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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 03:11:02 -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/2012/Dec/17/t1355731884r78r0kfkdxz9ufm.htm/, Retrieved Fri, 26 Apr 2024 01:09:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200697, Retrieved Fri, 26 Apr 2024 01:09:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact145
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 08:11:02] [c22edb53782261805d75305d7c9e625a] [Current]
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Dataseries X:
6,81
6,8
6,8
6,85
6,85
6,85
6,85
6,85
6,85
6,86
6,86
6,88
6,88
6,88
6,91
6,91
6,91
6,91
6,99
6,99
6,99
7,02
7,02
7,05
7,05
7,05
7,05
7,1
7,1
7,1
7,1
7,12
7,13
7,18
7,24
7,24
7,24
7,27
7,27
7,27
7,27
7,3
7,3
7,57
7,76
7,94
7,94
7,96
7,96
7,98
7,99
8
8
8,04
8,04
8,04
8,04
8,04
8,07
8,07
8,07
8,07
8,11
8,11
8,12
8,11
8,13
8,15
8,16
8,2
8,2
8,2




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=200697&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=200697&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200697&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
beta0.496972732866031
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.496972732866031 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200697&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]0.496972732866031[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200697&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200697&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
beta0.496972732866031
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
36.86.790.00999999999999979
46.856.794969727328660.0550302726713392
56.856.8723182723285-0.0223182723284987
66.856.86122669953656-0.0112266995365564
76.856.85564733598681-0.00564733598680789
86.856.85284076398803-0.00284076398803101
96.856.85142898174547-0.00142898174547224
106.866.850718816782210.0092811832177917
116.866.86533131177019-0.00533131177018564
126.886.862681795190.017318204810004
136.886.89128847076276-0.0112884707627572
146.886.88567840859791-0.00567840859791158
156.916.882856394358680.0271436056413226
166.916.92634602623408-0.0163460262340838
176.916.91822249690503-0.00822249690503085
186.916.91413614014716-0.00413614014715513
196.996.912080591274710.0779194087252932
206.997.03080441277222-0.0408044127722214
216.997.01052573224382-0.0205257322438168
227.027.000325002996530.0196749970034684
237.027.04010294002648-0.0201029400264758
247.057.030112326982880.0198876730171245
257.057.06999595819254-0.019995958192542
267.057.06005851220332-0.0100585122033197
277.057.05505970590507-0.00505970590506966
287.17.052545170033930.0474548299660711
297.17.12612892656986-0.0261289265698599
307.17.11314356252558-0.0131435625255811
317.17.10661157033765-0.0066115703376477
327.127.103325800158410.0166741998415896
337.137.13161242282204-0.00161242282204022
347.187.140811092645640.0391889073543643
357.247.210286911031570.0297130889684327
367.247.2850535060581-0.0450535060581014
377.247.26266314202721-0.0226631420272101
387.277.251400178398620.0185998216013825
