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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 21 May 2012 09:59:50 -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/2012/May/21/t1337608849vyaaioomrzs2nx9.htm/, Retrieved Fri, 03 May 2024 00:29:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166941, Retrieved Fri, 03 May 2024 00:29:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oef 2] [2012-05-21 13:59:50] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
92,8
90,61
88,49
88,33
87,7
87,33
87,33
87,33
85,47
86,1
86,1
86,13
83,31
83,31
83,55
84,11
84,11
77,59
77,59
76,44
72,71
72,9
72,39
72,46
72,48
72,48
72,48
72,3
72,3
72,3
71,14
71,14
68,99
68,42
68,42
69,28
65,22
70,21
70,21
71,2
68,94
68,94
68,93
68,93
68,93
68,93
59,94
61,04
60,2
60,2
60,12
60,25
58,03
62,37
62,16
62,16
62,16
62,16
62,29
64,39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166941&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166941&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166941&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.809356675163719
beta0.129073905393437
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.809356675163719 \tabularnewline
beta & 0.129073905393437 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166941&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]0.809356675163719[/C][/ROW]
[ROW][C]beta[/C][C]0.129073905393437[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166941&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166941&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
alpha0.809356675163719
beta0.129073905393437
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
388.4988.420.0699999999999932
488.3386.29396764514582.03603235485417
587.785.9718545398981.72814546010196
687.3385.58108499385951.74891500614045
787.3385.3898290197911.94017098020896
887.3385.55605085098381.7739491490162
985.4785.7730587722573-0.303058772257259
1086.184.27736687977221.82263312022775
1186.184.69252260852021.40747739147982
1286.1384.91870397402251.21129602597746
1383.3185.112644894107-1.80264489410705
1483.3182.67891601982190.631083980178147
1583.5582.28086919640711.2691308035929
1684.1182.53181189658741.57818810341263
1784.1183.19776048883070.912239511169346
1877.5983.4200179097485-5.83001790974852
1977.5977.57634080945840.0136591905416452
2076.4476.4637097100836-0.0237097100835797
2172.7175.3183569633646-2.60835696336463
2272.971.80861593382271.09138406617734
2372.3971.40729843326180.982701566738228
2472.4671.02067774079251.43932225920754
2572.4871.15398748312521.32601251687475
2672.4871.33411354923351.14588645076645
2772.4871.48816050288790.991839497112124
2872.371.62114285139030.678857148609694
2972.371.57172889917080.728271100829161
3072.371.63838863006730.6616113699327
3171.1471.7202133032689-0.580213303268906
3271.1470.73634584510270.403654154897268
3368.9970.5909465504148-1.60094655041476
3468.4268.6558644876548-0.235864487654837
3568.4267.80098068992760.619019310072403
3669.2867.70266978350551.57733021649454
3765.2268.5447528887999-3.32475288879991
3870.2165.07197592603225.1380240739678
