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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 computationTue, 28 Dec 2010 15:38:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/28/t1293550551x2otzlg4sq439wz.htm/, Retrieved Sat, 04 May 2024 23:54:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116388, Retrieved Sat, 04 May 2024 23:54:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-28 15:38:00] [a8b9961884f5001e2816791dd4ebd90c] [Current]
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Dataseries X:
11100
8962
9173
8738
8459
8078
8411
8291
7810
8616
8312
9692
9911
8915
9452
9112
8472
8230
8384
8625
8221
8649
8625
10443
10357
8586
8892
8329
8101
7922
8120
7838
7735
8406
8209
9451
10041
9411
10405
8467
8464
8102
7627
7513
7510
8291
8064
9383
9706
8579
9474
8318
8213
8059
9111
7708
7680
8014
8007
8718
9486
9113
9025
8476
7952
7759
7835
7600
7651
8319
8812
8630




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116388&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116388&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116388&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.135019238273121
beta0.0440917299700262
gamma0.0333766681540438

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.135019238273121 \tabularnewline
beta & 0.0440917299700262 \tabularnewline
gamma & 0.0333766681540438 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116388&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]0.135019238273121[/C][/ROW]
[ROW][C]beta[/C][C]0.0440917299700262[/C][/ROW]
[ROW][C]gamma[/C][C]0.0333766681540438[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116388&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116388&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
alpha0.135019238273121
beta0.0440917299700262
gamma0.0333766681540438







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1399119855.3944978632555.6055021367483
1489158868.5050503080446.4949496919617
1594529395.4122981142856.5877018857173
1691129059.5608080065352.4391919934733
1784728427.5447052515544.4552947484517
1882308162.7986087795767.2013912204302
1983848503.52373838579-119.523738385786
2086258434.15916403987190.840835960125
2182217985.6692311748235.330768825194
2286498814.04560710458-165.045607104577
2386258488.4642483113136.5357516887
24104439897.66500383773545.334996162268
251035710207.5800348888149.419965111239
2685869240.47675450445-654.476754504447
2788929676.24010234525-784.240102345255
2883299224.94465761887-895.944657618873
2981018457.20578773181-356.205787731811
3079228129.19198695794-207.19198695794
3181208416.01698300128-296.01698300128
3278388319.27103852083-481.271038520834
3377357764.80460021012-29.8046002101173
3484068527.73234758384-121.732347583844
3582098198.8723562186210.1276437813794
3694519584.22169187039-133.221691870385
37100419768.46277445654272.537225543463
3894118772.88139397185638.118606028147
39104059365.226152748241039.77384725176
4084679153.64399041275-686.643990412755
4184648427.65434712236.3456528779898
4281028157.1888010478-55.1888010477978
4376278463.12187198599-836.12187198599
4475138286.0368038243-773.036803824307
4575107701.40708453483-191.407084534827
