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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 08 Dec 2011 05:57:42 -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/2011/Dec/08/t1323341913iwfucx9nivydzqk.htm/, Retrieved Fri, 03 May 2024 08:39:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152828, Retrieved Fri, 03 May 2024 08:39:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact83
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
- RMPD        [Exponential Smoothing] [exponential smoot...] [2011-12-08 10:57:42] [02062aee8449a97abc7c7e765b9155b5] [Current]
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Post a new message
Dataseries X:
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152828&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]1 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=152828&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152828&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00799336056490778
beta1
gamma0.270233270260182

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00799336056490778 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.270233270260182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152828&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]0.00799336056490778[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.270233270260182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152828&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152828&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
alpha0.00799336056490778
beta1
gamma0.270233270260182







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134447.1768162393162-3.17681623931622
143638.0837799467682-2.08377994676819
157273.3578242829646-1.35782428296459
164546.7101511987917-1.71015119879171
175658.2543253167248-2.25432531672478
185456.3594633529693-2.35946335296927
195339.278234274994313.7217657250057
203526.35189794706048.64810205293963
216158.12080006058852.87919993941155
225270.3666037427136-18.3666037427136
234749.6291045027813-2.62910450278133
245159.7047187217436-8.70471872174356
255243.22723578724118.77276421275893
266334.479213567566728.5207864324333
277470.39361686130773.60638313869225
284543.93197214057181.0680278594282
295155.6154788029016-4.6154788029016
306453.917689100873310.0823108991267
313641.5904402121934-5.59044021219341
323027.33883387609312.66116612390686
335557.6547491391153-2.65474913911528
346464.2580095044485-0.258009504448466
353948.1259311420018-9.12593114200185
364056.7108436699862-16.7108436699862
376344.980552919149718.0194470808503
384541.80021359499753.19978640500252
395970.8307886969352-11.8307886969352
405543.43934466273911.560655337261
414053.641058811222-13.641058811222
426455.6969951117948.30300488820597
432739.0256436622636-12.0256436622636
442826.75475861491091.24524138508907
454555.4431091662208-10.4431091662208
465762.373168542764-5.37316854276402
474543.52861596540661.47138403459345
486949.955298266916119.0447017330839
496047.897254941011112.1027450589889
505640.725753455675615.2742465443244
515865.948951251318-7.94895125131799
525045.01558580477114.98441419522894
535148.51269375207152.48730624792845
545356.8129492463164-3.81294924631644
553734.73112159984132.26887840015873
562226.3822645161918-4.38226451619183
575552.09751428084092.90248571915906
587060.80525657138549.19474342861463
596244.340329804500817.6596701954992
605856.16508333961321.83491666038678
613952.5286963963152-13.5286963963152
624946.21779967883082.78220032116921
635865.231065282095-7.23106528209502
644747.891703263284-0.891703263283958
654250.7466401119039-8.74664011190388
666257.25257853889924.74742146110083
673936.92238769734222.07761230265781
684026.840315428650313.1596845713497
697254.840156563539217.1598434364608
