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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, 29 Nov 2011 08:45:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Nov/29/t1322574427dq30uuodvpwk957.htm/, Retrieved Thu, 25 Apr 2024 05:49:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=148351, Retrieved Thu, 25 Apr 2024 05:49:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact82
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Structural Time Series Models] [] [2011-11-29 13:23:42] [80bca13c5f9401fbb753952fd2952f4a]
- RMPD  [Exponential Smoothing] [] [2011-11-29 13:28:23] [80bca13c5f9401fbb753952fd2952f4a]
-    D      [Exponential Smoothing] [] [2011-11-29 13:45:43] [204816f6f70a8d342ddc2b9d4f4a80d3] [Current]
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Dataseries X:
6,11
6,13
6,15
6,15
6,16
6,18
6,21
6,22
6,23
6,26
6,28
6,28
6,29
6,32
6,36
6,37
6,38
6,38
6,4
6,41
6,42
6,43
6,44
6,47
6,47
6,48
6,51
6,54
6,56
6,57
6,6
6,62
6,65
6,71
6,76
6,78
6,8
6,83
6,86
6,86
6,87
6,88
6,9
6,92
6,93
6,94
6,96
6,98
6,99
7,01
7,06
7,07
7,08
7,08
7,1
7,11
7,22
7,24
7,25
7,26
7,27
7,3
7,32
7,34
7,35
7,36
7,39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148351&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148351&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148351&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.99994898197325
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.99994898197325 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148351&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]0.99994898197325[/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=148351&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148351&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
alpha0.99994898197325
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
26.136.110.0199999999999996
36.156.129998979639470.0200010203605352
46.156.149998979587411.02041259175678e-06
56.166.149999999947940.0100000000520595
66.186.159999489819730.02000051018027
76.216.179998979613440.0300010203865639
86.226.209998469407140.0100015305928602
96.236.219999489741640.0100005102583562
106.266.22999948979370.0300005102062997
116.286.259998469433170.0200015305668328
126.286.279998979561381.02043862160173e-06
136.296.279999999947940.0100000000520604
146.326.289999489819730.0300005101802707
156.366.319998469433170.0400015305668306
166.376.359997959200840.0100020407991561
176.386.369999489715610.0100005102843852
186.386.37999948979375.10206301207461e-07
196.46.379999999973970.0200000000260303
206.416.399998979639460.0100010203605363
216.426.409999489767680.0100005102323237
226.436.41999948979370.0100005102062983
236.446.42999948979370.0100005102062983
246.476.43999948979370.030000510206297
256.476.469998469433171.53056683238617e-06
266.486.469999999921910.0100000000780875
276.516.479999489819730.0300005101802707
286.546.509998469433170.0300015305668309
296.566.539998469381110.020001530618889
306.576.559998979561380.0100010204386249
316.66.569999489767670.0300005102323277
326.626.599998469433170.0200015305668337
336.656.619998979561380.0300010204386219
346.716.649998469407140.0600015305928627
356.766.70999693884030.0500030611596927
366.786.759997448942490.0200025510575124
376.86.779998979509320.0200010204906844
386.836.79999897958740.0300010204125991
396.866.829998469407140.0300015305928625
406.866.859998469381111.53061889029971e-06
416.876.859999999921910.0100000000780893