4682918435.09615523769-144.096155237687
4780648102.12504170216-38.1250417021565
4893839471.63515753307-88.6351575330718
4997069668.6903868375737.3096131624316
5085798645.58256306614-66.582563066142
5194749143.85912583628330.140874163722
5283188771.8804255021-453.880425502099
5382138084.83642706802128.163572931981
5480597811.31731168935247.682688310645
5591118124.59311036594986.406889634055
5677088195.25062554122-487.250625541223
5776807667.5455031886312.4544968113705
5880148432.8855319782-418.885531978196
5980078066.99593374934-59.9959337493392
6087189433.08858293744-715.088582937438
6194869546.4609336245-60.4609336244976
6291138503.83510699378609.164893006217
6390259105.50922047261-80.5092204726134
6484768653.71049770796-177.710497707958
6579528020.66304206782-68.6630420678202
6677597722.7519074008436.2480925991576
6778358026.28116891763-191.281168917627
6876007885.84644121834-285.846441218339
6976517391.42339227517259.576607724832
7083198170.81003207372148.189967926277
7188127888.35690790335923.643092096655
7286309370.71210645267-740.712106452673

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9911 & 9855.39449786325 & 55.6055021367483 \tabularnewline
14 & 8915 & 8868.50505030804 & 46.4949496919617 \tabularnewline
15 & 9452 & 9395.41229811428 & 56.5877018857173 \tabularnewline
16 & 9112 & 9059.56080800653 & 52.4391919934733 \tabularnewline
17 & 8472 & 8427.54470525155 & 44.4552947484517 \tabularnewline
18 & 8230 & 8162.79860877957 & 67.2013912204302 \tabularnewline
19 & 8384 & 8503.52373838579 & -119.523738385786 \tabularnewline
20 & 8625 & 8434.15916403987 & 190.840835960125 \tabularnewline
21 & 8221 & 7985.6692311748 & 235.330768825194 \tabularnewline
22 & 8649 & 8814.04560710458 & -165.045607104577 \tabularnewline
23 & 8625 & 8488.4642483113 & 136.5357516887 \tabularnewline
24 & 10443 & 9897.66500383773 & 545.334996162268 \tabularnewline
25 & 10357 & 10207.5800348888 & 149.419965111239 \tabularnewline
26 & 8586 & 9240.47675450445 & -654.476754504447 \tabularnewline
27 & 8892 & 9676.24010234525 & -784.240102345255 \tabularnewline
28 & 8329 & 9224.94465761887 & -895.944657618873 \tabularnewline
29 & 8101 & 8457.20578773181 & -356.205787731811 \tabularnewline
30 & 7922 & 8129.19198695794 & -207.19198695794 \tabularnewline
31 & 8120 & 8416.01698300128 & -296.01698300128 \tabularnewline
32 & 7838 & 8319.27103852083 & -481.271038520834 \tabularnewline
33 & 7735 & 7764.80460021012 & -29.8046002101173 \tabularnewline
34 & 8406 & 8527.73234758384 & -121.732347583844 \tabularnewline
35 & 8209 & 8198.87235621862 & 10.1276437813794 \tabularnewline
36 & 9451 & 9584.22169187039 & -133.221691870385 \tabularnewline
37 & 10041 & 9768.46277445654 & 272.537225543463 \tabularnewline
38 & 9411 & 8772.88139397185 & 638.118606028147 \tabularnewline
39 & 10405 & 9365.22615274824 & 1039.77384725176 \tabularnewline
40 & 8467 & 9153.64399041275 & -686.643990412755 \tabularnewline
41 & 8464 & 8427.654347122 & 36.3456528779898 \tabularnewline
42 & 8102 & 8157.1888010478 & -55.1888010477978 \tabularnewline
43 & 7627 & 8463.12187198599 & -836.12187198599 \tabularnewline
44 & 7513 & 8286.0368038243 & -773.036803824307 \tabularnewline
