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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 13:25:04 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t121182997174ssj75q6v3l738.htm/, Retrieved Tue, 14 May 2024 15:31:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13296, Retrieved Tue, 14 May 2024 15:31:09 +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)
-       [Exponential Smoothing] [Aantal inschrijvi...] [2008-05-26 19:25:04] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
42553




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 4 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13296&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13296&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 time4 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.341201512395321
beta0
gamma0.875658744185353

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.341201512395321 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.875658744185353 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13296&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]0.341201512395321[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.875658744185353[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13296&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
alpha0.341201512395321
beta0
gamma0.875658744185353







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133151432478.5095713308-964.509571330844
142707127633.7742594754-562.774259475369
152946229858.9789157948-396.9789157948
162610526330.1648576729-225.164857672855
172239722481.3197176804-84.3197176803551
182384323715.7001246415127.299875358458
192170521607.281587386897.718412613176
201808918073.508985442415.4910145576068
212076420410.3324553078353.667544692154
222531624471.6530318003844.346968199708
231770417130.465137269573.534862730987
241554815196.4047532664351.595246733594
252802932385.0996593921-4356.09965939209
262938326706.81409961032676.18590038965
273643830178.33451679156259.66548320847
283203428704.55353279933329.44646720072
292267925624.5654854751-2945.56548547514
302431926141.6085232899-1822.60852328993
311800423197.1778014374-5193.17780143743
321753717855.9746353464-318.974635346352
332036620225.0132730322140.986726967789
342278224397.1990318382-1615.19903183815
351916916489.00912869672679.99087130333
361380715176.5023585576-1369.50235855757
372974328198.49419227871544.50580772126
382559128537.0398580175-2946.03985801748
392909631673.3359923962-2577.33599239617
402648226188.2974754638293.702524536151
412240519745.35369278912659.64630721086
422704422584.96794119604459.03205880396
431797019658.4315366501-1688.43153665009
441873018296.8927127078433.107287292172
451968421325.3733064043-1641.37330640427
461978523917.1321619439-4132.1321619439
471847917634.8709733806844.12902661939
481069813583.343321264-2885.34332126400
493195626315.37190898675640.62809101327
502950625530.99772826633975.00227173373
513450631375.0867247413130.913275259
522716529177.6260856717-2012.62608567174
532673622842.14602008933893.85397991068
542369127229.5888103522-3538.58881035217
551815718195.9314115922-38.9314115921807
561732818620.8733458202-1292.87334582016
571820519792.5103910492-1587.51039104924
582099520771.6103722955223.389627704488
591738218766.0220572724-1384.02205727244
60936711714.4535764689-2347.45357646895
613112429291.61110669641832.38889330356
622655126320.8841670277230.115832972329
633065129965.1716088314685.828391168558
642585924678.65981012511180.34018987493
652510022911.06247311742188.93752688256
662577822472.65622834523305.34377165479
672041817885.16042988232532.83957011771
681868818436.2810108908251.718989109249
692042420027.6501251368396.349874863205
702477622983.55658364671792.44341635329