707065.65413885642994.34586114357012
715451.68640450513222.31359549486782
726559.29036361949265.70963638050743

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 44 & 47.1768162393162 & -3.17681623931622 \tabularnewline
14 & 36 & 38.0837799467682 & -2.08377994676819 \tabularnewline
15 & 72 & 73.3578242829646 & -1.35782428296459 \tabularnewline
16 & 45 & 46.7101511987917 & -1.71015119879171 \tabularnewline
17 & 56 & 58.2543253167248 & -2.25432531672478 \tabularnewline
18 & 54 & 56.3594633529693 & -2.35946335296927 \tabularnewline
19 & 53 & 39.2782342749943 & 13.7217657250057 \tabularnewline
20 & 35 & 26.3518979470604 & 8.64810205293963 \tabularnewline
21 & 61 & 58.1208000605885 & 2.87919993941155 \tabularnewline
22 & 52 & 70.3666037427136 & -18.3666037427136 \tabularnewline
23 & 47 & 49.6291045027813 & -2.62910450278133 \tabularnewline
24 & 51 & 59.7047187217436 & -8.70471872174356 \tabularnewline
25 & 52 & 43.2272357872411 & 8.77276421275893 \tabularnewline
26 & 63 & 34.4792135675667 & 28.5207864324333 \tabularnewline
27 & 74 & 70.3936168613077 & 3.60638313869225 \tabularnewline
28 & 45 & 43.9319721405718 & 1.0680278594282 \tabularnewline
29 & 51 & 55.6154788029016 & -4.6154788029016 \tabularnewline
30 & 64 & 53.9176891008733 & 10.0823108991267 \tabularnewline
31 & 36 & 41.5904402121934 & -5.59044021219341 \tabularnewline
32 & 30 & 27.3388338760931 & 2.66116612390686 \tabularnewline
33 & 55 & 57.6547491391153 & -2.65474913911528 \tabularnewline
34 & 64 & 64.2580095044485 & -0.258009504448466 \tabularnewline
35 & 39 & 48.1259311420018 & -9.12593114200185 \tabularnewline
36 & 40 & 56.7108436699862 & -16.7108436699862 \tabularnewline
37 & 63 & 44.9805529191497 & 18.0194470808503 \tabularnewline
38 & 45 & 41.8002135949975 & 3.19978640500252 \tabularnewline
39 & 59 & 70.8307886969352 & -11.8307886969352 \tabularnewline
40 & 55 & 43.439344662739 & 11.560655337261 \tabularnewline
41 & 40 & 53.641058811222 & -13.641058811222 \tabularnewline
42 & 64 & 55.696995111794 & 8.30300488820597 \tabularnewline
43 & 27 & 39.0256436622636 & -12.0256436622636 \tabularnewline
44 & 28 & 26.7547586149109 & 1.24524138508907 \tabularnewline
45 & 45 & 55.4431091662208 & -10.4431091662208 \tabularnewline
46 & 57 & 62.373168542764 & -5.37316854276402 \tabularnewline
47 & 45 & 43.5286159654066 & 1.47138403459345 \tabularnewline
48 & 69 & 49.9552982669161 & 19.0447017330839 \tabularnewline
49 & 60 & 47.8972549410111 & 12.1027450589889 \tabularnewline
50 & 56 & 40.7257534556756 & 15.2742465443244 \tabularnewline
51 & 58 & 65.948951251318 & -7.94895125131799 \tabularnewline
52 & 50 & 45.0155858047711 & 4.98441419522894 \tabularnewline
53 & 51 & 48.5126937520715 & 2.48730624792845 \tabularnewline
54 & 53 & 56.8129492463164 & -3.81294924631644 \tabularnewline
55 & 37 & 34.7311215998413 & 2.26887840015873 \tabularnewline
56 & 22 & 26.3822645161918 & -4.38226451619183 \tabularnewline
57 & 55 & 52.0975142808409 & 2.90248571915906 \tabularnewline
58 & 70 & 60.8052565713854 & 9.19474342861463 \tabularnewline
59 & 62 & 44.3403298045008 & 17.6596701954992 \tabularnewline
60 & 58 & 56.1650833396132 & 1.83491666038678 \tabularnewline
61 & 39 & 52.5286963963152 & -13.5286963963152 \tabularnewline
62 & 49 & 46.2177996788308 & 2.78220032116921 \tabularnewline
63 & 58 & 65.231065282095 & -7.23106528209502 \tabularnewline
64 & 47 & 47.891703263284 & -0.891703263283958 \tabularnewline
65 & 42 & 50.7466401119039 & -8.74664011190388 \tabularnewline
66 & 62 & 57.2525785388992 & 4.74742146110083 \tabularnewline
67 & 39 & 36.9223876973422 & 2.07761230265781 \tabularnewline
68 & 40 & 26.8403154286503 & 13.1596845713497 \tabularnewline
69 & 72 & 54.8401565635392 & 17.1598434364608 \tabularnewline
70 & 70 & 65.6541388564299 & 4.34586114357012 \tabularnewline
