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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 23 May 2012 11:52:18 -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/23/t1337788378bujytoq5udd71hi.htm/, Retrieved Sun, 28 Apr 2024 23:01:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167210, Retrieved Sun, 28 Apr 2024 23:01:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2012-04-25 11:26:19] [b2f271c918a5e9dab64646daf8888c88]
- RMPD    [Exponential Smoothing] [] [2012-05-23 15:52:18] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
4
4
4
4
4
4
4
4
4,06
4,07
4,07
4,07
4,07
4,07
4,3
4,44
4,52
4,52
4,52
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,61
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,66
4,7
4,72
4,73
4,73
4,74
4,74
4,74
4,76
4,88
4,88
4,88
4,88
4,89
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,98
5
5,03
5,04
5,04
5,05
5,05
5,06
5,06




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=167210&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=167210&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167210&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
alpha1
beta0.0718870055767105
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0718870055767105 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167210&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0718870055767105[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167210&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167210&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
alpha1
beta0.0718870055767105
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3440
4440
5440
6440
7440
8440
94.0640.0599999999999996
104.074.06431322033460.00568677966539788
114.074.07472202589612-0.00472202589612269
124.074.0743825735942-0.00438257359419492
134.074.07406752350179-0.00406752350178863
144.074.07377512141713-0.00377512141713154
154.34.073503739242770.226496260757234
164.444.319785877202920.120214122797075
174.524.468427710518840.051572289481161
184.524.55213508798037-0.0321350879803735
194.524.54982499273152-0.0298249927315206
204.534.5476809633127-0.0176809633127037
214.534.55640993180444-0.0264099318044426
224.534.55451140088954-0.0245114008895362
234.534.5527493496771-0.0227493496770972
244.534.55111396704999-0.0211139670499927
254.534.54959614718292-0.0195961471829236
264.534.5481874388411-0.0181874388411032
274.534.54687999832371-0.0168799983237067
284.614.545666545790080.0643334542099252
294.634.63029128517163-0.000291285171633682
304.634.65027034555288-0.0202703455528752
314.634.64881317110907-0.0188131711090742
324.634.64746074857264-0.0174607485726401
334.634.64620554764263-0.0162055476426257
344.634.64504057934887-0.0150405793488666
354.634.64395935713734-0.0139593571373373
364.634.64295586075296-0.0129558607529585
374.634.64202450271876-0.0120245027187593
384.634.64116009722476-0.0111600972247592
394.664.640357831253330.0196421687466746
404.74.671769847947560.0282301520524433
414.724.713799229045580.0062007709544174
424.734.73424498390176-0.00424498390176176
434.734.74393982472034-0.0139398247203433
444.744.74293773246293-0.00293773246293405
454.744.75272654767299-0.0127265476729876
464.744.75181167426945-0.0118116742694472
474.764.750962568375370.00903743162463044
484.884.771612242272970.108387757727032
494.884.89940391361714-0.0194039136171389
504.884.89800902437073-0.0180090243707332
514.884.89671440953536-0.0167144095353633
524.894.89551286068388-0.00551286068388368
