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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Dec 2014 19:26:37 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Dec/17/t1418844643ucyxyr14h56kpn4.htm/, Retrieved Thu, 16 May 2024 16:22:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270601, Retrieved Thu, 16 May 2024 16:22:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2014-11-30 15:49:42] [379af119b8c9c9402cda7215f859bbd6]
- R P     [Exponential Smoothing] [] [2014-12-17 19:26:37] [23f6b347f5ddfa38e8c261c083a091fc] [Current]
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Dataseries X:
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118
21925
20801
18785
20659
29367
23992
20645
22356
17902
15879
16963
21035
17988
10437
24470
22237
27053
26419
22311
20624
17336
15586
17733
19231
16102
11770




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270601&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270601&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270601&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.323584330510254
beta0.00540753489126229
gamma0.361207081356596

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.323584330510254 \tabularnewline
beta & 0.00540753489126229 \tabularnewline
gamma & 0.361207081356596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270601&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]0.323584330510254[/C][/ROW]
[ROW][C]beta[/C][C]0.00540753489126229[/C][/ROW]
[ROW][C]gamma[/C][C]0.361207081356596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270601&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270601&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
alpha0.323584330510254
beta0.00540753489126229
gamma0.361207081356596







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132544727690.562232906-2243.56223290599
142409025485.7395235942-1395.73952359418
152778628576.9417020401-790.941702040072
162619526542.7546606397-347.754660639697
172051620411.6175024569104.382497543091
182275922221.3841583919537.61584160812
191902817609.90405265691418.09594734308
201697115952.81488761641018.18511238363
212003619153.185789865882.814210135006
222248521566.5475319563918.452468043695
231873015177.25669141833552.74330858167
241453812460.30598957132077.69401042873
252756126550.31877313011010.68122686987
262598525621.3875415059363.612458494092
273467029448.45891214875221.54108785126
283206629497.42241516862568.57758483138
292718624454.85972709992731.14027290008
302958627259.47668019562326.52331980443
312135923484.1359332537-2125.13593325367
322155320618.7564949664934.243505033603
331957323794.69638852-4221.69638852
342425624591.8998325794-335.899832579391
352238018465.02545976753914.97454023249
361616715530.2069835719636.79301642807
372729728916.0593618587-1619.05936185871
382828726996.27965342391290.72034657609
393347432330.07993628941143.92006371062
402822930424.0782963366-2195.07829633661
412878523884.13153851374900.86846148635
422559727300.1186340384-1703.11863403836
431813021134.2797687466-3004.2797687466
442019818731.4587302261466.54126977396
452284920820.39164291832028.60835708174
462311824600.9147828647-1482.91478286471
