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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 26 May 2010 15:11:47 +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/May/26/t1274886799bw1nwjhw19r76fr.htm/, Retrieved Fri, 03 May 2024 09:59:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76501, Retrieved Fri, 03 May 2024 09:59:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDG2W61
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Inschrijvingen ni...] [2010-05-26 15:11:47] [b03685e875ed2700a03085f141fd8e3b] [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 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=76501&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=76501&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76501&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
alpha0.276932709155431
beta0
gamma0.577138618850172

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.276932709155431 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.577138618850172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76501&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]0.276932709155431[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.577138618850172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76501&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76501&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
alpha0.276932709155431
beta0
gamma0.577138618850172







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770240678.2345328283-2976.23453282829
143036432460.6011739035-2096.60117390354
153260934167.0670641293-1558.06706412932
163021231322.1289976808-1110.1289976808
172996530682.1979668410-717.197966841046
182835228822.4157242163-470.415724216327
192581422246.80888994643567.19111005355
202241421276.26412146211137.73587853791
212050621938.2570672756-1432.25706727559
222880627765.74323742791040.25676257205
232222823220.1160275709-992.116027570948
241397114690.4083149259-719.408314925868
253684537684.0013503702-839.001350370214
263533830425.31761441724912.68238558284
273502234297.6190903654724.380909634558
283477732271.69458509682505.30541490321
292688732796.9696720100-5909.96967200996
302397029602.1238049251-5632.12380492505
312278023282.0051084644-502.00510846444
321735120170.7307045642-2819.73070456416
332138218664.28780394552717.7121960545
342456126672.8410937893-2111.84109378929
351740920406.1652789812-2997.16527898118
361151411434.997516417779.0024835822751
373151434599.7892408052-3085.78924080518
382707129119.1319184530-2048.13191845304
392946229315.9359011925146.064098807492
402610527873.0542625796-1768.05426257959
412239723703.117345793-1306.11734579302
422384321899.17665074871943.82334925126
432170519817.93565269281887.06434730720
441808916401.06252359131687.93747640872
452076418453.77099997182310.22900002819
462531624334.0577029644981.94229703558
471770418554.6970174236-850.697017423641
481554811461.67227175144086.32772824861
492802934415.5240158981-6386.52401589813
502938328453.8101070086929.189892991424
513643830390.79195131006047.20804868996
523203429783.34925026082250.65074973920
532267926919.0941211718-4240.09412117184
542431925658.8722276831-1339.87222768305
551800422644.5824150959-4640.58241509589
561753717336.8927377133200.107262286729
572036619237.2608736831128.73912631699
582278224236.0469846087-1454.04698460875
591916917017.30236999972151.69763000032
601380712816.0089888519990.99101114807
612974330542.2343858723-799.234385872296
622559129180.7447235738-3589.74472357377
632909632002.0862132317-2906.08621323174
642648227330.8419313555-848.841931355491
652240520899.5827813071505.41721869300
662704422440.77267399884603.22732600125
671797019694.9019632502-1724.90196325023
681873017214.72806039411515.27193960594
691968419866.8357300826-182.835730082639
701978523424.5812421143-3639.58124211433
711847917105.30419734111373.69580265894
721069812204.1821164803-1506.1821164803

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 40678.2345328283 & -2976.23453282829 \tabularnewline
14 & 30364 & 32460.6011739035 & -2096.60117390354 \tabularnewline
15 & 32609 & 34167.0670641293 & -1558.06706412932 \tabularnewline
16 & 30212 & 31322.1289976808 & -1110.1289976808 \tabularnewline
17 & 29965 & 30682.1979668410 & -717.197966841046 \tabularnewline
18 & 28352 & 28822.4157242163 & -470.415724216327 \tabularnewline
19 & 25814 & 22246.8088899464 & 3567.19111005355 \tabularnewline
20 & 22414 & 21276.2641214621 & 1137.73587853791 \tabularnewline
21 & 20506 & 21938.2570672756 & -1432.25706727559 \tabularnewline
22 & 28806 & 27765.7432374279 & 1040.25676257205 \tabularnewline
23 & 22228 & 23220.1160275709 & -992.116027570948 \tabularnewline
24 & 13971 & 14690.4083149259 & -719.408314925868 \tabularnewline
25 & 36845 & 37684.0013503702 & -839.001350370214 \tabularnewline
26 & 35338 & 30425.3176144172 & 4912.68238558284 \tabularnewline
27 & 35022 & 34297.6190903654 & 724.380909634558 \tabularnewline
28 & 34777 & 32271.6945850968 & 2505.30541490321 \tabularnewline
29 & 26887 & 32796.9696720100 & -5909.96967200996 \tabularnewline
30 & 23970 & 29602.1238049251 & -5632.12380492505 \tabularnewline
31 & 22780 & 23282.0051084644 & -502.00510846444 \tabularnewline
32 & 17351 & 20170.7307045642 & -2819.73070456416 \tabularnewline
33 & 21382 & 18664.2878039455 & 2717.7121960545 \tabularnewline
34 & 24561 & 26672.8410937893 & -2111.84109378929 \tabularnewline
35 & 17409 & 20406.1652789812 & -2997.16527898118 \tabularnewline
36 & 11514 & 11434.9975164177 & 79.0024835822751 \tabularnewline
37 & 31514 & 34599.7892408052 & -3085.78924080518 \tabularnewline