71 & 54 & 51.6864045051322 & 2.31359549486782 \tabularnewline
72 & 65 & 59.2903636194926 & 5.70963638050743 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152828&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]44[/C][C]47.1768162393162[/C][C]-3.17681623931622[/C][/ROW]
[ROW][C]14[/C][C]36[/C][C]38.0837799467682[/C][C]-2.08377994676819[/C][/ROW]
[ROW][C]15[/C][C]72[/C][C]73.3578242829646[/C][C]-1.35782428296459[/C][/ROW]
[ROW][C]16[/C][C]45[/C][C]46.7101511987917[/C][C]-1.71015119879171[/C][/ROW]
[ROW][C]17[/C][C]56[/C][C]58.2543253167248[/C][C]-2.25432531672478[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]56.3594633529693[/C][C]-2.35946335296927[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]39.2782342749943[/C][C]13.7217657250057[/C][/ROW]
[ROW][C]20[/C][C]35[/C][C]26.3518979470604[/C][C]8.64810205293963[/C][/ROW]
[ROW][C]21[/C][C]61[/C][C]58.1208000605885[/C][C]2.87919993941155[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]70.3666037427136[/C][C]-18.3666037427136[/C][/ROW]
[ROW][C]23[/C][C]47[/C][C]49.6291045027813[/C][C]-2.62910450278133[/C][/ROW]
[ROW][C]24[/C][C]51[/C][C]59.7047187217436[/C][C]-8.70471872174356[/C][/ROW]
[ROW][C]25[/C][C]52[/C][C]43.2272357872411[/C][C]8.77276421275893[/C][/ROW]
[ROW][C]26[/C][C]63[/C][C]34.4792135675667[/C][C]28.5207864324333[/C][/ROW]
[ROW][C]27[/C][C]74[/C][C]70.3936168613077[/C][C]3.60638313869225[/C][/ROW]
[ROW][C]28[/C][C]45[/C][C]43.9319721405718[/C][C]1.0680278594282[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]55.6154788029016[/C][C]-4.6154788029016[/C][/ROW]
[ROW][C]30[/C][C]64[/C][C]53.9176891008733[/C][C]10.0823108991267[/C][/ROW]
[ROW][C]31[/C][C]36[/C][C]41.5904402121934[/C][C]-5.59044021219341[/C][/ROW]
[ROW][C]32[/C][C]30[/C][C]27.3388338760931[/C][C]2.66116612390686[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]57.6547491391153[/C][C]-2.65474913911528[/C][/ROW]
[ROW][C]34[/C][C]64[/C][C]64.2580095044485[/C][C]-0.258009504448466[/C][/ROW]
[ROW][C]35[/C][C]39[/C][C]48.1259311420018[/C][C]-9.12593114200185[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]56.7108436699862[/C][C]-16.7108436699862[/C][/ROW]
[ROW][C]37[/C][C]63[/C][C]44.9805529191497[/C][C]18.0194470808503[/C][/ROW]
[ROW][C]38[/C][C]45[/C][C]41.8002135949975[/C][C]3.19978640500252[/C][/ROW]
[ROW][C]39[/C][C]59[/C][C]70.8307886969352[/C][C]-11.8307886969352[/C][/ROW]
[ROW][C]40[/C][C]55[/C][C]43.439344662739[/C][C]11.560655337261[/C][/ROW]
[ROW][C]41[/C][C]40[/C][C]53.641058811222[/C][C]-13.641058811222[/C][/ROW]
[ROW][C]42[/C][C]64[/C][C]55.696995111794[/C][C]8.30300488820597[/C][/ROW]
[ROW][C]43[/C][C]27[/C][C]39.0256436622636[/C][C]-12.0256436622636[/C][/ROW]
[ROW][C]44[/C][C]28[/C][C]26.7547586149109[/C][C]1.24524138508907[/C][/ROW]
[ROW][C]45[/C][C]45[/C][C]55.4431091662208[/C][C]-10.4431091662208[/C][/ROW]
[ROW][C]46[/C][C]57[/C][C]62.373168542764[/C][C]-5.37316854276402[/C][/ROW]
[ROW][C]47[/C][C]45[/C][C]43.5286159654066[/C][C]1.47138403459345[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]49.9552982669161[/C][C]19.0447017330839[/C][/ROW]
[ROW][C]49[/C][C]60[/C][C]47.8972549410111[/C][C]12.1027450589889[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]40.7257534556756[/C][C]15.2742465443244[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]65.948951251318[/C][C]-7.94895125131799[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]45.0155858047711[/C][C]4.98441419522894[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]48.5126937520715[/C][C]2.48730624792845[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]56.8129492463164[/C][C]-3.81294924631644[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]34.7311215998413[/C][C]2.26887840015873[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]26.3822645161918