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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 computationSat, 16 Nov 2013 05:16:29 -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/2013/Nov/16/t13845970309isli6nwczqafn7.htm/, Retrieved Sat, 04 May 2024 20:55:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=225547, Retrieved Sat, 04 May 2024 20:55:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ws8] [2013-11-16 10:16:29] [16986792796a040c0e2998a7aab14aa2] [Current]
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Dataseries X:
0.7869
0.7439
0.7492
0.7804
0.7678
0.7573
0.7337
0.7136
0.7107
0.7015
0.6874
0.6754
0.6713
0.6849
0.7003
0.7309
0.7364
0.7439
0.7928
0.8188
0.784
0.7746
0.7677
0.7197
0.7304
0.7567
0.749
0.7328
0.7142
0.6927
0.6974
0.6953
0.699
0.6971
0.7246
0.7301
0.736
0.7585
0.7756
0.7564
0.7568
0.7593
0.779
0.7978
0.8125
0.8075
0.7781
0.771
0.7796
0.763
0.7531
0.7473
0.7707
0.7684
0.7702
0.759
0.7649
0.7508
0.7494
0.7334




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225547&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225547&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225547&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999955063609663
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999955063609663 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225547&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]0.999955063609663[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225547&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225547&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
alpha0.999955063609663
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
20.74390.7869-0.043
30.74920.7439019322647850.00529806773521546
40.78040.749199761923960.0312002380760398
50.76780.780398597973923-0.0125985979739232
60.75730.767800566135516-0.0105005661355163
70.73370.757300471857539-0.0236004718575386
80.71360.733701060520015-0.0201010605200155
90.71070.713600903269102-0.00290090326910175
100.70150.710700130356122-0.00920013035612166
110.68740.701500413420649-0.0141004134206488
120.67540.687400633621681-0.0120006336216814
130.67130.675400539265157-0.00410053926515674
140.68490.6713001842634330.013599815736567
150.70030.6848993888733720.0154006111266285
160.73090.7002993079521270.030600692047873
170.73640.7308986249153580.00550137508464255
180.74390.7363997527880620.00750024721193809
190.79280.7438996629659640.0489003370340363
200.81880.7927978025953670.0260021974046326
210.7840.818798831555108-0.0347988315551078
220.77460.784001563733878-0.00940156373387813
230.76770.774600422472338-0.00690042247233758
240.71970.767700310080078-0.0480003100800778
250.73040.719702156960670.01069784303933
260.75670.7303995192775490.0263004807224506
270.7490.756698818151332-0.00769881815133222
280.73280.749000345957098-0.0162003459570975
290.71420.73280072798507-0.0186007279850696
300.69270.714200835849573-0.0215008358495733
310.69740.6927009661699520.00469903383004777
320.69530.697399788842382-0.0020997888423816
330.6990.6953000943569310.00369990564306888
340.69710.698999833739596-0.00189983373959568
350.72460.6971000853716710.0274999146283295
360.73010.7245987642531020.00550123574689787
370.7360.7300997527943230.00590024720567683
380.75850.7359997348641880.0225002651358115
390.77560.7584989889193030.0171010110806968