711981420187.2471478846-373.247147884569
721273811764.9277139464973.072286053635
734255338377.21058150394175.78941849613

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31514 & 32478.5095713308 & -964.509571330844 \tabularnewline
14 & 27071 & 27633.7742594754 & -562.774259475369 \tabularnewline
15 & 29462 & 29858.9789157948 & -396.9789157948 \tabularnewline
16 & 26105 & 26330.1648576729 & -225.164857672855 \tabularnewline
17 & 22397 & 22481.3197176804 & -84.3197176803551 \tabularnewline
18 & 23843 & 23715.7001246415 & 127.299875358458 \tabularnewline
19 & 21705 & 21607.2815873868 & 97.718412613176 \tabularnewline
20 & 18089 & 18073.5089854424 & 15.4910145576068 \tabularnewline
21 & 20764 & 20410.3324553078 & 353.667544692154 \tabularnewline
22 & 25316 & 24471.6530318003 & 844.346968199708 \tabularnewline
23 & 17704 & 17130.465137269 & 573.534862730987 \tabularnewline
24 & 15548 & 15196.4047532664 & 351.595246733594 \tabularnewline
25 & 28029 & 32385.0996593921 & -4356.09965939209 \tabularnewline
26 & 29383 & 26706.8140996103 & 2676.18590038965 \tabularnewline
27 & 36438 & 30178.3345167915 & 6259.66548320847 \tabularnewline
28 & 32034 & 28704.5535327993 & 3329.44646720072 \tabularnewline
29 & 22679 & 25624.5654854751 & -2945.56548547514 \tabularnewline
30 & 24319 & 26141.6085232899 & -1822.60852328993 \tabularnewline
31 & 18004 & 23197.1778014374 & -5193.17780143743 \tabularnewline
32 & 17537 & 17855.9746353464 & -318.974635346352 \tabularnewline
33 & 20366 & 20225.0132730322 & 140.986726967789 \tabularnewline
34 & 22782 & 24397.1990318382 & -1615.19903183815 \tabularnewline
35 & 19169 & 16489.0091286967 & 2679.99087130333 \tabularnewline
36 & 13807 & 15176.5023585576 & -1369.50235855757 \tabularnewline
37 & 29743 & 28198.4941922787 & 1544.50580772126 \tabularnewline
38 & 25591 & 28537.0398580175 & -2946.03985801748 \tabularnewline
39 & 29096 & 31673.3359923962 & -2577.33599239617 \tabularnewline
40 & 26482 & 26188.2974754638 & 293.702524536151 \tabularnewline
41 & 22405 & 19745.3536927891 & 2659.64630721086 \tabularnewline
42 & 27044 & 22584.9679411960 & 4459.03205880396 \tabularnewline
43 & 17970 & 19658.4315366501 & -1688.43153665009 \tabularnewline
44 & 18730 & 18296.8927127078 & 433.107287292172 \tabularnewline
45 & 19684 & 21325.3733064043 & -1641.37330640427 \tabularnewline
46 & 19785 & 23917.1321619439 & -4132.1321619439 \tabularnewline
47 & 18479 & 17634.8709733806 & 844.12902661939 \tabularnewline
48 & 10698 & 13583.343321264 & -2885.34332126400 \tabularnewline
49 & 31956 & 26315.3719089867 & 5640.62809101327 \tabularnewline
50 & 29506 & 25530.9977282663 & 3975.00227173373 \tabularnewline
51 & 34506 & 31375.086724741 & 3130.913275259 \tabularnewline
52 & 27165 & 29177.6260856717 & -2012.62608567174 \tabularnewline
53 & 26736 & 22842.1460200893 & 3893.85397991068 \tabularnewline
54 & 23691 & 27229.5888103522 & -3538.58881035217 \tabularnewline
55 & 18157 & 18195.9314115922 & -38.9314115921807 \tabularnewline
56 & 17328 & 18620.8733458202 & -1292.87334582016 \tabularnewline
57 & 18205 & 19792.5103910492 & -1587.51039104924 \tabularnewline
58 & 20995 & 20771.6103722955 & 223.389627704488 \tabularnewline
59 & 17382 & 18766.0220572724 & -1384.02205727244 \tabularnewline
60 & 9367 & 11714.4535764689 & -2347.45357646895 \tabularnewline
61 & 31124 & 29291.6111066964 & 1832.38889330356 \tabularnewline
62 & 26551 & 26320.8841670277 & 230.115832972329 \tabularnewline
63 & 30651 & 29965.1716088314 & 685.828391168558 \tabularnewline
64 & 25859 & 24678.6598101251 & 1180.34018987493 \tabularnewline
65 & 25100 & 22911.0624731174 & 2188.93752688256 \tabularnewline
66 & 25778 & 22472.6562283452 & 3305.34377165479 \tabularnewline
67 & 20418 & 17885.1604298823 & 2532.83957011771 \tabularnewline