534.974.905116557637160.0648834423628424
544.974.98978083402013-0.0197808340201311
554.974.98835884909461-0.0183588490946143
564.974.98703908640737-0.0170390864073671
574.974.98581419750778-0.0158141975077788
584.974.98467736220335-0.0146773622033463
594.974.98362225058478-0.0136222505847829
604.974.98264298778103-0.0126429877810272
614.974.98173412124791-0.0117341212479065
624.974.98089059040832-0.0108905904083203
634.974.9801076984749-0.0101076984749033
644.984.979381086298270.000618913701730506
6554.9894255781510.0105744218490011
665.035.010185741673430.0198142583265728
675.045.04161012937225-0.00161012937224836
685.045.05149438199309-0.0114943819930868
695.055.05066808529065-0.000668085290648435
705.055.06062005863963-0.0106200586396339
715.065.059856614424980.000143385575017696
725.065.06986692198461-0.00986692198461281

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 4 & 4 & 0 \tabularnewline
4 & 4 & 4 & 0 \tabularnewline
5 & 4 & 4 & 0 \tabularnewline
6 & 4 & 4 & 0 \tabularnewline
7 & 4 & 4 & 0 \tabularnewline
8 & 4 & 4 & 0 \tabularnewline
9 & 4.06 & 4 & 0.0599999999999996 \tabularnewline
10 & 4.07 & 4.0643132203346 & 0.00568677966539788 \tabularnewline
11 & 4.07 & 4.07472202589612 & -0.00472202589612269 \tabularnewline
12 & 4.07 & 4.0743825735942 & -0.00438257359419492 \tabularnewline
13 & 4.07 & 4.07406752350179 & -0.00406752350178863 \tabularnewline
14 & 4.07 & 4.07377512141713 & -0.00377512141713154 \tabularnewline
15 & 4.3 & 4.07350373924277 & 0.226496260757234 \tabularnewline
16 & 4.44 & 4.31978587720292 & 0.120214122797075 \tabularnewline
17 & 4.52 & 4.46842771051884 & 0.051572289481161 \tabularnewline
18 & 4.52 & 4.55213508798037 & -0.0321350879803735 \tabularnewline
19 & 4.52 & 4.54982499273152 & -0.0298249927315206 \tabularnewline
20 & 4.53 & 4.5476809633127 & -0.0176809633127037 \tabularnewline
21 & 4.53 & 4.55640993180444 & -0.0264099318044426 \tabularnewline
22 & 4.53 & 4.55451140088954 & -0.0245114008895362 \tabularnewline
23 & 4.53 & 4.5527493496771 & -0.0227493496770972 \tabularnewline
24 & 4.53 & 4.55111396704999 & -0.0211139670499927 \tabularnewline
25 & 4.53 & 4.54959614718292 & -0.0195961471829236 \tabularnewline
26 & 4.53 & 4.5481874388411 & -0.0181874388411032 \tabularnewline
27 & 4.53 & 4.54687999832371 & -0.0168799983237067 \tabularnewline
28 & 4.61 & 4.54566654579008 & 0.0643334542099252 \tabularnewline
29 & 4.63 & 4.63029128517163 & -0.000291285171633682 \tabularnewline
30 & 4.63 & 4.65027034555288 & -0.0202703455528752 \tabularnewline
31 & 4.63 & 4.64881317110907 & -0.0188131711090742 \tabularnewline
32 & 4.63 & 4.64746074857264 & -0.0174607485726401 \tabularnewline
33 & 4.63 & 4.64620554764263 & -0.0162055476426257 \tabularnewline
34 & 4.63 & 4.64504057934887 & -0.0150405793488666 \tabularnewline
35 & 4.63 & 4.64395935713734 & -0.0139593571373373 \tabularnewline
36 & 4.63 & 4.64295586075296 & -0.0129558607529585 \tabularnewline
37 & 4.63 & 4.64202450271876 & -0.0120245027187593 \tabularnewline
38 & 4.63 & 4.64116009722476 & -0.0111600972247592 \tabularnewline
39 & 4.66 & 4.64035783125333 & 0.0196421687466746 \tabularnewline
40 & 4.7 & 4.67176984794756 & 0.0282301520524433 \tabularnewline
41 & 4.72 & 4.71379922904558 & 0.0062007709544174 \tabularnewline
42 & 4.73 & 4.73424498390176 & -0.00424498390176176 \tabularnewline
43 & 4.73 & 4.74393982472034 & -0.0139398247203433 \tabularnewline
44 & 4.74 & 4.74293773246293 & -0.00293773246293405 \tabularnewline
