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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 computationSat, 11 Dec 2010 16:41:33 +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/2010/Dec/11/t129208563269o9lny8up6ld8r.htm/, Retrieved Mon, 06 May 2024 22:00:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=108256, Retrieved Mon, 06 May 2024 22:00:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Exponential Smoothing] [Births] [2010-11-30 13:57:06] [b98453cac15ba1066b407e146608df68]
-    D            [Exponential Smoothing] [Tripple Exponenti...] [2010-12-11 16:41:33] [bff44ea937c3f909b1dc9a8bfab919e2] [Current]
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Dataseries X:
46
62
66
59
58
61
41
27
58
70
49
59
44
36
72
45
56
54
53
35
61
52
47
51
52
63
74
45
51
64
36
30
55
64
39
40
63
45
59
55
40
64
27
28
45
57
45
69
60
56
58
50
51
53
37
22
55
70
62
58
39
49
58
47
42
62
39
40
72
70
54
65




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108256&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108256&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108256&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' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00547273897852051
beta0
gamma0.283796808383624

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00547273897852051 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.283796808383624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108256&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]0.00547273897852051[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.283796808383624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108256&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108256&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
alpha0.00547273897852051
beta0
gamma0.283796808383624







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134447.3857323232323-3.38573232323233
143638.5338697606428-2.53386976064281
157274.061669219504-2.06166921950393
164547.6753862420055-2.67538624200552
175659.4940778847696-3.49407788476964
185457.8916223752023-3.89162237520234
195341.120324541739911.8796754582601
203528.35200557133916.64799442866086
216160.22172164291120.778278357088801
225272.5593142905455-20.5593142905455
234752.1134651965227-5.11346519652266
245162.4604805362263-11.4604805362263
255246.23382549309995.76617450690009
266337.672481737383525.3275182626165
277473.48603491065420.513965089345817
284546.9406299672454-1.94062996724536
295158.5322722115789-7.53227221157892
306456.79551230551877.20448769448126
313644.5362894494873-8.53628944948731
323030.1796304171774-0.179630417177368
335560.3552905180826-5.35529051808256
346466.6369154458488-2.63691544584883
353950.64864398173-11.6486439817300
364059.1684891381623-19.1684891381623
376347.761764388398715.2382356116013
384544.77332405628750.226675943712529
395973.4460387434385-14.4460387434385
405546.12596770513888.87403229486119
414056.1985901865845-16.1985901865845
426458.57375887403045.42624112596959
432741.862069546533-14.862069546533
442829.8294052226966-1.82940522269663
454558.5352392738363-13.5352392738363
465765.5393416137178-8.53934161371778
474546.9752644441634-1.97526444416337
486953.42562084324715.5743791567530
496051.92011475200668.07988524799342
505644.655581055909911.3444189440901
515869.2478595159965-11.2478595159965
525048.52723353808741.47276646191262
535151.4827620251635-0.482762025163474
545360.0474109291823-7.0474109291823
553737.5412094491569-0.541209449156923
562229.2653063658442-7.26530636584425
575554.6374936733710.36250632662896
587063.12771520052276.87228479947728
596246.500651021016315.4993489789837
605857.99991710410628.28958938114965e-05
613954.2939035450508-15.2939035450508
624947.82284515078441.17715484921555
635865.9829534109177-7.9829534109177
644748.8705114775701-1.87051147757007