68 & 18688 & 18436.2810108908 & 251.718989109249 \tabularnewline
69 & 20424 & 20027.6501251368 & 396.349874863205 \tabularnewline
70 & 24776 & 22983.5565836467 & 1792.44341635329 \tabularnewline
71 & 19814 & 20187.2471478846 & -373.247147884569 \tabularnewline
72 & 12738 & 11764.9277139464 & 973.072286053635 \tabularnewline
73 & 42553 & 38377.2105815039 & 4175.78941849613 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13296&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]31514[/C][C]32478.5095713308[/C][C]-964.509571330844[/C][/ROW]
[ROW][C]14[/C][C]27071[/C][C]27633.7742594754[/C][C]-562.774259475369[/C][/ROW]
[ROW][C]15[/C][C]29462[/C][C]29858.9789157948[/C][C]-396.9789157948[/C][/ROW]
[ROW][C]16[/C][C]26105[/C][C]26330.1648576729[/C][C]-225.164857672855[/C][/ROW]
[ROW][C]17[/C][C]22397[/C][C]22481.3197176804[/C][C]-84.3197176803551[/C][/ROW]
[ROW][C]18[/C][C]23843[/C][C]23715.7001246415[/C][C]127.299875358458[/C][/ROW]
[ROW][C]19[/C][C]21705[/C][C]21607.2815873868[/C][C]97.718412613176[/C][/ROW]
[ROW][C]20[/C][C]18089[/C][C]18073.5089854424[/C][C]15.4910145576068[/C][/ROW]
[ROW][C]21[/C][C]20764[/C][C]20410.3324553078[/C][C]353.667544692154[/C][/ROW]
[ROW][C]22[/C][C]25316[/C][C]24471.6530318003[/C][C]844.346968199708[/C][/ROW]
[ROW][C]23[/C][C]17704[/C][C]17130.465137269[/C][C]573.534862730987[/C][/ROW]
[ROW][C]24[/C][C]15548[/C][C]15196.4047532664[/C][C]351.595246733594[/C][/ROW]
[ROW][C]25[/C][C]28029[/C][C]32385.0996593921[/C][C]-4356.09965939209[/C][/ROW]
[ROW][C]26[/C][C]29383[/C][C]26706.8140996103[/C][C]2676.18590038965[/C][/ROW]
[ROW][C]27[/C][C]36438[/C][C]30178.3345167915[/C][C]6259.66548320847[/C][/ROW]
[ROW][C]28[/C][C]32034[/C][C]28704.5535327993[/C][C]3329.44646720072[/C][/ROW]
[ROW][C]29[/C][C]22679[/C][C]25624.5654854751[/C][C]-2945.56548547514[/C][/ROW]
[ROW][C]30[/C][C]24319[/C][C]26141.6085232899[/C][C]-1822.60852328993[/C][/ROW]
[ROW][C]31[/C][C]18004[/C][C]23197.1778014374[/C][C]-5193.17780143743[/C][/ROW]
[ROW][C]32[/C][C]17537[/C][C]17855.9746353464[/C][C]-318.974635346352[/C][/ROW]
[ROW][C]33[/C][C]20366[/C][C]20225.0132730322[/C][C]140.986726967789[/C][/ROW]
[ROW][C]34[/C][C]22782[/C][C]24397.1990318382[/C][C]-1615.19903183815[/C][/ROW]
[ROW][C]35[/C][C]19169[/C][C]16489.0091286967[/C][C]2679.99087130333[/C][/ROW]
[ROW][C]36[/C][C]13807[/C][C]15176.5023585576[/C][C]-1369.50235855757[/C][/ROW]
[ROW][C]37[/C][C]29743[/C][C]28198.4941922787[/C][C]1544.50580772126[/C][/ROW]
[ROW][C]38[/C][C]25591[/C][C]28537.0398580175[/C][C]-2946.03985801748[/C][/ROW]
[ROW][C]39[/C][C]29096[/C][C]31673.3359923962[/C][C]-2577.33599239617[/C][/ROW]
[ROW][C]40[/C][C]26482[/C][C]26188.2974754638[/C][C]293.702524536151[/C][/ROW]
[ROW][C]41[/C][C]22405[/C][C]19745.3536927891[/C][C]2659.64630721086[/C][/ROW]
[ROW][C]42[/C][C]27044[/C][C]22584.9679411960[/C][C]4459.03205880396[/C][/ROW]
[ROW][C]43[/C][C]17970[/C][C]19658.4315366501[/C][C]-1688.43153665009[/C][/ROW]
[ROW][C]44[/C][C]18730[/C][C]18296.8927127078[/C][C]433.107287292172[/C][/ROW]
[ROW][C]45[/C][C]19684[/C][C]21325.3733064043[/C][C]-1641.37330640427[/C][/ROW]
[ROW][C]46[/C][C]19785[/C][C]23917.1321619439[/C][C]-4132.1321619439[/C][/ROW]
[ROW][C]47[/C][C]18479[/C][C]17634.8709733806[/C][C]844.12902661939[/C][/ROW]
[ROW][C]48[/C][C]10698[/C][C]13583.343321264[/C][C]-2885.34332126400[/C][/ROW]
[ROW][C]49[/C][C]31956[/C][C]26315.3719089867[/C][C]5640.62809101327[/C][/ROW]
[ROW][C]50[/C][C]29506[/C][C]25530.9977282663[/C][C]3975.00227173373[/C][/ROW]
[ROW][C]51[/C][C]34506[/C][C]31375.086724741[/C][C]3130.913275259[/C][/ROW]
[ROW][C]52[/C][C]27165[/C][C]29177.6260856717[/C][C]-2012.62608567174[/C][/ROW]
[ROW][C]53[/C][C]26736[/C][C]22842.1460200893[/C][C]3893.85397991068[/C][/ROW]
[ROW][C]54[/C][C]23691[/C][C]27229.5888103522[/C][C]-3538.58881035217[/C][/ROW]
