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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 02 Jun 2010 08:45:25 +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/Jun/02/t1275468425fcwjldby5x4le33.htm/, Retrieved Thu, 31 Oct 2024 23:50:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76902, Retrieved Thu, 31 Oct 2024 23:50:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W61
Estimated Impact230
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opgave 10 oefening 1] [2010-01-19 17:45:21] [acb4d9171c10fb50d016574efb6916c7]
-    D    [Exponential Smoothing] [inschrijvingen ni...] [2010-06-02 08:45:25] [26ddb8a30b965ed6738d4d4bc4c527d5] [Current]
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Dataseries X:
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server184.73.236.201 @ 184.73.236.201

\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 & 184.73.236.201 @ 184.73.236.201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76902&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]184.73.236.201 @ 184.73.236.201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76902&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76902&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 Server184.73.236.201 @ 184.73.236.201







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.225679028753732
beta0.00094149628696139
gamma0.443442884267825

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.225679028753732 \tabularnewline
beta & 0.00094149628696139 \tabularnewline
gamma & 0.443442884267825 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76902&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]0.225679028753732[/C][/ROW]
[ROW][C]beta[/C][C]0.00094149628696139[/C][/ROW]
[ROW][C]gamma[/C][C]0.443442884267825[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76902&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76902&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
alpha0.225679028753732
beta0.00094149628696139
gamma0.443442884267825







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036432384.2423306432-2020.24233064318
153260934048.8239474283-1439.82394742829
163021230953.0817784316-741.081778431551
172996530167.1615625239-202.161562523925
182835228194.2876712464157.712328753587
192581422076.54434447373737.45565552631
202241420801.92075326921612.07924673078
212050621128.7820231174-622.782023117405
222880626754.5259191592051.47408084105
232222822076.0673310009151.932668999121
241397113470.8643970099500.1356029901
253684537059.4733194599-214.473319459903
263533829795.48397041035542.51602958971
273502233348.72441949681673.27558050316
283477731163.74413083673613.25586916331
292688731542.0186569803-4655.01865698035
302397028668.3449958561-4698.34499585611
312278022752.225994223627.7740057763804
321735120061.35455277-2710.35455277003
332138218709.04253007082672.95746992922
342456125498.9960342699-937.996034269905
351740920022.1189854628-2613.11898546284
361151411945.6711210855-431.671121085454
373151431811.142739522-297.142739522031
382707127135.223971572-64.2239715719661
392946227863.02418044031598.97581955968
402610526585.9480635963-480.948063596261
412239723768.4474504715-1371.44745047153
422384321869.56385517591973.43614482408
432170519509.10820626882195.89179373124
441808916761.2809759651327.71902403496
452076418040.74222789362723.25777210641
462531623196.82850721342119.17149278664
471770418102.3007276661-398.300727666137
481554811461.22353787174086.77646212826
492802933585.8002125576-5556.8002125576
502938327714.04861898681668.9513810132
513643829460.21037802946977.78962197057
523203428524.13301245923509.86698754081
532267925984.1070779241-3305.10707792409
542431924768.3603312277-449.360331227745
551800421738.5190502831-3734.51905028314
561753717326.1475284391210.852471560949
572036618790.72385674411575.27614325593
582278223364.3485694361-582.348569436119
591916917096.1467294062072.85327059405
601380712536.44630626261270.55369373736
612974329375.0615334862367.938466513806
622559127375.1673515005-1784.16735150052
632909629845.1799392579-749.179939257865
642648226329.5061513023152.493848697704
652240521403.18892294651001.81107705352
662704422062.65158253634981.3484174637
671797019291.1739870894-1321.17398708937
681873016843.79259252391886.2074074761
691968419125.9670976035558.032902396455
701978522648.0790967245-2863.07909672453
711847916985.57738857371493.42261142634
721069812280.7803828348-1582.78038283481