472192519150.89437526312774.10562473692
482080115053.37725178335747.62274821672
491878529558.2073245228-10773.2073245228
502065925387.5630799221-4728.5630799221
512936728727.5570058598639.442994140201
522399225831.4337995272-1839.43379952721
532064521129.8393958981-484.839395898085
542235621169.69149458991186.30850541006
551790215606.09649508942295.90350491056
561587916005.1225240476-126.122524047581
571696317707.6876426482-744.687642648205
582103519719.67167664771315.32832335226
591798816206.92944121481781.07055878525
601043712504.5612844794-2067.56128447942
612447020420.3464565924049.65354340796
622223722525.2458672056-288.245867205598
632705328623.6042636879-1570.6042636879
642641924412.82614484162006.17385515845
652231121299.43807004731011.56192995269
662062422247.2908247769-1623.29082477694
671733616056.22387589211279.77612410789
681558615543.472064688642.5279353114165
691773317158.5626152285574.437384771532
701923120112.1031701664-881.103170166407
711610216009.972420428292.0275795718389
721177010825.3289245881944.671075411919

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 25447 & 27690.562232906 & -2243.56223290599 \tabularnewline
14 & 24090 & 25485.7395235942 & -1395.73952359418 \tabularnewline
15 & 27786 & 28576.9417020401 & -790.941702040072 \tabularnewline
16 & 26195 & 26542.7546606397 & -347.754660639697 \tabularnewline
17 & 20516 & 20411.6175024569 & 104.382497543091 \tabularnewline
18 & 22759 & 22221.3841583919 & 537.61584160812 \tabularnewline
19 & 19028 & 17609.9040526569 & 1418.09594734308 \tabularnewline
20 & 16971 & 15952.8148876164 & 1018.18511238363 \tabularnewline
21 & 20036 & 19153.185789865 & 882.814210135006 \tabularnewline
22 & 22485 & 21566.5475319563 & 918.452468043695 \tabularnewline
23 & 18730 & 15177.2566914183 & 3552.74330858167 \tabularnewline
24 & 14538 & 12460.3059895713 & 2077.69401042873 \tabularnewline
25 & 27561 & 26550.3187731301 & 1010.68122686987 \tabularnewline
26 & 25985 & 25621.3875415059 & 363.612458494092 \tabularnewline
27 & 34670 & 29448.4589121487 & 5221.54108785126 \tabularnewline
28 & 32066 & 29497.4224151686 & 2568.57758483138 \tabularnewline
29 & 27186 & 24454.8597270999 & 2731.14027290008 \tabularnewline
30 & 29586 & 27259.4766801956 & 2326.52331980443 \tabularnewline
31 & 21359 & 23484.1359332537 & -2125.13593325367 \tabularnewline
32 & 21553 & 20618.7564949664 & 934.243505033603 \tabularnewline
33 & 19573 & 23794.69638852 & -4221.69638852 \tabularnewline
34 & 24256 & 24591.8998325794 & -335.899832579391 \tabularnewline
35 & 22380 & 18465.0254597675 & 3914.97454023249 \tabularnewline
36 & 16167 & 15530.2069835719 & 636.79301642807 \tabularnewline
37 & 27297 & 28916.0593618587 & -1619.05936185871 \tabularnewline
38 & 28287 & 26996.2796534239 & 1290.72034657609 \tabularnewline
39 & 33474 & 32330.0799362894 & 1143.92006371062 \tabularnewline
40 & 28229 & 30424.0782963366 & -2195.07829633661 \tabularnewline
41 & 28785 & 23884.1315385137 & 4900.86846148635 \tabularnewline
42 & 25597 & 27300.1186340384 & -1703.11863403836 \tabularnewline
43 & 18130 & 21134.2797687466 & -3004.2797687466 \tabularnewline
44 & 20198 & 18731.458730226 & 1466.54126977396 \tabularnewline
45 & 22849 & 20820.3916429183 & 2028.60835708174 \tabularnewline