45 & 7510 & 7701.40708453483 & -191.407084534827 \tabularnewline
46 & 8291 & 8435.09615523769 & -144.096155237687 \tabularnewline
47 & 8064 & 8102.12504170216 & -38.1250417021565 \tabularnewline
48 & 9383 & 9471.63515753307 & -88.6351575330718 \tabularnewline
49 & 9706 & 9668.69038683757 & 37.3096131624316 \tabularnewline
50 & 8579 & 8645.58256306614 & -66.582563066142 \tabularnewline
51 & 9474 & 9143.85912583628 & 330.140874163722 \tabularnewline
52 & 8318 & 8771.8804255021 & -453.880425502099 \tabularnewline
53 & 8213 & 8084.83642706802 & 128.163572931981 \tabularnewline
54 & 8059 & 7811.31731168935 & 247.682688310645 \tabularnewline
55 & 9111 & 8124.59311036594 & 986.406889634055 \tabularnewline
56 & 7708 & 8195.25062554122 & -487.250625541223 \tabularnewline
57 & 7680 & 7667.54550318863 & 12.4544968113705 \tabularnewline
58 & 8014 & 8432.8855319782 & -418.885531978196 \tabularnewline
59 & 8007 & 8066.99593374934 & -59.9959337493392 \tabularnewline
60 & 8718 & 9433.08858293744 & -715.088582937438 \tabularnewline
61 & 9486 & 9546.4609336245 & -60.4609336244976 \tabularnewline
62 & 9113 & 8503.83510699378 & 609.164893006217 \tabularnewline
63 & 9025 & 9105.50922047261 & -80.5092204726134 \tabularnewline
64 & 8476 & 8653.71049770796 & -177.710497707958 \tabularnewline
65 & 7952 & 8020.66304206782 & -68.6630420678202 \tabularnewline
66 & 7759 & 7722.75190740084 & 36.2480925991576 \tabularnewline
67 & 7835 & 8026.28116891763 & -191.281168917627 \tabularnewline
68 & 7600 & 7885.84644121834 & -285.846441218339 \tabularnewline
69 & 7651 & 7391.42339227517 & 259.576607724832 \tabularnewline
70 & 8319 & 8170.81003207372 & 148.189967926277 \tabularnewline
71 & 8812 & 7888.35690790335 & 923.643092096655 \tabularnewline
72 & 8630 & 9370.71210645267 & -740.712106452673 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116388&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]9911[/C][C]9855.39449786325[/C][C]55.6055021367483[/C][/ROW]
[ROW][C]14[/C][C]8915[/C][C]8868.50505030804[/C][C]46.4949496919617[/C][/ROW]
[ROW][C]15[/C][C]9452[/C][C]9395.41229811428[/C][C]56.5877018857173[/C][/ROW]
[ROW][C]16[/C][C]9112[/C][C]9059.56080800653[/C][C]52.4391919934733[/C][/ROW]
[ROW][C]17[/C][C]8472[/C][C]8427.54470525155[/C][C]44.4552947484517[/C][/ROW]
[ROW][C]18[/C][C]8230[/C][C]8162.79860877957[/C][C]67.2013912204302[/C][/ROW]
[ROW][C]19[/C][C]8384[/C][C]8503.52373838579[/C][C]-119.523738385786[/C][/ROW]
[ROW][C]20[/C][C]8625[/C][C]8434.15916403987[/C][C]190.840835960125[/C][/ROW]
[ROW][C]21[/C][C]8221[/C][C]7985.6692311748[/C][C]235.330768825194[/C][/ROW]
[ROW][C]22[/C][C]8649[/C][C]8814.04560710458[/C][C]-165.045607104577[/C][/ROW]
[ROW][C]23[/C][C]8625[/C][C]8488.4642483113[/C][C]136.5357516887[/C][/ROW]
[ROW][C]24[/C][C]10443[/C][C]9897.66500383773[/C][C]545.334996162268[/C][/ROW]
[ROW][C]25[/C][C]10357[/C][C]10207.5800348888[/C][C]149.419965111239[/C][/ROW]
[ROW][C]26[/C][C]8586[/C][C]9240.47675450445[/C][C]-654.476754504447[/C][/ROW]
[ROW][C]27[/C][C]8892[/C][C]9676.24010234525[/C][C]-784.240102345255[/C][/ROW]
[ROW][C]28[/C][C]8329[/C][C]9224.94465761887[/C][C]-895.944657618873[/C][/ROW]
[ROW][C]29[/C][C]8101[/C][C]8457.20578773181[/C][C]-356.205787731811[/C][/ROW]
