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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 07 Dec 2010 09:58:27 +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/07/t1291715800elkh2z8z8b5t1y0.htm/, Retrieved Sat, 04 May 2024 04:13:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=106105, Retrieved Sat, 04 May 2024 04:13:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD    [Exponential Smoothing] [WS09 - Exponentia...] [2009-12-02 20:49:23] [df6326eec97a6ca984a853b142930499]
- R PD        [Exponential Smoothing] [] [2010-12-07 09:58:27] [44163a3390d803b6e1dc8c2f0815c192] [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=106105&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=106105&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106105&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
alpha0.00486104141907233
beta0.816160950605529
gamma0.253859759879226

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00486104141907233 \tabularnewline
beta & 0.816160950605529 \tabularnewline
gamma & 0.253859759879226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106105&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]0.00486104141907233[/C][/ROW]
[ROW][C]beta[/C][C]0.816160950605529[/C][/ROW]
[ROW][C]gamma[/C][C]0.253859759879226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106105&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106105&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
alpha0.00486104141907233
beta0.816160950605529
gamma0.253859759879226







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134446.6829275162342-2.68292751623424
143637.4196383690258-1.41963836902578
157273.8547395004858-1.85473950048576
164546.5003158720121-1.50031587201206
175658.5293158416863-2.52931584168627
185456.6179340105627-2.61793401056273
195339.825869690735213.1741303092648
203526.7436464175698.25635358243098
216158.30266627102122.69733372897877
225270.667386235984-18.6673862359840
234749.8742525002373-2.87425250023728
245160.2580225998112-9.25802259981117
255243.88711655824388.11288344175625
266335.419364207753827.5806357922462
277470.68919633858383.31080366141622
284544.62910981452910.370890185470877
295156.2747338131084-5.2747338131084
306454.61095231604359.38904768395653
313642.3713431831259-6.37134318312594
323028.3315118057261.66848819427402
335558.0298335364493-3.02983353644935
346464.9666781000709-0.966678100070894
353948.6148066632519-9.61480666325193
364057.3813612933541-17.3813612933541
376345.554295734300817.4457042656992
384542.15560803022532.84439196977471
395970.9117520359552-11.9117520359552
405544.241096990614810.7589030093852
414054.3989780908847-14.3989780908847
426456.319500689847.68049931015996
432740.237866253895-13.2378662538950
442828.3092091538995-0.309209153899509
454556.2456489846546-11.2456489846546
465763.3572291256966-6.35722912569665
474545.0549821644299-0.0549821644299016
486951.623107205678617.3768927943214
496048.83677367443311.1632263255670
505641.871317707152614.1286822928474
515866.4498641015078-8.44986410150784
525046.00471250467523.99528749532485
535149.70609807620211.29390192379785
545357.2169843150172-4.21698431501715
553736.21467178145530.785328218544734
562227.8192640714578-5.81926407145777
575552.63774541666852.36225458333146
587061.07513148409788.92486851590216
596244.745638714964717.2543612850353
605856.00907963593721.99092036406280
613951.7658097966268-12.7658097966268
624945.50490764904423.49509235095576
635864.37374008907-6.37374008907004
644747.0997914298967-0.0997914298967402
654250.1236187423505-8.12361874235045
666256.18280732034175.81719267965832
673936.47831959689372.52168040310625