397.277.29064378257068-0.0206437825706764
407.277.28038438552983-0.0103843855298349
417.277.27522362907394-0.0052236290739387
427.37.272627627857580.0273723721424153
437.37.31623095044623-0.0162309504462268
447.577.308164610645950.261835389354048
457.767.708289659654270.0517103403457249
467.947.923988288813320.0160117111866782
477.948.11194567267963-0.171945672679628
487.968.02649336182355-0.0664933618235457
497.968.01344797408065-0.0534479740806484
507.987.98688578833564-0.00688578833563458
517.998.00346373928854-0.0134637392885377
5288.00677262797972-0.00677262797971778
5388.01340681654395-0.0134068165439523
548.048.006743994287070.0332560057129285
558.048.06327132233043-0.0232713223304337
568.048.05170610967447-0.0117061096744706
578.048.04588849235832-0.00588849235832001
588.048.04296207221854-0.00296207221854417
598.078.041490003093150.0285099969068536
608.078.08565869416995-0.0156586941699484
618.078.0778767501352-0.00787675013519618
628.078.0739622200944-0.0039622200944045
638.118.071993104745870.0380068952541279
648.118.13088149534807-0.0208814953480676
658.128.12050396153861-0.000503961538608877
668.118.13025350639551-0.0202535063955072
678.138.110188065972010.0198119340279881
688.158.140034056969260.0099659430307355
698.168.16498685891284-0.00498685891283657
708.28.172508526010510.0274914739894925
718.28.22617103896958-0.0261710389695793
728.28.21316474621092-0.0131647462109239

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6.8 & 6.79 & 0.00999999999999979 \tabularnewline
4 & 6.85 & 6.79496972732866 & 0.0550302726713392 \tabularnewline
5 & 6.85 & 6.8723182723285 & -0.0223182723284987 \tabularnewline
6 & 6.85 & 6.86122669953656 & -0.0112266995365564 \tabularnewline
7 & 6.85 & 6.85564733598681 & -0.00564733598680789 \tabularnewline
8 & 6.85 & 6.85284076398803 & -0.00284076398803101 \tabularnewline
9 & 6.85 & 6.85142898174547 & -0.00142898174547224 \tabularnewline
10 & 6.86 & 6.85071881678221 & 0.0092811832177917 \tabularnewline
11 & 6.86 & 6.86533131177019 & -0.00533131177018564 \tabularnewline
12 & 6.88 & 6.86268179519 & 0.017318204810004 \tabularnewline
13 & 6.88 & 6.89128847076276 & -0.0112884707627572 \tabularnewline
14 & 6.88 & 6.88567840859791 & -0.00567840859791158 \tabularnewline
15 & 6.91 & 6.88285639435868 & 0.0271436056413226 \tabularnewline
16 & 6.91 & 6.92634602623408 & -0.0163460262340838 \tabularnewline
17 & 6.91 & 6.91822249690503 & -0.00822249690503085 \tabularnewline
18 & 6.91 & 6.91413614014716 & -0.00413614014715513 \tabularnewline
19 & 6.99 & 6.91208059127471 & 0.0779194087252932 \tabularnewline
20 & 6.99 & 7.03080441277222 & -0.0408044127722214 \tabularnewline
21 & 6.99 & 7.01052573224382 & -0.0205257322438168 \tabularnewline
22 & 7.02 & 7.00032500299653 & 0.0196749970034684 \tabularnewline
23 & 7.02 & 7.04010294002648 & -0.0201029400264758 \tabularnewline
24 & 7.05 & 7.03011232698288 & 0.0198876730171245 \tabularnewline
25 & 7.05 & 7.06999595819254 & -0.019995958192542 \tabularnewline
26 & 7.05 & 7.06005851220332 & -0.0100585122033197 \tabularnewline
27 & 7.05 & 7.05505970590507 & -0.00505970590506966 \tabularnewline
