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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 14:57:40 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211835514k4dirjiaqwxslvn.htm/, Retrieved Tue, 14 May 2024 11:39:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13300, Retrieved Tue, 14 May 2024 11:39:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [neerslag in Notin...] [2008-05-26 20:57:40] [e6054d98fbbc73c68fb360666fa70916] [Current]
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Dataseries X:
29.90
28.77
15.64
23.73
25.65
21.81
28.97
24.29
25.33
28.84
19.99
19.75
22.70
23.28
24.15
20.38
27.75
27.31
25.61
22.64
26.05
28.07
21.02
25.00
17.93
35.45
17.70
28.53
26.55
26.51
30.78
26.83
27.49
25.89
20.44
19.79
18.14
27.98
35.90
34.38
21.58
21.53
31.14
28.25
25.16
20.51
30.05
20.17
32.37
22.46
25.40
19.82
18.14
20.10
20.25
19.73
24.74
26.17
20.14
31.71
26.66
20.75
20.01
26.67
23.91
26.81
29.31
31.76
22.99
23.94
27.04
20.28
23.32




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 7 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13300&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13300&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13300&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 time7 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0059609824078949
beta0
gamma0.149848445764807

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0059609824078949 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.149848445764807 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13300&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]0.0059609824078949[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.149848445764807[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13300&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13300&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
alpha0.0059609824078949
beta0
gamma0.149848445764807







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1322.721.83764812641930.862351873580732
1423.2822.59535256213740.684647437862608
1524.1523.48184066715790.668159332842098
1620.3819.82122663950130.558773360498666
1727.7526.98151691826310.768483081736893
1827.3126.27196655271461.0380334472854
1925.6124.62210131775650.987898682243461
2022.6421.49905751983341.14094248016659
2126.0524.50765775235911.54234224764089
2228.0726.34286140752841.72713859247157
2321.0219.50762500501551.51237499498450
242523.28898744446461.71101255553539
2517.9322.0404407121803-4.1104407121803
2635.4522.743491122506412.7065088774936
2717.723.7037352652812-6.00373526528117
2828.5319.97415178106998.55584821893014
2926.5527.2557072182352-0.705707218235155
3026.5126.5737299013003-0.0637299013002917
3130.7824.90094690013685.87905309986323
3226.8321.80963562559305.02036437440704
3327.4924.92419415636572.56580584363426
3425.8926.8073718865538-0.917371886553806
3520.4419.87478813160180.565211868398251
3619.7923.7062178522269-3.91621785222694
3718.1421.5446794857404-3.40467948574039
3827.9824.76882276066343.21117723933658
3935.922.878267544932613.0217324550674
4034.3821.415345139586212.9646548604138
4121.5827.3966351700835-5.81663517008354
4221.5326.7751943751373-5.24519437513732
4331.1425.95015790136265.18984209863742