400.75640.775599231542291-0.019199231542291
410.75680.7564008627441630.00039913725583729
420.75930.7567999820642130.00250001793578747
430.7790.7592998876582180.0197001123417818
440.79780.7789991147480620.0188008852519378
450.81250.7977991551560820.0147008448439184
460.80750.812499339397098-0.00499933939709785
470.77810.807500224652267-0.0294002246522665
480.7710.778101321139971-0.00710132113997097
490.77960.7710003191077390.00859968089226126
500.7630.779599613561383-0.0165996135613826
510.75310.763000745926714-0.00990074592671442
520.74730.753100444903784-0.00580044490378362
530.77070.7473002606510560.0233997393489438
540.76840.770698948500179-0.00229894850017887
550.77020.7684001033064470.00179989669355285
560.7590.77019991911914-0.0111999191191396
570.76490.7590005032839370.00589949671606271
580.75080.764899734897913-0.0140997348979128
590.74940.750800633591191-0.00140063359119114
600.73340.749400062939418-0.0160000629394177

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 0.7439 & 0.7869 & -0.043 \tabularnewline
3 & 0.7492 & 0.743901932264785 & 0.00529806773521546 \tabularnewline
4 & 0.7804 & 0.74919976192396 & 0.0312002380760398 \tabularnewline
5 & 0.7678 & 0.780398597973923 & -0.0125985979739232 \tabularnewline
6 & 0.7573 & 0.767800566135516 & -0.0105005661355163 \tabularnewline
7 & 0.7337 & 0.757300471857539 & -0.0236004718575386 \tabularnewline
8 & 0.7136 & 0.733701060520015 & -0.0201010605200155 \tabularnewline
9 & 0.7107 & 0.713600903269102 & -0.00290090326910175 \tabularnewline
10 & 0.7015 & 0.710700130356122 & -0.00920013035612166 \tabularnewline
11 & 0.6874 & 0.701500413420649 & -0.0141004134206488 \tabularnewline
12 & 0.6754 & 0.687400633621681 & -0.0120006336216814 \tabularnewline
13 & 0.6713 & 0.675400539265157 & -0.00410053926515674 \tabularnewline
14 & 0.6849 & 0.671300184263433 & 0.013599815736567 \tabularnewline
15 & 0.7003 & 0.684899388873372 & 0.0154006111266285 \tabularnewline
16 & 0.7309 & 0.700299307952127 & 0.030600692047873 \tabularnewline
17 & 0.7364 & 0.730898624915358 & 0.00550137508464255 \tabularnewline
18 & 0.7439 & 0.736399752788062 & 0.00750024721193809 \tabularnewline
19 & 0.7928 & 0.743899662965964 & 0.0489003370340363 \tabularnewline
20 & 0.8188 & 0.792797802595367 & 0.0260021974046326 \tabularnewline
21 & 0.784 & 0.818798831555108 & -0.0347988315551078 \tabularnewline
22 & 0.7746 & 0.784001563733878 & -0.00940156373387813 \tabularnewline
23 & 0.7677 & 0.774600422472338 & -0.00690042247233758 \tabularnewline
24 & 0.7197 & 0.767700310080078 & -0.0480003100800778 \tabularnewline
25 & 0.7304 & 0.71970215696067 & 0.01069784303933 \tabularnewline
26 & 0.7567 & 0.730399519277549 & 0.0263004807224506 \tabularnewline
27 & 0.749 & 0.756698818151332 & -0.00769881815133222 \tabularnewline
28 & 0.7328 & 0.749000345957098 & -0.0162003459570975 \tabularnewline
29 & 0.7142 & 0.73280072798507 & -0.0186007279850696 \tabularnewline
30 & 0.6927 & 0.714200835849573 & -0.0215008358495733 \tabularnewline
31 & 0.6974 & 0.692700966169952 & 0.00469903383004777 \tabularnewline
32 & 0.6953 & 0.697399788842382 & -0.0020997888423816 \tabularnewline
33 & 0.699 & 0.695300094356931 & 0.00369990564306888 \tabularnewline
34 & 0.6971 & 0.698999833739596 & -0.00189983373959568 \tabularnewline
35 & 0.7246 & 0.697100085371671 & 0.0274999146283295 \tabularnewline