45 & 4.74 & 4.75272654767299 & -0.0127265476729876 \tabularnewline
46 & 4.74 & 4.75181167426945 & -0.0118116742694472 \tabularnewline
47 & 4.76 & 4.75096256837537 & 0.00903743162463044 \tabularnewline
48 & 4.88 & 4.77161224227297 & 0.108387757727032 \tabularnewline
49 & 4.88 & 4.89940391361714 & -0.0194039136171389 \tabularnewline
50 & 4.88 & 4.89800902437073 & -0.0180090243707332 \tabularnewline
51 & 4.88 & 4.89671440953536 & -0.0167144095353633 \tabularnewline
52 & 4.89 & 4.89551286068388 & -0.00551286068388368 \tabularnewline
53 & 4.97 & 4.90511655763716 & 0.0648834423628424 \tabularnewline
54 & 4.97 & 4.98978083402013 & -0.0197808340201311 \tabularnewline
55 & 4.97 & 4.98835884909461 & -0.0183588490946143 \tabularnewline
56 & 4.97 & 4.98703908640737 & -0.0170390864073671 \tabularnewline
57 & 4.97 & 4.98581419750778 & -0.0158141975077788 \tabularnewline
58 & 4.97 & 4.98467736220335 & -0.0146773622033463 \tabularnewline
59 & 4.97 & 4.98362225058478 & -0.0136222505847829 \tabularnewline
60 & 4.97 & 4.98264298778103 & -0.0126429877810272 \tabularnewline
61 & 4.97 & 4.98173412124791 & -0.0117341212479065 \tabularnewline
62 & 4.97 & 4.98089059040832 & -0.0108905904083203 \tabularnewline
63 & 4.97 & 4.9801076984749 & -0.0101076984749033 \tabularnewline
64 & 4.98 & 4.97938108629827 & 0.000618913701730506 \tabularnewline
65 & 5 & 4.989425578151 & 0.0105744218490011 \tabularnewline
66 & 5.03 & 5.01018574167343 & 0.0198142583265728 \tabularnewline
67 & 5.04 & 5.04161012937225 & -0.00161012937224836 \tabularnewline
68 & 5.04 & 5.05149438199309 & -0.0114943819930868 \tabularnewline
69 & 5.05 & 5.05066808529065 & -0.000668085290648435 \tabularnewline
70 & 5.05 & 5.06062005863963 & -0.0106200586396339 \tabularnewline
71 & 5.06 & 5.05985661442498 & 0.000143385575017696 \tabularnewline
72 & 5.06 & 5.06986692198461 & -0.00986692198461281 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167210&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]4[/C][C]4[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]4[/C][C]4[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]4[/C][C]4[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]4[/C][C]4[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]4[/C][C]4[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]4[/C][C]4[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]4.06[/C][C]4[/C][C]0.0599999999999996[/C][/ROW]
[ROW][C]10[/C][C]4.07[/C][C]4.0643132203346[/C][C]0.00568677966539788[/C][/ROW]
[ROW][C]11[/C][C]4.07[/C][C]4.07472202589612[/C][C]-0.00472202589612269[/C][/ROW]
[ROW][C]12[/C][C]4.07[/C][C]4.0743825735942[/C][C]-0.00438257359419492[/C][/ROW]
[ROW][C]13[/C][C]4.07[/C][C]4.07406752350179[/C][C]-0.00406752350178863[/C][/ROW]
[ROW][C]14[/C][C]4.07[/C][C]4.07377512141713[/C][C]-0.00377512141713154[/C][/ROW]
[ROW][C]15[/C][C]4.3[/C][C]4.07350373924277[/C][C]0.226496260757234[/C][/ROW]
[ROW][C]16[/C][C]4.44[/C][C]4.31978587720292[/C][C]0.120214122797075[/C][/ROW]
[ROW][C]17[/C][C]4.52[/C][C]4.46842771051884[/C][C]0.051572289481161[/C][/ROW]
[ROW][C]18[/C][C]4.52[/C][C]4.55213508798037[/C][C]-0.0321350879803735[/C][/ROW]
[ROW][C]19[/C][C]4.52[/C][C]4.54982499273152[/C][C]-0.0298249927315206[/C][/ROW]
[ROW][C]20[/C][C]4.53[/C][C]4.5476809633127[/C][C]-0.0176809633127037[/C][/ROW]
[ROW][C]21[/C][C]4.53[/C][C]4.55640993180444[/C][C]-0.0264099318044426[/C][/ROW]
[ROW][C]22[/C][C]4.53[/C][C]4.55451140088954[/C][C]-0.0245114008895362[/C][/ROW]
[ROW][C]23[/C][C]4.53[/C][C]4.5527493496771[/C][C]-0.0227493496770972[/C][/ROW]