3970.2168.98535706014641.22464293985364
4071.269.85935161294151.34064838705852
4168.9470.9672892317982-2.02728923179816
4268.9469.1375795840039-0.197579584003904
4368.9368.76811714105840.161882858941624
4468.9368.70649941438780.2235005856122
4568.9368.71810080310010.21189919689995
4668.9368.74244896714380.187551032856177
4759.9468.7666836433788-8.82668364337879
4861.0460.57309168046350.466908319536465
4960.259.9501068395860.249893160414025
5060.259.17758487659831.02241512340167
5160.1259.13711718480170.982882815198273
5260.2559.16733240441371.08266759558633
5358.0359.391411950432-1.36141195043204
5462.3757.49513701465724.87486298534277
5562.1661.15549429405471.00450570594533
5662.1661.78828959782610.371710402173932
5762.1661.9477592047260.212240795274042
5862.1662.00033314322090.159666856779133
5962.2962.02703590354720.262964096452784
6064.3962.16481399907962.22518600092036

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 88.49 & 88.42 & 0.0699999999999932 \tabularnewline
4 & 88.33 & 86.2939676451458 & 2.03603235485417 \tabularnewline
5 & 87.7 & 85.971854539898 & 1.72814546010196 \tabularnewline
6 & 87.33 & 85.5810849938595 & 1.74891500614045 \tabularnewline
7 & 87.33 & 85.389829019791 & 1.94017098020896 \tabularnewline
8 & 87.33 & 85.5560508509838 & 1.7739491490162 \tabularnewline
9 & 85.47 & 85.7730587722573 & -0.303058772257259 \tabularnewline
10 & 86.1 & 84.2773668797722 & 1.82263312022775 \tabularnewline
11 & 86.1 & 84.6925226085202 & 1.40747739147982 \tabularnewline
12 & 86.13 & 84.9187039740225 & 1.21129602597746 \tabularnewline
13 & 83.31 & 85.112644894107 & -1.80264489410705 \tabularnewline
14 & 83.31 & 82.6789160198219 & 0.631083980178147 \tabularnewline
15 & 83.55 & 82.2808691964071 & 1.2691308035929 \tabularnewline
16 & 84.11 & 82.5318118965874 & 1.57818810341263 \tabularnewline
17 & 84.11 & 83.1977604888307 & 0.912239511169346 \tabularnewline
18 & 77.59 & 83.4200179097485 & -5.83001790974852 \tabularnewline
19 & 77.59 & 77.5763408094584 & 0.0136591905416452 \tabularnewline
20 & 76.44 & 76.4637097100836 & -0.0237097100835797 \tabularnewline
21 & 72.71 & 75.3183569633646 & -2.60835696336463 \tabularnewline
22 & 72.9 & 71.8086159338227 & 1.09138406617734 \tabularnewline
23 & 72.39 & 71.4072984332618 & 0.982701566738228 \tabularnewline
24 & 72.46 & 71.0206777407925 & 1.43932225920754 \tabularnewline
25 & 72.48 & 71.1539874831252 & 1.32601251687475 \tabularnewline
26 & 72.48 & 71.3341135492335 & 1.14588645076645 \tabularnewline
27 & 72.48 & 71.4881605028879 & 0.991839497112124 \tabularnewline
28 & 72.3 & 71.6211428513903 & 0.678857148609694 \tabularnewline
29 & 72.3 & 71.5717288991708 & 0.728271100829161 \tabularnewline
30 & 72.3 & 71.6383886300673 & 0.6616113699327 \tabularnewline
31 & 71.14 & 71.7202133032689 & -0.580213303268906 \tabularnewline
32 & 71.14 & 70.7363458451027 & 0.403654154897268 \tabularnewline
33 & 68.99 & 70.5909465504148 & -1.60094655041476 \tabularnewline
34 & 68.42 & 68.6558644876548 & -0.235864487654837 \tabularnewline
35 & 68.42 & 67.8009806899276 & 0.619019310072403 \tabularnewline
