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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 05:15:18 -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/t13557393408oykvoxmt8ps7ds.htm/, Retrieved Fri, 19 Apr 2024 13:14:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200749, Retrieved Fri, 19 Apr 2024 13:14:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact107
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [Maximumprijs tick...] [2012-11-26 16:33:35] [895815dea0e464124282c4efec6b6e6c]
- RMPD    [Exponential Smoothing] [Gemiddelde Consum...] [2012-12-17 10:15:18] [76c30f62b7052b57088120e90a652e05] [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=200749&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=200749&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200749&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
beta0.136416350245047
gamma0.0670226125538515

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.136416350245047 \tabularnewline
gamma & 0.0670226125538515 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200749&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]0.136416350245047[/C][/ROW]
[ROW][C]gamma[/C][C]0.0670226125538515[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200749&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200749&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
beta0.136416350245047
gamma0.0670226125538515







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136.886.843448183760680.0365518162393181
146.886.88237699963193-0.00237699963193005
156.916.91205273801761-0.00205273801760697
166.916.9109393776559-0.000939377655903684
176.916.909977897851252.21021487512019e-05
186.916.909564246279050.000435753720950949
196.996.965873690211270.0241263097887323
206.997.00041491333753-0.0104149133375273
216.996.99732748220524-0.00732748220523671
227.027.007161227159650.012838772840353
237.027.03099597902548-0.010995979025485
247.057.049495947699460.000504052300542845
257.057.0562313753413-0.00623137534129636
267.057.0520479805269-0.00204798052689714
277.057.08176860249804-0.0317686024980439
287.17.046601512359540.0533984876404574
297.17.10305260581872-0.00305260581872435
307.17.10221951380753-0.00221951380753183
317.17.15816673583459-0.0581667358345914
327.127.101481842026370.0185181579736327
337.137.122341354883720.00765864511627523
347.187.144219452631640.0357805473683568
357.247.191183837646740.0488161623532637
367.247.27784316034794-0.0378431603479381
377.247.2493474011982-0.00934740119820088
387.277.244738929509130.025261070490866
397.277.30818495254878-0.0381849525487796
407.277.27214256735446-0.00214256735446217
417.277.27101695280248-0.00101695280247771
427.37.270461557146130.0295384428538732
437.37.36074108371217-0.0607410837121751
447.577.303705006762230.26629499323777
457.767.608365331161590.15163466883841
467.947.829884112588480.110115887411524
477.948.01698905338648-0.076989053386483
487.968.02648648771468-0.0664864877146778
497.968.0140833103867-0.0540833103866953
507.988.00337212924124-0.0233721292412401
517.998.05018378867269-0.0601837886726937
5288.02114040254471-0.0211404025447131
5388.02742317265352-0.0274231726535188