46 & 23118 & 24600.9147828647 & -1482.91478286471 \tabularnewline
47 & 21925 & 19150.8943752631 & 2774.10562473692 \tabularnewline
48 & 20801 & 15053.3772517833 & 5747.62274821672 \tabularnewline
49 & 18785 & 29558.2073245228 & -10773.2073245228 \tabularnewline
50 & 20659 & 25387.5630799221 & -4728.5630799221 \tabularnewline
51 & 29367 & 28727.5570058598 & 639.442994140201 \tabularnewline
52 & 23992 & 25831.4337995272 & -1839.43379952721 \tabularnewline
53 & 20645 & 21129.8393958981 & -484.839395898085 \tabularnewline
54 & 22356 & 21169.6914945899 & 1186.30850541006 \tabularnewline
55 & 17902 & 15606.0964950894 & 2295.90350491056 \tabularnewline
56 & 15879 & 16005.1225240476 & -126.122524047581 \tabularnewline
57 & 16963 & 17707.6876426482 & -744.687642648205 \tabularnewline
58 & 21035 & 19719.6716766477 & 1315.32832335226 \tabularnewline
59 & 17988 & 16206.9294412148 & 1781.07055878525 \tabularnewline
60 & 10437 & 12504.5612844794 & -2067.56128447942 \tabularnewline
61 & 24470 & 20420.346456592 & 4049.65354340796 \tabularnewline
62 & 22237 & 22525.2458672056 & -288.245867205598 \tabularnewline
63 & 27053 & 28623.6042636879 & -1570.6042636879 \tabularnewline
64 & 26419 & 24412.8261448416 & 2006.17385515845 \tabularnewline
65 & 22311 & 21299.4380700473 & 1011.56192995269 \tabularnewline
66 & 20624 & 22247.2908247769 & -1623.29082477694 \tabularnewline
67 & 17336 & 16056.2238758921 & 1279.77612410789 \tabularnewline
68 & 15586 & 15543.4720646886 & 42.5279353114165 \tabularnewline
69 & 17733 & 17158.5626152285 & 574.437384771532 \tabularnewline
70 & 19231 & 20112.1031701664 & -881.103170166407 \tabularnewline
71 & 16102 & 16009.9724204282 & 92.0275795718389 \tabularnewline
72 & 11770 & 10825.3289245881 & 944.671075411919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270601&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]25447[/C][C]27690.562232906[/C][C]-2243.56223290599[/C][/ROW]
[ROW][C]14[/C][C]24090[/C][C]25485.7395235942[/C][C]-1395.73952359418[/C][/ROW]
[ROW][C]15[/C][C]27786[/C][C]28576.9417020401[/C][C]-790.941702040072[/C][/ROW]
[ROW][C]16[/C][C]26195[/C][C]26542.7546606397[/C][C]-347.754660639697[/C][/ROW]
[ROW][C]17[/C][C]20516[/C][C]20411.6175024569[/C][C]104.382497543091[/C][/ROW]
[ROW][C]18[/C][C]22759[/C][C]22221.3841583919[/C][C]537.61584160812[/C][/ROW]
[ROW][C]19[/C][C]19028[/C][C]17609.9040526569[/C][C]1418.09594734308[/C][/ROW]
[ROW][C]20[/C][C]16971[/C][C]15952.8148876164[/C][C]1018.18511238363[/C][/ROW]
[ROW][C]21[/C][C]20036[/C][C]19153.185789865[/C][C]882.814210135006[/C][/ROW]
[ROW][C]22[/C][C]22485[/C][C]21566.5475319563[/C][C]918.452468043695[/C][/ROW]
[ROW][C]23[/C][C]18730[/C][C]15177.2566914183[/C][C]3552.74330858167[/C][/ROW]
[ROW][C]24[/C][C]14538[/C][C]12460.3059895713[/C][C]2077.69401042873[/C][/ROW]
[ROW][C]25[/C][C]27561[/C][C]26550.3187731301[/C][C]1010.68122686987[/C][/ROW]
[ROW][C]26[/C][C]25985[/C][C]25621.3875415059[/C][C]363.612458494092[/C][/ROW]
[ROW][C]27[/C][C]34670[/C][C]29448.4589121487[/C][C]5221.54108785126[/C][/ROW]
[ROW][C]28[/C][C]32066[/C][C]29497.4224151686[/C][C]2568.57758483138[/C][/ROW]
[ROW][C]29[/C][C]27186[/C][C]24454.8597270999[/C][C]2731.14027290008[/C][/ROW]