654251.2558075547797-9.25580755477974
666257.9196133206854.08038667931505
673937.31064550724681.68935449275322
684027.149115977201312.8508840227987
697254.784295735371617.2157042646284
707065.20409413421664.79590586578341
715451.00060066567712.99939933432294
726558.05688816132356.94311183867649

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 44 & 47.3857323232323 & -3.38573232323233 \tabularnewline
14 & 36 & 38.5338697606428 & -2.53386976064281 \tabularnewline
15 & 72 & 74.061669219504 & -2.06166921950393 \tabularnewline
16 & 45 & 47.6753862420055 & -2.67538624200552 \tabularnewline
17 & 56 & 59.4940778847696 & -3.49407788476964 \tabularnewline
18 & 54 & 57.8916223752023 & -3.89162237520234 \tabularnewline
19 & 53 & 41.1203245417399 & 11.8796754582601 \tabularnewline
20 & 35 & 28.3520055713391 & 6.64799442866086 \tabularnewline
21 & 61 & 60.2217216429112 & 0.778278357088801 \tabularnewline
22 & 52 & 72.5593142905455 & -20.5593142905455 \tabularnewline
23 & 47 & 52.1134651965227 & -5.11346519652266 \tabularnewline
24 & 51 & 62.4604805362263 & -11.4604805362263 \tabularnewline
25 & 52 & 46.2338254930999 & 5.76617450690009 \tabularnewline
26 & 63 & 37.6724817373835 & 25.3275182626165 \tabularnewline
27 & 74 & 73.4860349106542 & 0.513965089345817 \tabularnewline
28 & 45 & 46.9406299672454 & -1.94062996724536 \tabularnewline
29 & 51 & 58.5322722115789 & -7.53227221157892 \tabularnewline
30 & 64 & 56.7955123055187 & 7.20448769448126 \tabularnewline
31 & 36 & 44.5362894494873 & -8.53628944948731 \tabularnewline
32 & 30 & 30.1796304171774 & -0.179630417177368 \tabularnewline
33 & 55 & 60.3552905180826 & -5.35529051808256 \tabularnewline
34 & 64 & 66.6369154458488 & -2.63691544584883 \tabularnewline
35 & 39 & 50.64864398173 & -11.6486439817300 \tabularnewline
36 & 40 & 59.1684891381623 & -19.1684891381623 \tabularnewline
37 & 63 & 47.7617643883987 & 15.2382356116013 \tabularnewline
38 & 45 & 44.7733240562875 & 0.226675943712529 \tabularnewline
39 & 59 & 73.4460387434385 & -14.4460387434385 \tabularnewline
40 & 55 & 46.1259677051388 & 8.87403229486119 \tabularnewline
41 & 40 & 56.1985901865845 & -16.1985901865845 \tabularnewline
42 & 64 & 58.5737588740304 & 5.42624112596959 \tabularnewline
43 & 27 & 41.862069546533 & -14.862069546533 \tabularnewline
44 & 28 & 29.8294052226966 & -1.82940522269663 \tabularnewline
45 & 45 & 58.5352392738363 & -13.5352392738363 \tabularnewline
46 & 57 & 65.5393416137178 & -8.53934161371778 \tabularnewline
47 & 45 & 46.9752644441634 & -1.97526444416337 \tabularnewline
48 & 69 & 53.425620843247 & 15.5743791567530 \tabularnewline
49 & 60 & 51.9201147520066 & 8.07988524799342 \tabularnewline
50 & 56 & 44.6555810559099 & 11.3444189440901 \tabularnewline
51 & 58 & 69.2478595159965 & -11.2478595159965 \tabularnewline
52 & 50 & 48.5272335380874 & 1.47276646191262 \tabularnewline
53 & 51 & 51.4827620251635 & -0.482762025163474 \tabularnewline
54 & 53 & 60.0474109291823 & -7.0474109291823 \tabularnewline
55 & 37 & 37.5412094491569 & -0.541209449156923 \tabularnewline
56 & 22 & 29.2653063658442 & -7.26530636584425 \tabularnewline
57 & 55 & 54.637493673371 & 0.36250632662896 \tabularnewline
58 & 70 & 63.1277152005227 & 6.87228479947728 \tabularnewline
59 & 62 & 46.5006510210163 & 15.4993489789837 \tabularnewline
60 & 58 & 57.9999171041062 & 8.28958938114965e-05 \tabularnewline
61 & 39 & 54.2939035450508 & -15.2939035450508 \tabularnewline
62 & 49 & 47.8228451507844 & 1.17715484921555 \tabularnewline
63 & 58 & 65.9829534109177 & -7.9829534109177 \tabularnewline
64 & 47 & 48.8705114775701 & -1.87051147757007 \tabularnewline
65 & 42 & 51.2558075547797 & -9.25580755477974 \tabularnewline
66 & 62 & 57.919613320685 & 4.08038667931505 \tabularnewline
67 & 39 & 37.3106455072468 & 1.68935449275322 \tabularnewline
68 & 40 & 27.1491159772013 & 12.8508840227987 \tabularnewline