548.048.023265536861320.016734463138679
558.048.12179839124601-0.081798391246009
568.048.06188975325631-0.0218897532563123
578.048.05723696634265-0.0172369663426544
588.048.06571889563823-0.0257188956382262
598.078.054293751096260.0157062489037418
608.078.10643634024775-0.0364363402477466
618.078.07813249436153-0.0081324943615293
628.078.07368975582901-0.00368975582900788
638.118.103186412805520.00681358719448077
648.118.11328256416933-0.00328256416933215
658.128.112001435412570.00799856458742632
668.118.12267590373412-0.0126759037341238
678.138.16719670321066-0.0371967032106557
688.158.133372464717510.0166275352824883
698.168.153974065727650.00602593427234765
708.28.175629435021240.0243705649787636
718.28.21103731188238-0.011037311882383
728.28.22953164207887-0.0295316420788687

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6.88 & 6.84344818376068 & 0.0365518162393181 \tabularnewline
14 & 6.88 & 6.88237699963193 & -0.00237699963193005 \tabularnewline
15 & 6.91 & 6.91205273801761 & -0.00205273801760697 \tabularnewline
16 & 6.91 & 6.9109393776559 & -0.000939377655903684 \tabularnewline
17 & 6.91 & 6.90997789785125 & 2.21021487512019e-05 \tabularnewline
18 & 6.91 & 6.90956424627905 & 0.000435753720950949 \tabularnewline
19 & 6.99 & 6.96587369021127 & 0.0241263097887323 \tabularnewline
20 & 6.99 & 7.00041491333753 & -0.0104149133375273 \tabularnewline
21 & 6.99 & 6.99732748220524 & -0.00732748220523671 \tabularnewline
22 & 7.02 & 7.00716122715965 & 0.012838772840353 \tabularnewline
23 & 7.02 & 7.03099597902548 & -0.010995979025485 \tabularnewline
24 & 7.05 & 7.04949594769946 & 0.000504052300542845 \tabularnewline
25 & 7.05 & 7.0562313753413 & -0.00623137534129636 \tabularnewline
26 & 7.05 & 7.0520479805269 & -0.00204798052689714 \tabularnewline
27 & 7.05 & 7.08176860249804 & -0.0317686024980439 \tabularnewline
28 & 7.1 & 7.04660151235954 & 0.0533984876404574 \tabularnewline
29 & 7.1 & 7.10305260581872 & -0.00305260581872435 \tabularnewline
30 & 7.1 & 7.10221951380753 & -0.00221951380753183 \tabularnewline
31 & 7.1 & 7.15816673583459 & -0.0581667358345914 \tabularnewline
32 & 7.12 & 7.10148184202637 & 0.0185181579736327 \tabularnewline
33 & 7.13 & 7.12234135488372 & 0.00765864511627523 \tabularnewline
34 & 7.18 & 7.14421945263164 & 0.0357805473683568 \tabularnewline
35 & 7.24 & 7.19118383764674 & 0.0488161623532637 \tabularnewline
36 & 7.24 & 7.27784316034794 & -0.0378431603479381 \tabularnewline
37 & 7.24 & 7.2493474011982 & -0.00934740119820088 \tabularnewline
38 & 7.27 & 7.24473892950913 & 0.025261070490866 \tabularnewline
39 & 7.27 & 7.30818495254878 & -0.0381849525487796 \tabularnewline
40 & 7.27 & 7.27214256735446 & -0.00214256735446217 \tabularnewline
41 & 7.27 & 7.27101695280248 & -0.00101695280247771 \tabularnewline
42 & 7.3 & 7.27046155714613 & 0.0295384428538732 \tabularnewline
43 & 7.3 & 7.36074108371217 & -0.0607410837121751 \tabularnewline
44 & 7.57 & 7.30370500676223 & 0.26629499323777 \tabularnewline
45 & 7.76 & 7.60836533116159 & 0.15163466883841 \tabularnewline
46 & 7.94 & 7.82988411258848 & 0.110115887411524 \tabularnewline
47 & 7.94 & 8.01698905338648 & -0.076989053386483 \tabularnewline
48 & 7.96 & 8.02648648771468 & -0.0664864877146778 \tabularnewline