36 & 0.7301 & 0.724598764253102 & 0.00550123574689787 \tabularnewline
37 & 0.736 & 0.730099752794323 & 0.00590024720567683 \tabularnewline
38 & 0.7585 & 0.735999734864188 & 0.0225002651358115 \tabularnewline
39 & 0.7756 & 0.758498988919303 & 0.0171010110806968 \tabularnewline
40 & 0.7564 & 0.775599231542291 & -0.019199231542291 \tabularnewline
41 & 0.7568 & 0.756400862744163 & 0.00039913725583729 \tabularnewline
42 & 0.7593 & 0.756799982064213 & 0.00250001793578747 \tabularnewline
43 & 0.779 & 0.759299887658218 & 0.0197001123417818 \tabularnewline
44 & 0.7978 & 0.778999114748062 & 0.0188008852519378 \tabularnewline
45 & 0.8125 & 0.797799155156082 & 0.0147008448439184 \tabularnewline
46 & 0.8075 & 0.812499339397098 & -0.00499933939709785 \tabularnewline
47 & 0.7781 & 0.807500224652267 & -0.0294002246522665 \tabularnewline
48 & 0.771 & 0.778101321139971 & -0.00710132113997097 \tabularnewline
49 & 0.7796 & 0.771000319107739 & 0.00859968089226126 \tabularnewline
50 & 0.763 & 0.779599613561383 & -0.0165996135613826 \tabularnewline
51 & 0.7531 & 0.763000745926714 & -0.00990074592671442 \tabularnewline
52 & 0.7473 & 0.753100444903784 & -0.00580044490378362 \tabularnewline
53 & 0.7707 & 0.747300260651056 & 0.0233997393489438 \tabularnewline
54 & 0.7684 & 0.770698948500179 & -0.00229894850017887 \tabularnewline
55 & 0.7702 & 0.768400103306447 & 0.00179989669355285 \tabularnewline
56 & 0.759 & 0.77019991911914 & -0.0111999191191396 \tabularnewline
57 & 0.7649 & 0.759000503283937 & 0.00589949671606271 \tabularnewline
58 & 0.7508 & 0.764899734897913 & -0.0140997348979128 \tabularnewline
59 & 0.7494 & 0.750800633591191 & -0.00140063359119114 \tabularnewline
60 & 0.7334 & 0.749400062939418 & -0.0160000629394177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225547&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]2[/C][C]0.7439[/C][C]0.7869[/C][C]-0.043[/C][/ROW]
[ROW][C]3[/C][C]0.7492[/C][C]0.743901932264785[/C][C]0.00529806773521546[/C][/ROW]
[ROW][C]4[/C][C]0.7804[/C][C]0.74919976192396[/C][C]0.0312002380760398[/C][/ROW]
[ROW][C]5[/C][C]0.7678[/C][C]0.780398597973923[/C][C]-0.0125985979739232[/C][/ROW]
[ROW][C]6[/C][C]0.7573[/C][C]0.767800566135516[/C][C]-0.0105005661355163[/C][/ROW]
[ROW][C]7[/C][C]0.7337[/C][C]0.757300471857539[/C][C]-0.0236004718575386[/C][/ROW]
[ROW][C]8[/C][C]0.7136[/C][C]0.733701060520015[/C][C]-0.0201010605200155[/C][/ROW]
[ROW][C]9[/C][C]0.7107[/C][C]0.713600903269102[/C][C]-0.00290090326910175[/C][/ROW]
[ROW][C]10[/C][C]0.7015[/C][C]0.710700130356122[/C][C]-0.00920013035612166[/C][/ROW]
[ROW][C]11[/C][C]0.6874[/C][C]0.701500413420649[/C][C]-0.0141004134206488[/C][/ROW]
[ROW][C]12[/C][C]0.6754[/C][C]0.687400633621681[/C][C]-0.0120006336216814[/C][/ROW]
[ROW][C]13[/C][C]0.6713[/C][C]0.675400539265157[/C][C]-0.00410053926515674[/C][/ROW]
[ROW][C]14[/C][C]0.6849[/C][C]0.671300184263433[/C][C]0.013599815736567[/C][/ROW]
[ROW][C]15[/C][C]0.7003[/C][C]0.684899388873372[/C][C]0.0154006111266285[/C][/ROW]
[ROW][C]16[/C][C]0.7309[/C][C]0.700299307952127[/C][C]0.030600692047873[/C][/ROW]
[ROW][C]17[/C][C]0.7364[/C][C]0.730898624915358[/C][C]0.00550137508464255[/C][/ROW]
[ROW][C]18[/C][C]0.7439[/C][C]0.736399752788062[/C][C]0.00750024721193809[/C][/ROW]
[ROW][C]19[/C][C]0.7928[/C][C]0.743899662965964[/C][C]0.0489003370340363[/C][/ROW]