[ROW][C]30[/C][C]29586[/C][C]27259.4766801956[/C][C]2326.52331980443[/C][/ROW]
[ROW][C]31[/C][C]21359[/C][C]23484.1359332537[/C][C]-2125.13593325367[/C][/ROW]
[ROW][C]32[/C][C]21553[/C][C]20618.7564949664[/C][C]934.243505033603[/C][/ROW]
[ROW][C]33[/C][C]19573[/C][C]23794.69638852[/C][C]-4221.69638852[/C][/ROW]
[ROW][C]34[/C][C]24256[/C][C]24591.8998325794[/C][C]-335.899832579391[/C][/ROW]
[ROW][C]35[/C][C]22380[/C][C]18465.0254597675[/C][C]3914.97454023249[/C][/ROW]
[ROW][C]36[/C][C]16167[/C][C]15530.2069835719[/C][C]636.79301642807[/C][/ROW]
[ROW][C]37[/C][C]27297[/C][C]28916.0593618587[/C][C]-1619.05936185871[/C][/ROW]
[ROW][C]38[/C][C]28287[/C][C]26996.2796534239[/C][C]1290.72034657609[/C][/ROW]
[ROW][C]39[/C][C]33474[/C][C]32330.0799362894[/C][C]1143.92006371062[/C][/ROW]
[ROW][C]40[/C][C]28229[/C][C]30424.0782963366[/C][C]-2195.07829633661[/C][/ROW]
[ROW][C]41[/C][C]28785[/C][C]23884.1315385137[/C][C]4900.86846148635[/C][/ROW]
[ROW][C]42[/C][C]25597[/C][C]27300.1186340384[/C][C]-1703.11863403836[/C][/ROW]
[ROW][C]43[/C][C]18130[/C][C]21134.2797687466[/C][C]-3004.2797687466[/C][/ROW]
[ROW][C]44[/C][C]20198[/C][C]18731.458730226[/C][C]1466.54126977396[/C][/ROW]
[ROW][C]45[/C][C]22849[/C][C]20820.3916429183[/C][C]2028.60835708174[/C][/ROW]
[ROW][C]46[/C][C]23118[/C][C]24600.9147828647[/C][C]-1482.91478286471[/C][/ROW]
[ROW][C]47[/C][C]21925[/C][C]19150.8943752631[/C][C]2774.10562473692[/C][/ROW]
[ROW][C]48[/C][C]20801[/C][C]15053.3772517833[/C][C]5747.62274821672[/C][/ROW]
[ROW][C]49[/C][C]18785[/C][C]29558.2073245228[/C][C]-10773.2073245228[/C][/ROW]
[ROW][C]50[/C][C]20659[/C][C]25387.5630799221[/C][C]-4728.5630799221[/C][/ROW]
[ROW][C]51[/C][C]29367[/C][C]28727.5570058598[/C][C]639.442994140201[/C][/ROW]
[ROW][C]52[/C][C]23992[/C][C]25831.4337995272[/C][C]-1839.43379952721[/C][/ROW]
[ROW][C]53[/C][C]20645[/C][C]21129.8393958981[/C][C]-484.839395898085[/C][/ROW]
[ROW][C]54[/C][C]22356[/C][C]21169.6914945899[/C][C]1186.30850541006[/C][/ROW]
[ROW][C]55[/C][C]17902[/C][C]15606.0964950894[/C][C]2295.90350491056[/C][/ROW]
[ROW][C]56[/C][C]15879[/C][C]16005.1225240476[/C][C]-126.122524047581[/C][/ROW]
[ROW][C]57[/C][C]16963[/C][C]17707.6876426482[/C][C]-744.687642648205[/C][/ROW]
[ROW][C]58[/C][C]21035[/C][C]19719.6716766477[/C][C]1315.32832335226[/C][/ROW]
[ROW][C]59[/C][C]17988[/C][C]16206.9294412148[/C][C]1781.07055878525[/C][/ROW]
[ROW][C]60[/C][C]10437[/C][C]12504.5612844794[/C][C]-2067.56128447942[/C][/ROW]
[ROW][C]61[/C][C]24470[/C][C]20420.346456592[/C][C]4049.65354340796[/C][/ROW]
[ROW][C]62[/C][C]22237[/C][C]22525.2458672056[/C][C]-288.245867205598[/C][/ROW]
[ROW][C]63[/C][C]27053[/C][C]28623.6042636879[/C][C]-1570.6042636879[/C][/ROW]
[ROW][C]64[/C][C]26419[/C][C]24412.8261448416[/C][C]2006.17385515845[/C][/ROW]
[ROW][C]65[/C][C]22311[/C][C]21299.4380700473[/C][C]1011.56192995269[/C][/ROW]
[ROW][C]66[/C][C]20624[/C][C]22247.2908247769[/C][C]-1623.29082477694[/C][/ROW]
[ROW][C]67[/C][C]17336[/C][C]16056.2238758921[/C][C]1279.77612410789[/C][/ROW]
[ROW][C]68[/C][C]15586[/C][C]15543.4720646886[/C][C]42.5279353114165[/C][/ROW]
[ROW][C]69[/C][C]17733[/C][C]17158.5626152285[/C][C]574.437384771532[/C][/ROW]