426.886.869999489819730.0100005101802711
436.96.87999948979370.0200005102062963
446.926.899998979613440.0200010203865642
456.936.91999897958740.0100010204125933
466.946.929999489767670.0100005102323273
476.966.93999948979370.0200005102062981
486.986.959998979613440.020001020386565
496.996.979998979587410.0100010204125933
507.016.989999489767670.0200005102323262
517.067.009998979613430.0500010203865662
527.077.05999744904660.0100025509533967
537.087.069999489689590.0100005103104115
547.087.07999948979375.10206302095639e-07
557.17.079999999973970.0200000000260294
567.117.099998979639460.0100010203605372
577.227.109999489767680.110000510232323
587.247.219994387991030.0200056120089744
597.257.239998979353150.0100010206468486
607.267.249999489767660.0100005102323388
617.277.25999948979370.0100005102062983
627.37.26999948979370.0300005102062979
637.327.299998469433170.0200015305668328
647.347.319998979561380.0200010204386212
657.357.33999897958740.010001020412596
667.367.349999489767670.0100005102323273
677.397.35999948979370.0300005102062979

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 6.13 & 6.11 & 0.0199999999999996 \tabularnewline
3 & 6.15 & 6.12999897963947 & 0.0200010203605352 \tabularnewline
4 & 6.15 & 6.14999897958741 & 1.02041259175678e-06 \tabularnewline
5 & 6.16 & 6.14999999994794 & 0.0100000000520595 \tabularnewline
6 & 6.18 & 6.15999948981973 & 0.02000051018027 \tabularnewline
7 & 6.21 & 6.17999897961344 & 0.0300010203865639 \tabularnewline
8 & 6.22 & 6.20999846940714 & 0.0100015305928602 \tabularnewline
9 & 6.23 & 6.21999948974164 & 0.0100005102583562 \tabularnewline
10 & 6.26 & 6.2299994897937 & 0.0300005102062997 \tabularnewline
11 & 6.28 & 6.25999846943317 & 0.0200015305668328 \tabularnewline
12 & 6.28 & 6.27999897956138 & 1.02043862160173e-06 \tabularnewline
13 & 6.29 & 6.27999999994794 & 0.0100000000520604 \tabularnewline
14 & 6.32 & 6.28999948981973 & 0.0300005101802707 \tabularnewline
15 & 6.36 & 6.31999846943317 & 0.0400015305668306 \tabularnewline
16 & 6.37 & 6.35999795920084 & 0.0100020407991561 \tabularnewline
17 & 6.38 & 6.36999948971561 & 0.0100005102843852 \tabularnewline
18 & 6.38 & 6.3799994897937 & 5.10206301207461e-07 \tabularnewline
19 & 6.4 & 6.37999999997397 & 0.0200000000260303 \tabularnewline
20 & 6.41 & 6.39999897963946 & 0.0100010203605363 \tabularnewline
21 & 6.42 & 6.40999948976768 & 0.0100005102323237 \tabularnewline
22 & 6.43 & 6.4199994897937 & 0.0100005102062983 \tabularnewline
23 & 6.44 & 6.4299994897937 & 0.0100005102062983 \tabularnewline
24 & 6.47 & 6.4399994897937 & 0.030000510206297 \tabularnewline
25 & 6.47 & 6.46999846943317 & 1.53056683238617e-06 \tabularnewline
26 & 6.48 & 6.46999999992191 & 0.0100000000780875 \tabularnewline
27 & 6.51 & 6.47999948981973 & 0.0300005101802707 \tabularnewline
28 & 6.54 & 6.50999846943317 & 0.0300015305668309 \tabularnewline
29 & 6.56 & 6.53999846938111 & 0.020001530618889 \tabularnewline
30 & 6.57 & 6.55999897956138 & 0.0100010204386249 \tabularnewline
31 & 6.6 & 6.56999948976767 & 0.0300005102323277 \tabularnewline
32 & 6.62 & 6.59999846943317 & 0.0200015305668337 \tabularnewline
33 & 6.65 & 6.61999897956138 & 0.0300010204386219 \tabularnewline
34 & 6.71 & 6.64999846940714 & 0.0600015305928627 \tabularnewline
35 & 6.76 & 6.7099969388403 & 0.0500030611596927 \tabularnewline
36 & 6.78 & 6.75999744894249 & 0.0200025510575124 \tabularnewline
37 & 6.8 & 6.77999897950932 & 0.0200010204906844 \tabularnewline