36 & 69.28 & 67.7026697835055 & 1.57733021649454 \tabularnewline
37 & 65.22 & 68.5447528887999 & -3.32475288879991 \tabularnewline
38 & 70.21 & 65.0719759260322 & 5.1380240739678 \tabularnewline
39 & 70.21 & 68.9853570601464 & 1.22464293985364 \tabularnewline
40 & 71.2 & 69.8593516129415 & 1.34064838705852 \tabularnewline
41 & 68.94 & 70.9672892317982 & -2.02728923179816 \tabularnewline
42 & 68.94 & 69.1375795840039 & -0.197579584003904 \tabularnewline
43 & 68.93 & 68.7681171410584 & 0.161882858941624 \tabularnewline
44 & 68.93 & 68.7064994143878 & 0.2235005856122 \tabularnewline
45 & 68.93 & 68.7181008031001 & 0.21189919689995 \tabularnewline
46 & 68.93 & 68.7424489671438 & 0.187551032856177 \tabularnewline
47 & 59.94 & 68.7666836433788 & -8.82668364337879 \tabularnewline
48 & 61.04 & 60.5730916804635 & 0.466908319536465 \tabularnewline
49 & 60.2 & 59.950106839586 & 0.249893160414025 \tabularnewline
50 & 60.2 & 59.1775848765983 & 1.02241512340167 \tabularnewline
51 & 60.12 & 59.1371171848017 & 0.982882815198273 \tabularnewline
52 & 60.25 & 59.1673324044137 & 1.08266759558633 \tabularnewline
53 & 58.03 & 59.391411950432 & -1.36141195043204 \tabularnewline
54 & 62.37 & 57.4951370146572 & 4.87486298534277 \tabularnewline
55 & 62.16 & 61.1554942940547 & 1.00450570594533 \tabularnewline
56 & 62.16 & 61.7882895978261 & 0.371710402173932 \tabularnewline
57 & 62.16 & 61.947759204726 & 0.212240795274042 \tabularnewline
58 & 62.16 & 62.0003331432209 & 0.159666856779133 \tabularnewline
59 & 62.29 & 62.0270359035472 & 0.262964096452784 \tabularnewline
60 & 64.39 & 62.1648139990796 & 2.22518600092036 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166941&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]3[/C][C]88.49[/C][C]88.42[/C][C]0.0699999999999932[/C][/ROW]
[ROW][C]4[/C][C]88.33[/C][C]86.2939676451458[/C][C]2.03603235485417[/C][/ROW]
[ROW][C]5[/C][C]87.7[/C][C]85.971854539898[/C][C]1.72814546010196[/C][/ROW]
[ROW][C]6[/C][C]87.33[/C][C]85.5810849938595[/C][C]1.74891500614045[/C][/ROW]
[ROW][C]7[/C][C]87.33[/C][C]85.389829019791[/C][C]1.94017098020896[/C][/ROW]
[ROW][C]8[/C][C]87.33[/C][C]85.5560508509838[/C][C]1.7739491490162[/C][/ROW]
[ROW][C]9[/C][C]85.47[/C][C]85.7730587722573[/C][C]-0.303058772257259[/C][/ROW]
[ROW][C]10[/C][C]86.1[/C][C]84.2773668797722[/C][C]1.82263312022775[/C][/ROW]
[ROW][C]11[/C][C]86.1[/C][C]84.6925226085202[/C][C]1.40747739147982[/C][/ROW]
[ROW][C]12[/C][C]86.13[/C][C]84.9187039740225[/C][C]1.21129602597746[/C][/ROW]
[ROW][C]13[/C][C]83.31[/C][C]85.112644894107[/C][C]-1.80264489410705[/C][/ROW]
[ROW][C]14[/C][C]83.31[/C][C]82.6789160198219[/C][C]0.631083980178147[/C][/ROW]
[ROW][C]15[/C][C]83.55[/C][C]82.2808691964071[/C][C]1.2691308035929[/C][/ROW]
[ROW][C]16[/C][C]84.11[/C][C]82.5318118965874[/C][C]1.57818810341263[/C][/ROW]
[ROW][C]17[/C][C]84.11[/C][C]83.1977604888307[/C][C]0.912239511169346[/C][/ROW]
[ROW][C]18[/C][C]77.59[/C][C]83.4200179097485[/C][C]-5.83001790974852[/C][/ROW]
[ROW][C]19[/C][C]77.59[/C][C]77.5763408094584[/C][C]0.0136591905416452[/C][/ROW]
[ROW][C]20[/C][C]76.44[/C][C]76.4637097100836[/C][C]-0.0237097100835797[/C][/ROW]