[ROW][C]70[/C][C]19231[/C][C]20112.1031701664[/C][C]-881.103170166407[/C][/ROW]
[ROW][C]71[/C][C]16102[/C][C]16009.9724204282[/C][C]92.0275795718389[/C][/ROW]
[ROW][C]72[/C][C]11770[/C][C]10825.3289245881[/C][C]944.671075411919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270601&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270601&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
132544727690.562232906-2243.56223290599
142409025485.7395235942-1395.73952359418
152778628576.9417020401-790.941702040072
162619526542.7546606397-347.754660639697
172051620411.6175024569104.382497543091
182275922221.3841583919537.61584160812
191902817609.90405265691418.09594734308
201697115952.81488761641018.18511238363
212003619153.185789865882.814210135006
222248521566.5475319563918.452468043695
231873015177.25669141833552.74330858167
241453812460.30598957132077.69401042873
252756126550.31877313011010.68122686987
262598525621.3875415059363.612458494092
273467029448.45891214875221.54108785126
283206629497.42241516862568.57758483138
292718624454.85972709992731.14027290008
302958627259.47668019562326.52331980443
312135923484.1359332537-2125.13593325367
322155320618.7564949664934.243505033603
331957323794.69638852-4221.69638852
342425624591.8998325794-335.899832579391
352238018465.02545976753914.97454023249
361616715530.2069835719636.79301642807
372729728916.0593618587-1619.05936185871
382828726996.27965342391290.72034657609
393347432330.07993628941143.92006371062
402822930424.0782963366-2195.07829633661
412878523884.13153851374900.86846148635
422559727300.1186340384-1703.11863403836
431813021134.2797687466-3004.2797687466
442019818731.4587302261466.54126977396
452284920820.39164291832028.60835708174
462311824600.9147828647-1482.91478286471
472192519150.89437526312774.10562473692
482080115053.37725178335747.62274821672
491878529558.2073245228-10773.2073245228
502065925387.5630799221-4728.5630799221
512936728727.5570058598639.442994140201
522399225831.4337995272-1839.43379952721
532064521129.8393958981-484.839395898085
542235621169.69149458991186.30850541006
551790215606.09649508942295.90350491056
561587916005.1225240476-126.122524047581
571696317707.6876426482-744.687642648205
582103519719.67167664771315.32832335226
591798816206.92944121481781.07055878525
601043712504.5612844794-2067.56128447942
612447020420.3464565924049.65354340796
622223722525.2458672056-288.245867205598
632705328623.6042636879-1570.6042636879
642641924412.82614484162006.17385515845
652231121299.43807004731011.56192995269
662062422247.2908247769-1623.29082477694
671733616056.22387589211279.77612410789
681558615543.472064688642.5279353114165
691773317158.5626152285574.437384771532
701923120112.1031701664-881.103170166407
711610216009.972420428292.0275795718389
721177010825.3289245881944.671075411919







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7321220.285322468316152.224457086126288.3461878505
7420957.696680915915628.172714027126287.2206478046
7526839.296182904321257.922455663332420.6699101453
7624016.672504752918191.801765527229841.5432439786
7720013.629090508213952.594332706426074.66384831
7819991.143621422213700.439401074426281.8478417701
7915038.23442528848523.6562983844121552.8125521925