[ROW][C]24[/C][C]4.53[/C][C]4.55111396704999[/C][C]-0.0211139670499927[/C][/ROW]
[ROW][C]25[/C][C]4.53[/C][C]4.54959614718292[/C][C]-0.0195961471829236[/C][/ROW]
[ROW][C]26[/C][C]4.53[/C][C]4.5481874388411[/C][C]-0.0181874388411032[/C][/ROW]
[ROW][C]27[/C][C]4.53[/C][C]4.54687999832371[/C][C]-0.0168799983237067[/C][/ROW]
[ROW][C]28[/C][C]4.61[/C][C]4.54566654579008[/C][C]0.0643334542099252[/C][/ROW]
[ROW][C]29[/C][C]4.63[/C][C]4.63029128517163[/C][C]-0.000291285171633682[/C][/ROW]
[ROW][C]30[/C][C]4.63[/C][C]4.65027034555288[/C][C]-0.0202703455528752[/C][/ROW]
[ROW][C]31[/C][C]4.63[/C][C]4.64881317110907[/C][C]-0.0188131711090742[/C][/ROW]
[ROW][C]32[/C][C]4.63[/C][C]4.64746074857264[/C][C]-0.0174607485726401[/C][/ROW]
[ROW][C]33[/C][C]4.63[/C][C]4.64620554764263[/C][C]-0.0162055476426257[/C][/ROW]
[ROW][C]34[/C][C]4.63[/C][C]4.64504057934887[/C][C]-0.0150405793488666[/C][/ROW]
[ROW][C]35[/C][C]4.63[/C][C]4.64395935713734[/C][C]-0.0139593571373373[/C][/ROW]
[ROW][C]36[/C][C]4.63[/C][C]4.64295586075296[/C][C]-0.0129558607529585[/C][/ROW]
[ROW][C]37[/C][C]4.63[/C][C]4.64202450271876[/C][C]-0.0120245027187593[/C][/ROW]
[ROW][C]38[/C][C]4.63[/C][C]4.64116009722476[/C][C]-0.0111600972247592[/C][/ROW]
[ROW][C]39[/C][C]4.66[/C][C]4.64035783125333[/C][C]0.0196421687466746[/C][/ROW]
[ROW][C]40[/C][C]4.7[/C][C]4.67176984794756[/C][C]0.0282301520524433[/C][/ROW]
[ROW][C]41[/C][C]4.72[/C][C]4.71379922904558[/C][C]0.0062007709544174[/C][/ROW]
[ROW][C]42[/C][C]4.73[/C][C]4.73424498390176[/C][C]-0.00424498390176176[/C][/ROW]
[ROW][C]43[/C][C]4.73[/C][C]4.74393982472034[/C][C]-0.0139398247203433[/C][/ROW]
[ROW][C]44[/C][C]4.74[/C][C]4.74293773246293[/C][C]-0.00293773246293405[/C][/ROW]
[ROW][C]45[/C][C]4.74[/C][C]4.75272654767299[/C][C]-0.0127265476729876[/C][/ROW]
[ROW][C]46[/C][C]4.74[/C][C]4.75181167426945[/C][C]-0.0118116742694472[/C][/ROW]
[ROW][C]47[/C][C]4.76[/C][C]4.75096256837537[/C][C]0.00903743162463044[/C][/ROW]
[ROW][C]48[/C][C]4.88[/C][C]4.77161224227297[/C][C]0.108387757727032[/C][/ROW]
[ROW][C]49[/C][C]4.88[/C][C]4.89940391361714[/C][C]-0.0194039136171389[/C][/ROW]
[ROW][C]50[/C][C]4.88[/C][C]4.89800902437073[/C][C]-0.0180090243707332[/C][/ROW]
[ROW][C]51[/C][C]4.88[/C][C]4.89671440953536[/C][C]-0.0167144095353633[/C][/ROW]
[ROW][C]52[/C][C]4.89[/C][C]4.89551286068388[/C][C]-0.00551286068388368[/C][/ROW]
[ROW][C]53[/C][C]4.97[/C][C]4.90511655763716[/C][C]0.0648834423628424[/C][/ROW]
[ROW][C]54[/C][C]4.97[/C][C]4.98978083402013[/C][C]-0.0197808340201311[/C][/ROW]
[ROW][C]55[/C][C]4.97[/C][C]4.98835884909461[/C][C]-0.0183588490946143[/C][/ROW]
[ROW][C]56[/C][C]4.97[/C][C]4.98703908640737[/C][C]-0.0170390864073671[/C][/ROW]
[ROW][C]57[/C][C]4.97[/C][C]4.98581419750778[/C][C]-0.0158141975077788[/C][/ROW]
[ROW][C]58[/C][C]4.97[/C][C]4.98467736220335[/C][C]-0.0146773622033463[/C][/ROW]
[ROW][C]59[/C][C]4.97[/C][C]4.98362225058478[/C][C]-0.0136222505847829[/C][/ROW]
[ROW][C]60[/C][C]4.97[/C][C]4.98264298778103[/C][C]-0.0126429877810272[/C][/ROW]
[ROW][C]61[/C][C]4.97[/C][C]4.98173412124791[/C][C]-0.0117341212479065[/C][/ROW]
[ROW][C]62[/C][C]4.97[/C][C]4.98089059040832[/C][C]-0.0108905904083203[/C][/ROW]
[ROW][C]63[/C][C]4.97[/C][C]4.9801076984749[/C][C]-0.0101076984749033[/C][/ROW]
[ROW][C]64[/C][C]4.98[/C][C]4.97938108629827[/C][C]0.000618913701730506[/C][/ROW]
[ROW][C]65[/C][C]5[/C][C]4.989425578151[/C][C]0.0105744218490011[/C][/ROW]
[ROW][C]66[/C][C]5.03[/C][C]5.01018574167343[/C][C]0.0198142583265728[/C][/ROW]