38 & 6.83 & 6.7999989795874 & 0.0300010204125991 \tabularnewline
39 & 6.86 & 6.82999846940714 & 0.0300015305928625 \tabularnewline
40 & 6.86 & 6.85999846938111 & 1.53061889029971e-06 \tabularnewline
41 & 6.87 & 6.85999999992191 & 0.0100000000780893 \tabularnewline
42 & 6.88 & 6.86999948981973 & 0.0100005101802711 \tabularnewline
43 & 6.9 & 6.8799994897937 & 0.0200005102062963 \tabularnewline
44 & 6.92 & 6.89999897961344 & 0.0200010203865642 \tabularnewline
45 & 6.93 & 6.9199989795874 & 0.0100010204125933 \tabularnewline
46 & 6.94 & 6.92999948976767 & 0.0100005102323273 \tabularnewline
47 & 6.96 & 6.9399994897937 & 0.0200005102062981 \tabularnewline
48 & 6.98 & 6.95999897961344 & 0.020001020386565 \tabularnewline
49 & 6.99 & 6.97999897958741 & 0.0100010204125933 \tabularnewline
50 & 7.01 & 6.98999948976767 & 0.0200005102323262 \tabularnewline
51 & 7.06 & 7.00999897961343 & 0.0500010203865662 \tabularnewline
52 & 7.07 & 7.0599974490466 & 0.0100025509533967 \tabularnewline
53 & 7.08 & 7.06999948968959 & 0.0100005103104115 \tabularnewline
54 & 7.08 & 7.0799994897937 & 5.10206302095639e-07 \tabularnewline
55 & 7.1 & 7.07999999997397 & 0.0200000000260294 \tabularnewline
56 & 7.11 & 7.09999897963946 & 0.0100010203605372 \tabularnewline
57 & 7.22 & 7.10999948976768 & 0.110000510232323 \tabularnewline
58 & 7.24 & 7.21999438799103 & 0.0200056120089744 \tabularnewline
59 & 7.25 & 7.23999897935315 & 0.0100010206468486 \tabularnewline
60 & 7.26 & 7.24999948976766 & 0.0100005102323388 \tabularnewline
61 & 7.27 & 7.2599994897937 & 0.0100005102062983 \tabularnewline
62 & 7.3 & 7.2699994897937 & 0.0300005102062979 \tabularnewline
63 & 7.32 & 7.29999846943317 & 0.0200015305668328 \tabularnewline
64 & 7.34 & 7.31999897956138 & 0.0200010204386212 \tabularnewline
65 & 7.35 & 7.3399989795874 & 0.010001020412596 \tabularnewline
66 & 7.36 & 7.34999948976767 & 0.0100005102323273 \tabularnewline
67 & 7.39 & 7.3599994897937 & 0.0300005102062979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148351&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]6.13[/C][C]6.11[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]3[/C][C]6.15[/C][C]6.12999897963947[/C][C]0.0200010203605352[/C][/ROW]
[ROW][C]4[/C][C]6.15[/C][C]6.14999897958741[/C][C]1.02041259175678e-06[/C][/ROW]
[ROW][C]5[/C][C]6.16[/C][C]6.14999999994794[/C][C]0.0100000000520595[/C][/ROW]
[ROW][C]6[/C][C]6.18[/C][C]6.15999948981973[/C][C]0.02000051018027[/C][/ROW]
[ROW][C]7[/C][C]6.21[/C][C]6.17999897961344[/C][C]0.0300010203865639[/C][/ROW]
[ROW][C]8[/C][C]6.22[/C][C]6.20999846940714[/C][C]0.0100015305928602[/C][/ROW]
[ROW][C]9[/C][C]6.23[/C][C]6.21999948974164[/C][C]0.0100005102583562[/C][/ROW]
[ROW][C]10[/C][C]6.26[/C][C]6.2299994897937[/C][C]0.0300005102062997[/C][/ROW]
[ROW][C]11[/C][C]6.28[/C][C]6.25999846943317[/C][C]0.0200015305668328[/C][/ROW]
[ROW][C]12[/C][C]6.28[/C][C]6.27999897956138[/C][C]1.02043862160173e-06[/C][/ROW]
[ROW][C]13[/C][C]6.29[/C][C]6.27999999994794[/C][C]0.0100000000520604[/C][/ROW]
[ROW][C]14[/C][C]6.32[/C][C]6.28999948981973[/C][C]0.0300005101802707[/C][/ROW]
[ROW][C]15[/C][C]6.36[/C][C]6.31999846943317[/C][C]0.0400015305668306[/C][/ROW]
[ROW][C]16[/C][C]6.37[/C][C]6.35999795920084[/C][C]0.0100020407991561[/C][/ROW]
[ROW][C]17[/C][C]6.38[/C][C]6.36999948971561[/C][C]0.0100005102843852[/C][/ROW]
[ROW][C]18[/C][C]6.38[/C][C]6.3799994897937[/C][C]5.10206301207461e-07[/C][/ROW]