28 & 7.1 & 7.05254517003393 & 0.0474548299660711 \tabularnewline
29 & 7.1 & 7.12612892656986 & -0.0261289265698599 \tabularnewline
30 & 7.1 & 7.11314356252558 & -0.0131435625255811 \tabularnewline
31 & 7.1 & 7.10661157033765 & -0.0066115703376477 \tabularnewline
32 & 7.12 & 7.10332580015841 & 0.0166741998415896 \tabularnewline
33 & 7.13 & 7.13161242282204 & -0.00161242282204022 \tabularnewline
34 & 7.18 & 7.14081109264564 & 0.0391889073543643 \tabularnewline
35 & 7.24 & 7.21028691103157 & 0.0297130889684327 \tabularnewline
36 & 7.24 & 7.2850535060581 & -0.0450535060581014 \tabularnewline
37 & 7.24 & 7.26266314202721 & -0.0226631420272101 \tabularnewline
38 & 7.27 & 7.25140017839862 & 0.0185998216013825 \tabularnewline
39 & 7.27 & 7.29064378257068 & -0.0206437825706764 \tabularnewline
40 & 7.27 & 7.28038438552983 & -0.0103843855298349 \tabularnewline
41 & 7.27 & 7.27522362907394 & -0.0052236290739387 \tabularnewline
42 & 7.3 & 7.27262762785758 & 0.0273723721424153 \tabularnewline
43 & 7.3 & 7.31623095044623 & -0.0162309504462268 \tabularnewline
44 & 7.57 & 7.30816461064595 & 0.261835389354048 \tabularnewline
45 & 7.76 & 7.70828965965427 & 0.0517103403457249 \tabularnewline
46 & 7.94 & 7.92398828881332 & 0.0160117111866782 \tabularnewline
47 & 7.94 & 8.11194567267963 & -0.171945672679628 \tabularnewline
48 & 7.96 & 8.02649336182355 & -0.0664933618235457 \tabularnewline
49 & 7.96 & 8.01344797408065 & -0.0534479740806484 \tabularnewline
50 & 7.98 & 7.98688578833564 & -0.00688578833563458 \tabularnewline
51 & 7.99 & 8.00346373928854 & -0.0134637392885377 \tabularnewline
52 & 8 & 8.00677262797972 & -0.00677262797971778 \tabularnewline
53 & 8 & 8.01340681654395 & -0.0134068165439523 \tabularnewline
54 & 8.04 & 8.00674399428707 & 0.0332560057129285 \tabularnewline
55 & 8.04 & 8.06327132233043 & -0.0232713223304337 \tabularnewline
56 & 8.04 & 8.05170610967447 & -0.0117061096744706 \tabularnewline
57 & 8.04 & 8.04588849235832 & -0.00588849235832001 \tabularnewline
58 & 8.04 & 8.04296207221854 & -0.00296207221854417 \tabularnewline
59 & 8.07 & 8.04149000309315 & 0.0285099969068536 \tabularnewline
60 & 8.07 & 8.08565869416995 & -0.0156586941699484 \tabularnewline
61 & 8.07 & 8.0778767501352 & -0.00787675013519618 \tabularnewline
62 & 8.07 & 8.0739622200944 & -0.0039622200944045 \tabularnewline
63 & 8.11 & 8.07199310474587 & 0.0380068952541279 \tabularnewline
64 & 8.11 & 8.13088149534807 & -0.0208814953480676 \tabularnewline
65 & 8.12 & 8.12050396153861 & -0.000503961538608877 \tabularnewline
66 & 8.11 & 8.13025350639551 & -0.0202535063955072 \tabularnewline
67 & 8.13 & 8.11018806597201 & 0.0198119340279881 \tabularnewline
68 & 8.15 & 8.14003405696926 & 0.0099659430307355 \tabularnewline
69 & 8.16 & 8.16498685891284 & -0.00498685891283657 \tabularnewline
70 & 8.2 & 8.17250852601051 & 0.0274914739894925 \tabularnewline
71 & 8.2 & 8.22617103896958 & -0.0261710389695793 \tabularnewline