49 & 7.96 & 8.0140833103867 & -0.0540833103866953 \tabularnewline
50 & 7.98 & 8.00337212924124 & -0.0233721292412401 \tabularnewline
51 & 7.99 & 8.05018378867269 & -0.0601837886726937 \tabularnewline
52 & 8 & 8.02114040254471 & -0.0211404025447131 \tabularnewline
53 & 8 & 8.02742317265352 & -0.0274231726535188 \tabularnewline
54 & 8.04 & 8.02326553686132 & 0.016734463138679 \tabularnewline
55 & 8.04 & 8.12179839124601 & -0.081798391246009 \tabularnewline
56 & 8.04 & 8.06188975325631 & -0.0218897532563123 \tabularnewline
57 & 8.04 & 8.05723696634265 & -0.0172369663426544 \tabularnewline
58 & 8.04 & 8.06571889563823 & -0.0257188956382262 \tabularnewline
59 & 8.07 & 8.05429375109626 & 0.0157062489037418 \tabularnewline
60 & 8.07 & 8.10643634024775 & -0.0364363402477466 \tabularnewline
61 & 8.07 & 8.07813249436153 & -0.0081324943615293 \tabularnewline
62 & 8.07 & 8.07368975582901 & -0.00368975582900788 \tabularnewline
63 & 8.11 & 8.10318641280552 & 0.00681358719448077 \tabularnewline
64 & 8.11 & 8.11328256416933 & -0.00328256416933215 \tabularnewline
65 & 8.12 & 8.11200143541257 & 0.00799856458742632 \tabularnewline
66 & 8.11 & 8.12267590373412 & -0.0126759037341238 \tabularnewline
67 & 8.13 & 8.16719670321066 & -0.0371967032106557 \tabularnewline
68 & 8.15 & 8.13337246471751 & 0.0166275352824883 \tabularnewline
69 & 8.16 & 8.15397406572765 & 0.00602593427234765 \tabularnewline
70 & 8.2 & 8.17562943502124 & 0.0243705649787636 \tabularnewline
71 & 8.2 & 8.21103731188238 & -0.011037311882383 \tabularnewline
72 & 8.2 & 8.22953164207887 & -0.0295316420788687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200749&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]13[/C][C]6.88[/C][C]6.84344818376068[/C][C]0.0365518162393181[/C][/ROW]
[ROW][C]14[/C][C]6.88[/C][C]6.88237699963193[/C][C]-0.00237699963193005[/C][/ROW]
[ROW][C]15[/C][C]6.91[/C][C]6.91205273801761[/C][C]-0.00205273801760697[/C][/ROW]
[ROW][C]16[/C][C]6.91[/C][C]6.9109393776559[/C][C]-0.000939377655903684[/C][/ROW]
[ROW][C]17[/C][C]6.91[/C][C]6.90997789785125[/C][C]2.21021487512019e-05[/C][/ROW]
[ROW][C]18[/C][C]6.91[/C][C]6.90956424627905[/C][C]0.000435753720950949[/C][/ROW]
[ROW][C]19[/C][C]6.99[/C][C]6.96587369021127[/C][C]0.0241263097887323[/C][/ROW]
[ROW][C]20[/C][C]6.99[/C][C]7.00041491333753[/C][C]-0.0104149133375273[/C][/ROW]
[ROW][C]21[/C][C]6.99[/C][C]6.99732748220524[/C][C]-0.00732748220523671[/C][/ROW]
[ROW][C]22[/C][C]7.02[/C][C]7.00716122715965[/C][C]0.012838772840353[/C][/ROW]
[ROW][C]23[/C][C]7.02[/C][C]7.03099597902548[/C][C]-0.010995979025485[/C][/ROW]
[ROW][C]24[/C][C]7.05[/C][C]7.04949594769946[/C][C]0.000504052300542845[/C][/ROW]
[ROW][C]25[/C][C]7.05[/C][C]7.0562313753413[/C][C]-0.00623137534129636[/C][/ROW]
[ROW][C]26[/C][C]7.05[/C][C]7.0520479805269[/C][C]-0.00204798052689714[/C][/ROW]
[ROW][C]27[/C][C]7.05[/C][C]7.08176860249804[/C][C]-0.0317686024980439[/C][/ROW]
[ROW][C]28[/C][C]7.1[/C][C]7.04660151235954[/C][C]0.0533984876404574[/C][/ROW]
[ROW][C]29[/C][C]7.1[/C][C]7.10305260581872[/C][C]-0.00305260581872435[/C][/ROW]
[ROW][C]30[/C][C]7.1[/C][C]7.10221951380753[/C][C]-0.00221951380753183[/C][/ROW]
[ROW][C]31[/C][C]7.1[/C][C]7.15816673583459[/C][C]-0.0581667358345914[/C][/ROW]