69 & 72 & 54.7842957353716 & 17.2157042646284 \tabularnewline
70 & 70 & 65.2040941342166 & 4.79590586578341 \tabularnewline
71 & 54 & 51.0006006656771 & 2.99939933432294 \tabularnewline
72 & 65 & 58.0568881613235 & 6.94311183867649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108256&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]44[/C][C]47.3857323232323[/C][C]-3.38573232323233[/C][/ROW]
[ROW][C]14[/C][C]36[/C][C]38.5338697606428[/C][C]-2.53386976064281[/C][/ROW]
[ROW][C]15[/C][C]72[/C][C]74.061669219504[/C][C]-2.06166921950393[/C][/ROW]
[ROW][C]16[/C][C]45[/C][C]47.6753862420055[/C][C]-2.67538624200552[/C][/ROW]
[ROW][C]17[/C][C]56[/C][C]59.4940778847696[/C][C]-3.49407788476964[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]57.8916223752023[/C][C]-3.89162237520234[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]41.1203245417399[/C][C]11.8796754582601[/C][/ROW]
[ROW][C]20[/C][C]35[/C][C]28.3520055713391[/C][C]6.64799442866086[/C][/ROW]
[ROW][C]21[/C][C]61[/C][C]60.2217216429112[/C][C]0.778278357088801[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]72.5593142905455[/C][C]-20.5593142905455[/C][/ROW]
[ROW][C]23[/C][C]47[/C][C]52.1134651965227[/C][C]-5.11346519652266[/C][/ROW]
[ROW][C]24[/C][C]51[/C][C]62.4604805362263[/C][C]-11.4604805362263[/C][/ROW]
[ROW][C]25[/C][C]52[/C][C]46.2338254930999[/C][C]5.76617450690009[/C][/ROW]
[ROW][C]26[/C][C]63[/C][C]37.6724817373835[/C][C]25.3275182626165[/C][/ROW]
[ROW][C]27[/C][C]74[/C][C]73.4860349106542[/C][C]0.513965089345817[/C][/ROW]
[ROW][C]28[/C][C]45[/C][C]46.9406299672454[/C][C]-1.94062996724536[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]58.5322722115789[/C][C]-7.53227221157892[/C][/ROW]
[ROW][C]30[/C][C]64[/C][C]56.7955123055187[/C][C]7.20448769448126[/C][/ROW]
[ROW][C]31[/C][C]36[/C][C]44.5362894494873[/C][C]-8.53628944948731[/C][/ROW]
[ROW][C]32[/C][C]30[/C][C]30.1796304171774[/C][C]-0.179630417177368[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]60.3552905180826[/C][C]-5.35529051808256[/C][/ROW]
[ROW][C]34[/C][C]64[/C][C]66.6369154458488[/C][C]-2.63691544584883[/C][/ROW]
[ROW][C]35[/C][C]39[/C][C]50.64864398173[/C][C]-11.6486439817300[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]59.1684891381623[/C][C]-19.1684891381623[/C][/ROW]
[ROW][C]37[/C][C]63[/C][C]47.7617643883987[/C][C]15.2382356116013[/C][/ROW]
[ROW][C]38[/C][C]45[/C][C]44.7733240562875[/C][C]0.226675943712529[/C][/ROW]
[ROW][C]39[/C][C]59[/C][C]73.4460387434385[/C][C]-14.4460387434385[/C][/ROW]
[ROW][C]40[/C][C]55[/C][C]46.1259677051388[/C][C]8.87403229486119[/C][/ROW]
[ROW][C]41[/C][C]40[/C][C]56.1985901865845[/C][C]-16.1985901865845[/C][/ROW]
[ROW][C]42[/C][C]64[/C][C]58.5737588740304[/C][C]5.42624112596959[/C][/ROW]
[ROW][C]43[/C][C]27[/C][C]41.862069546533[/C][C]-14.862069546533[/C][/ROW]
[ROW][C]44[/C][C]28[/C][C]29.8294052226966[/C][C]-1.82940522269663[/C][/ROW]
[ROW][C]45[/C][C]45[/C][C]58.5352392738363[/C][C]-13.5352392738363[/C][/ROW]
[ROW][C]46[/C][C]57[/C][C]65.5393416137178[/C][C]-8.53934161371778[/C][/ROW]
[ROW][C]47[/C][C]45[/C][C]46.9752644441634[/C][C]-1.97526444416337[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]53.425620843247[/C][C]15.5743791567530[/C][/ROW]
[ROW][C]49[/C][C]60[/C][C]51.9201147520066[/C][C]8.07988524799342[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]44.6555810559099[/C][C]11.3444189440901[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]69.2478595159965[/C][C]-11.2478595159965[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]48.5272335380874[/C][C]1.47276646191262[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]51.4827620251635[/C][C]-0.482762025163474[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]60.0474109291823[/C][C]-7.0474109291823[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]37.5412094