[ROW][C]20[/C][C]0.8188[/C][C]0.792797802595367[/C][C]0.0260021974046326[/C][/ROW]
[ROW][C]21[/C][C]0.784[/C][C]0.818798831555108[/C][C]-0.0347988315551078[/C][/ROW]
[ROW][C]22[/C][C]0.7746[/C][C]0.784001563733878[/C][C]-0.00940156373387813[/C][/ROW]
[ROW][C]23[/C][C]0.7677[/C][C]0.774600422472338[/C][C]-0.00690042247233758[/C][/ROW]
[ROW][C]24[/C][C]0.7197[/C][C]0.767700310080078[/C][C]-0.0480003100800778[/C][/ROW]
[ROW][C]25[/C][C]0.7304[/C][C]0.71970215696067[/C][C]0.01069784303933[/C][/ROW]
[ROW][C]26[/C][C]0.7567[/C][C]0.730399519277549[/C][C]0.0263004807224506[/C][/ROW]
[ROW][C]27[/C][C]0.749[/C][C]0.756698818151332[/C][C]-0.00769881815133222[/C][/ROW]
[ROW][C]28[/C][C]0.7328[/C][C]0.749000345957098[/C][C]-0.0162003459570975[/C][/ROW]
[ROW][C]29[/C][C]0.7142[/C][C]0.73280072798507[/C][C]-0.0186007279850696[/C][/ROW]
[ROW][C]30[/C][C]0.6927[/C][C]0.714200835849573[/C][C]-0.0215008358495733[/C][/ROW]
[ROW][C]31[/C][C]0.6974[/C][C]0.692700966169952[/C][C]0.00469903383004777[/C][/ROW]
[ROW][C]32[/C][C]0.6953[/C][C]0.697399788842382[/C][C]-0.0020997888423816[/C][/ROW]
[ROW][C]33[/C][C]0.699[/C][C]0.695300094356931[/C][C]0.00369990564306888[/C][/ROW]
[ROW][C]34[/C][C]0.6971[/C][C]0.698999833739596[/C][C]-0.00189983373959568[/C][/ROW]
[ROW][C]35[/C][C]0.7246[/C][C]0.697100085371671[/C][C]0.0274999146283295[/C][/ROW]
[ROW][C]36[/C][C]0.7301[/C][C]0.724598764253102[/C][C]0.00550123574689787[/C][/ROW]
[ROW][C]37[/C][C]0.736[/C][C]0.730099752794323[/C][C]0.00590024720567683[/C][/ROW]
[ROW][C]38[/C][C]0.7585[/C][C]0.735999734864188[/C][C]0.0225002651358115[/C][/ROW]
[ROW][C]39[/C][C]0.7756[/C][C]0.758498988919303[/C][C]0.0171010110806968[/C][/ROW]
[ROW][C]40[/C][C]0.7564[/C][C]0.775599231542291[/C][C]-0.019199231542291[/C][/ROW]
[ROW][C]41[/C][C]0.7568[/C][C]0.756400862744163[/C][C]0.00039913725583729[/C][/ROW]
[ROW][C]42[/C][C]0.7593[/C][C]0.756799982064213[/C][C]0.00250001793578747[/C][/ROW]
[ROW][C]43[/C][C]0.779[/C][C]0.759299887658218[/C][C]0.0197001123417818[/C][/ROW]
[ROW][C]44[/C][C]0.7978[/C][C]0.778999114748062[/C][C]0.0188008852519378[/C][/ROW]
[ROW][C]45[/C][C]0.8125[/C][C]0.797799155156082[/C][C]0.0147008448439184[/C][/ROW]
[ROW][C]46[/C][C]0.8075[/C][C]0.812499339397098[/C][C]-0.00499933939709785[/C][/ROW]
[ROW][C]47[/C][C]0.7781[/C][C]0.807500224652267[/C][C]-0.0294002246522665[/C][/ROW]
[ROW][C]48[/C][C]0.771[/C][C]0.778101321139971[/C][C]-0.00710132113997097[/C][/ROW]
[ROW][C]49[/C][C]0.7796[/C][C]0.771000319107739[/C][C]0.00859968089226126[/C][/ROW]
[ROW][C]50[/C][C]0.763[/C][C]0.779599613561383[/C][C]-0.0165996135613826[/C][/ROW]
[ROW][C]51[/C][C]0.7531[/C][C]0.763000745926714[/C][C]-0.00990074592671442[/C][/ROW]
[ROW][C]52[/C][C]0.7473[/C][C]0.753100444903784[/C][C]-0.00580044490378362[/C][/ROW]
[ROW][C]53[/C][C]0.7707[/C][C]0.747300260651056[/C][C]0.0233997393489438[/C][/ROW]
[ROW][C]54[/C][C]0.7684[/C][C]0.770698948500179[/C][C]-0.00229894850017887[/C][/ROW]
[ROW][C]55[/C][C]0.7702[/C][C]0.768400103306447[/C][C]0.00179989669355285[/C][/ROW]
[ROW][C]56[/C][C]0.759[/C][C]0.77019991911914[/C][C]-0.0111999191191396[/C][/ROW]
[ROW][C]57[/C][C]0.7649[/C][C]0.759000503283937[/C][C]0.00589949671606271[/C][/ROW]
[ROW][C]58[/C][C]0.7508[/C][C]0.764899734897913[/C][C]-0.0140997348979128[/C][/ROW]
[ROW][C]59[/C][C]0.7494[/C][C]0.750800633591191[/C][C]-0.00140063359119114[/C][/ROW]