72 & 8.2 & 8.21316474621092 & -0.0131647462109239 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200697&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]6.8[/C][C]6.79[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]6.85[/C][C]6.79496972732866[/C][C]0.0550302726713392[/C][/ROW]
[ROW][C]5[/C][C]6.85[/C][C]6.8723182723285[/C][C]-0.0223182723284987[/C][/ROW]
[ROW][C]6[/C][C]6.85[/C][C]6.86122669953656[/C][C]-0.0112266995365564[/C][/ROW]
[ROW][C]7[/C][C]6.85[/C][C]6.85564733598681[/C][C]-0.00564733598680789[/C][/ROW]
[ROW][C]8[/C][C]6.85[/C][C]6.85284076398803[/C][C]-0.00284076398803101[/C][/ROW]
[ROW][C]9[/C][C]6.85[/C][C]6.85142898174547[/C][C]-0.00142898174547224[/C][/ROW]
[ROW][C]10[/C][C]6.86[/C][C]6.85071881678221[/C][C]0.0092811832177917[/C][/ROW]
[ROW][C]11[/C][C]6.86[/C][C]6.86533131177019[/C][C]-0.00533131177018564[/C][/ROW]
[ROW][C]12[/C][C]6.88[/C][C]6.86268179519[/C][C]0.017318204810004[/C][/ROW]
[ROW][C]13[/C][C]6.88[/C][C]6.89128847076276[/C][C]-0.0112884707627572[/C][/ROW]
[ROW][C]14[/C][C]6.88[/C][C]6.88567840859791[/C][C]-0.00567840859791158[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.88285639435868[/C][C]0.0271436056413226[/C][/ROW]
[ROW][C]16[/C][C]6.91[/C][C]6.92634602623408[/C][C]-0.0163460262340838[/C][/ROW]
[ROW][C]17[/C][C]6.91[/C][C]6.91822249690503[/C][C]-0.00822249690503085[/C][/ROW]
[ROW][C]18[/C][C]6.91[/C][C]6.91413614014716[/C][C]-0.00413614014715513[/C][/ROW]
[ROW][C]19[/C][C]6.99[/C][C]6.91208059127471[/C][C]0.0779194087252932[/C][/ROW]
[ROW][C]20[/C][C]6.99[/C][C]7.03080441277222[/C][C]-0.0408044127722214[/C][/ROW]
[ROW][C]21[/C][C]6.99[/C][C]7.01052573224382[/C][C]-0.0205257322438168[/C][/ROW]
[ROW][C]22[/C][C]7.02[/C][C]7.00032500299653[/C][C]0.0196749970034684[/C][/ROW]
[ROW][C]23[/C][C]7.02[/C][C]7.04010294002648[/C][C]-0.0201029400264758[/C][/ROW]
[ROW][C]24[/C][C]7.05[/C][C]7.03011232698288[/C][C]0.0198876730171245[/C][/ROW]
[ROW][C]25[/C][C]7.05[/C][C]7.06999595819254[/C][C]-0.019995958192542[/C][/ROW]
[ROW][C]26[/C][C]7.05[/C][C]7.06005851220332[/C][C]-0.0100585122033197[/C][/ROW]
[ROW][C]27[/C][C]7.05[/C][C]7.05505970590507[/C][C]-0.00505970590506966[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.05254517003393[/C][C]0.0474548299660711[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.12612892656986[/C][C]-0.0261289265698599[/C][/ROW]
[ROW][C]30[/C][C]7.1[/C][C]7.11314356252558[/C][C]-0.0131435625255811[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]7.10661157033765[/C][C]-0.0066115703376477[/C][/ROW]
[ROW][C]32[/C][C]7.12[/C][C]7.10332580015841[/C][C]0.0166741998415896[/C][/ROW]
[ROW][C]33[/C][C]7.13[/C][C]7.13161242282204[/C][C]-0.00161242282204022[/C][/ROW]
[ROW][C]34[/C][C]7.18[/C][C]7.14081109264564[/C][C]0.0391889073543643[/C][/ROW]
[ROW][C]35[/C][C]7.24[/C][C]7.21028691103157[/C][C]0.0297130889684327[/C][/ROW]
[ROW][C]36[/C][C]7.24[/C][C]7.2850535060581[/C][C]-0.0450535060581014[/C][/ROW]
[ROW][C]37[/C][C]7.24[/C][C]7.26266314202721[/C][C]-0.0226631420272101[/C][/ROW]
[ROW][C]38[/C][C]7.27[/C][C]7.25140017839862[/C][C]0.0185998216013825[/C][/ROW]
[ROW][C]39[/C][C]7.27[/C][C]7.29064378257068[/C][C]-0.0206437825706764[/C][/ROW]
[ROW][C]40[/C][C]7.27[/C][C]7.28038438552983[/C][C]-0.0103843855298349[/C][/ROW]