[ROW][C]19[/C][C]6.4[/C][C]6.37999999997397[/C][C]0.0200000000260303[/C][/ROW]
[ROW][C]20[/C][C]6.41[/C][C]6.39999897963946[/C][C]0.0100010203605363[/C][/ROW]
[ROW][C]21[/C][C]6.42[/C][C]6.40999948976768[/C][C]0.0100005102323237[/C][/ROW]
[ROW][C]22[/C][C]6.43[/C][C]6.4199994897937[/C][C]0.0100005102062983[/C][/ROW]
[ROW][C]23[/C][C]6.44[/C][C]6.4299994897937[/C][C]0.0100005102062983[/C][/ROW]
[ROW][C]24[/C][C]6.47[/C][C]6.4399994897937[/C][C]0.030000510206297[/C][/ROW]
[ROW][C]25[/C][C]6.47[/C][C]6.46999846943317[/C][C]1.53056683238617e-06[/C][/ROW]
[ROW][C]26[/C][C]6.48[/C][C]6.46999999992191[/C][C]0.0100000000780875[/C][/ROW]
[ROW][C]27[/C][C]6.51[/C][C]6.47999948981973[/C][C]0.0300005101802707[/C][/ROW]
[ROW][C]28[/C][C]6.54[/C][C]6.50999846943317[/C][C]0.0300015305668309[/C][/ROW]
[ROW][C]29[/C][C]6.56[/C][C]6.53999846938111[/C][C]0.020001530618889[/C][/ROW]
[ROW][C]30[/C][C]6.57[/C][C]6.55999897956138[/C][C]0.0100010204386249[/C][/ROW]
[ROW][C]31[/C][C]6.6[/C][C]6.56999948976767[/C][C]0.0300005102323277[/C][/ROW]
[ROW][C]32[/C][C]6.62[/C][C]6.59999846943317[/C][C]0.0200015305668337[/C][/ROW]
[ROW][C]33[/C][C]6.65[/C][C]6.61999897956138[/C][C]0.0300010204386219[/C][/ROW]
[ROW][C]34[/C][C]6.71[/C][C]6.64999846940714[/C][C]0.0600015305928627[/C][/ROW]
[ROW][C]35[/C][C]6.76[/C][C]6.7099969388403[/C][C]0.0500030611596927[/C][/ROW]
[ROW][C]36[/C][C]6.78[/C][C]6.75999744894249[/C][C]0.0200025510575124[/C][/ROW]
[ROW][C]37[/C][C]6.8[/C][C]6.77999897950932[/C][C]0.0200010204906844[/C][/ROW]
[ROW][C]38[/C][C]6.83[/C][C]6.7999989795874[/C][C]0.0300010204125991[/C][/ROW]
[ROW][C]39[/C][C]6.86[/C][C]6.82999846940714[/C][C]0.0300015305928625[/C][/ROW]
[ROW][C]40[/C][C]6.86[/C][C]6.85999846938111[/C][C]1.53061889029971e-06[/C][/ROW]
[ROW][C]41[/C][C]6.87[/C][C]6.85999999992191[/C][C]0.0100000000780893[/C][/ROW]
[ROW][C]42[/C][C]6.88[/C][C]6.86999948981973[/C][C]0.0100005101802711[/C][/ROW]
[ROW][C]43[/C][C]6.9[/C][C]6.8799994897937[/C][C]0.0200005102062963[/C][/ROW]
[ROW][C]44[/C][C]6.92[/C][C]6.89999897961344[/C][C]0.0200010203865642[/C][/ROW]
[ROW][C]45[/C][C]6.93[/C][C]6.9199989795874[/C][C]0.0100010204125933[/C][/ROW]
[ROW][C]46[/C][C]6.94[/C][C]6.92999948976767[/C][C]0.0100005102323273[/C][/ROW]
[ROW][C]47[/C][C]6.96[/C][C]6.9399994897937[/C][C]0.0200005102062981[/C][/ROW]
[ROW][C]48[/C][C]6.98[/C][C]6.95999897961344[/C][C]0.020001020386565[/C][/ROW]
[ROW][C]49[/C][C]6.99[/C][C]6.97999897958741[/C][C]0.0100010204125933[/C][/ROW]
[ROW][C]50[/C][C]7.01[/C][C]6.98999948976767[/C][C]0.0200005102323262[/C][/ROW]
[ROW][C]51[/C][C]7.06[/C][C]7.00999897961343[/C][C]0.0500010203865662[/C][/ROW]
[ROW][C]52[/C][C]7.07[/C][C]7.0599974490466[/C][C]0.0100025509533967[/C][/ROW]
[ROW][C]53[/C][C]7.08[/C][C]7.06999948968959[/C][C]0.0100005103104115[/C][/ROW]
[ROW][C]54[/C][C]7.08[/C][C]7.0799994897937[/C][C]5.10206302095639e-07[/C][/ROW]
[ROW][C]55[/C][C]7.1[/C][C]7.07999999997397[/C][C]0.0200000000260294[/C][/ROW]
[ROW][C]56[/C][C]7.11[/C][C]7.09999897963946[/C][C]0.0100010203605372[/C][/ROW]
[ROW][C]57[/C][C]7.22[/C][C]7.10999948976768[/C][C]0.110000510232323[/C][/ROW]
[ROW][C]58[/C][C]7.24[/C][C]7.21999438799103[/C][C]0.0200056120089744[/C][/ROW]
[ROW][C]59[/C][C]7.25[/C][C]7.23999897935315[/C][C]0.0100010206468486[/C][/ROW]
[ROW][C]60[/C][C]7.26[/C][C]7.24999948976766[/C][C]0.0100005102323388[/C][/ROW]
[ROW][C]61[/C][C]7.27[/C][C]7.2599994897937[/C][C]0.0100005102062983[/C][/ROW]
[ROW][C]62[/C][C]7.3[/C][C]7.2699994897937[/C][C]0.0300005102062979[/C][/ROW]