38 & 27071 & 29119.1319184530 & -2048.13191845304 \tabularnewline
39 & 29462 & 29315.9359011925 & 146.064098807492 \tabularnewline
40 & 26105 & 27873.0542625796 & -1768.05426257959 \tabularnewline
41 & 22397 & 23703.117345793 & -1306.11734579302 \tabularnewline
42 & 23843 & 21899.1766507487 & 1943.82334925126 \tabularnewline
43 & 21705 & 19817.9356526928 & 1887.06434730720 \tabularnewline
44 & 18089 & 16401.0625235913 & 1687.93747640872 \tabularnewline
45 & 20764 & 18453.7709999718 & 2310.22900002819 \tabularnewline
46 & 25316 & 24334.0577029644 & 981.94229703558 \tabularnewline
47 & 17704 & 18554.6970174236 & -850.697017423641 \tabularnewline
48 & 15548 & 11461.6722717514 & 4086.32772824861 \tabularnewline
49 & 28029 & 34415.5240158981 & -6386.52401589813 \tabularnewline
50 & 29383 & 28453.8101070086 & 929.189892991424 \tabularnewline
51 & 36438 & 30390.7919513100 & 6047.20804868996 \tabularnewline
52 & 32034 & 29783.3492502608 & 2250.65074973920 \tabularnewline
53 & 22679 & 26919.0941211718 & -4240.09412117184 \tabularnewline
54 & 24319 & 25658.8722276831 & -1339.87222768305 \tabularnewline
55 & 18004 & 22644.5824150959 & -4640.58241509589 \tabularnewline
56 & 17537 & 17336.8927377133 & 200.107262286729 \tabularnewline
57 & 20366 & 19237.260873683 & 1128.73912631699 \tabularnewline
58 & 22782 & 24236.0469846087 & -1454.04698460875 \tabularnewline
59 & 19169 & 17017.3023699997 & 2151.69763000032 \tabularnewline
60 & 13807 & 12816.0089888519 & 990.99101114807 \tabularnewline
61 & 29743 & 30542.2343858723 & -799.234385872296 \tabularnewline
62 & 25591 & 29180.7447235738 & -3589.74472357377 \tabularnewline
63 & 29096 & 32002.0862132317 & -2906.08621323174 \tabularnewline
64 & 26482 & 27330.8419313555 & -848.841931355491 \tabularnewline
65 & 22405 & 20899.582781307 & 1505.41721869300 \tabularnewline
66 & 27044 & 22440.7726739988 & 4603.22732600125 \tabularnewline
67 & 17970 & 19694.9019632502 & -1724.90196325023 \tabularnewline
68 & 18730 & 17214.7280603941 & 1515.27193960594 \tabularnewline
69 & 19684 & 19866.8357300826 & -182.835730082639 \tabularnewline
70 & 19785 & 23424.5812421143 & -3639.58124211433 \tabularnewline
71 & 18479 & 17105.3041973411 & 1373.69580265894 \tabularnewline
72 & 10698 & 12204.1821164803 & -1506.1821164803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76501&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]40678.2345328283[/C][C]-2976.23453282829[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]32460.6011739035[/C][C]-2096.60117390354[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]34167.0670641293[/C][C]-1558.06706412932[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]31322.1289976808[/C][C]-1110.1289976808[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30682.1979668410[/C][C]-717.197966841046[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28822.4157242163[/C][C]-470.415724216327[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]22246.8088899464[/C][C]3567.19111005355[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]21276.2641214621[/C][C]1137.73587853791[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21938.2570672756[/C][C]-1432.25706727559[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]27765.7432374279[/C][C]1040.25676257205[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]23220.1160275709[/C][C]-992.116027570948[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]14690.4083149259[/C][C]-719.408314925868[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]37684.0013503702[/C][C]-839.001350370214[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]30425.3176144172[/C][C]4912.68238558284[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]34297.6190903654[/C][C]724.380909634558[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]32271.6945850968[/C][C]2505.30541490321[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]32796.9696720100[/C][C]-5909.96967200996[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]29602.1238049251[/C][C]-5632.12380492505[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]23282.0051084644[/C][C]-502.00510846444[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]20170.7307045642[/C][C]-2819.73070456416[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]18664.2878039455[/C][C]2717.7121960545[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]26672.8410937893[/C][C]-2111.84109378929[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]20406.1652789812[/C][C]-2997.16527898118[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]11434.9975164177[/C][C]79.0024835822751[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]34599.7892408052[/C][C]-3085.78924080518[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]29119.1319184530[/C][C]-2048.13191845304[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]29315.9359011925[/C][C]146.064098807492[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27873.0542625796[/C][C]-1768.05426257959[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]23703.117345793[/C][C]-1306.11734579302[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]21899.1766507487[/C][C]1943.82334925126[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]19817.9356526928[/C][C]1887.06434730720[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]16401.0625235913[/C][C]1687.93747640872[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]18453.7709999718[/C][C]2310.22900002819[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]24334.0577029644[/C][C]981.94229703558[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