4428.2522.70444485353695.54555514646314
4525.1625.474351175511-0.314351175510978
4620.5126.8295288302594-6.31952883025937
4730.0520.05372687748949.99627312251055
4820.1723.2971649588303-3.12716495883026
4932.3721.200066705544711.1699332944553
5022.4625.5463776645605-3.08637766456047
5125.425.06834555334260.331654446657375
5219.8223.5034081196583-3.68340811965834
5318.1426.5944361904885-8.45443619048846
5420.126.0405573195039-5.94055731950387
5520.2526.7660522996157-6.51605229961571
5619.7323.5055920427926-3.77559204279258
5724.7425.3407038205359-0.600703820535934
5826.1725.79674258388650.373257416113482
5920.1421.4953500595627-1.35535005956267
6031.7122.70940078603729.00059921396284
6126.6622.80891376647483.85108623352523
6220.7524.9784441593524-4.22844415935237
6320.0125.0025068992166-4.99250689921658
6426.6722.81992521065563.85007478934439
6523.9125.2333903694891-1.32339036948913
6626.8125.09557486771951.71442513228055
6729.3125.77917931233553.53082068766451
6831.7622.98150996669458.7784900333055
6922.9925.3758643609065-2.38586436090646
7023.9425.9690638901831-2.02906389018307
7127.0421.37772467400525.6622753259948
7220.2824.1893790324116-3.90937903241156
7323.3223.4424457585962-0.122445758596172

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 22.7 & 21.8376481264193 & 0.862351873580732 \tabularnewline
14 & 23.28 & 22.5953525621374 & 0.684647437862608 \tabularnewline
15 & 24.15 & 23.4818406671579 & 0.668159332842098 \tabularnewline
16 & 20.38 & 19.8212266395013 & 0.558773360498666 \tabularnewline
17 & 27.75 & 26.9815169182631 & 0.768483081736893 \tabularnewline
18 & 27.31 & 26.2719665527146 & 1.0380334472854 \tabularnewline
19 & 25.61 & 24.6221013177565 & 0.987898682243461 \tabularnewline
20 & 22.64 & 21.4990575198334 & 1.14094248016659 \tabularnewline
21 & 26.05 & 24.5076577523591 & 1.54234224764089 \tabularnewline
22 & 28.07 & 26.3428614075284 & 1.72713859247157 \tabularnewline
23 & 21.02 & 19.5076250050155 & 1.51237499498450 \tabularnewline
24 & 25 & 23.2889874444646 & 1.71101255553539 \tabularnewline
25 & 17.93 & 22.0404407121803 & -4.1104407121803 \tabularnewline
26 & 35.45 & 22.7434911225064 & 12.7065088774936 \tabularnewline
27 & 17.7 & 23.7037352652812 & -6.00373526528117 \tabularnewline
28 & 28.53 & 19.9741517810699 & 8.55584821893014 \tabularnewline
29 & 26.55 & 27.2557072182352 & -0.705707218235155 \tabularnewline
30 & 26.51 & 26.5737299013003 & -0.0637299013002917 \tabularnewline
31 & 30.78 & 24.9009469001368 & 5.87905309986323 \tabularnewline
32 & 26.83 & 21.8096356255930 & 5.02036437440704 \tabularnewline
33 & 27.49 & 24.9241941563657 & 2.56580584363426 \tabularnewline
34 & 25.89 & 26.8073718865538 & -0.917371886553806 \tabularnewline
35 & 20.44 & 19.8747881316018 & 0.565211868398251 \tabularnewline
36 & 19.79 & 23.7062178522269 & -3.91621785222694 \tabularnewline
37 & 18.14 & 21.5446794857404 & -3.40467948574039 \tabularnewline
38 & 27.98 & 24.7688227606634 & 3.21117723933658 \tabularnewline
39 & 35.9 & 22.8782675449326 & 13.0217324550674 \tabularnewline
40 & 34.38 & 21.4153451395862 & 12.9646548604138 \tabularnewline
41 & 21.58 & 27.3966351700835 & -5.81663517008354 \tabularnewline
42 & 21.53 & 26.7751943751373 & -5.24519437513732 \tabularnewline
43 & 31.14 & 25.9501579013626 & 5.18984209863742 \tabularnewline