[ROW][C]41[/C][C]7.27[/C][C]7.27522362907394[/C][C]-0.0052236290739387[/C][/ROW]
[ROW][C]42[/C][C]7.3[/C][C]7.27262762785758[/C][C]0.0273723721424153[/C][/ROW]
[ROW][C]43[/C][C]7.3[/C][C]7.31623095044623[/C][C]-0.0162309504462268[/C][/ROW]
[ROW][C]44[/C][C]7.57[/C][C]7.30816461064595[/C][C]0.261835389354048[/C][/ROW]
[ROW][C]45[/C][C]7.76[/C][C]7.70828965965427[/C][C]0.0517103403457249[/C][/ROW]
[ROW][C]46[/C][C]7.94[/C][C]7.92398828881332[/C][C]0.0160117111866782[/C][/ROW]
[ROW][C]47[/C][C]7.94[/C][C]8.11194567267963[/C][C]-0.171945672679628[/C][/ROW]
[ROW][C]48[/C][C]7.96[/C][C]8.02649336182355[/C][C]-0.0664933618235457[/C][/ROW]
[ROW][C]49[/C][C]7.96[/C][C]8.01344797408065[/C][C]-0.0534479740806484[/C][/ROW]
[ROW][C]50[/C][C]7.98[/C][C]7.98688578833564[/C][C]-0.00688578833563458[/C][/ROW]
[ROW][C]51[/C][C]7.99[/C][C]8.00346373928854[/C][C]-0.0134637392885377[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]8.00677262797972[/C][C]-0.00677262797971778[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]8.01340681654395[/C][C]-0.0134068165439523[/C][/ROW]
[ROW][C]54[/C][C]8.04[/C][C]8.00674399428707[/C][C]0.0332560057129285[/C][/ROW]
[ROW][C]55[/C][C]8.04[/C][C]8.06327132233043[/C][C]-0.0232713223304337[/C][/ROW]
[ROW][C]56[/C][C]8.04[/C][C]8.05170610967447[/C][C]-0.0117061096744706[/C][/ROW]
[ROW][C]57[/C][C]8.04[/C][C]8.04588849235832[/C][C]-0.00588849235832001[/C][/ROW]
[ROW][C]58[/C][C]8.04[/C][C]8.04296207221854[/C][C]-0.00296207221854417[/C][/ROW]
[ROW][C]59[/C][C]8.07[/C][C]8.04149000309315[/C][C]0.0285099969068536[/C][/ROW]
[ROW][C]60[/C][C]8.07[/C][C]8.08565869416995[/C][C]-0.0156586941699484[/C][/ROW]
[ROW][C]61[/C][C]8.07[/C][C]8.0778767501352[/C][C]-0.00787675013519618[/C][/ROW]
[ROW][C]62[/C][C]8.07[/C][C]8.0739622200944[/C][C]-0.0039622200944045[/C][/ROW]
[ROW][C]63[/C][C]8.11[/C][C]8.07199310474587[/C][C]0.0380068952541279[/C][/ROW]
[ROW][C]64[/C][C]8.11[/C][C]8.13088149534807[/C][C]-0.0208814953480676[/C][/ROW]
[ROW][C]65[/C][C]8.12[/C][C]8.12050396153861[/C][C]-0.000503961538608877[/C][/ROW]
[ROW][C]66[/C][C]8.11[/C][C]8.13025350639551[/C][C]-0.0202535063955072[/C][/ROW]
[ROW][C]67[/C][C]8.13[/C][C]8.11018806597201[/C][C]0.0198119340279881[/C][/ROW]
[ROW][C]68[/C][C]8.15[/C][C]8.14003405696926[/C][C]0.0099659430307355[/C][/ROW]
[ROW][C]69[/C][C]8.16[/C][C]8.16498685891284[/C][C]-0.00498685891283657[/C][/ROW]
[ROW][C]70[/C][C]8.2[/C][C]8.17250852601051[/C][C]0.0274914739894925[/C][/ROW]
[ROW][C]71[/C][C]8.2[/C][C]8.22617103896958[/C][C]-0.0261710389695793[/C][/ROW]
[ROW][C]72[/C][C]8.2[/C][C]8.21316474621092[/C][C]-0.0131647462109239[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200697&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200697&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
36.86.790.00999999999999979
46.856.794969727328660.0550302726713392
56.856.8723182723285-0.0223182723284987
66.856.86122669953656-0.0112266995365564
76.856.85564733598681-0.00564733598680789
86.856.85284076398803-0.00284076398803101
96.856.85142898174547-0.00142898174547224
106.866.850718816782210.0092811832177917