684026.415682442467813.5843175575322
697253.74313603243318.2568639675670
707064.3185543765825.68144562341796
715450.06643977630463.93356022369539
726557.7210271947887.27897280521199

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 44 & 46.6829275162342 & -2.68292751623424 \tabularnewline
14 & 36 & 37.4196383690258 & -1.41963836902578 \tabularnewline
15 & 72 & 73.8547395004858 & -1.85473950048576 \tabularnewline
16 & 45 & 46.5003158720121 & -1.50031587201206 \tabularnewline
17 & 56 & 58.5293158416863 & -2.52931584168627 \tabularnewline
18 & 54 & 56.6179340105627 & -2.61793401056273 \tabularnewline
19 & 53 & 39.8258696907352 & 13.1741303092648 \tabularnewline
20 & 35 & 26.743646417569 & 8.25635358243098 \tabularnewline
21 & 61 & 58.3026662710212 & 2.69733372897877 \tabularnewline
22 & 52 & 70.667386235984 & -18.6673862359840 \tabularnewline
23 & 47 & 49.8742525002373 & -2.87425250023728 \tabularnewline
24 & 51 & 60.2580225998112 & -9.25802259981117 \tabularnewline
25 & 52 & 43.8871165582438 & 8.11288344175625 \tabularnewline
26 & 63 & 35.4193642077538 & 27.5806357922462 \tabularnewline
27 & 74 & 70.6891963385838 & 3.31080366141622 \tabularnewline
28 & 45 & 44.6291098145291 & 0.370890185470877 \tabularnewline
29 & 51 & 56.2747338131084 & -5.2747338131084 \tabularnewline
30 & 64 & 54.6109523160435 & 9.38904768395653 \tabularnewline
31 & 36 & 42.3713431831259 & -6.37134318312594 \tabularnewline
32 & 30 & 28.331511805726 & 1.66848819427402 \tabularnewline
33 & 55 & 58.0298335364493 & -3.02983353644935 \tabularnewline
34 & 64 & 64.9666781000709 & -0.966678100070894 \tabularnewline
35 & 39 & 48.6148066632519 & -9.61480666325193 \tabularnewline
36 & 40 & 57.3813612933541 & -17.3813612933541 \tabularnewline
37 & 63 & 45.5542957343008 & 17.4457042656992 \tabularnewline
38 & 45 & 42.1556080302253 & 2.84439196977471 \tabularnewline
39 & 59 & 70.9117520359552 & -11.9117520359552 \tabularnewline
40 & 55 & 44.2410969906148 & 10.7589030093852 \tabularnewline
41 & 40 & 54.3989780908847 & -14.3989780908847 \tabularnewline
42 & 64 & 56.31950068984 & 7.68049931015996 \tabularnewline
43 & 27 & 40.237866253895 & -13.2378662538950 \tabularnewline
44 & 28 & 28.3092091538995 & -0.309209153899509 \tabularnewline
45 & 45 & 56.2456489846546 & -11.2456489846546 \tabularnewline
46 & 57 & 63.3572291256966 & -6.35722912569665 \tabularnewline
47 & 45 & 45.0549821644299 & -0.0549821644299016 \tabularnewline
48 & 69 & 51.6231072056786 & 17.3768927943214 \tabularnewline
49 & 60 & 48.836773674433 & 11.1632263255670 \tabularnewline
50 & 56 & 41.8713177071526 & 14.1286822928474 \tabularnewline
51 & 58 & 66.4498641015078 & -8.44986410150784 \tabularnewline
52 & 50 & 46.0047125046752 & 3.99528749532485 \tabularnewline
53 & 51 & 49.7060980762021 & 1.29390192379785 \tabularnewline
54 & 53 & 57.2169843150172 & -4.21698431501715 \tabularnewline
55 & 37 & 36.2146717814553 & 0.785328218544734 \tabularnewline
56 & 22 & 27.8192640714578 & -5.81926407145777 \tabularnewline
57 & 55 & 52.6377454166685 & 2.36225458333146 \tabularnewline
58 & 70 & 61.0751314840978 & 8.92486851590216 \tabularnewline
59 & 62 & 44.7456387149647 & 17.2543612850353 \tabularnewline
60 & 58 & 56.0090796359372 & 1.99092036406280 \tabularnewline
61 & 39 & 51.7658097966268 & -12.7658097966268 \tabularnewline
62 & 49 & 45.5049076490442 & 3.49509235095576 \tabularnewline
63 & 58 & 64.37374008907 & -6.37374008907004 \tabularnewline
64 & 47 & 47.0997914298967 & -0.0997914298967402 \tabularnewline
65 & 42 & 50.1236187423505 & -8.12361874235045 \tabularnewline
66 & 62 & 56.1828073203417 & 5.81719267965832 \tabularnewline
67 & 39 & 36.4783195968937 & 2.52168040310625 \tabularnewline