[/C][C]-4.38226451619183[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]52.0975142808409[/C][C]2.90248571915906[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]60.8052565713854[/C][C]9.19474342861463[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]44.3403298045008[/C][C]17.6596701954992[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]56.1650833396132[/C][C]1.83491666038678[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]52.5286963963152[/C][C]-13.5286963963152[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]46.2177996788308[/C][C]2.78220032116921[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]65.231065282095[/C][C]-7.23106528209502[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]47.891703263284[/C][C]-0.891703263283958[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]50.7466401119039[/C][C]-8.74664011190388[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]57.2525785388992[/C][C]4.74742146110083[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]36.9223876973422[/C][C]2.07761230265781[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]26.8403154286503[/C][C]13.1596845713497[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]54.8401565635392[/C][C]17.1598434364608[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]65.6541388564299[/C][C]4.34586114357012[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]51.6864045051322[/C][C]2.31359549486782[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]59.2903636194926[/C][C]5.70963638050743[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152828&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152828&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
134447.1768162393162-3.17681623931622
143638.0837799467682-2.08377994676819
157273.3578242829646-1.35782428296459
164546.7101511987917-1.71015119879171
175658.2543253167248-2.25432531672478
185456.3594633529693-2.35946335296927
195339.278234274994313.7217657250057
203526.35189794706048.64810205293963
216158.12080006058852.87919993941155
225270.3666037427136-18.3666037427136
234749.6291045027813-2.62910450278133
245159.7047187217436-8.70471872174356
255243.22723578724118.77276421275893
266334.479213567566728.5207864324333
277470.39361686130773.60638313869225
284543.93197214057181.0680278594282
295155.6154788029016-4.6154788029016
306453.917689100873310.0823108991267
313641.5904402121934-5.59044021219341
323027.33883387609312.66116612390686
335557.6547491391153-2.65474913911528
346464.2580095044485-0.258009504448466
353948.1259311420018-9.12593114200185
364056.7108436699862-16.7108436699862
376344.980552919149718.0194470808503
384541.80021359499753.19978640500252
395970.8307886969352-11.8307886969352
405543.43934466273911.560655337261
414053.641058811222-13.641058811222
426455.6969951117948.30300488820597
432739.0256436622636-12.0256436622636
442826.75475861491091.24524138508907
454555.4431091662208-10.4431091662208
465762.373168542764-5.37316854276402
474543.52861596540661.47138403459345
486949.955298266916119.0447017330839
496047.897254941011112.1027450589889
505640.725753455675615.2742465443244
515865.948951251318-7.94895125131799
525045.01558580477114.98441419522894
535148.51269375207152.48730624792845
545356.8129492463164-3.81294924631644
553734.73112159984132.26887840015873
562226.3822645161918-4.38226451619183
575552.09751428084092.90248571915906
587060.80525657138549.19474342861463
596244.340329804500817.6596701954992
605856.16508333961321.83491666038678
613952.5286963963152-13.5286963963152
624946.21779967883082.78220032116921
635865.231065282095-7.23106528209502
644747.891703263284-0.891703263283958
654250.7466401119039-8.74664011190388
666257.25257853889924.74742146110083
673936.92238769734222.07761230265781