[ROW][C]67[/C][C]5.04[/C][C]5.04161012937225[/C][C]-0.00161012937224836[/C][/ROW]
[ROW][C]68[/C][C]5.04[/C][C]5.05149438199309[/C][C]-0.0114943819930868[/C][/ROW]
[ROW][C]69[/C][C]5.05[/C][C]5.05066808529065[/C][C]-0.000668085290648435[/C][/ROW]
[ROW][C]70[/C][C]5.05[/C][C]5.06062005863963[/C][C]-0.0106200586396339[/C][/ROW]
[ROW][C]71[/C][C]5.06[/C][C]5.05985661442498[/C][C]0.000143385575017696[/C][/ROW]
[ROW][C]72[/C][C]5.06[/C][C]5.06986692198461[/C][C]-0.00986692198461281[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167210&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167210&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
3440
4440
5440
6440
7440
8440
94.0640.0599999999999996
104.074.06431322033460.00568677966539788
114.074.07472202589612-0.00472202589612269
124.074.0743825735942-0.00438257359419492
134.074.07406752350179-0.00406752350178863
144.074.07377512141713-0.00377512141713154
154.34.073503739242770.226496260757234
164.444.319785877202920.120214122797075
174.524.468427710518840.051572289481161
184.524.55213508798037-0.0321350879803735
194.524.54982499273152-0.0298249927315206
204.534.5476809633127-0.0176809633127037
214.534.55640993180444-0.0264099318044426
224.534.55451140088954-0.0245114008895362
234.534.5527493496771-0.0227493496770972
244.534.55111396704999-0.0211139670499927
254.534.54959614718292-0.0195961471829236
264.534.5481874388411-0.0181874388411032
274.534.54687999832371-0.0168799983237067
284.614.545666545790080.0643334542099252
294.634.63029128517163-0.000291285171633682
304.634.65027034555288-0.0202703455528752
314.634.64881317110907-0.0188131711090742
324.634.64746074857264-0.0174607485726401
334.634.64620554764263-0.0162055476426257
344.634.64504057934887-0.0150405793488666
354.634.64395935713734-0.0139593571373373
364.634.64295586075296-0.0129558607529585
374.634.64202450271876-0.0120245027187593
384.634.64116009722476-0.0111600972247592
394.664.640357831253330.0196421687466746
404.74.671769847947560.0282301520524433
414.724.713799229045580.0062007709544174
424.734.73424498390176-0.00424498390176176
434.734.74393982472034-0.0139398247203433
444.744.74293773246293-0.00293773246293405
454.744.75272654767299-0.0127265476729876
464.744.75181167426945-0.0118116742694472
474.764.750962568375370.00903743162463044
484.884.771612242272970.108387757727032
494.884.89940391361714-0.0194039136171389
504.884.89800902437073-0.0180090243707332
514.884.89671440953536-0.0167144095353633
524.894.89551286068388-0.00551286068388368
534.974.905116557637160.0648834423628424
544.974.98978083402013-0.0197808340201311
554.974.98835884909461-0.0183588490946143
564.974.98703908640737-0.0170390864073671
574.974.98581419750778-0.0158141975077788
584.974.98467736220335-0.0146773622033463
594.974.98362225058478-0.0136222505847829
604.974.98264298778103-0.0126429877810272
614.974.98173412124791-0.0117341212479065
624.974.98089059040832-0.0108905904083203
634.974.9801076984749-0.0101076984749033
644.984.979381086298270.000618913701730506
6554.9894255781510.0105744218490011
665.035.010185741673430.0198142583265728
675.045.04161012937225-0.00161012937224836
685.045.05149438199309-0.0114943819930868
695.055.05066808529065-0.000668085290648435
705.055.06062005863963-0.0106200586396339
715.065.059856614424980.000143385575017696
725.065.06986692198461-0.00986692198461281







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.069157618508884.992503443936995.14581179308076
745.078315237017764.965945818513315.1906846555222