68 & 40 & 26.4156824424678 & 13.5843175575322 \tabularnewline
69 & 72 & 53.743136032433 & 18.2568639675670 \tabularnewline
70 & 70 & 64.318554376582 & 5.68144562341796 \tabularnewline
71 & 54 & 50.0664397763046 & 3.93356022369539 \tabularnewline
72 & 65 & 57.721027194788 & 7.27897280521199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106105&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]46.6829275162342[/C][C]-2.68292751623424[/C][/ROW]
[ROW][C]14[/C][C]36[/C][C]37.4196383690258[/C][C]-1.41963836902578[/C][/ROW]
[ROW][C]15[/C][C]72[/C][C]73.8547395004858[/C][C]-1.85473950048576[/C][/ROW]
[ROW][C]16[/C][C]45[/C][C]46.5003158720121[/C][C]-1.50031587201206[/C][/ROW]
[ROW][C]17[/C][C]56[/C][C]58.5293158416863[/C][C]-2.52931584168627[/C][/ROW]
[ROW][C]18[/C][C]54[/C][C]56.6179340105627[/C][C]-2.61793401056273[/C][/ROW]
[ROW][C]19[/C][C]53[/C][C]39.8258696907352[/C][C]13.1741303092648[/C][/ROW]
[ROW][C]20[/C][C]35[/C][C]26.743646417569[/C][C]8.25635358243098[/C][/ROW]
[ROW][C]21[/C][C]61[/C][C]58.3026662710212[/C][C]2.69733372897877[/C][/ROW]
[ROW][C]22[/C][C]52[/C][C]70.667386235984[/C][C]-18.6673862359840[/C][/ROW]
[ROW][C]23[/C][C]47[/C][C]49.8742525002373[/C][C]-2.87425250023728[/C][/ROW]
[ROW][C]24[/C][C]51[/C][C]60.2580225998112[/C][C]-9.25802259981117[/C][/ROW]
[ROW][C]25[/C][C]52[/C][C]43.8871165582438[/C][C]8.11288344175625[/C][/ROW]
[ROW][C]26[/C][C]63[/C][C]35.4193642077538[/C][C]27.5806357922462[/C][/ROW]
[ROW][C]27[/C][C]74[/C][C]70.6891963385838[/C][C]3.31080366141622[/C][/ROW]
[ROW][C]28[/C][C]45[/C][C]44.6291098145291[/C][C]0.370890185470877[/C][/ROW]
[ROW][C]29[/C][C]51[/C][C]56.2747338131084[/C][C]-5.2747338131084[/C][/ROW]
[ROW][C]30[/C][C]64[/C][C]54.6109523160435[/C][C]9.38904768395653[/C][/ROW]
[ROW][C]31[/C][C]36[/C][C]42.3713431831259[/C][C]-6.37134318312594[/C][/ROW]
[ROW][C]32[/C][C]30[/C][C]28.331511805726[/C][C]1.66848819427402[/C][/ROW]
[ROW][C]33[/C][C]55[/C][C]58.0298335364493[/C][C]-3.02983353644935[/C][/ROW]
[ROW][C]34[/C][C]64[/C][C]64.9666781000709[/C][C]-0.966678100070894[/C][/ROW]
[ROW][C]35[/C][C]39[/C][C]48.6148066632519[/C][C]-9.61480666325193[/C][/ROW]
[ROW][C]36[/C][C]40[/C][C]57.3813612933541[/C][C]-17.3813612933541[/C][/ROW]
[ROW][C]37[/C][C]63[/C][C]45.5542957343008[/C][C]17.4457042656992[/C][/ROW]
[ROW][C]38[/C][C]45[/C][C]42.1556080302253[/C][C]2.84439196977471[/C][/ROW]
[ROW][C]39[/C][C]59[/C][C]70.9117520359552[/C][C]-11.9117520359552[/C][/ROW]
[ROW][C]40[/C][C]55[/C][C]44.2410969906148[/C][C]10.7589030093852[/C][/ROW]
[ROW][C]41[/C][C]40[/C][C]54.3989780908847[/C][C]-14.3989780908847[/C][/ROW]
[ROW][C]42[/C][C]64[/C][C]56.31950068984[/C][C]7.68049931015996[/C][/ROW]
[ROW][C]43[/C][C]27[/C][C]40.237866253895[/C][C]-13.2378662538950[/C][/ROW]
[ROW][C]44[/C][C]28[/C][C]28.3092091538995[/C][C]-0.309209153899509[/C][/ROW]
[ROW][C]45[/C][C]45[/C][C]56.2456489846546[/C][C]-11.2456489846546[/C][/ROW]
[ROW][C]46[/C][C]57[/C][C]63.3572291256966[/C][C]-6.35722912569665[/C][/ROW]
[ROW][C]47[/C][C]45[/C][C]45.0549821644299[/C][C]-0.0549821644299016[/C][/ROW]
[ROW][C]48[/C][C]69[/C][C]51.6231072056786[/C][C]17.3768927943214[/C][/ROW]
[ROW][C]49[/C][C]60[/C][C]48.836773674433[/C][C]11.1632263255670[/C][/ROW]
[ROW][C]50[/C][C]56[/C][C]41.8713177071526[/C][C]14.1286822928474[/C][/ROW]
[ROW][C]51[/C][C]58[/C][C]66.4498641015078[/C][C]-8.44986410150784[/C][/ROW]
[ROW][C]52[/C][C]50[/C][C]46.0047125046752[/C][C]3.99528749532485[/C][/ROW]
[ROW][C]53[/C][C]51[/C][C]49.7060980762021[/C][C]1.29390192379785[/C][/ROW]
[ROW][C]54[/C][C]53[/C][C]57.2169843150172[/C][C]-4.21698431501715[/C][/ROW]
[ROW][C]55[/C][C]37[/C][C]36.2146717814553[/C][C]0.785328218544734[/C][/ROW]