[ROW][C]32[/C][C]7.12[/C][C]7.10148184202637[/C][C]0.0185181579736327[/C][/ROW]
[ROW][C]33[/C][C]7.13[/C][C]7.12234135488372[/C][C]0.00765864511627523[/C][/ROW]
[ROW][C]34[/C][C]7.18[/C][C]7.14421945263164[/C][C]0.0357805473683568[/C][/ROW]
[ROW][C]35[/C][C]7.24[/C][C]7.19118383764674[/C][C]0.0488161623532637[/C][/ROW]
[ROW][C]36[/C][C]7.24[/C][C]7.27784316034794[/C][C]-0.0378431603479381[/C][/ROW]
[ROW][C]37[/C][C]7.24[/C][C]7.2493474011982[/C][C]-0.00934740119820088[/C][/ROW]
[ROW][C]38[/C][C]7.27[/C][C]7.24473892950913[/C][C]0.025261070490866[/C][/ROW]
[ROW][C]39[/C][C]7.27[/C][C]7.30818495254878[/C][C]-0.0381849525487796[/C][/ROW]
[ROW][C]40[/C][C]7.27[/C][C]7.27214256735446[/C][C]-0.00214256735446217[/C][/ROW]
[ROW][C]41[/C][C]7.27[/C][C]7.27101695280248[/C][C]-0.00101695280247771[/C][/ROW]
[ROW][C]42[/C][C]7.3[/C][C]7.27046155714613[/C][C]0.0295384428538732[/C][/ROW]
[ROW][C]43[/C][C]7.3[/C][C]7.36074108371217[/C][C]-0.0607410837121751[/C][/ROW]
[ROW][C]44[/C][C]7.57[/C][C]7.30370500676223[/C][C]0.26629499323777[/C][/ROW]
[ROW][C]45[/C][C]7.76[/C][C]7.60836533116159[/C][C]0.15163466883841[/C][/ROW]
[ROW][C]46[/C][C]7.94[/C][C]7.82988411258848[/C][C]0.110115887411524[/C][/ROW]
[ROW][C]47[/C][C]7.94[/C][C]8.01698905338648[/C][C]-0.076989053386483[/C][/ROW]
[ROW][C]48[/C][C]7.96[/C][C]8.02648648771468[/C][C]-0.0664864877146778[/C][/ROW]
[ROW][C]49[/C][C]7.96[/C][C]8.0140833103867[/C][C]-0.0540833103866953[/C][/ROW]
[ROW][C]50[/C][C]7.98[/C][C]8.00337212924124[/C][C]-0.0233721292412401[/C][/ROW]
[ROW][C]51[/C][C]7.99[/C][C]8.05018378867269[/C][C]-0.0601837886726937[/C][/ROW]
[ROW][C]52[/C][C]8[/C][C]8.02114040254471[/C][C]-0.0211404025447131[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]8.02742317265352[/C][C]-0.0274231726535188[/C][/ROW]
[ROW][C]54[/C][C]8.04[/C][C]8.02326553686132[/C][C]0.016734463138679[/C][/ROW]
[ROW][C]55[/C][C]8.04[/C][C]8.12179839124601[/C][C]-0.081798391246009[/C][/ROW]
[ROW][C]56[/C][C]8.04[/C][C]8.06188975325631[/C][C]-0.0218897532563123[/C][/ROW]
[ROW][C]57[/C][C]8.04[/C][C]8.05723696634265[/C][C]-0.0172369663426544[/C][/ROW]
[ROW][C]58[/C][C]8.04[/C][C]8.06571889563823[/C][C]-0.0257188956382262[/C][/ROW]
[ROW][C]59[/C][C]8.07[/C][C]8.05429375109626[/C][C]0.0157062489037418[/C][/ROW]
[ROW][C]60[/C][C]8.07[/C][C]8.10643634024775[/C][C]-0.0364363402477466[/C][/ROW]
[ROW][C]61[/C][C]8.07[/C][C]8.07813249436153[/C][C]-0.0081324943615293[/C][/ROW]
[ROW][C]62[/C][C]8.07[/C][C]8.07368975582901[/C][C]-0.00368975582900788[/C][/ROW]
[ROW][C]63[/C][C]8.11[/C][C]8.10318641280552[/C][C]0.00681358719448077[/C][/ROW]
[ROW][C]64[/C][C]8.11[/C][C]8.11328256416933[/C][C]-0.00328256416933215[/C][/ROW]
[ROW][C]65[/C][C]8.12[/C][C]8.11200143541257[/C][C]0.00799856458742632[/C][/ROW]
[ROW][C]66[/C][C]8.11[/C][C]8.12267590373412[/C][C]-0.0126759037341238[/C][/ROW]
[ROW][C]67[/C][C]8.13[/C][C]8.16719670321066[/C][C]-0.0371967032106557[/C][/ROW]
[ROW][C]68[/C][C]8.15[/C][C]8.13337246471751[/C][C]0.0166275352824883[/C][/ROW]
[ROW][C]69[/C][C]8.16[/C][C]8.15397406572765[/C][C]0.00602593427234765[/C][/ROW]
[ROW][C]70[/C][C]8.2[/C][C]8.17562943502124[/C][C]0.0243705649787636[/C][/ROW]