44 & 28.25 & 22.7044448535369 & 5.54555514646314 \tabularnewline
45 & 25.16 & 25.474351175511 & -0.314351175510978 \tabularnewline
46 & 20.51 & 26.8295288302594 & -6.31952883025937 \tabularnewline
47 & 30.05 & 20.0537268774894 & 9.99627312251055 \tabularnewline
48 & 20.17 & 23.2971649588303 & -3.12716495883026 \tabularnewline
49 & 32.37 & 21.2000667055447 & 11.1699332944553 \tabularnewline
50 & 22.46 & 25.5463776645605 & -3.08637766456047 \tabularnewline
51 & 25.4 & 25.0683455533426 & 0.331654446657375 \tabularnewline
52 & 19.82 & 23.5034081196583 & -3.68340811965834 \tabularnewline
53 & 18.14 & 26.5944361904885 & -8.45443619048846 \tabularnewline
54 & 20.1 & 26.0405573195039 & -5.94055731950387 \tabularnewline
55 & 20.25 & 26.7660522996157 & -6.51605229961571 \tabularnewline
56 & 19.73 & 23.5055920427926 & -3.77559204279258 \tabularnewline
57 & 24.74 & 25.3407038205359 & -0.600703820535934 \tabularnewline
58 & 26.17 & 25.7967425838865 & 0.373257416113482 \tabularnewline
59 & 20.14 & 21.4953500595627 & -1.35535005956267 \tabularnewline
60 & 31.71 & 22.7094007860372 & 9.00059921396284 \tabularnewline
61 & 26.66 & 22.8089137664748 & 3.85108623352523 \tabularnewline
62 & 20.75 & 24.9784441593524 & -4.22844415935237 \tabularnewline
63 & 20.01 & 25.0025068992166 & -4.99250689921658 \tabularnewline
64 & 26.67 & 22.8199252106556 & 3.85007478934439 \tabularnewline
65 & 23.91 & 25.2333903694891 & -1.32339036948913 \tabularnewline
66 & 26.81 & 25.0955748677195 & 1.71442513228055 \tabularnewline
67 & 29.31 & 25.7791793123355 & 3.53082068766451 \tabularnewline
68 & 31.76 & 22.9815099666945 & 8.7784900333055 \tabularnewline
69 & 22.99 & 25.3758643609065 & -2.38586436090646 \tabularnewline
70 & 23.94 & 25.9690638901831 & -2.02906389018307 \tabularnewline
71 & 27.04 & 21.3777246740052 & 5.6622753259948 \tabularnewline
72 & 20.28 & 24.1893790324116 & -3.90937903241156 \tabularnewline
73 & 23.32 & 23.4424457585962 & -0.122445758596172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13300&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]22.7[/C][C]21.8376481264193[/C][C]0.862351873580732[/C][/ROW]
[ROW][C]14[/C][C]23.28[/C][C]22.5953525621374[/C][C]0.684647437862608[/C][/ROW]
[ROW][C]15[/C][C]24.15[/C][C]23.4818406671579[/C][C]0.668159332842098[/C][/ROW]
[ROW][C]16[/C][C]20.38[/C][C]19.8212266395013[/C][C]0.558773360498666[/C][/ROW]
[ROW][C]17[/C][C]27.75[/C][C]26.9815169182631[/C][C]0.768483081736893[/C][/ROW]
[ROW][C]18[/C][C]27.31[/C][C]26.2719665527146[/C][C]1.0380334472854[/C][/ROW]
[ROW][C]19[/C][C]25.61[/C][C]24.6221013177565[/C][C]0.987898682243461[/C][/ROW]
[ROW][C]20[/C][C]22.64[/C][C]21.4990575198334[/C][C]1.14094248016659[/C][/ROW]
[ROW][C]21[/C][C]26.05[/C][C]24.5076577523591[/C][C]1.54234224764089[/C][/ROW]
[ROW][C]22[/C][C]28.07[/C][C]26.3428614075284[/C][C]1.72713859247157[/C][/ROW]
[ROW][C]23[/C][C]21.02[/C][C]19.5076250050155[/C][C]1.51237499498450[/C][/ROW]
[ROW][C]24[/C][C]25[/C][C]23.2889874444646[/C][C]1.71101255553539[/C][/ROW]
[ROW][C]25[/C][C]17.93[/C][C]22.0404407121803[/C][C]-4.1104407121803[/C][/ROW]
[ROW][C]26[/C][C]35.45[/C][C]22.7434911225064[/C][C]12.7065088774936[/C][/ROW]
[ROW][C]27[/C][C]17.7[/C][C]23.7037352652812[/C][C]-6.00373526528117[/C][/ROW]
