][C]43[/C][C]4730788[/C][C]4457031.25834129[/C][C]273756.741658715[/C][/ROW]
[ROW][C]44[/C][C]4642726[/C][C]4484978.72151743[/C][C]157747.27848257[/C][/ROW]
[ROW][C]45[/C][C]4246919[/C][C]4176776.58208721[/C][C]70142.4179127901[/C][/ROW]
[ROW][C]46[/C][C]4308117[/C][C]4162209.65932592[/C][C]145907.340674081[/C][/ROW]
[ROW][C]47[/C][C]3508154[/C][C]3350221.14915685[/C][C]157932.850843154[/C][/ROW]
[ROW][C]48[/C][C]3236641[/C][C]3302591.01499831[/C][C]-65950.0149983079[/C][/ROW]
[ROW][C]49[/C][C]3257275[/C][C]3113786.1823176[/C][C]143488.817682403[/C][/ROW]
[ROW][C]50[/C][C]3045631[/C][C]3138915.88075209[/C][C]-93284.8807520871[/C][/ROW]
[ROW][C]51[/C][C]3657692[/C][C]3680068.73512522[/C][C]-22376.7351252167[/C][/ROW]
[ROW][C]52[/C][C]4125747[/C][C]3851500.15450347[/C][C]274246.845496533[/C][/ROW]
[ROW][C]53[/C][C]4472507[/C][C]4486461.8399014[/C][C]-13954.8399014045[/C][/ROW]
[ROW][C]54[/C][C]4513455[/C][C]4493852.43285519[/C][C]19602.5671448121[/C][/ROW]
[ROW][C]55[/C][C]5150896[/C][C]5006358.02387848[/C][C]144537.97612152[/C][/ROW]
[ROW][C]56[/C][C]5057815[/C][C]4962674.17364123[/C][C]95140.8263587737[/C][/ROW]
[ROW][C]57[/C][C]4681742[/C][C]4587438.31433263[/C][C]94303.6856673677[/C][/ROW]
[ROW][C]58[/C][C]4603682[/C][C]4579635.94563634[/C][C]24046.0543636642[/C][/ROW]
[ROW][C]59[/C][C]3580181[/C][C]3635280.26013979[/C][C]-55099.2601397862[/C][/ROW]
[ROW][C]60[/C][C]3534002[/C][C]3480547.12690185[/C][C]53454.8730981476[/C][/ROW]
[ROW][C]61[/C][C]3422762[/C][C]3336894.27577312[/C][C]85867.7242268813[/C][/ROW]
[ROW][C]62[/C][C]3295209[/C][C]3332256.52033048[/C][C]-37047.520330478[/C][/ROW]
[ROW][C]63[/C][C]3868093[/C][C]3941622.09423663[/C][C]-73529.0942366323[/C][/ROW]
[ROW][C]64[/C][C]4189245[/C][C]4100757.56474928[/C][C]88487.4352507219[/C][/ROW]
[ROW][C]65[/C][C]4544332[/C][C]4668587.83935144[/C][C]-124255.839351444[/C][/ROW]
[ROW][C]66[/C][C]4612845[/C][C]4624349.06804308[/C][C]-11504.0680430802[/C][/ROW]
[ROW][C]67[/C][C]5221595[/C][C]5135150.95704227[/C][C]86444.0429577315[/C][/ROW]
[ROW][C]68[/C][C]5137505[/C][C]5061834.24570352[/C][C]75670.7542964779[/C][/ROW]
[ROW][C]69[/C][C]4760439[/C][C]4669882.50191081[/C][C]90556.4980891896[/C][/ROW]
[ROW][C]70[/C][C]4643697[/C][C]4659423.61259163[/C][C]-15726.612591628[/C][/ROW]
[ROW][C]71[/C][C]3692267[/C][C]3683604.30826777[/C][C]8662.69173222873[/C][/ROW]
[ROW][C]72[/C][C]3587603[/C][C]3556200.52461254[/C][C]31402.4753874578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210555&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
1332009443167204.6994387833739.3005612171
1431531703140498.1000458812671.8999541239
1537414983741453.332560444.6674395971932
1639187193927064.1223945-8345.12239449937
1744034494421241.26383444-17792.2638344411
1844004074426590.06782568-26183.0678256759
1948474734907515.77871157-60042.7787115667
2047161364771496.41039374-55360.4103937391
2142974404347134.76042137-49694.7604213692
2242722534274738.36834083-2485.36834082566
2332718343383859.46242806-112025.462428062
2431683883212094.14024116-43706.1402411629
2529117483037622.05780152-125874.057801517
2627209992938239.65758258-217240.657582576
2731999183371761.03571613-171843.03571613
2836726233453707.53335248218915.466647517
2938920134008571.30229496-116558.302294957
3038508453965714.05185492-114869.051854919
3145324674348410.60911505184056.390884953
3244847394337293.01067192147445.989328079
3340149724036984.40166577-22012.40166577
3439837583980925.242399122832.75760087976
3531584593153128.53798155330.46201849543
3631005693042971.3308169457597.6691830624
3729354042922135.8657640913268.1342359073
3828557192889097.25657061-33378.2565706149
3934656113416560.2707745249050.7292254777
4030069853610240.34483207-603255.344832074
4140951103747445.49874398347664.501256025
4241047933923614.73640148181178.263598524
4347307884457031.25834129273756.741658715
4446427264484978.72151743157747.27848257
4542469194176776.5820872170142.4179127901
4643081174162209.65932592145907.340674081
4735081543350221.14915685157932.850843154
4832366413302591.01499831-65950.0149983079
4932572753113786.1823176143488.817682403
5030456313138915.88075209-93284.8807520871
5136576923680068.73512522-22376.7351252167
5241257473851500.15450347274246.845496533
5344725074486461.8399014-13954.8399014045
5445134554493852.4328551919602.5671448121
5551508965006358.02387848144537.97612152
5650578154962674.1736412395140.8263587737
5746817424587438.3143326394303.6856673677
5846036824579635.9456363424046.0543636642
5935801813635280.26013979-55099.2601397862
6035340023480547.1269018553454.8730981476
6134227623336894.2757731285867.7242268813
6232952093332256.52033048-37047.520330478
6338680933941622.09423663-73529.0942366323
6441892454100757.5647492888487.4352507219
6545443324668587.83935144-124255.839351444
6646128454624349.06804308-11504.0680430802
6752215955135150.9570422786444.0429577315
6851375055061834.2457035275670.7542964779
6947604394669882.5019108190556.4980891896
7046436974659423.61259163-15726.612591628
7136922673683604.308267778662.69173222873
7235876033556200.5246125431402.4753874578