[ROW][C]56[/C][C]22[/C][C]27.8192640714578[/C][C]-5.81926407145777[/C][/ROW]
[ROW][C]57[/C][C]55[/C][C]52.6377454166685[/C][C]2.36225458333146[/C][/ROW]
[ROW][C]58[/C][C]70[/C][C]61.0751314840978[/C][C]8.92486851590216[/C][/ROW]
[ROW][C]59[/C][C]62[/C][C]44.7456387149647[/C][C]17.2543612850353[/C][/ROW]
[ROW][C]60[/C][C]58[/C][C]56.0090796359372[/C][C]1.99092036406280[/C][/ROW]
[ROW][C]61[/C][C]39[/C][C]51.7658097966268[/C][C]-12.7658097966268[/C][/ROW]
[ROW][C]62[/C][C]49[/C][C]45.5049076490442[/C][C]3.49509235095576[/C][/ROW]
[ROW][C]63[/C][C]58[/C][C]64.37374008907[/C][C]-6.37374008907004[/C][/ROW]
[ROW][C]64[/C][C]47[/C][C]47.0997914298967[/C][C]-0.0997914298967402[/C][/ROW]
[ROW][C]65[/C][C]42[/C][C]50.1236187423505[/C][C]-8.12361874235045[/C][/ROW]
[ROW][C]66[/C][C]62[/C][C]56.1828073203417[/C][C]5.81719267965832[/C][/ROW]
[ROW][C]67[/C][C]39[/C][C]36.4783195968937[/C][C]2.52168040310625[/C][/ROW]
[ROW][C]68[/C][C]40[/C][C]26.4156824424678[/C][C]13.5843175575322[/C][/ROW]
[ROW][C]69[/C][C]72[/C][C]53.743136032433[/C][C]18.2568639675670[/C][/ROW]
[ROW][C]70[/C][C]70[/C][C]64.318554376582[/C][C]5.68144562341796[/C][/ROW]
[ROW][C]71[/C][C]54[/C][C]50.0664397763046[/C][C]3.93356022369539[/C][/ROW]
[ROW][C]72[/C][C]65[/C][C]57.721027194788[/C][C]7.27897280521199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106105&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106105&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
134446.6829275162342-2.68292751623424
143637.4196383690258-1.41963836902578
157273.8547395004858-1.85473950048576
164546.5003158720121-1.50031587201206
175658.5293158416863-2.52931584168627
185456.6179340105627-2.61793401056273
195339.825869690735213.1741303092648
203526.7436464175698.25635358243098
216158.30266627102122.69733372897877
225270.667386235984-18.6673862359840
234749.8742525002373-2.87425250023728
245160.2580225998112-9.25802259981117
255243.88711655824388.11288344175625
266335.419364207753827.5806357922462
277470.68919633858383.31080366141622
284544.62910981452910.370890185470877
295156.2747338131084-5.2747338131084
306454.61095231604359.38904768395653
313642.3713431831259-6.37134318312594
323028.3315118057261.66848819427402
335558.0298335364493-3.02983353644935
346464.9666781000709-0.966678100070894
353948.6148066632519-9.61480666325193
364057.3813612933541-17.3813612933541
376345.554295734300817.4457042656992
384542.15560803022532.84439196977471
395970.9117520359552-11.9117520359552
405544.241096990614810.7589030093852
414054.3989780908847-14.3989780908847
426456.319500689847.68049931015996
432740.237866253895-13.2378662538950
442828.3092091538995-0.309209153899509
454556.2456489846546-11.2456489846546
465763.3572291256966-6.35722912569665
474545.0549821644299-0.0549821644299016
486951.623107205678617.3768927943214
496048.83677367443311.1632263255670
505641.871317707152614.1286822928474
515866.4498641015078-8.44986410150784
525046.00471250467523.99528749532485
535149.70609807620211.29390192379785
545357.2169843150172-4.21698431501715
553736.21467178145530.785328218544734
562227.8192640714578-5.81926407145777
575552.63774541666852.36225458333146
587061.07513148409788.92486851590216
596244.745638714964717.2543612850353
605856.00907963593721.99092036406280
613951.7658097966268-12.7658097966268
624945.50490764904423.49509235095576
635864.37374008907-6.37374008907004
644747.0997914298967-0.0997914298967402
654250.1236187423505-8.12361874235045
666256.18280732034175.81719267965832
673936.47831959689372.52168040310625
684026.415682442467813.5843175575322
697253.74313603243318.2568639675670
707064.3185543765825.68144562341796
715450.06643977630463.93356022369539