[ROW][C]28[/C][C]28.53[/C][C]19.9741517810699[/C][C]8.55584821893014[/C][/ROW]
[ROW][C]29[/C][C]26.55[/C][C]27.2557072182352[/C][C]-0.705707218235155[/C][/ROW]
[ROW][C]30[/C][C]26.51[/C][C]26.5737299013003[/C][C]-0.0637299013002917[/C][/ROW]
[ROW][C]31[/C][C]30.78[/C][C]24.9009469001368[/C][C]5.87905309986323[/C][/ROW]
[ROW][C]32[/C][C]26.83[/C][C]21.8096356255930[/C][C]5.02036437440704[/C][/ROW]
[ROW][C]33[/C][C]27.49[/C][C]24.9241941563657[/C][C]2.56580584363426[/C][/ROW]
[ROW][C]34[/C][C]25.89[/C][C]26.8073718865538[/C][C]-0.917371886553806[/C][/ROW]
[ROW][C]35[/C][C]20.44[/C][C]19.8747881316018[/C][C]0.565211868398251[/C][/ROW]
[ROW][C]36[/C][C]19.79[/C][C]23.7062178522269[/C][C]-3.91621785222694[/C][/ROW]
[ROW][C]37[/C][C]18.14[/C][C]21.5446794857404[/C][C]-3.40467948574039[/C][/ROW]
[ROW][C]38[/C][C]27.98[/C][C]24.7688227606634[/C][C]3.21117723933658[/C][/ROW]
[ROW][C]39[/C][C]35.9[/C][C]22.8782675449326[/C][C]13.0217324550674[/C][/ROW]
[ROW][C]40[/C][C]34.38[/C][C]21.4153451395862[/C][C]12.9646548604138[/C][/ROW]
[ROW][C]41[/C][C]21.58[/C][C]27.3966351700835[/C][C]-5.81663517008354[/C][/ROW]
[ROW][C]42[/C][C]21.53[/C][C]26.7751943751373[/C][C]-5.24519437513732[/C][/ROW]
[ROW][C]43[/C][C]31.14[/C][C]25.9501579013626[/C][C]5.18984209863742[/C][/ROW]
[ROW][C]44[/C][C]28.25[/C][C]22.7044448535369[/C][C]5.54555514646314[/C][/ROW]
[ROW][C]45[/C][C]25.16[/C][C]25.474351175511[/C][C]-0.314351175510978[/C][/ROW]
[ROW][C]46[/C][C]20.51[/C][C]26.8295288302594[/C][C]-6.31952883025937[/C][/ROW]
[ROW][C]47[/C][C]30.05[/C][C]20.0537268774894[/C][C]9.99627312251055[/C][/ROW]
[ROW][C]48[/C][C]20.17[/C][C]23.2971649588303[/C][C]-3.12716495883026[/C][/ROW]
[ROW][C]49[/C][C]32.37[/C][C]21.2000667055447[/C][C]11.1699332944553[/C][/ROW]
[ROW][C]50[/C][C]22.46[/C][C]25.5463776645605[/C][C]-3.08637766456047[/C][/ROW]
[ROW][C]51[/C][C]25.4[/C][C]25.0683455533426[/C][C]0.331654446657375[/C][/ROW]
[ROW][C]52[/C][C]19.82[/C][C]23.5034081196583[/C][C]-3.68340811965834[/C][/ROW]
[ROW][C]53[/C][C]18.14[/C][C]26.5944361904885[/C][C]-8.45443619048846[/C][/ROW]
[ROW][C]54[/C][C]20.1[/C][C]26.0405573195039[/C][C]-5.94055731950387[/C][/ROW]
[ROW][C]55[/C][C]20.25[/C][C]26.7660522996157[/C][C]-6.51605229961571[/C][/ROW]
[ROW][C]56[/C][C]19.73[/C][C]23.5055920427926[/C][C]-3.77559204279258[/C][/ROW]
[ROW][C]57[/C][C]24.74[/C][C]25.3407038205359[/C][C]-0.600703820535934[/C][/ROW]
[ROW][C]58[/C][C]26.17[/C][C]25.7967425838865[/C][C]0.373257416113482[/C][/ROW]
[ROW][C]59[/C][C]20.14[/C][C]21.4953500595627[/C][C]-1.35535005956267[/C][/ROW]
[ROW][C]60[/C][C]31.71[/C][C]22.7094007860372[/C][C]9.00059921396284[/C][/ROW]
[ROW][C]61[/C][C]26.66[/C][C]22.8089137664748[/C][C]3.85108623352523[/C][/ROW]
[ROW][C]62[/C][C]20.75[/C][C]24.9784441593524[/C][C]-4.22844415935237[/C][/ROW]
[ROW][C]63[/C][C]20.01[/C][C]25.0025068992166[/C][C]-4.99250689921658[/C][/ROW]
[ROW][C]64[/C][C]26.67[/C][C]22.8199252106556[/C][C]3.85007478934439[/C][/ROW]
[ROW][C]65[/C][C]23.91[/C][C]25.2333903694891[/C][C]-1.32339036948913[/C][/ROW]
[ROW][C]66[/C][C]26.81[/C][C]25.0955748677195[/C][C]1.71442513228055[/C][/ROW]
[ROW][C]67[/C][C]29.31[/C][C]25.7791793123355[/C][C]3.53082068766451[/C][/ROW]
[ROW][C]68[/C][C]31.76[/C][C]22.9815099666945[/C][C]8.7784900333055[/C][/ROW]