[ROW][C]60[/C][C]0.7334[/C][C]0.749400062939418[/C][C]-0.0160000629394177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225547&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225547&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
20.74390.7869-0.043
30.74920.7439019322647850.00529806773521546
40.78040.749199761923960.0312002380760398
50.76780.780398597973923-0.0125985979739232
60.75730.767800566135516-0.0105005661355163
70.73370.757300471857539-0.0236004718575386
80.71360.733701060520015-0.0201010605200155
90.71070.713600903269102-0.00290090326910175
100.70150.710700130356122-0.00920013035612166
110.68740.701500413420649-0.0141004134206488
120.67540.687400633621681-0.0120006336216814
130.67130.675400539265157-0.00410053926515674
140.68490.6713001842634330.013599815736567
150.70030.6848993888733720.0154006111266285
160.73090.7002993079521270.030600692047873
170.73640.7308986249153580.00550137508464255
180.74390.7363997527880620.00750024721193809
190.79280.7438996629659640.0489003370340363
200.81880.7927978025953670.0260021974046326
210.7840.818798831555108-0.0347988315551078
220.77460.784001563733878-0.00940156373387813
230.76770.774600422472338-0.00690042247233758
240.71970.767700310080078-0.0480003100800778
250.73040.719702156960670.01069784303933
260.75670.7303995192775490.0263004807224506
270.7490.756698818151332-0.00769881815133222
280.73280.749000345957098-0.0162003459570975
290.71420.73280072798507-0.0186007279850696
300.69270.714200835849573-0.0215008358495733
310.69740.6927009661699520.00469903383004777
320.69530.697399788842382-0.0020997888423816
330.6990.6953000943569310.00369990564306888
340.69710.698999833739596-0.00189983373959568
350.72460.6971000853716710.0274999146283295
360.73010.7245987642531020.00550123574689787
370.7360.7300997527943230.00590024720567683
380.75850.7359997348641880.0225002651358115
390.77560.7584989889193030.0171010110806968
400.75640.775599231542291-0.019199231542291
410.75680.7564008627441630.00039913725583729
420.75930.7567999820642130.00250001793578747
430.7790.7592998876582180.0197001123417818
440.79780.7789991147480620.0188008852519378
450.81250.7977991551560820.0147008448439184
460.80750.812499339397098-0.00499933939709785
470.77810.807500224652267-0.0294002246522665
480.7710.778101321139971-0.00710132113997097
490.77960.7710003191077390.00859968089226126
500.7630.779599613561383-0.0165996135613826
510.75310.763000745926714-0.00990074592671442
520.74730.753100444903784-0.00580044490378362
530.77070.7473002606510560.0233997393489438
540.76840.770698948500179-0.00229894850017887
550.77020.7684001033064470.00179989669355285
560.7590.77019991911914-0.0111999191191396
570.76490.7590005032839370.00589949671606271
580.75080.764899734897913-0.0140997348979128
590.74940.750800633591191-0.00140063359119114
600.73340.749400062939418-0.0160000629394177







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
610.7334007189850740.6968463373363190.769955100633829
620.7334007189850740.6817061781893220.785095259780826
630.7334007189850740.6700885694524250.796712868517723
640.7334007189850740.6602944196066660.806507018363481
650.7334007189850740.6516655751412770.815135862828871
660.7334007189850740.643864489058150.822936948911998
670.7334007189850740.6366906409172330.830110797052914