116.866.86533131177019-0.00533131177018564
126.886.862681795190.017318204810004
136.886.89128847076276-0.0112884707627572
146.886.88567840859791-0.00567840859791158
156.916.882856394358680.0271436056413226
166.916.92634602623408-0.0163460262340838
176.916.91822249690503-0.00822249690503085
186.916.91413614014716-0.00413614014715513
196.996.912080591274710.0779194087252932
206.997.03080441277222-0.0408044127722214
216.997.01052573224382-0.0205257322438168
227.027.000325002996530.0196749970034684
237.027.04010294002648-0.0201029400264758
247.057.030112326982880.0198876730171245
257.057.06999595819254-0.019995958192542
267.057.06005851220332-0.0100585122033197
277.057.05505970590507-0.00505970590506966
287.17.052545170033930.0474548299660711
297.17.12612892656986-0.0261289265698599
307.17.11314356252558-0.0131435625255811
317.17.10661157033765-0.0066115703376477
327.127.103325800158410.0166741998415896
337.137.13161242282204-0.00161242282204022
347.187.140811092645640.0391889073543643
357.247.210286911031570.0297130889684327
367.247.2850535060581-0.0450535060581014
377.247.26266314202721-0.0226631420272101
387.277.251400178398620.0185998216013825
397.277.29064378257068-0.0206437825706764
407.277.28038438552983-0.0103843855298349
417.277.27522362907394-0.0052236290739387
427.37.272627627857580.0273723721424153
437.37.31623095044623-0.0162309504462268
447.577.308164610645950.261835389354048
457.767.708289659654270.0517103403457249
467.947.923988288813320.0160117111866782
477.948.11194567267963-0.171945672679628
487.968.02649336182355-0.0664933618235457
497.968.01344797408065-0.0534479740806484
507.987.98688578833564-0.00688578833563458
517.998.00346373928854-0.0134637392885377
5288.00677262797972-0.00677262797971778
5388.01340681654395-0.0134068165439523
548.048.006743994287070.0332560057129285
558.048.06327132233043-0.0232713223304337
568.048.05170610967447-0.0117061096744706
578.048.04588849235832-0.00588849235832001
588.048.04296207221854-0.00296207221854417
598.078.041490003093150.0285099969068536
608.078.08565869416995-0.0156586941699484
618.078.0778767501352-0.00787675013519618
628.078.0739622200944-0.0039622200944045
638.118.071993104745870.0380068952541279
648.118.13088149534807-0.0208814953480676
658.128.12050396153861-0.000503961538608877
668.118.13025350639551-0.0202535063955072
678.138.110188065972010.0198119340279881
688.158.140034056969260.0099659430307355
698.168.16498685891284-0.00498685891283657
708.28.172508526010510.0274914739894925
718.28.22617103896958-0.0261710389695793
728.28.21316474621092-0.0131647462109239







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.206622226308998.117772147637938.29547230498006
748.213244452617998.053291424794668.37319748044132
758.219866678926987.98117981231718.45855354553686
768.226488905235977.900984373119318.55199343735263
778.233111131544977.81307562361598.65314663947404
788.239733357853967.717908847915678.76155786779225
798.246355584162957.615906783241068.87680438508485
808.252977810471957.507441789505948.99851383143796
818.259600036780947.392838743519459.12636133004244