726557.7210271947887.27897280521199







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7349.767755753690444.972350825860354.5631606815204
7447.830331798597443.032348703388752.6283148938061
7564.954047705819660.143620457396669.7644749542427
7648.958077200170744.145470295495953.7706841048456
7750.214979671072245.387149802398555.0428095397458
7860.576485582196755.70494519010565.4480259742883
7939.158503224865934.315376391998144.0016300577338
8031.607055872534326.766507555788336.4476041892803
8161.790548334183856.754604238701566.8264924296661
8269.581249767776464.379624583401374.7828749521514
8354.038959206827148.919594805601359.1583236080529
8463.024726540055439.485705973781886.5637471063289

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 49.7677557536904 & 44.9723508258603 & 54.5631606815204 \tabularnewline
74 & 47.8303317985974 & 43.0323487033887 & 52.6283148938061 \tabularnewline
75 & 64.9540477058196 & 60.1436204573966 & 69.7644749542427 \tabularnewline
76 & 48.9580772001707 & 44.1454702954959 & 53.7706841048456 \tabularnewline
77 & 50.2149796710722 & 45.3871498023985 & 55.0428095397458 \tabularnewline
78 & 60.5764855821967 & 55.704945190105 & 65.4480259742883 \tabularnewline
79 & 39.1585032248659 & 34.3153763919981 & 44.0016300577338 \tabularnewline
80 & 31.6070558725343 & 26.7665075557883 & 36.4476041892803 \tabularnewline
81 & 61.7905483341838 & 56.7546042387015 & 66.8264924296661 \tabularnewline
82 & 69.5812497677764 & 64.3796245834013 & 74.7828749521514 \tabularnewline
83 & 54.0389592068271 & 48.9195948056013 & 59.1583236080529 \tabularnewline
84 & 63.0247265400554 & 39.4857059737818 & 86.5637471063289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=106105&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]49.7677557536904[/C][C]44.9723508258603[/C][C]54.5631606815204[/C][/ROW]
[ROW][C]74[/C][C]47.8303317985974[/C][C]43.0323487033887[/C][C]52.6283148938061[/C][/ROW]
[ROW][C]75[/C][C]64.9540477058196[/C][C]60.1436204573966[/C][C]69.7644749542427[/C][/ROW]
[ROW][C]76[/C][C]48.9580772001707[/C][C]44.1454702954959[/C][C]53.7706841048456[/C][/ROW]
[ROW][C]77[/C][C]50.2149796710722[/C][C]45.3871498023985[/C][C]55.0428095397458[/C][/ROW]
[ROW][C]78[/C][C]60.5764855821967[/C][C]55.704945190105[/C][C]65.4480259742883[/C][/ROW]
[ROW][C]79[/C][C]39.1585032248659[/C][C]34.3153763919981[/C][C]44.0016300577338[/C][/ROW]
[ROW][C]80[/C][C]31.6070558725343[/C][C]26.7665075557883[/C][C]36.4476041892803[/C][/ROW]
[ROW][C]81[/C][C]61.7905483341838[/C][C]56.7546042387015[/C][C]66.8264924296661[/C][/ROW]
[ROW][C]82[/C][C]69.5812497677764[/C][C]64.3796245834013[/C][C]74.7828749521514[/C][/ROW]
[ROW][C]83[/C][C]54.0389592068271[/C][C]48.9195948056013[/C][C]59.1583236080529[/C][/ROW]
[ROW][C]84[/C][C]63.0247265400554[/C][C]39.4857059737818[/C][C]86.5637471063289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=106105&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=106105&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
7349.767755753690444.972350825860354.5631606815204
7447.830331798597443.032348703388752.6283148938061
7564.954047705819660.143620457396669.7644749542427
7648.958077200170744.145470295495953.7706841048456
7750.214979671072245.387149802398555.0428095397458
7860.576485582196755.70494519010565.4480259742883
7939.158503224865934.315376391998144.0016300577338
8031.607055872534326.766507555788336.4476041892803
8161.790548334183856.754604238701566.8264924296661
8269.581249767776464.379624583401374.7828749521514
8354.038959206827148.919594805601359.1583236080529
8463.024726540055439.485705973781886.5637471063289



Parameters (Session):
par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')