[ROW][C]69[/C][C]22.99[/C][C]25.3758643609065[/C][C]-2.38586436090646[/C][/ROW]
[ROW][C]70[/C][C]23.94[/C][C]25.9690638901831[/C][C]-2.02906389018307[/C][/ROW]
[ROW][C]71[/C][C]27.04[/C][C]21.3777246740052[/C][C]5.6622753259948[/C][/ROW]
[ROW][C]72[/C][C]20.28[/C][C]24.1893790324116[/C][C]-3.90937903241156[/C][/ROW]
[ROW][C]73[/C][C]23.32[/C][C]23.4424457585962[/C][C]-0.122445758596172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13300&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13300&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
1322.721.83764812641930.862351873580732
1423.2822.59535256213740.684647437862608
1524.1523.48184066715790.668159332842098
1620.3819.82122663950130.558773360498666
1727.7526.98151691826310.768483081736893
1827.3126.27196655271461.0380334472854
1925.6124.62210131775650.987898682243461
2022.6421.49905751983341.14094248016659
2126.0524.50765775235911.54234224764089
2228.0726.34286140752841.72713859247157
2321.0219.50762500501551.51237499498450
242523.28898744446461.71101255553539
2517.9322.0404407121803-4.1104407121803
2635.4522.743491122506412.7065088774936
2717.723.7037352652812-6.00373526528117
2828.5319.97415178106998.55584821893014
2926.5527.2557072182352-0.705707218235155
3026.5126.5737299013003-0.0637299013002917
3130.7824.90094690013685.87905309986323
3226.8321.80963562559305.02036437440704
3327.4924.92419415636572.56580584363426
3425.8926.8073718865538-0.917371886553806
3520.4419.87478813160180.565211868398251
3619.7923.7062178522269-3.91621785222694
3718.1421.5446794857404-3.40467948574039
3827.9824.76882276066343.21117723933658
3935.922.878267544932613.0217324550674
4034.3821.415345139586212.9646548604138
4121.5827.3966351700835-5.81663517008354
4221.5326.7751943751373-5.24519437513732
4331.1425.95015790136265.18984209863742
4428.2522.70444485353695.54555514646314
4525.1625.474351175511-0.314351175510978
4620.5126.8295288302594-6.31952883025937
4730.0520.05372687748949.99627312251055
4820.1723.2971649588303-3.12716495883026
4932.3721.200066705544711.1699332944553
5022.4625.5463776645605-3.08637766456047
5125.425.06834555334260.331654446657375
5219.8223.5034081196583-3.68340811965834
5318.1426.5944361904885-8.45443619048846
5420.126.0405573195039-5.94055731950387
5520.2526.7660522996157-6.51605229961571
5619.7323.5055920427926-3.77559204279258
5724.7425.3407038205359-0.600703820535934
5826.1725.79674258388650.373257416113482
5920.1421.4953500595627-1.35535005956267
6031.7122.70940078603729.00059921396284
6126.6622.80891376647483.85108623352523
6220.7524.9784441593524-4.22844415935237
6320.0125.0025068992166-4.99250689921658
6426.6722.81992521065563.85007478934439
6523.9125.2333903694891-1.32339036948913
6626.8125.09557486771951.71442513228055
6729.3125.77917931233553.53082068766451
6831.7622.98150996669458.7784900333055
6922.9925.3758643609065-2.38586436090646
7023.9425.9690638901831-2.02906389018307
7127.0421.37772467400525.6622753259948
7220.2824.1893790324116-3.90937903241156
7323.3223.4424457585962-0.122445758596172







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7424.385623593142822.824554362394325.9466928238913
7524.320027261945322.757881129113425.8821733947772
7623.480639431595021.917019724330225.0442591388597
7725.104924446747723.540055439473226.6697934540223