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733399011.836629053271462.486025373526561.18723274
743353551.597868793174345.740246483532757.45549109
753987756.776085443739350.598888884236162.953282
764185644.124723063895315.643482774475972.60596336
774717186.28867884365916.623677345068455.95368025
784731979.733186924357136.292196545106823.17417729
795260887.32796324824946.689833995696827.96609241
805144910.708305914699788.64091735590032.77569452
814713273.312297434285897.584078125140649.04051674
824660053.569462824218552.912679575101554.22624606
833689984.296065473317751.074112954062217.51801799
843558409.645309993199343.161307143917476.12931284

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3399011.83662905 & 3271462.48602537 & 3526561.18723274 \tabularnewline
74 & 3353551.59786879 & 3174345.74024648 & 3532757.45549109 \tabularnewline
75 & 3987756.77608544 & 3739350.59888888 & 4236162.953282 \tabularnewline
76 & 4185644.12472306 & 3895315.64348277 & 4475972.60596336 \tabularnewline
77 & 4717186.2886788 & 4365916.62367734 & 5068455.95368025 \tabularnewline
78 & 4731979.73318692 & 4357136.29219654 & 5106823.17417729 \tabularnewline
79 & 5260887.3279632 & 4824946.68983399 & 5696827.96609241 \tabularnewline
80 & 5144910.70830591 & 4699788.6409173 & 5590032.77569452 \tabularnewline
81 & 4713273.31229743 & 4285897.58407812 & 5140649.04051674 \tabularnewline
82 & 4660053.56946282 & 4218552.91267957 & 5101554.22624606 \tabularnewline
83 & 3689984.29606547 & 3317751.07411295 & 4062217.51801799 \tabularnewline
84 & 3558409.64530999 & 3199343.16130714 & 3917476.12931284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210555&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]3399011.83662905[/C][C]3271462.48602537[/C][C]3526561.18723274[/C][/ROW]
[ROW][C]74[/C][C]3353551.59786879[/C][C]3174345.74024648[/C][C]3532757.45549109[/C][/ROW]
[ROW][C]75[/C][C]3987756.77608544[/C][C]3739350.59888888[/C][C]4236162.953282[/C][/ROW]
[ROW][C]76[/C][C]4185644.12472306[/C][C]3895315.64348277[/C][C]4475972.60596336[/C][/ROW]
[ROW][C]77[/C][C]4717186.2886788[/C][C]4365916.62367734[/C][C]5068455.95368025[/C][/ROW]
[ROW][C]78[/C][C]4731979.73318692[/C][C]4357136.29219654[/C][C]5106823.17417729[/C][/ROW]
[ROW][C]79[/C][C]5260887.3279632[/C][C]4824946.68983399[/C][C]5696827.96609241[/C][/ROW]
[ROW][C]80[/C][C]5144910.70830591[/C][C]4699788.6409173[/C][C]5590032.77569452[/C][/ROW]
[ROW][C]81[/C][C]4713273.31229743[/C][C]4285897.58407812[/C][C]5140649.04051674[/C][/ROW]
[ROW][C]82[/C][C]4660053.56946282[/C][C]4218552.91267957[/C][C]5101554.22624606[/C][/ROW]
[ROW][C]83[/C][C]3689984.29606547[/C][C]3317751.07411295[/C][C]4062217.51801799[/C][/ROW]
[ROW][C]84[/C][C]3558409.64530999[/C][C]3199343.16130714[/C][C]3917476.12931284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210555&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210555&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
733399011.836629053271462.486025373526561.18723274
743353551.597868793174345.740246483532757.45549109
753987756.776085443739350.598888884236162.953282
764185644.124723063895315.643482774475972.60596336
774717186.28867884365916.623677345068455.95368025
784731979.733186924357136.292196545106823.17417729
795260887.32796324824946.689833995696827.96609241
805144910.708305914699788.64091735590032.77569452
814713273.312297434285897.584078125140649.04051674
824660053.569462824218552.912679575101554.22624606
833689984.296065473317751.074112954062217.51801799
843558409.645309993199343.161307143917476.12931284



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')