755.087472855526644.944946362954955.22999934809833
765.096630474035524.92634442949235.26691651857873
775.10578809254444.90896780970555.3026083753833
785.114945711053284.892241442404885.33764997970167
795.124103329562164.875839418660755.37236724046357
805.133260948071044.859559855344085.40696204079799
815.142418566579924.843269979313655.44156715384619
825.15157618508884.826878684876545.47627368530105
835.160733803597684.810321494767675.51114611242769
845.169891422106564.79355172748555.54623111672762

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.06915761850888 & 4.99250344393699 & 5.14581179308076 \tabularnewline
74 & 5.07831523701776 & 4.96594581851331 & 5.1906846555222 \tabularnewline
75 & 5.08747285552664 & 4.94494636295495 & 5.22999934809833 \tabularnewline
76 & 5.09663047403552 & 4.9263444294923 & 5.26691651857873 \tabularnewline
77 & 5.1057880925444 & 4.9089678097055 & 5.3026083753833 \tabularnewline
78 & 5.11494571105328 & 4.89224144240488 & 5.33764997970167 \tabularnewline
79 & 5.12410332956216 & 4.87583941866075 & 5.37236724046357 \tabularnewline
80 & 5.13326094807104 & 4.85955985534408 & 5.40696204079799 \tabularnewline
81 & 5.14241856657992 & 4.84326997931365 & 5.44156715384619 \tabularnewline
82 & 5.1515761850888 & 4.82687868487654 & 5.47627368530105 \tabularnewline
83 & 5.16073380359768 & 4.81032149476767 & 5.51114611242769 \tabularnewline
84 & 5.16989142210656 & 4.7935517274855 & 5.54623111672762 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167210&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]5.06915761850888[/C][C]4.99250344393699[/C][C]5.14581179308076[/C][/ROW]
[ROW][C]74[/C][C]5.07831523701776[/C][C]4.96594581851331[/C][C]5.1906846555222[/C][/ROW]
[ROW][C]75[/C][C]5.08747285552664[/C][C]4.94494636295495[/C][C]5.22999934809833[/C][/ROW]
[ROW][C]76[/C][C]5.09663047403552[/C][C]4.9263444294923[/C][C]5.26691651857873[/C][/ROW]
[ROW][C]77[/C][C]5.1057880925444[/C][C]4.9089678097055[/C][C]5.3026083753833[/C][/ROW]
[ROW][C]78[/C][C]5.11494571105328[/C][C]4.89224144240488[/C][C]5.33764997970167[/C][/ROW]
[ROW][C]79[/C][C]5.12410332956216[/C][C]4.87583941866075[/C][C]5.37236724046357[/C][/ROW]
[ROW][C]80[/C][C]5.13326094807104[/C][C]4.85955985534408[/C][C]5.40696204079799[/C][/ROW]
[ROW][C]81[/C][C]5.14241856657992[/C][C]4.84326997931365[/C][C]5.44156715384619[/C][/ROW]
[ROW][C]82[/C][C]5.1515761850888[/C][C]4.82687868487654[/C][C]5.47627368530105[/C][/ROW]
[ROW][C]83[/C][C]5.16073380359768[/C][C]4.81032149476767[/C][C]5.51114611242769[/C][/ROW]
[ROW][C]84[/C][C]5.16989142210656[/C][C]4.7935517274855[/C][C]5.54623111672762[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167210&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167210&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
735.069157618508884.992503443936995.14581179308076
745.078315237017764.965945818513315.1906846555222
755.087472855526644.944946362954955.22999934809833
765.096630474035524.92634442949235.26691651857873
775.10578809254444.90896780970555.3026083753833
785.114945711053284.892241442404885.33764997970167
795.124103329562164.875839418660755.37236724046357
805.133260948071044.859559855344085.40696204079799
815.142418566579924.843269979313655.44156715384619
825.15157618508884.826878684876545.47627368530105
835.160733803597684.810321494767675.51114611242769
845.169891422106564.79355172748555.54623111672762



Parameters (Session):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')