7825.428378379279823.861982238473426.9947745200862
7926.374396166715924.807812108193927.940980225238
8024.330638904017422.762527522342225.8987502856926
8125.009175693881823.439477022886926.5788743648767
8225.669680897213124.101270765265427.2380910291608
8322.232770417216820.662151033820923.8033898006127
8423.583018653314922.011394822941125.1546424836886
8523.4234769289001NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 24.3856235931428 & 22.8245543623943 & 25.9466928238913 \tabularnewline
75 & 24.3200272619453 & 22.7578811291134 & 25.8821733947772 \tabularnewline
76 & 23.4806394315950 & 21.9170197243302 & 25.0442591388597 \tabularnewline
77 & 25.1049244467477 & 23.5400554394732 & 26.6697934540223 \tabularnewline
78 & 25.4283783792798 & 23.8619822384734 & 26.9947745200862 \tabularnewline
79 & 26.3743961667159 & 24.8078121081939 & 27.940980225238 \tabularnewline
80 & 24.3306389040174 & 22.7625275223422 & 25.8987502856926 \tabularnewline
81 & 25.0091756938818 & 23.4394770228869 & 26.5788743648767 \tabularnewline
82 & 25.6696808972131 & 24.1012707652654 & 27.2380910291608 \tabularnewline
83 & 22.2327704172168 & 20.6621510338209 & 23.8033898006127 \tabularnewline
84 & 23.5830186533149 & 22.0113948229411 & 25.1546424836886 \tabularnewline
85 & 23.4234769289001 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13300&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]74[/C][C]24.3856235931428[/C][C]22.8245543623943[/C][C]25.9466928238913[/C][/ROW]
[ROW][C]75[/C][C]24.3200272619453[/C][C]22.7578811291134[/C][C]25.8821733947772[/C][/ROW]
[ROW][C]76[/C][C]23.4806394315950[/C][C]21.9170197243302[/C][C]25.0442591388597[/C][/ROW]
[ROW][C]77[/C][C]25.1049244467477[/C][C]23.5400554394732[/C][C]26.6697934540223[/C][/ROW]
[ROW][C]78[/C][C]25.4283783792798[/C][C]23.8619822384734[/C][C]26.9947745200862[/C][/ROW]
[ROW][C]79[/C][C]26.3743961667159[/C][C]24.8078121081939[/C][C]27.940980225238[/C][/ROW]
[ROW][C]80[/C][C]24.3306389040174[/C][C]22.7625275223422[/C][C]25.8987502856926[/C][/ROW]
[ROW][C]81[/C][C]25.0091756938818[/C][C]23.4394770228869[/C][C]26.5788743648767[/C][/ROW]
[ROW][C]82[/C][C]25.6696808972131[/C][C]24.1012707652654[/C][C]27.2380910291608[/C][/ROW]
[ROW][C]83[/C][C]22.2327704172168[/C][C]20.6621510338209[/C][C]23.8033898006127[/C][/ROW]
[ROW][C]84[/C][C]23.5830186533149[/C][C]22.0113948229411[/C][C]25.1546424836886[/C][/ROW]
[ROW][C]85[/C][C]23.4234769289001[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13300&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13300&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
7424.385623593142822.824554362394325.9466928238913
7524.320027261945322.757881129113425.8821733947772
7623.480639431595021.917019724330225.0442591388597
7725.104924446747723.540055439473226.6697934540223
7825.428378379279823.861982238473426.9947745200862
7926.374396166715924.807812108193927.940980225238
8024.330638904017422.762527522342225.8987502856926
8125.009175693881823.439477022886926.5788743648767
8225.669680897213124.101270765265427.2380910291608
8322.232770417216820.662151033820923.8033898006127
8423.583018653314922.011394822941125.1546424836886
8523.4234769289001NANA



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=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')