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 41487.9961256583 & -3785.99612565827 \tabularnewline
14 & 30364 & 32384.2423306432 & -2020.24233064318 \tabularnewline
15 & 32609 & 34048.8239474283 & -1439.82394742829 \tabularnewline
16 & 30212 & 30953.0817784316 & -741.081778431551 \tabularnewline
17 & 29965 & 30167.1615625239 & -202.161562523925 \tabularnewline
18 & 28352 & 28194.2876712464 & 157.712328753587 \tabularnewline
19 & 25814 & 22076.5443444737 & 3737.45565552631 \tabularnewline
20 & 22414 & 20801.9207532692 & 1612.07924673078 \tabularnewline
21 & 20506 & 21128.7820231174 & -622.782023117405 \tabularnewline
22 & 28806 & 26754.525919159 & 2051.47408084105 \tabularnewline
23 & 22228 & 22076.0673310009 & 151.932668999121 \tabularnewline
24 & 13971 & 13470.8643970099 & 500.1356029901 \tabularnewline
25 & 36845 & 37059.4733194599 & -214.473319459903 \tabularnewline
26 & 35338 & 29795.4839704103 & 5542.51602958971 \tabularnewline
27 & 35022 & 33348.7244194968 & 1673.27558050316 \tabularnewline
28 & 34777 & 31163.7441308367 & 3613.25586916331 \tabularnewline
29 & 26887 & 31542.0186569803 & -4655.01865698035 \tabularnewline
30 & 23970 & 28668.3449958561 & -4698.34499585611 \tabularnewline
31 & 22780 & 22752.2259942236 & 27.7740057763804 \tabularnewline
32 & 17351 & 20061.35455277 & -2710.35455277003 \tabularnewline
33 & 21382 & 18709.0425300708 & 2672.95746992922 \tabularnewline
34 & 24561 & 25498.9960342699 & -937.996034269905 \tabularnewline
35 & 17409 & 20022.1189854628 & -2613.11898546284 \tabularnewline
36 & 11514 & 11945.6711210855 & -431.671121085454 \tabularnewline
37 & 31514 & 31811.142739522 & -297.142739522031 \tabularnewline
38 & 27071 & 27135.223971572 & -64.2239715719661 \tabularnewline
39 & 29462 & 27863.0241804403 & 1598.97581955968 \tabularnewline
40 & 26105 & 26585.9480635963 & -480.948063596261 \tabularnewline
41 & 22397 & 23768.4474504715 & -1371.44745047153 \tabularnewline
42 & 23843 & 21869.5638551759 & 1973.43614482408 \tabularnewline
43 & 21705 & 19509.1082062688 & 2195.89179373124 \tabularnewline
44 & 18089 & 16761.280975965 & 1327.71902403496 \tabularnewline
45 & 20764 & 18040.7422278936 & 2723.25777210641 \tabularnewline
46 & 25316 & 23196.8285072134 & 2119.17149278664 \tabularnewline
47 & 17704 & 18102.3007276661 & -398.300727666137 \tabularnewline
48 & 15548 & 11461.2235378717 & 4086.77646212826 \tabularnewline
49 & 28029 & 33585.8002125576 & -5556.8002125576 \tabularnewline
50 & 29383 & 27714.0486189868 & 1668.9513810132 \tabularnewline
51 & 36438 & 29460.2103780294 & 6977.78962197057 \tabularnewline
52 & 32034 & 28524.1330124592 & 3509.86698754081 \tabularnewline
53 & 22679 & 25984.1070779241 & -3305.10707792409 \tabularnewline
54 & 24319 & 24768.3603312277 & -449.360331227745 \tabularnewline
55 & 18004 & 21738.5190502831 & -3734.51905028314 \tabularnewline
56 & 17537 & 17326.1475284391 & 210.852471560949 \tabularnewline
57 & 20366 & 18790.7238567441 & 1575.27614325593 \tabularnewline
58 & 22782 & 23364.3485694361 & -582.348569436119 \tabularnewline
59 & 19169 & 17096.146729406 & 2072.85327059405 \tabularnewline
60 & 13807 & 12536.4463062626 & 1270.55369373736 \tabularnewline
61 & 29743 & 29375.0615334862 & 367.938466513806 \tabularnewline
62 & 25591 & 27375.1673515005 & -1784.16735150052 \tabularnewline
63 & 29096 & 29845.1799392579 & -749.179939257865 \tabularnewline
64 & 26482 & 26329.5061513023 & 152.493848697704 \tabularnewline
65 & 22405 & 21403.1889229465 & 1001.81107705352 \tabularnewline
66 & 27044 & 22062.6515825363 & 4981.3484174637 \tabularnewline
67 & 17970 & 19291.1739870894 & -1321.17398708937 \tabularnewline
68 & 18730 & 16843.7925925239 & 1886.2074074761 \tabularnewline
69 & 19684 & 19125.9670976035 & 558.032902396455 \tabularnewline
70 & 19785 & 22648.0790967245 & -2863.07909672453 \tabularnewline
71 & 18479 & 16985.5773885737 & 1493.42261142634 \tabularnewline
72 & 10698 & 12280.7803828348 & -1582.78038283481 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76902&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]37702[/C][C]41487.9961256583[/C][C]-3785.99612565827[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]32384.2423306432[/C][C]-2020.24233064318[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]34048.8239474283[/C][C]-1439.82394742829[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30953.0817784316[/C][C]-741.081778431551[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30167.1615625239[/C][C]-202.161562523925[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28194.2876712464[/C][C]157.712328753587[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]22076.5443444737[/C][C]3737.45565552631[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]20801.9207532692[/C][C]1612.07924673078[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21128.7820231174[/C][C]-622.782023117405[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]26754.525919159[/C][C]2051.47408084105[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]22076.0673310009[/C][C]151.932668999121[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]13470.8643970099[/C][C]500.1356029901[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]37059.4733194599[/C][C]-214.473319459903[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]29795.4839704103[/C][C]5542.51602958971[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]33348.7244194968[/C][C]1673.27558050316[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]31163.7441308367[/C][C]3613.25586916331[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]31542.0186569803[/C][C]-4655.01865698035[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]28668.3449958561[/C][C]-4698.34499585611[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]22752.2259942236[/C][C]27.7740057763804[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]20061.35455277[/C][C]-2710.35455277003[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18709.0425300708[/C][C]2672.95746992922[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]25498.9960342699[/C][C]-937.996034269905[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