684026.840315428650313.1596845713497
697254.840156563539217.1598434364608
707065.65413885642994.34586114357012
715451.68640450513222.31359549486782
726559.29036361949265.70963638050743







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7351.741412430312933.079435681963870.403389178662
7450.194346071245831.529984705539668.858707436952
7566.762021638253748.092295997109885.4317472793976
7651.4986109248232.819352597719370.1778692519206
7752.580842883211533.886699465781271.2749863006418
7863.169873097836144.454315948364481.8854302473077
7942.443862768982323.699198459411761.1885270785529
8035.657215492724216.874601600659654.4398293847888
8164.86023734075646.029703159494183.6907715220179
8272.200840222040553.311312874982791.0903675690984
8357.717704468701638.757040802416876.6783681349864
8466.259196904105947.214221401871285.3041724063406

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 51.7414124303129 & 33.0794356819638 & 70.403389178662 \tabularnewline
74 & 50.1943460712458 & 31.5299847055396 & 68.858707436952 \tabularnewline
75 & 66.7620216382537 & 48.0922959971098 & 85.4317472793976 \tabularnewline
76 & 51.49861092482 & 32.8193525977193 & 70.1778692519206 \tabularnewline
77 & 52.5808428832115 & 33.8866994657812 & 71.2749863006418 \tabularnewline
78 & 63.1698730978361 & 44.4543159483644 & 81.8854302473077 \tabularnewline
79 & 42.4438627689823 & 23.6991984594117 & 61.1885270785529 \tabularnewline
80 & 35.6572154927242 & 16.8746016006596 & 54.4398293847888 \tabularnewline
81 & 64.860237340756 & 46.0297031594941 & 83.6907715220179 \tabularnewline
82 & 72.2008402220405 & 53.3113128749827 & 91.0903675690984 \tabularnewline
83 & 57.7177044687016 & 38.7570408024168 & 76.6783681349864 \tabularnewline
84 & 66.2591969041059 & 47.2142214018712 & 85.3041724063406 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152828&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]51.7414124303129[/C][C]33.0794356819638[/C][C]70.403389178662[/C][/ROW]
[ROW][C]74[/C][C]50.1943460712458[/C][C]31.5299847055396[/C][C]68.858707436952[/C][/ROW]
[ROW][C]75[/C][C]66.7620216382537[/C][C]48.0922959971098[/C][C]85.4317472793976[/C][/ROW]
[ROW][C]76[/C][C]51.49861092482[/C][C]32.8193525977193[/C][C]70.1778692519206[/C][/ROW]
[ROW][C]77[/C][C]52.5808428832115[/C][C]33.8866994657812[/C][C]71.2749863006418[/C][/ROW]
[ROW][C]78[/C][C]63.1698730978361[/C][C]44.4543159483644[/C][C]81.8854302473077[/C][/ROW]
[ROW][C]79[/C][C]42.4438627689823[/C][C]23.6991984594117[/C][C]61.1885270785529[/C][/ROW]
[ROW][C]80[/C][C]35.6572154927242[/C][C]16.8746016006596[/C][C]54.4398293847888[/C][/ROW]
[ROW][C]81[/C][C]64.860237340756[/C][C]46.0297031594941[/C][C]83.6907715220179[/C][/ROW]
[ROW][C]82[/C][C]72.2008402220405[/C][C]53.3113128749827[/C][C]91.0903675690984[/C][/ROW]
[ROW][C]83[/C][C]57.7177044687016[/C][C]38.7570408024168[/C][C]76.6783681349864[/C][/ROW]
[ROW][C]84[/C][C]66.2591969041059[/C][C]47.2142214018712[/C][C]85.3041724063406[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152828&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152828&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
7351.741412430312933.079435681963870.403389178662
7450.194346071245831.529984705539668.858707436952
7566.762021638253748.092295997109885.4317472793976
7651.4986109248232.819352597719370.1778692519206
7752.580842883211533.886699465781271.2749863006418
7863.169873097836144.454315948364481.8854302473077
7942.443862768982323.699198459411761.1885270785529
8035.657215492724216.874601600659654.4398293847888
8164.86023734075646.029703159494183.6907715220179
8272.200840222040553.311312874982791.0903675690984
8357.717704468701638.757040802416876.6783681349864
8466.259196904105947.214221401871285.3041724063406



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')