828.266222263089937.272381858497029.26006266768285
838.272844489398937.146321384498239.39936759429963
848.279466715707927.014879303102739.54405412831312

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.20662222630899 & 8.11777214763793 & 8.29547230498006 \tabularnewline
74 & 8.21324445261799 & 8.05329142479466 & 8.37319748044132 \tabularnewline
75 & 8.21986667892698 & 7.9811798123171 & 8.45855354553686 \tabularnewline
76 & 8.22648890523597 & 7.90098437311931 & 8.55199343735263 \tabularnewline
77 & 8.23311113154497 & 7.8130756236159 & 8.65314663947404 \tabularnewline
78 & 8.23973335785396 & 7.71790884791567 & 8.76155786779225 \tabularnewline
79 & 8.24635558416295 & 7.61590678324106 & 8.87680438508485 \tabularnewline
80 & 8.25297781047195 & 7.50744178950594 & 8.99851383143796 \tabularnewline
81 & 8.25960003678094 & 7.39283874351945 & 9.12636133004244 \tabularnewline
82 & 8.26622226308993 & 7.27238185849702 & 9.26006266768285 \tabularnewline
83 & 8.27284448939893 & 7.14632138449823 & 9.39936759429963 \tabularnewline
84 & 8.27946671570792 & 7.01487930310273 & 9.54405412831312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200697&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]8.20662222630899[/C][C]8.11777214763793[/C][C]8.29547230498006[/C][/ROW]
[ROW][C]74[/C][C]8.21324445261799[/C][C]8.05329142479466[/C][C]8.37319748044132[/C][/ROW]
[ROW][C]75[/C][C]8.21986667892698[/C][C]7.9811798123171[/C][C]8.45855354553686[/C][/ROW]
[ROW][C]76[/C][C]8.22648890523597[/C][C]7.90098437311931[/C][C]8.55199343735263[/C][/ROW]
[ROW][C]77[/C][C]8.23311113154497[/C][C]7.8130756236159[/C][C]8.65314663947404[/C][/ROW]
[ROW][C]78[/C][C]8.23973335785396[/C][C]7.71790884791567[/C][C]8.76155786779225[/C][/ROW]
[ROW][C]79[/C][C]8.24635558416295[/C][C]7.61590678324106[/C][C]8.87680438508485[/C][/ROW]
[ROW][C]80[/C][C]8.25297781047195[/C][C]7.50744178950594[/C][C]8.99851383143796[/C][/ROW]
[ROW][C]81[/C][C]8.25960003678094[/C][C]7.39283874351945[/C][C]9.12636133004244[/C][/ROW]
[ROW][C]82[/C][C]8.26622226308993[/C][C]7.27238185849702[/C][C]9.26006266768285[/C][/ROW]
[ROW][C]83[/C][C]8.27284448939893[/C][C]7.14632138449823[/C][C]9.39936759429963[/C][/ROW]
[ROW][C]84[/C][C]8.27946671570792[/C][C]7.01487930310273[/C][C]9.54405412831312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200697&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200697&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
738.206622226308998.117772147637938.29547230498006
748.213244452617998.053291424794668.37319748044132
758.219866678926987.98117981231718.45855354553686
768.226488905235977.900984373119318.55199343735263
778.233111131544977.81307562361598.65314663947404
788.239733357853967.717908847915678.76155786779225
798.246355584162957.615906783241068.87680438508485
808.252977810471957.507441789505948.99851383143796
818.259600036780947.392838743519459.12636133004244
828.266222263089937.272381858497029.26006266768285
838.272844489398937.146321384498239.39936759429963
848.279466715707927.014879303102739.54405412831312



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')