]20022.1189854628[/C][C]-2613.11898546284[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]11945.6711210855[/C][C]-431.671121085454[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]31811.142739522[/C][C]-297.142739522031[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]27135.223971572[/C][C]-64.2239715719661[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]27863.0241804403[/C][C]1598.97581955968[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]26585.9480635963[/C][C]-480.948063596261[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]23768.4474504715[/C][C]-1371.44745047153[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21869.5638551759[/C][C]1973.43614482408[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19509.1082062688[/C][C]2195.89179373124[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]16761.280975965[/C][C]1327.71902403496[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18040.7422278936[/C][C]2723.25777210641[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]23196.8285072134[/C][C]2119.17149278664[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]18102.3007276661[/C][C]-398.300727666137[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]11461.2235378717[/C][C]4086.77646212826[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]33585.8002125576[/C][C]-5556.8002125576[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]27714.0486189868[/C][C]1668.9513810132[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]29460.2103780294[/C][C]6977.78962197057[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]28524.1330124592[/C][C]3509.86698754081[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]25984.1070779241[/C][C]-3305.10707792409[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]24768.3603312277[/C][C]-449.360331227745[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]21738.5190502831[/C][C]-3734.51905028314[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]17326.1475284391[/C][C]210.852471560949[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18790.7238567441[/C][C]1575.27614325593[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]23364.3485694361[/C][C]-582.348569436119[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]17096.146729406[/C][C]2072.85327059405[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12536.4463062626[/C][C]1270.55369373736[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]29375.0615334862[/C][C]367.938466513806[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]27375.1673515005[/C][C]-1784.16735150052[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]29845.1799392579[/C][C]-749.179939257865[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]26329.5061513023[/C][C]152.493848697704[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]21403.1889229465[/C][C]1001.81107705352[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]22062.6515825363[/C][C]4981.3484174637[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19291.1739870894[/C][C]-1321.17398708937[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]16843.7925925239[/C][C]1886.2074074761[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19125.9670976035[/C][C]558.032902396455[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]22648.0790967245[/C][C]-2863.07909672453[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]16985.5773885737[/C][C]1493.42261142634[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]12280.7803828348[/C][C]-1582.78038283481[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76902&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76902&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
133770241487.9961256583-3785.99612565827
143036432384.2423306432-2020.24233064318
153260934048.8239474283-1439.82394742829
163021230953.0817784316-741.081778431551
172996530167.1615625239-202.161562523925
182835228194.2876712464157.712328753587
192581422076.54434447373737.45565552631
202241420801.92075326921612.07924673078
212050621128.7820231174-622.782023117405
222880626754.5259191592051.47408084105
232222822076.0673310009151.932668999121
241397113470.8643970099500.1356029901
253684537059.4733194599-214.473319459903
263533829795.48397041035542.51602958971
273502233348.72441949681673.27558050316
283477731163.74413083673613.25586916331
292688731542.0186569803-4655.01865698035
302397028668.3449958561-4698.34499585611
312278022752.225994223627.7740057763804
321735120061.35455277-2710.35455277003
332138218709.04253007082672.95746992922
342456125498.9960342699-937.996034269905
351740920022.1189854628-2613.11898546284
361151411945.6711210855-431.671121085454
373151431811.142739522-297.142739522031
382707127135.223971572-64.2239715719661
392946227863.02418044031598.97581955968
402610526585.9480635963-480.948063596261
412239723768.4474504715-1371.44745047153
422384321869.56385517591973.43614482408
432170519509.10820626882195.89179373124
441808916761.2809759651327.71902403496
452076418040.74222789362723.25777210641
462531623196.82850721342119.17149278664
471770418102.3007276661-398.300727666137
481554811461.22353787174086.77646212826
492802933585.8002125576-5556.8002125576
502938327714.04861898681668.9513810132
513643829460.21037802946977.78962197057
523203428524.13301245923509.86698754081
532267925984.1070779241-3305.10707792409
542431924768.3603312277-449.360331227745
551800421738.5190502831-3734.51905028314
561753717326.1475284391210.852471560949
572036618790.72385674411575.27614325593
582278223364.3485694361-582.348569436119
591916917096.1467294062072.85327059405
601380712536.44630626261270.55369373736
612974329375.0615334862367.938466513806
622559127375.1673515005-1784.16735150052
632909629845.1799392579-749.179939257865
642648226329.5061513023152.493848697704
652240521403.18892294651001.81107705352
662704422062.65158253634981.3484174637
671797019291.1739870894-1321.17398708937
681873016843.79259252391886.2074074761
691968419125.9670976035558.032902396455
701978522648.0790967245-2863.07909672453
711847916985.57738857371493.42261142634
721069812280.7803828348-1582.78038283481