[ROW][C]71[/C][C]8.2[/C][C]8.21103731188238[/C][C]-0.011037311882383[/C][/ROW]
[ROW][C]72[/C][C]8.2[/C][C]8.22953164207887[/C][C]-0.0295316420788687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200749&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200749&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
136.886.843448183760680.0365518162393181
146.886.88237699963193-0.00237699963193005
156.916.91205273801761-0.00205273801760697
166.916.9109393776559-0.000939377655903684
176.916.909977897851252.21021487512019e-05
186.916.909564246279050.000435753720950949
196.996.965873690211270.0241263097887323
206.997.00041491333753-0.0104149133375273
216.996.99732748220524-0.00732748220523671
227.027.007161227159650.012838772840353
237.027.03099597902548-0.010995979025485
247.057.049495947699460.000504052300542845
257.057.0562313753413-0.00623137534129636
267.057.0520479805269-0.00204798052689714
277.057.08176860249804-0.0317686024980439
287.17.046601512359540.0533984876404574
297.17.10305260581872-0.00305260581872435
307.17.10221951380753-0.00221951380753183
317.17.15816673583459-0.0581667358345914
327.127.101481842026370.0185181579736327
337.137.122341354883720.00765864511627523
347.187.144219452631640.0357805473683568
357.247.191183837646740.0488161623532637
367.247.27784316034794-0.0378431603479381
377.247.2493474011982-0.00934740119820088
387.277.244738929509130.025261070490866
397.277.30818495254878-0.0381849525487796
407.277.27214256735446-0.00214256735446217
417.277.27101695280248-0.00101695280247771
427.37.270461557146130.0295384428538732
437.37.36074108371217-0.0607410837121751
447.577.303705006762230.26629499323777
457.767.608365331161590.15163466883841
467.947.829884112588480.110115887411524
477.948.01698905338648-0.076989053386483
487.968.02648648771468-0.0664864877146778
497.968.0140833103867-0.0540833103866953
507.988.00337212924124-0.0233721292412401
517.998.05018378867269-0.0601837886726937
5288.02114040254471-0.0211404025447131
5388.02742317265352-0.0274231726535188
548.048.023265536861320.016734463138679
558.048.12179839124601-0.081798391246009
568.048.06188975325631-0.0218897532563123
578.048.05723696634265-0.0172369663426544
588.048.06571889563823-0.0257188956382262
598.078.054293751096260.0157062489037418
608.078.10643634024775-0.0364363402477466
618.078.07813249436153-0.0081324943615293
628.078.07368975582901-0.00368975582900788
638.118.103186412805520.00681358719448077
648.118.11328256416933-0.00328256416933215
658.128.112001435412570.00799856458742632
668.118.12267590373412-0.0126759037341238
678.138.16719670321066-0.0371967032106557
688.158.133372464717510.0166275352824883
698.168.153974065727650.00602593427234765
708.28.175629435021240.0243705649787636
718.28.21103731188238-0.011037311882383
728.28.22953164207887-0.0295316420788687







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
738.202169709916398.100031627857078.30430779197572
748.201006086499468.046394461594758.35561771140416
758.229842463082528.027837576536688.43184734962835
768.227845506332247.979804943829738.47588606883476
778.225015216248647.930995713712128.51903471878516
788.221768259498367.881232960585288.56230355841145
798.274771302748097.886875878193758.66266672730244