[ROW][C]30[/C][C]7922[/C][C]8129.19198695794[/C][C]-207.19198695794[/C][/ROW]
[ROW][C]31[/C][C]8120[/C][C]8416.01698300128[/C][C]-296.01698300128[/C][/ROW]
[ROW][C]32[/C][C]7838[/C][C]8319.27103852083[/C][C]-481.271038520834[/C][/ROW]
[ROW][C]33[/C][C]7735[/C][C]7764.80460021012[/C][C]-29.8046002101173[/C][/ROW]
[ROW][C]34[/C][C]8406[/C][C]8527.73234758384[/C][C]-121.732347583844[/C][/ROW]
[ROW][C]35[/C][C]8209[/C][C]8198.87235621862[/C][C]10.1276437813794[/C][/ROW]
[ROW][C]36[/C][C]9451[/C][C]9584.22169187039[/C][C]-133.221691870385[/C][/ROW]
[ROW][C]37[/C][C]10041[/C][C]9768.46277445654[/C][C]272.537225543463[/C][/ROW]
[ROW][C]38[/C][C]9411[/C][C]8772.88139397185[/C][C]638.118606028147[/C][/ROW]
[ROW][C]39[/C][C]10405[/C][C]9365.22615274824[/C][C]1039.77384725176[/C][/ROW]
[ROW][C]40[/C][C]8467[/C][C]9153.64399041275[/C][C]-686.643990412755[/C][/ROW]
[ROW][C]41[/C][C]8464[/C][C]8427.654347122[/C][C]36.3456528779898[/C][/ROW]
[ROW][C]42[/C][C]8102[/C][C]8157.1888010478[/C][C]-55.1888010477978[/C][/ROW]
[ROW][C]43[/C][C]7627[/C][C]8463.12187198599[/C][C]-836.12187198599[/C][/ROW]
[ROW][C]44[/C][C]7513[/C][C]8286.0368038243[/C][C]-773.036803824307[/C][/ROW]
[ROW][C]45[/C][C]7510[/C][C]7701.40708453483[/C][C]-191.407084534827[/C][/ROW]
[ROW][C]46[/C][C]8291[/C][C]8435.09615523769[/C][C]-144.096155237687[/C][/ROW]
[ROW][C]47[/C][C]8064[/C][C]8102.12504170216[/C][C]-38.1250417021565[/C][/ROW]
[ROW][C]48[/C][C]9383[/C][C]9471.63515753307[/C][C]-88.6351575330718[/C][/ROW]
[ROW][C]49[/C][C]9706[/C][C]9668.69038683757[/C][C]37.3096131624316[/C][/ROW]
[ROW][C]50[/C][C]8579[/C][C]8645.58256306614[/C][C]-66.582563066142[/C][/ROW]
[ROW][C]51[/C][C]9474[/C][C]9143.85912583628[/C][C]330.140874163722[/C][/ROW]
[ROW][C]52[/C][C]8318[/C][C]8771.8804255021[/C][C]-453.880425502099[/C][/ROW]
[ROW][C]53[/C][C]8213[/C][C]8084.83642706802[/C][C]128.163572931981[/C][/ROW]
[ROW][C]54[/C][C]8059[/C][C]7811.31731168935[/C][C]247.682688310645[/C][/ROW]
[ROW][C]55[/C][C]9111[/C][C]8124.59311036594[/C][C]986.406889634055[/C][/ROW]
[ROW][C]56[/C][C]7708[/C][C]8195.25062554122[/C][C]-487.250625541223[/C][/ROW]
[ROW][C]57[/C][C]7680[/C][C]7667.54550318863[/C][C]12.4544968113705[/C][/ROW]
[ROW][C]58[/C][C]8014[/C][C]8432.8855319782[/C][C]-418.885531978196[/C][/ROW]
[ROW][C]59[/C][C]8007[/C][C]8066.99593374934[/C][C]-59.9959337493392[/C][/ROW]
[ROW][C]60[/C][C]8718[/C][C]9433.08858293744[/C][C]-715.088582937438[/C][/ROW]
[ROW][C]61[/C][C]9486[/C][C]9546.4609336245[/C][C]-60.4609336244976[/C][/ROW]
[ROW][C]62[/C][C]9113[/C][C]8503.83510699378[/C][C]609.164893006217[/C][/ROW]
[ROW][C]63[/C][C]9025[/C][C]9105.50922047261[/C][C]-80.5092204726134[/C][/ROW]
[ROW][C]64[/C][C]8476[/C][C]8653.71049770796[/C][C]-177.710497707958[/C][/ROW]
[ROW][C]65[/C][C]7952[/C][C]8020.66304206782[/C][C]-68.6630420678202[/C][/ROW]
[ROW][C]66[/C][C]7759[/C][C]7722.75190740084[/C][C]36.2480925991576[/C][/ROW]
[ROW][C]67[/C][C]7835[/C][C]8026.28116891763[/C][C]-191.281168917627[/C][/ROW]
[ROW][C]68[/C][C]7600[/C][C]7885.84644121834[/C][C]-285.846441218339[/C][/ROW]
[ROW][C]69[/C][C]7651[/C][C]7391.42339227517[/C][C]259.576607724832[/C][/ROW]