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7326498.981865143423698.880672300829299.083057986
7423934.863394318520956.288363419126913.4384252178
7526836.693618630423556.492578439430116.8946588213
7624042.23331480820686.841609152927397.6250204631
7719769.007584472216442.31068039923095.7044885454
7821288.45675620117662.497386310724914.4161260914
7916072.176615045812656.443904693519487.9093253982
8015124.888989784911597.600805588718652.1771739811
8116273.780768290912429.524494834220118.0370417475
8218070.92652369313805.659849372122336.193198014
8315008.434190426611001.710892847819015.1574880055
849842.625886158257798.833920993911886.4178513226

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 26498.9818651434 & 23698.8806723008 & 29299.083057986 \tabularnewline
74 & 23934.8633943185 & 20956.2883634191 & 26913.4384252178 \tabularnewline
75 & 26836.6936186304 & 23556.4925784394 & 30116.8946588213 \tabularnewline
76 & 24042.233314808 & 20686.8416091529 & 27397.6250204631 \tabularnewline
77 & 19769.0075844722 & 16442.310680399 & 23095.7044885454 \tabularnewline
78 & 21288.456756201 & 17662.4973863107 & 24914.4161260914 \tabularnewline
79 & 16072.1766150458 & 12656.4439046935 & 19487.9093253982 \tabularnewline
80 & 15124.8889897849 & 11597.6008055887 & 18652.1771739811 \tabularnewline
81 & 16273.7807682909 & 12429.5244948342 & 20118.0370417475 \tabularnewline
82 & 18070.926523693 & 13805.6598493721 & 22336.193198014 \tabularnewline
83 & 15008.4341904266 & 11001.7108928478 & 19015.1574880055 \tabularnewline
84 & 9842.62588615825 & 7798.8339209939 & 11886.4178513226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76902&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]26498.9818651434[/C][C]23698.8806723008[/C][C]29299.083057986[/C][/ROW]
[ROW][C]74[/C][C]23934.8633943185[/C][C]20956.2883634191[/C][C]26913.4384252178[/C][/ROW]
[ROW][C]75[/C][C]26836.6936186304[/C][C]23556.4925784394[/C][C]30116.8946588213[/C][/ROW]
[ROW][C]76[/C][C]24042.233314808[/C][C]20686.8416091529[/C][C]27397.6250204631[/C][/ROW]
[ROW][C]77[/C][C]19769.0075844722[/C][C]16442.310680399[/C][C]23095.7044885454[/C][/ROW]
[ROW][C]78[/C][C]21288.456756201[/C][C]17662.4973863107[/C][C]24914.4161260914[/C][/ROW]
[ROW][C]79[/C][C]16072.1766150458[/C][C]12656.4439046935[/C][C]19487.9093253982[/C][/ROW]
[ROW][C]80[/C][C]15124.8889897849[/C][C]11597.6008055887[/C][C]18652.1771739811[/C][/ROW]
[ROW][C]81[/C][C]16273.7807682909[/C][C]12429.5244948342[/C][C]20118.0370417475[/C][/ROW]
[ROW][C]82[/C][C]18070.926523693[/C][C]13805.6598493721[/C][C]22336.193198014[/C][/ROW]
[ROW][C]83[/C][C]15008.4341904266[/C][C]11001.7108928478[/C][C]19015.1574880055[/C][/ROW]
[ROW][C]84[/C][C]9842.62588615825[/C][C]7798.8339209939[/C][C]11886.4178513226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76902&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76902&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
7326498.981865143423698.880672300829299.083057986
7423934.863394318520956.288363419126913.4384252178
7526836.693618630423556.492578439430116.8946588213
7624042.23331480820686.841609152927397.6250204631
7719769.007584472216442.31068039923095.7044885454
7821288.45675620117662.497386310724914.4161260914
7916072.176615045812656.443904693519487.9093253982
8015124.888989784911597.600805588718652.1771739811
8116273.780768290912429.524494834220118.0370417475
8218070.92652369313805.659849372122336.193198014
8315008.434190426611001.710892847819015.1574880055
849842.625886158257798.833920993911886.4178513226



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=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')