[ROW][C]21[/C][C]72.71[/C][C]75.3183569633646[/C][C]-2.60835696336463[/C][/ROW]
[ROW][C]22[/C][C]72.9[/C][C]71.8086159338227[/C][C]1.09138406617734[/C][/ROW]
[ROW][C]23[/C][C]72.39[/C][C]71.4072984332618[/C][C]0.982701566738228[/C][/ROW]
[ROW][C]24[/C][C]72.46[/C][C]71.0206777407925[/C][C]1.43932225920754[/C][/ROW]
[ROW][C]25[/C][C]72.48[/C][C]71.1539874831252[/C][C]1.32601251687475[/C][/ROW]
[ROW][C]26[/C][C]72.48[/C][C]71.3341135492335[/C][C]1.14588645076645[/C][/ROW]
[ROW][C]27[/C][C]72.48[/C][C]71.4881605028879[/C][C]0.991839497112124[/C][/ROW]
[ROW][C]28[/C][C]72.3[/C][C]71.6211428513903[/C][C]0.678857148609694[/C][/ROW]
[ROW][C]29[/C][C]72.3[/C][C]71.5717288991708[/C][C]0.728271100829161[/C][/ROW]
[ROW][C]30[/C][C]72.3[/C][C]71.6383886300673[/C][C]0.6616113699327[/C][/ROW]
[ROW][C]31[/C][C]71.14[/C][C]71.7202133032689[/C][C]-0.580213303268906[/C][/ROW]
[ROW][C]32[/C][C]71.14[/C][C]70.7363458451027[/C][C]0.403654154897268[/C][/ROW]
[ROW][C]33[/C][C]68.99[/C][C]70.5909465504148[/C][C]-1.60094655041476[/C][/ROW]
[ROW][C]34[/C][C]68.42[/C][C]68.6558644876548[/C][C]-0.235864487654837[/C][/ROW]
[ROW][C]35[/C][C]68.42[/C][C]67.8009806899276[/C][C]0.619019310072403[/C][/ROW]
[ROW][C]36[/C][C]69.28[/C][C]67.7026697835055[/C][C]1.57733021649454[/C][/ROW]
[ROW][C]37[/C][C]65.22[/C][C]68.5447528887999[/C][C]-3.32475288879991[/C][/ROW]
[ROW][C]38[/C][C]70.21[/C][C]65.0719759260322[/C][C]5.1380240739678[/C][/ROW]
[ROW][C]39[/C][C]70.21[/C][C]68.9853570601464[/C][C]1.22464293985364[/C][/ROW]
[ROW][C]40[/C][C]71.2[/C][C]69.8593516129415[/C][C]1.34064838705852[/C][/ROW]
[ROW][C]41[/C][C]68.94[/C][C]70.9672892317982[/C][C]-2.02728923179816[/C][/ROW]
[ROW][C]42[/C][C]68.94[/C][C]69.1375795840039[/C][C]-0.197579584003904[/C][/ROW]
[ROW][C]43[/C][C]68.93[/C][C]68.7681171410584[/C][C]0.161882858941624[/C][/ROW]
[ROW][C]44[/C][C]68.93[/C][C]68.7064994143878[/C][C]0.2235005856122[/C][/ROW]
[ROW][C]45[/C][C]68.93[/C][C]68.7181008031001[/C][C]0.21189919689995[/C][/ROW]
[ROW][C]46[/C][C]68.93[/C][C]68.7424489671438[/C][C]0.187551032856177[/C][/ROW]
[ROW][C]47[/C][C]59.94[/C][C]68.7666836433788[/C][C]-8.82668364337879[/C][/ROW]
[ROW][C]48[/C][C]61.04[/C][C]60.5730916804635[/C][C]0.466908319536465[/C][/ROW]
[ROW][C]49[/C][C]60.2[/C][C]59.950106839586[/C][C]0.249893160414025[/C][/ROW]
[ROW][C]50[/C][C]60.2[/C][C]59.1775848765983[/C][C]1.02241512340167[/C][/ROW]
[ROW][C]51[/C][C]60.12[/C][C]59.1371171848017[/C][C]0.982882815198273[/C][/ROW]
[ROW][C]52[/C][C]60.25[/C][C]59.1673324044137[/C][C]1.08266759558633[/C][/ROW]
[ROW][C]53[/C][C]58.03[/C][C]59.391411950432[/C][C]-1.36141195043204[/C][/ROW]
[ROW][C]54[/C][C]62.37[/C][C]57.4951370146572[/C][C]4.87486298534277[/C][/ROW]
[ROW][C]55[/C][C]62.16[/C][C]61.1554942940547[/C][C]1.00450570594533[/C][/ROW]
[ROW][C]56[/C][C]62.16[/C][C]61.7882895978261[/C][C]0.371710402173932[/C][/ROW]
[ROW][C]57[/C][C]62.16[/C][C]61.947759204726[/C][C]0.212240795274042[/C][/ROW]
[ROW][C]58[/C][C]62.16[/C][C]62.0003331432209[/C][C]0.159666856779133[/C][/ROW]
[ROW][C]59[/C][C]62.29[/C][C]62.0270359035472[/C][C]0.262964096452784[/C][/ROW]