808.279024345997827.842754413998618.71529427799704
818.281610722580887.795855286917358.76736615824441
828.295030432497287.758624053469178.83143681152539
838.300533475747017.712281737063328.8887852144307
848.326036518996747.684731964962288.96734107303119

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 8.20216970991639 & 8.10003162785707 & 8.30430779197572 \tabularnewline
74 & 8.20100608649946 & 8.04639446159475 & 8.35561771140416 \tabularnewline
75 & 8.22984246308252 & 8.02783757653668 & 8.43184734962835 \tabularnewline
76 & 8.22784550633224 & 7.97980494382973 & 8.47588606883476 \tabularnewline
77 & 8.22501521624864 & 7.93099571371212 & 8.51903471878516 \tabularnewline
78 & 8.22176825949836 & 7.88123296058528 & 8.56230355841145 \tabularnewline
79 & 8.27477130274809 & 7.88687587819375 & 8.66266672730244 \tabularnewline
80 & 8.27902434599782 & 7.84275441399861 & 8.71529427799704 \tabularnewline
81 & 8.28161072258088 & 7.79585528691735 & 8.76736615824441 \tabularnewline
82 & 8.29503043249728 & 7.75862405346917 & 8.83143681152539 \tabularnewline
83 & 8.30053347574701 & 7.71228173706332 & 8.8887852144307 \tabularnewline
84 & 8.32603651899674 & 7.68473196496228 & 8.96734107303119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200749&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]8.20216970991639[/C][C]8.10003162785707[/C][C]8.30430779197572[/C][/ROW]
[ROW][C]74[/C][C]8.20100608649946[/C][C]8.04639446159475[/C][C]8.35561771140416[/C][/ROW]
[ROW][C]75[/C][C]8.22984246308252[/C][C]8.02783757653668[/C][C]8.43184734962835[/C][/ROW]
[ROW][C]76[/C][C]8.22784550633224[/C][C]7.97980494382973[/C][C]8.47588606883476[/C][/ROW]
[ROW][C]77[/C][C]8.22501521624864[/C][C]7.93099571371212[/C][C]8.51903471878516[/C][/ROW]
[ROW][C]78[/C][C]8.22176825949836[/C][C]7.88123296058528[/C][C]8.56230355841145[/C][/ROW]
[ROW][C]79[/C][C]8.27477130274809[/C][C]7.88687587819375[/C][C]8.66266672730244[/C][/ROW]
[ROW][C]80[/C][C]8.27902434599782[/C][C]7.84275441399861[/C][C]8.71529427799704[/C][/ROW]
[ROW][C]81[/C][C]8.28161072258088[/C][C]7.79585528691735[/C][C]8.76736615824441[/C][/ROW]
[ROW][C]82[/C][C]8.29503043249728[/C][C]7.75862405346917[/C][C]8.83143681152539[/C][/ROW]
[ROW][C]83[/C][C]8.30053347574701[/C][C]7.71228173706332[/C][C]8.8887852144307[/C][/ROW]
[ROW][C]84[/C][C]8.32603651899674[/C][C]7.68473196496228[/C][C]8.96734107303119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200749&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200749&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
738.202169709916398.100031627857078.30430779197572
748.201006086499468.046394461594758.35561771140416
758.229842463082528.027837576536688.43184734962835
768.227845506332247.979804943829738.47588606883476
778.225015216248647.930995713712128.51903471878516
788.221768259498367.881232960585288.56230355841145
798.274771302748097.886875878193758.66266672730244
808.279024345997827.842754413998618.71529427799704
818.281610722580887.795855286917358.76736615824441
828.295030432497287.758624053469178.83143681152539
838.300533475747017.712281737063328.8887852144307
848.326036518996747.684731964962288.96734107303119



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