[ROW][C]70[/C][C]8319[/C][C]8170.81003207372[/C][C]148.189967926277[/C][/ROW]
[ROW][C]71[/C][C]8812[/C][C]7888.35690790335[/C][C]923.643092096655[/C][/ROW]
[ROW][C]72[/C][C]8630[/C][C]9370.71210645267[/C][C]-740.712106452673[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116388&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116388&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
1399119855.3944978632555.6055021367483
1489158868.5050503080446.4949496919617
1594529395.4122981142856.5877018857173
1691129059.5608080065352.4391919934733
1784728427.5447052515544.4552947484517
1882308162.7986087795767.2013912204302
1983848503.52373838579-119.523738385786
2086258434.15916403987190.840835960125
2182217985.6692311748235.330768825194
2286498814.04560710458-165.045607104577
2386258488.4642483113136.5357516887
24104439897.66500383773545.334996162268
251035710207.5800348888149.419965111239
2685869240.47675450445-654.476754504447
2788929676.24010234525-784.240102345255
2883299224.94465761887-895.944657618873
2981018457.20578773181-356.205787731811
3079228129.19198695794-207.19198695794
3181208416.01698300128-296.01698300128
3278388319.27103852083-481.271038520834
3377357764.80460021012-29.8046002101173
3484068527.73234758384-121.732347583844
3582098198.8723562186210.1276437813794
3694519584.22169187039-133.221691870385
37100419768.46277445654272.537225543463
3894118772.88139397185638.118606028147
39104059365.226152748241039.77384725176
4084679153.64399041275-686.643990412755
4184648427.65434712236.3456528779898
4281028157.1888010478-55.1888010477978
4376278463.12187198599-836.12187198599
4475138286.0368038243-773.036803824307
4575107701.40708453483-191.407084534827
4682918435.09615523769-144.096155237687
4780648102.12504170216-38.1250417021565
4893839471.63515753307-88.6351575330718
4997069668.6903868375737.3096131624316
5085798645.58256306614-66.582563066142
5194749143.85912583628330.140874163722
5283188771.8804255021-453.880425502099
5382138084.83642706802128.163572931981
5480597811.31731168935247.682688310645
5591118124.59311036594986.406889634055
5677088195.25062554122-487.250625541223
5776807667.5455031886312.4544968113705
5880148432.8855319782-418.885531978196
5980078066.99593374934-59.9959337493392
6087189433.08858293744-715.088582937438
6194869546.4609336245-60.4609336244976
6291138503.83510699378609.164893006217
6390259105.50922047261-80.5092204726134
6484768653.71049770796-177.710497707958
6579528020.66304206782-68.6630420678202
6677597722.7519074008436.2480925991576
6778358026.28116891763-191.281168917627
6876007885.84644121834-285.846441218339
6976517391.42339227517259.576607724832
7083198170.81003207372148.189967926277
7188127888.35690790335923.643092096655
7286309370.71210645267-740.712106452673







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
739501.736458417648679.8222321994510323.6506846358
748489.17862886397659.13753257869319.2197251492
758987.638642275328148.85900642949826.41827812125
768543.329177917977695.190010671079391.46834516488
777937.907412067517079.780140711888796.03468342315
787653.187813485386784.43798655928521.93764041155
797945.930183605137065.919118541368825.9412486689