[ROW][C]60[/C][C]64.39[/C][C]62.1648139990796[/C][C]2.22518600092036[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166941&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166941&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
388.4988.420.0699999999999932
488.3386.29396764514582.03603235485417
587.785.9718545398981.72814546010196
687.3385.58108499385951.74891500614045
787.3385.3898290197911.94017098020896
887.3385.55605085098381.7739491490162
985.4785.7730587722573-0.303058772257259
1086.184.27736687977221.82263312022775
1186.184.69252260852021.40747739147982
1286.1384.91870397402251.21129602597746
1383.3185.112644894107-1.80264489410705
1483.3182.67891601982190.631083980178147
1583.5582.28086919640711.2691308035929
1684.1182.53181189658741.57818810341263
1784.1183.19776048883070.912239511169346
1877.5983.4200179097485-5.83001790974852
1977.5977.57634080945840.0136591905416452
2076.4476.4637097100836-0.0237097100835797
2172.7175.3183569633646-2.60835696336463
2272.971.80861593382271.09138406617734
2372.3971.40729843326180.982701566738228
2472.4671.02067774079251.43932225920754
2572.4871.15398748312521.32601251687475
2672.4871.33411354923351.14588645076645
2772.4871.48816050288790.991839497112124
2872.371.62114285139030.678857148609694
2972.371.57172889917080.728271100829161
3072.371.63838863006730.6616113699327
3171.1471.7202133032689-0.580213303268906
3271.1470.73634584510270.403654154897268
3368.9970.5909465504148-1.60094655041476
3468.4268.6558644876548-0.235864487654837
3568.4267.80098068992760.619019310072403
3669.2867.70266978350551.57733021649454
3765.2268.5447528887999-3.32475288879991
3870.2165.07197592603225.1380240739678
3970.2168.98535706014641.22464293985364
4071.269.85935161294151.34064838705852
4168.9470.9672892317982-2.02728923179816
4268.9469.1375795840039-0.197579584003904
4368.9368.76811714105840.161882858941624
4468.9368.70649941438780.2235005856122
4568.9368.71810080310010.21189919689995
4668.9368.74244896714380.187551032856177
4759.9468.7666836433788-8.82668364337879
4861.0460.57309168046350.466908319536465
4960.259.9501068395860.249893160414025
5060.259.17758487659831.02241512340167
5160.1259.13711718480170.982882815198273
5260.2559.16733240441371.08266759558633
5358.0359.391411950432-1.36141195043204
5462.3757.49513701465724.87486298534277
5562.1661.15549429405471.00450570594533
5662.1661.78828959782610.371710402173932
5762.1661.9477592047260.212240795274042
5862.1662.00033314322090.159666856779133
5962.2962.02703590354720.262964096452784
6064.3962.16481399907962.22518600092036







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6164.123187611967560.112955769003568.1334194549315
6264.280592081529658.848136295737669.7130478673216
6364.437996551091757.641879722078771.2341133801046
6464.595401020653856.443109393526772.7476926477808
6564.752805490215855.230171642515674.2754393379161
6664.910209959777953.99232056223975.8280993573169
6765.0676144293452.723784620699277.4114442379809
6865.225018898902151.421358267999479.0286795298049
6965.382423368464250.083271059443780.6815756774847