[ROW][C]63[/C][C]7.32[/C][C]7.29999846943317[/C][C]0.0200015305668328[/C][/ROW]
[ROW][C]64[/C][C]7.34[/C][C]7.31999897956138[/C][C]0.0200010204386212[/C][/ROW]
[ROW][C]65[/C][C]7.35[/C][C]7.3399989795874[/C][C]0.010001020412596[/C][/ROW]
[ROW][C]66[/C][C]7.36[/C][C]7.34999948976767[/C][C]0.0100005102323273[/C][/ROW]
[ROW][C]67[/C][C]7.39[/C][C]7.3599994897937[/C][C]0.0300005102062979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148351&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148351&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
26.136.110.0199999999999996
36.156.129998979639470.0200010203605352
46.156.149998979587411.02041259175678e-06
56.166.149999999947940.0100000000520595
66.186.159999489819730.02000051018027
76.216.179998979613440.0300010203865639
86.226.209998469407140.0100015305928602
96.236.219999489741640.0100005102583562
106.266.22999948979370.0300005102062997
116.286.259998469433170.0200015305668328
126.286.279998979561381.02043862160173e-06
136.296.279999999947940.0100000000520604
146.326.289999489819730.0300005101802707
156.366.319998469433170.0400015305668306
166.376.359997959200840.0100020407991561
176.386.369999489715610.0100005102843852
186.386.37999948979375.10206301207461e-07
196.46.379999999973970.0200000000260303
206.416.399998979639460.0100010203605363
216.426.409999489767680.0100005102323237
226.436.41999948979370.0100005102062983
236.446.42999948979370.0100005102062983
246.476.43999948979370.030000510206297
256.476.469998469433171.53056683238617e-06
266.486.469999999921910.0100000000780875
276.516.479999489819730.0300005101802707
286.546.509998469433170.0300015305668309
296.566.539998469381110.020001530618889
306.576.559998979561380.0100010204386249
316.66.569999489767670.0300005102323277
326.626.599998469433170.0200015305668337
336.656.619998979561380.0300010204386219
346.716.649998469407140.0600015305928627
356.766.70999693884030.0500030611596927
366.786.759997448942490.0200025510575124
376.86.779998979509320.0200010204906844
386.836.79999897958740.0300010204125991
396.866.829998469407140.0300015305928625
406.866.859998469381111.53061889029971e-06
416.876.859999999921910.0100000000780893
426.886.869999489819730.0100005101802711
436.96.87999948979370.0200005102062963
446.926.899998979613440.0200010203865642
456.936.91999897958740.0100010204125933
466.946.929999489767670.0100005102323273
476.966.93999948979370.0200005102062981
486.986.959998979613440.020001020386565
496.996.979998979587410.0100010204125933
507.016.989999489767670.0200005102323262
517.067.009998979613430.0500010203865662
527.077.05999744904660.0100025509533967
537.087.069999489689590.0100005103104115
547.087.07999948979375.10206302095639e-07
557.17.079999999973970.0200000000260294
567.117.099998979639460.0100010203605372
577.227.109999489767680.110000510232323
587.247.219994387991030.0200056120089744
597.257.239998979353150.0100010206468486
607.267.249999489767660.0100005102323388
617.277.25999948979370.0100005102062983
627.37.26999948979370.0300005102062979
637.327.299998469433170.0200015305668328
647.347.319998979561380.0200010204386212
657.357.33999897958740.010001020412596
667.367.349999489767670.0100005102323273
677.397.35999948979370.0300005102062979







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
687.389998469433177.357404514741967.42259242412437
697.389998469433177.343904832475697.43609210639065
707.389998469433177.333546003999647.4464509348667