8013810.42687416017077.1806012863820543.6731470338
8115542.99283520578595.7812743143622490.2043960971
8217955.300123052110798.393336013125112.2069100912
8314377.85583120457015.1483457815321740.5633166274
849373.409717405721808.4678121840816938.3516226274

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 21220.2853224683 & 16152.2244570861 & 26288.3461878505 \tabularnewline
74 & 20957.6966809159 & 15628.1727140271 & 26287.2206478046 \tabularnewline
75 & 26839.2961829043 & 21257.9224556633 & 32420.6699101453 \tabularnewline
76 & 24016.6725047529 & 18191.8017655272 & 29841.5432439786 \tabularnewline
77 & 20013.6290905082 & 13952.5943327064 & 26074.66384831 \tabularnewline
78 & 19991.1436214222 & 13700.4394010744 & 26281.8478417701 \tabularnewline
79 & 15038.2344252884 & 8523.65629838441 & 21552.8125521925 \tabularnewline
80 & 13810.4268741601 & 7077.18060128638 & 20543.6731470338 \tabularnewline
81 & 15542.9928352057 & 8595.78127431436 & 22490.2043960971 \tabularnewline
82 & 17955.3001230521 & 10798.3933360131 & 25112.2069100912 \tabularnewline
83 & 14377.8558312045 & 7015.14834578153 & 21740.5633166274 \tabularnewline
84 & 9373.40971740572 & 1808.46781218408 & 16938.3516226274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270601&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]21220.2853224683[/C][C]16152.2244570861[/C][C]26288.3461878505[/C][/ROW]
[ROW][C]74[/C][C]20957.6966809159[/C][C]15628.1727140271[/C][C]26287.2206478046[/C][/ROW]
[ROW][C]75[/C][C]26839.2961829043[/C][C]21257.9224556633[/C][C]32420.6699101453[/C][/ROW]
[ROW][C]76[/C][C]24016.6725047529[/C][C]18191.8017655272[/C][C]29841.5432439786[/C][/ROW]
[ROW][C]77[/C][C]20013.6290905082[/C][C]13952.5943327064[/C][C]26074.66384831[/C][/ROW]
[ROW][C]78[/C][C]19991.1436214222[/C][C]13700.4394010744[/C][C]26281.8478417701[/C][/ROW]
[ROW][C]79[/C][C]15038.2344252884[/C][C]8523.65629838441[/C][C]21552.8125521925[/C][/ROW]
[ROW][C]80[/C][C]13810.4268741601[/C][C]7077.18060128638[/C][C]20543.6731470338[/C][/ROW]
[ROW][C]81[/C][C]15542.9928352057[/C][C]8595.78127431436[/C][C]22490.2043960971[/C][/ROW]
[ROW][C]82[/C][C]17955.3001230521[/C][C]10798.3933360131[/C][C]25112.2069100912[/C][/ROW]
[ROW][C]83[/C][C]14377.8558312045[/C][C]7015.14834578153[/C][C]21740.5633166274[/C][/ROW]
[ROW][C]84[/C][C]9373.40971740572[/C][C]1808.46781218408[/C][C]16938.3516226274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270601&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270601&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
7321220.285322468316152.224457086126288.3461878505
7420957.696680915915628.172714027126287.2206478046
7526839.296182904321257.922455663332420.6699101453
7624016.672504752918191.801765527229841.5432439786
7720013.629090508213952.594332706426074.66384831
7819991.143621422213700.439401074426281.8478417701
7915038.23442528848523.6562983844121552.8125521925
8013810.42687416017077.1806012863820543.6731470338
8115542.99283520578595.7812743143622490.2043960971
8217955.300123052110798.393336013125112.2069100912
8314377.85583120457015.1483457815321740.5633166274
849373.409717405721808.4678121840816938.3516226274



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')