680.7334007189850740.6300133796719420.836788058298205
690.7334007189850740.6237419543531050.843059483617042
700.7334007189850740.6178102894895040.848991148480643
710.7334007189850740.6121685032941480.854632934675999
720.7334007189850740.6067778424907690.860023595479378

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 0.733400718985074 & 0.696846337336319 & 0.769955100633829 \tabularnewline
62 & 0.733400718985074 & 0.681706178189322 & 0.785095259780826 \tabularnewline
63 & 0.733400718985074 & 0.670088569452425 & 0.796712868517723 \tabularnewline
64 & 0.733400718985074 & 0.660294419606666 & 0.806507018363481 \tabularnewline
65 & 0.733400718985074 & 0.651665575141277 & 0.815135862828871 \tabularnewline
66 & 0.733400718985074 & 0.64386448905815 & 0.822936948911998 \tabularnewline
67 & 0.733400718985074 & 0.636690640917233 & 0.830110797052914 \tabularnewline
68 & 0.733400718985074 & 0.630013379671942 & 0.836788058298205 \tabularnewline
69 & 0.733400718985074 & 0.623741954353105 & 0.843059483617042 \tabularnewline
70 & 0.733400718985074 & 0.617810289489504 & 0.848991148480643 \tabularnewline
71 & 0.733400718985074 & 0.612168503294148 & 0.854632934675999 \tabularnewline
72 & 0.733400718985074 & 0.606777842490769 & 0.860023595479378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=225547&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]0.733400718985074[/C][C]0.696846337336319[/C][C]0.769955100633829[/C][/ROW]
[ROW][C]62[/C][C]0.733400718985074[/C][C]0.681706178189322[/C][C]0.785095259780826[/C][/ROW]
[ROW][C]63[/C][C]0.733400718985074[/C][C]0.670088569452425[/C][C]0.796712868517723[/C][/ROW]
[ROW][C]64[/C][C]0.733400718985074[/C][C]0.660294419606666[/C][C]0.806507018363481[/C][/ROW]
[ROW][C]65[/C][C]0.733400718985074[/C][C]0.651665575141277[/C][C]0.815135862828871[/C][/ROW]
[ROW][C]66[/C][C]0.733400718985074[/C][C]0.64386448905815[/C][C]0.822936948911998[/C][/ROW]
[ROW][C]67[/C][C]0.733400718985074[/C][C]0.636690640917233[/C][C]0.830110797052914[/C][/ROW]
[ROW][C]68[/C][C]0.733400718985074[/C][C]0.630013379671942[/C][C]0.836788058298205[/C][/ROW]
[ROW][C]69[/C][C]0.733400718985074[/C][C]0.623741954353105[/C][C]0.843059483617042[/C][/ROW]
[ROW][C]70[/C][C]0.733400718985074[/C][C]0.617810289489504[/C][C]0.848991148480643[/C][/ROW]
[ROW][C]71[/C][C]0.733400718985074[/C][C]0.612168503294148[/C][C]0.854632934675999[/C][/ROW]
[ROW][C]72[/C][C]0.733400718985074[/C][C]0.606777842490769[/C][C]0.860023595479378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=225547&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=225547&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
610.7334007189850740.6968463373363190.769955100633829
620.7334007189850740.6817061781893220.785095259780826
630.7334007189850740.6700885694524250.796712868517723
640.7334007189850740.6602944196066660.806507018363481
650.7334007189850740.6516655751412770.815135862828871
660.7334007189850740.643864489058150.822936948911998
670.7334007189850740.6366906409172330.830110797052914
680.7334007189850740.6300133796719420.836788058298205
690.7334007189850740.6237419543531050.843059483617042
700.7334007189850740.6178102894895040.848991148480643
710.7334007189850740.6121685032941480.854632934675999
720.7334007189850740.6067778424907690.860023595479378



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