491569[/C][C]-0.541209449156923[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]29.2653063658442[/C][C]-7.26530636584425[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]54.637493673371[/C][C]0.36250632662896[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]63.1277152005227[/C][C]6.87228479947728[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]46.5006510210163[/C][C]15.4993489789837[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]57.9999171041062[/C][C]8.28958938114965e-05[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]54.2939035450508[/C][C]-15.2939035450508[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]47.8228451507844[/C][C]1.17715484921555[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]65.9829534109177[/C][C]-7.9829534109177[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]48.8705114775701[/C][C]-1.87051147757007[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]51.2558075547797[/C][C]-9.25580755477974[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]57.919613320685[/C][C]4.08038667931505[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]37.3106455072468[/C][C]1.68935449275322[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]27.1491159772013[/C][C]12.8508840227987[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]54.7842957353716[/C][C]17.2157042646284[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]65.2040941342166[/C][C]4.79590586578341[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]51.0006006656771[/C][C]2.99939933432294[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]58.0568881613235[/C][C]6.94311183867649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108256&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108256&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
134447.3857323232323-3.38573232323233
143638.5338697606428-2.53386976064281
157274.061669219504-2.06166921950393
164547.6753862420055-2.67538624200552
175659.4940778847696-3.49407788476964
185457.8916223752023-3.89162237520234
195341.120324541739911.8796754582601
203528.35200557133916.64799442866086
216160.22172164291120.778278357088801
225272.5593142905455-20.5593142905455
234752.1134651965227-5.11346519652266
245162.4604805362263-11.4604805362263
255246.23382549309995.76617450690009
266337.672481737383525.3275182626165
277473.48603491065420.513965089345817
284546.9406299672454-1.94062996724536
295158.5322722115789-7.53227221157892
306456.79551230551877.20448769448126
313644.5362894494873-8.53628944948731
323030.1796304171774-0.179630417177368
335560.3552905180826-5.35529051808256
346466.6369154458488-2.63691544584883
353950.64864398173-11.6486439817300
364059.1684891381623-19.1684891381623
376347.761764388398715.2382356116013
384544.77332405628750.226675943712529
395973.4460387434385-14.4460387434385
405546.12596770513888.87403229486119
414056.1985901865845-16.1985901865845
426458.57375887403045.42624112596959
432741.862069546533-14.862069546533
442829.8294052226966-1.82940522269663
454558.5352392738363-13.5352392738363
465765.5393416137178-8.53934161371778
474546.9752644441634-1.97526444416337
486953.42562084324715.5743791567530
496051.92011475200668.07988524799342
505644.655581055909911.3444189440901
515869.2478595159965-11.2478595159965
525048.52723353808741.47276646191262
535151.4827620251635-0.482762025163474
545360.0474109291823-7.0474109291823
553737.5412094491569-0.541209449156923
562229.2653063658442-7.26530636584425
575554.6374936733710.36250632662896
587063.12771520052276.87228479947728
596246.500651021016315.4993489789837
605857.99991710410628.28958938114965e-05
613954.2939035450508-15.2939035450508
624947.82284515078441.17715484921555
635865.9829534109177-7.9829534109177
644748.8705114775701-1.87051147757007
654251.2558075547797-9.25580755477974
666257.9196133206854.08038667931505