807830.406826969756938.493189787348722.32046415216
817393.841565618166489.382871009868298.30026022646
828136.935857479237219.289879657249054.58183530122
837857.950735333126926.47682208098789.42464858533
849163.136489039838217.1967735090110109.0762045706

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 9501.73645841764 & 8679.82223219945 & 10323.6506846358 \tabularnewline
74 & 8489.1786288639 & 7659.1375325786 & 9319.2197251492 \tabularnewline
75 & 8987.63864227532 & 8148.8590064294 & 9826.41827812125 \tabularnewline
76 & 8543.32917791797 & 7695.19001067107 & 9391.46834516488 \tabularnewline
77 & 7937.90741206751 & 7079.78014071188 & 8796.03468342315 \tabularnewline
78 & 7653.18781348538 & 6784.4379865592 & 8521.93764041155 \tabularnewline
79 & 7945.93018360513 & 7065.91911854136 & 8825.9412486689 \tabularnewline
80 & 7830.40682696975 & 6938.49318978734 & 8722.32046415216 \tabularnewline
81 & 7393.84156561816 & 6489.38287100986 & 8298.30026022646 \tabularnewline
82 & 8136.93585747923 & 7219.28987965724 & 9054.58183530122 \tabularnewline
83 & 7857.95073533312 & 6926.4768220809 & 8789.42464858533 \tabularnewline
84 & 9163.13648903983 & 8217.19677350901 & 10109.0762045706 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116388&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]9501.73645841764[/C][C]8679.82223219945[/C][C]10323.6506846358[/C][/ROW]
[ROW][C]74[/C][C]8489.1786288639[/C][C]7659.1375325786[/C][C]9319.2197251492[/C][/ROW]
[ROW][C]75[/C][C]8987.63864227532[/C][C]8148.8590064294[/C][C]9826.41827812125[/C][/ROW]
[ROW][C]76[/C][C]8543.32917791797[/C][C]7695.19001067107[/C][C]9391.46834516488[/C][/ROW]
[ROW][C]77[/C][C]7937.90741206751[/C][C]7079.78014071188[/C][C]8796.03468342315[/C][/ROW]
[ROW][C]78[/C][C]7653.18781348538[/C][C]6784.4379865592[/C][C]8521.93764041155[/C][/ROW]
[ROW][C]79[/C][C]7945.93018360513[/C][C]7065.91911854136[/C][C]8825.9412486689[/C][/ROW]
[ROW][C]80[/C][C]7830.40682696975[/C][C]6938.49318978734[/C][C]8722.32046415216[/C][/ROW]
[ROW][C]81[/C][C]7393.84156561816[/C][C]6489.38287100986[/C][C]8298.30026022646[/C][/ROW]
[ROW][C]82[/C][C]8136.93585747923[/C][C]7219.28987965724[/C][C]9054.58183530122[/C][/ROW]
[ROW][C]83[/C][C]7857.95073533312[/C][C]6926.4768220809[/C][C]8789.42464858533[/C][/ROW]
[ROW][C]84[/C][C]9163.13648903983[/C][C]8217.19677350901[/C][C]10109.0762045706[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116388&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116388&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
739501.736458417648679.8222321994510323.6506846358
748489.17862886397659.13753257869319.2197251492
758987.638642275328148.85900642949826.41827812125
768543.329177917977695.190010671079391.46834516488
777937.907412067517079.780140711888796.03468342315
787653.187813485386784.43798655928521.93764041155
797945.930183605137065.919118541368825.9412486689
807830.406826969756938.493189787348722.32046415216
817393.841565618166489.382871009868298.30026022646
828136.935857479237219.289879657249054.58183530122
837857.950735333126926.47682208098789.42464858533
849163.136489039838217.1967735090110109.0762045706



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')