717.389998469433177.324813054353727.45518388451261
727.389998469433177.317119145721747.4628777931446
737.389998469433177.310163306063947.46983363280239
747.389998469433177.303766742118067.47623019674827
757.389998469433177.297812959284877.48218397958146
767.389998469433177.292221039691657.48777589917469
777.389998469433177.286932067281877.49306487158447
787.389998469433177.281901565046557.49809537381978
797.389998469433177.277094978683227.50290196018312

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
68 & 7.38999846943317 & 7.35740451474196 & 7.42259242412437 \tabularnewline
69 & 7.38999846943317 & 7.34390483247569 & 7.43609210639065 \tabularnewline
70 & 7.38999846943317 & 7.33354600399964 & 7.4464509348667 \tabularnewline
71 & 7.38999846943317 & 7.32481305435372 & 7.45518388451261 \tabularnewline
72 & 7.38999846943317 & 7.31711914572174 & 7.4628777931446 \tabularnewline
73 & 7.38999846943317 & 7.31016330606394 & 7.46983363280239 \tabularnewline
74 & 7.38999846943317 & 7.30376674211806 & 7.47623019674827 \tabularnewline
75 & 7.38999846943317 & 7.29781295928487 & 7.48218397958146 \tabularnewline
76 & 7.38999846943317 & 7.29222103969165 & 7.48777589917469 \tabularnewline
77 & 7.38999846943317 & 7.28693206728187 & 7.49306487158447 \tabularnewline
78 & 7.38999846943317 & 7.28190156504655 & 7.49809537381978 \tabularnewline
79 & 7.38999846943317 & 7.27709497868322 & 7.50290196018312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=148351&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]68[/C][C]7.38999846943317[/C][C]7.35740451474196[/C][C]7.42259242412437[/C][/ROW]
[ROW][C]69[/C][C]7.38999846943317[/C][C]7.34390483247569[/C][C]7.43609210639065[/C][/ROW]
[ROW][C]70[/C][C]7.38999846943317[/C][C]7.33354600399964[/C][C]7.4464509348667[/C][/ROW]
[ROW][C]71[/C][C]7.38999846943317[/C][C]7.32481305435372[/C][C]7.45518388451261[/C][/ROW]
[ROW][C]72[/C][C]7.38999846943317[/C][C]7.31711914572174[/C][C]7.4628777931446[/C][/ROW]
[ROW][C]73[/C][C]7.38999846943317[/C][C]7.31016330606394[/C][C]7.46983363280239[/C][/ROW]
[ROW][C]74[/C][C]7.38999846943317[/C][C]7.30376674211806[/C][C]7.47623019674827[/C][/ROW]
[ROW][C]75[/C][C]7.38999846943317[/C][C]7.29781295928487[/C][C]7.48218397958146[/C][/ROW]
[ROW][C]76[/C][C]7.38999846943317[/C][C]7.29222103969165[/C][C]7.48777589917469[/C][/ROW]
[ROW][C]77[/C][C]7.38999846943317[/C][C]7.28693206728187[/C][C]7.49306487158447[/C][/ROW]
[ROW][C]78[/C][C]7.38999846943317[/C][C]7.28190156504655[/C][C]7.49809537381978[/C][/ROW]
[ROW][C]79[/C][C]7.38999846943317[/C][C]7.27709497868322[/C][C]7.50290196018312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=148351&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=148351&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
687.389998469433177.357404514741967.42259242412437
697.389998469433177.343904832475697.43609210639065
707.389998469433177.333546003999647.4464509348667
717.389998469433177.324813054353727.45518388451261
727.389998469433177.317119145721747.4628777931446
737.389998469433177.310163306063947.46983363280239
747.389998469433177.303766742118067.47623019674827
757.389998469433177.297812959284877.48218397958146
767.389998469433177.292221039691657.48777589917469
777.389998469433177.286932067281877.49306487158447
787.389998469433177.281901565046557.49809537381978
797.389998469433177.277094978683227.50290196018312



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')