673937.31064550724681.68935449275322
684027.149115977201312.8508840227987
697254.784295735371617.2157042646284
707065.20409413421664.79590586578341
715451.00060066567712.99939933432294
726558.05688816132356.94311183867649







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7350.072241239640331.342357930085868.8021245491948
7448.333734234355729.603570438733267.0638980299781
7563.902017728765245.17157345127582.6324620062553
7648.558462413973429.827737658815767.2891871691312
7748.869542298567830.138537069942367.6005475271933
7859.348058988076940.616773290183378.0793446859704
7938.041906601852919.310340438890756.773472764815
8031.021402649605312.289556025773949.7532492734368
8159.818195725207841.086068644706178.5503228057094
8266.638367680326647.905960147353785.3707752132995
8351.901574887622533.168886906377170.6342628688679
8460.054535314807641.321566889488378.787503740127

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 50.0722412396403 & 31.3423579300858 & 68.8021245491948 \tabularnewline
74 & 48.3337342343557 & 29.6035704387332 & 67.0638980299781 \tabularnewline
75 & 63.9020177287652 & 45.171573451275 & 82.6324620062553 \tabularnewline
76 & 48.5584624139734 & 29.8277376588157 & 67.2891871691312 \tabularnewline
77 & 48.8695422985678 & 30.1385370699423 & 67.6005475271933 \tabularnewline
78 & 59.3480589880769 & 40.6167732901833 & 78.0793446859704 \tabularnewline
79 & 38.0419066018529 & 19.3103404388907 & 56.773472764815 \tabularnewline
80 & 31.0214026496053 & 12.2895560257739 & 49.7532492734368 \tabularnewline
81 & 59.8181957252078 & 41.0860686447061 & 78.5503228057094 \tabularnewline
82 & 66.6383676803266 & 47.9059601473537 & 85.3707752132995 \tabularnewline
83 & 51.9015748876225 & 33.1688869063771 & 70.6342628688679 \tabularnewline
84 & 60.0545353148076 & 41.3215668894883 & 78.787503740127 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=108256&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]50.0722412396403[/C][C]31.3423579300858[/C][C]68.8021245491948[/C][/ROW]
[ROW][C]74[/C][C]48.3337342343557[/C][C]29.6035704387332[/C][C]67.0638980299781[/C][/ROW]
[ROW][C]75[/C][C]63.9020177287652[/C][C]45.171573451275[/C][C]82.6324620062553[/C][/ROW]
[ROW][C]76[/C][C]48.5584624139734[/C][C]29.8277376588157[/C][C]67.2891871691312[/C][/ROW]
[ROW][C]77[/C][C]48.8695422985678[/C][C]30.1385370699423[/C][C]67.6005475271933[/C][/ROW]
[ROW][C]78[/C][C]59.3480589880769[/C][C]40.6167732901833[/C][C]78.0793446859704[/C][/ROW]
[ROW][C]79[/C][C]38.0419066018529[/C][C]19.3103404388907[/C][C]56.773472764815[/C][/ROW]
[ROW][C]80[/C][C]31.0214026496053[/C][C]12.2895560257739[/C][C]49.7532492734368[/C][/ROW]
[ROW][C]81[/C][C]59.8181957252078[/C][C]41.0860686447061[/C][C]78.5503228057094[/C][/ROW]
[ROW][C]82[/C][C]66.6383676803266[/C][C]47.9059601473537[/C][C]85.3707752132995[/C][/ROW]
[ROW][C]83[/C][C]51.9015748876225[/C][C]33.1688869063771[/C][C]70.6342628688679[/C][/ROW]
[ROW][C]84[/C][C]60.0545353148076[/C][C]41.3215668894883[/C][C]78.787503740127[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=108256&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=108256&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
7350.072241239640331.342357930085868.8021245491948
7448.333734234355729.603570438733267.0638980299781
7563.902017728765245.17157345127582.6324620062553
7648.558462413973429.827737658815767.2891871691312
7748.869542298567830.138537069942367.6005475271933
7859.348058988076940.616773290183378.0793446859704
7938.041906601852919.310340438890756.773472764815
8031.021402649605312.289556025773949.7532492734368
8159.818195725207841.086068644706178.5503228057094
8266.638367680326647.905960147353785.3707752132995
8351.901574887622533.168886906377170.6342628688679
8460.054535314807641.321566889488378.787503740127



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')