[ROW][C]55[/C][C]18157[/C][C]18195.9314115922[/C][C]-38.9314115921807[/C][/ROW]
[ROW][C]56[/C][C]17328[/C][C]18620.8733458202[/C][C]-1292.87334582016[/C][/ROW]
[ROW][C]57[/C][C]18205[/C][C]19792.5103910492[/C][C]-1587.51039104924[/C][/ROW]
[ROW][C]58[/C][C]20995[/C][C]20771.6103722955[/C][C]223.389627704488[/C][/ROW]
[ROW][C]59[/C][C]17382[/C][C]18766.0220572724[/C][C]-1384.02205727244[/C][/ROW]
[ROW][C]60[/C][C]9367[/C][C]11714.4535764689[/C][C]-2347.45357646895[/C][/ROW]
[ROW][C]61[/C][C]31124[/C][C]29291.6111066964[/C][C]1832.38889330356[/C][/ROW]
[ROW][C]62[/C][C]26551[/C][C]26320.8841670277[/C][C]230.115832972329[/C][/ROW]
[ROW][C]63[/C][C]30651[/C][C]29965.1716088314[/C][C]685.828391168558[/C][/ROW]
[ROW][C]64[/C][C]25859[/C][C]24678.6598101251[/C][C]1180.34018987493[/C][/ROW]
[ROW][C]65[/C][C]25100[/C][C]22911.0624731174[/C][C]2188.93752688256[/C][/ROW]
[ROW][C]66[/C][C]25778[/C][C]22472.6562283452[/C][C]3305.34377165479[/C][/ROW]
[ROW][C]67[/C][C]20418[/C][C]17885.1604298823[/C][C]2532.83957011771[/C][/ROW]
[ROW][C]68[/C][C]18688[/C][C]18436.2810108908[/C][C]251.718989109249[/C][/ROW]
[ROW][C]69[/C][C]20424[/C][C]20027.6501251368[/C][C]396.349874863205[/C][/ROW]
[ROW][C]70[/C][C]24776[/C][C]22983.5565836467[/C][C]1792.44341635329[/C][/ROW]
[ROW][C]71[/C][C]19814[/C][C]20187.2471478846[/C][C]-373.247147884569[/C][/ROW]
[ROW][C]72[/C][C]12738[/C][C]11764.9277139464[/C][C]973.072286053635[/C][/ROW]
[ROW][C]73[/C][C]42553[/C][C]38377.2105815039[/C][C]4175.78941849613[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13296&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
133151432478.5095713308-964.509571330844
142707127633.7742594754-562.774259475369
152946229858.9789157948-396.9789157948
162610526330.1648576729-225.164857672855
172239722481.3197176804-84.3197176803551
182384323715.7001246415127.299875358458
192170521607.281587386897.718412613176
201808918073.508985442415.4910145576068
212076420410.3324553078353.667544692154
222531624471.6530318003844.346968199708
231770417130.465137269573.534862730987
241554815196.4047532664351.595246733594
252802932385.0996593921-4356.09965939209
262938326706.81409961032676.18590038965
273643830178.33451679156259.66548320847
283203428704.55353279933329.44646720072
292267925624.5654854751-2945.56548547514
302431926141.6085232899-1822.60852328993
311800423197.1778014374-5193.17780143743
321753717855.9746353464-318.974635346352
332036620225.0132730322140.986726967789
342278224397.1990318382-1615.19903183815
351916916489.00912869672679.99087130333
361380715176.5023585576-1369.50235855757
372974328198.49419227871544.50580772126
382559128537.0398580175-2946.03985801748
392909631673.3359923962-2577.33599239617
402648226188.2974754638293.702524536151
412240519745.35369278912659.64630721086
422704422584.96794119604459.03205880396
431797019658.4315366501-1688.43153665009
441873018296.8927127078433.107287292172
451968421325.3733064043-1641.37330640427
461978523917.1321619439-4132.1321619439
471847917634.8709733806844.12902661939
481069813583.343321264-2885.34332126400
493195626315.37190898675640.62809101327
502950625530.99772826633975.00227173373
513450631375.0867247413130.913275259
522716529177.6260856717-2012.62608567174
532673622842.14602008933893.85397991068
542369127229.5888103522-3538.58881035217
551815718195.9314115922-38.9314115921807
561732818620.8733458202-1292.87334582016
571820519792.5103910492-1587.51039104924
582099520771.6103722955223.389627704488
591738218766.0220572724-1384.02205727244
60936711714.4535764689-2347.45357646895
613112429291.61110669641832.38889330356
622655126320.8841670277230.115832972329
633065129965.1716088314685.828391168558
642585924678.65981012511180.34018987493
652510022911.06247311742188.93752688256
662577822472.65622834523305.34377165479