7065.539827838026348.708601112041982.3710545640107
7165.697232307588447.296948150375984.0975164648009
7265.854636777150545.848241091245285.8610324630558

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 64.1231876119675 & 60.1129557690035 & 68.1334194549315 \tabularnewline
62 & 64.2805920815296 & 58.8481362957376 & 69.7130478673216 \tabularnewline
63 & 64.4379965510917 & 57.6418797220787 & 71.2341133801046 \tabularnewline
64 & 64.5954010206538 & 56.4431093935267 & 72.7476926477808 \tabularnewline
65 & 64.7528054902158 & 55.2301716425156 & 74.2754393379161 \tabularnewline
66 & 64.9102099597779 & 53.992320562239 & 75.8280993573169 \tabularnewline
67 & 65.06761442934 & 52.7237846206992 & 77.4114442379809 \tabularnewline
68 & 65.2250188989021 & 51.4213582679994 & 79.0286795298049 \tabularnewline
69 & 65.3824233684642 & 50.0832710594437 & 80.6815756774847 \tabularnewline
70 & 65.5398278380263 & 48.7086011120419 & 82.3710545640107 \tabularnewline
71 & 65.6972323075884 & 47.2969481503759 & 84.0975164648009 \tabularnewline
72 & 65.8546367771505 & 45.8482410912452 & 85.8610324630558 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166941&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]61[/C][C]64.1231876119675[/C][C]60.1129557690035[/C][C]68.1334194549315[/C][/ROW]
[ROW][C]62[/C][C]64.2805920815296[/C][C]58.8481362957376[/C][C]69.7130478673216[/C][/ROW]
[ROW][C]63[/C][C]64.4379965510917[/C][C]57.6418797220787[/C][C]71.2341133801046[/C][/ROW]
[ROW][C]64[/C][C]64.5954010206538[/C][C]56.4431093935267[/C][C]72.7476926477808[/C][/ROW]
[ROW][C]65[/C][C]64.7528054902158[/C][C]55.2301716425156[/C][C]74.2754393379161[/C][/ROW]
[ROW][C]66[/C][C]64.9102099597779[/C][C]53.992320562239[/C][C]75.8280993573169[/C][/ROW]
[ROW][C]67[/C][C]65.06761442934[/C][C]52.7237846206992[/C][C]77.4114442379809[/C][/ROW]
[ROW][C]68[/C][C]65.2250188989021[/C][C]51.4213582679994[/C][C]79.0286795298049[/C][/ROW]
[ROW][C]69[/C][C]65.3824233684642[/C][C]50.0832710594437[/C][C]80.6815756774847[/C][/ROW]
[ROW][C]70[/C][C]65.5398278380263[/C][C]48.7086011120419[/C][C]82.3710545640107[/C][/ROW]
[ROW][C]71[/C][C]65.6972323075884[/C][C]47.2969481503759[/C][C]84.0975164648009[/C][/ROW]
[ROW][C]72[/C][C]65.8546367771505[/C][C]45.8482410912452[/C][C]85.8610324630558[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166941&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166941&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
6164.123187611967560.112955769003568.1334194549315
6264.280592081529658.848136295737669.7130478673216
6364.437996551091757.641879722078771.2341133801046
6464.595401020653856.443109393526772.7476926477808
6564.752805490215855.230171642515674.2754393379161
6664.910209959777953.99232056223975.8280993573169
6765.0676144293452.723784620699277.4114442379809
6865.225018898902151.421358267999479.0286795298049
6965.382423368464250.083271059443780.6815756774847
7065.539827838026348.708601112041982.3710545640107
7165.697232307588447.296948150375984.0975164648009
7265.854636777150545.848241091245285.8610324630558



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')