672041817885.16042988232532.83957011771
681868818436.2810108908251.718989109249
692042420027.6501251368396.349874863205
702477622983.55658364671792.44341635329
711981420187.2471478846-373.247147884569
721273811764.9277139464973.072286053635
734255338377.21058150394175.78941849613







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7433992.870869480829630.556298043138355.1854409185
7538894.210444120534329.77500605643458.6458821849
7632224.915933597527437.450504000437012.3813631946
7730188.081733027125165.969628320935210.1938377332
7829422.063234473824516.097205535434328.0292634122
7922237.877406477817187.109324763127288.6454881925
8020444.698599120714990.006269721425899.3909285200
8122183.216849413216058.545704354928307.8879944714
8226098.713389792920362.052853509031835.3739260767
8321162.139053961216123.996404296726200.2817036257
8413128.23945331782550.8803300085523705.5985766271
8542210.9367385439NANA

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 33992.8708694808 & 29630.5562980431 & 38355.1854409185 \tabularnewline
75 & 38894.2104441205 & 34329.775006056 & 43458.6458821849 \tabularnewline
76 & 32224.9159335975 & 27437.4505040004 & 37012.3813631946 \tabularnewline
77 & 30188.0817330271 & 25165.9696283209 & 35210.1938377332 \tabularnewline
78 & 29422.0632344738 & 24516.0972055354 & 34328.0292634122 \tabularnewline
79 & 22237.8774064778 & 17187.1093247631 & 27288.6454881925 \tabularnewline
80 & 20444.6985991207 & 14990.0062697214 & 25899.3909285200 \tabularnewline
81 & 22183.2168494132 & 16058.5457043549 & 28307.8879944714 \tabularnewline
82 & 26098.7133897929 & 20362.0528535090 & 31835.3739260767 \tabularnewline
83 & 21162.1390539612 & 16123.9964042967 & 26200.2817036257 \tabularnewline
84 & 13128.2394533178 & 2550.88033000855 & 23705.5985766271 \tabularnewline
85 & 42210.9367385439 & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13296&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]74[/C][C]33992.8708694808[/C][C]29630.5562980431[/C][C]38355.1854409185[/C][/ROW]
[ROW][C]75[/C][C]38894.2104441205[/C][C]34329.775006056[/C][C]43458.6458821849[/C][/ROW]
[ROW][C]76[/C][C]32224.9159335975[/C][C]27437.4505040004[/C][C]37012.3813631946[/C][/ROW]
[ROW][C]77[/C][C]30188.0817330271[/C][C]25165.9696283209[/C][C]35210.1938377332[/C][/ROW]
[ROW][C]78[/C][C]29422.0632344738[/C][C]24516.0972055354[/C][C]34328.0292634122[/C][/ROW]
[ROW][C]79[/C][C]22237.8774064778[/C][C]17187.1093247631[/C][C]27288.6454881925[/C][/ROW]
[ROW][C]80[/C][C]20444.6985991207[/C][C]14990.0062697214[/C][C]25899.3909285200[/C][/ROW]
[ROW][C]81[/C][C]22183.2168494132[/C][C]16058.5457043549[/C][C]28307.8879944714[/C][/ROW]
[ROW][C]82[/C][C]26098.7133897929[/C][C]20362.0528535090[/C][C]31835.3739260767[/C][/ROW]
[ROW][C]83[/C][C]21162.1390539612[/C][C]16123.9964042967[/C][C]26200.2817036257[/C][/ROW]
[ROW][C]84[/C][C]13128.2394533178[/C][C]2550.88033000855[/C][C]23705.5985766271[/C][/ROW]
[ROW][C]85[/C][C]42210.9367385439[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13296&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13296&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
7433992.870869480829630.556298043138355.1854409185
7538894.210444120534329.77500605643458.6458821849
7632224.915933597527437.450504000437012.3813631946
7730188.081733027125165.969628320935210.1938377332
7829422.063234473824516.097205535434328.0292634122
7922237.877406477817187.109324763127288.6454881925
8020444.698599120714990.006269721425899.3909285200
8122183.216849413216058.545704354928307.8879944714
8226098.713389792920362.052853509031835.3739260767
8321162.139053961216123.996404296726200.2817036257
8413128.23945331782550.8803300085523705.5985766271
8542210.9367385439NANA



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')