]18554.6970174236[/C][C]-850.697017423641[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]11461.6722717514[/C][C]4086.32772824861[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]34415.5240158981[/C][C]-6386.52401589813[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]28453.8101070086[/C][C]929.189892991424[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]30390.7919513100[/C][C]6047.20804868996[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]29783.3492502608[/C][C]2250.65074973920[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]26919.0941211718[/C][C]-4240.09412117184[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]25658.8722276831[/C][C]-1339.87222768305[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]22644.5824150959[/C][C]-4640.58241509589[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]17336.8927377133[/C][C]200.107262286729[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]19237.260873683[/C][C]1128.73912631699[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]24236.0469846087[/C][C]-1454.04698460875[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]17017.3023699997[/C][C]2151.69763000032[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12816.0089888519[/C][C]990.99101114807[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]30542.2343858723[/C][C]-799.234385872296[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]29180.7447235738[/C][C]-3589.74472357377[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]32002.0862132317[/C][C]-2906.08621323174[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]27330.8419313555[/C][C]-848.841931355491[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]20899.582781307[/C][C]1505.41721869300[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]22440.7726739988[/C][C]4603.22732600125[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]19694.9019632502[/C][C]-1724.90196325023[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]17214.7280603941[/C][C]1515.27193960594[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19866.8357300826[/C][C]-182.835730082639[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]23424.5812421143[/C][C]-3639.58124211433[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]17105.3041973411[/C][C]1373.69580265894[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]12204.1821164803[/C][C]-1506.1821164803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76501&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76501&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
133770240678.2345328283-2976.23453282829
143036432460.6011739035-2096.60117390354
153260934167.0670641293-1558.06706412932
163021231322.1289976808-1110.1289976808
172996530682.1979668410-717.197966841046
182835228822.4157242163-470.415724216327
192581422246.80888994643567.19111005355
202241421276.26412146211137.73587853791
212050621938.2570672756-1432.25706727559
222880627765.74323742791040.25676257205
232222823220.1160275709-992.116027570948
241397114690.4083149259-719.408314925868
253684537684.0013503702-839.001350370214
263533830425.31761441724912.68238558284
273502234297.6190903654724.380909634558
283477732271.69458509682505.30541490321
292688732796.9696720100-5909.96967200996
302397029602.1238049251-5632.12380492505
312278023282.0051084644-502.00510846444
321735120170.7307045642-2819.73070456416
332138218664.28780394552717.7121960545
342456126672.8410937893-2111.84109378929
351740920406.1652789812-2997.16527898118
361151411434.997516417779.0024835822751
373151434599.7892408052-3085.78924080518
382707129119.1319184530-2048.13191845304
392946229315.9359011925146.064098807492
402610527873.0542625796-1768.05426257959
412239723703.117345793-1306.11734579302
422384321899.17665074871943.82334925126
432170519817.93565269281887.06434730720
441808916401.06252359131687.93747640872
452076418453.77099997182310.22900002819
462531624334.0577029644981.94229703558
471770418554.6970174236-850.697017423641
481554811461.67227175144086.32772824861
492802934415.5240158981-6386.52401589813
502938328453.8101070086929.189892991424
513643830390.79195131006047.20804868996
523203429783.34925026082250.65074973920
532267926919.0941211718-4240.09412117184
542431925658.8722276831-1339.87222768305
551800422644.5824150959-4640.58241509589
561753717336.8927377133200.107262286729
572036619237.2608736831128.73912631699
582278224236.0469846087-1454.04698460875
591916917017.30236999972151.69763000032
601380712816.0089888519990.99101114807
612974330542.2343858723-799.234385872296
622559129180.7447235738-3589.74472357377
632909632002.0862132317-2906.08621323174
642648227330.8419313555-848.841931355491
652240520899.5827813071505.41721869300
662704422440.77267399884603.22732600125
671797019694.9019632502-1724.90196325023
681873017214.72806039411515.27193960594
691968419866.8357300826-182.835730082639
701978523424.5812421143-3639.58124211433
711847917105.30419734111373.69580265894
721069812204.1821164803-1506.1821164803







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7328491.779530535823325.366781081433658.1922799902
7426187.115982280720826.252014494831547.9799500666
7530287.872775726024739.368088471435836.3774629805
7627279.927551632321549.923533495333009.9315697693
7722066.196518729116160.268324850927972.1247126074
7824483.234456872418406.473015559630559.9958981853
7917821.787533844311578.865830186024064.7092375025
8017171.452562648410766.679874926623576.2252503703
8118695.294459590512132.661225532125257.9276936489
8220861.138497040614144.353793914627577.9232001667
8317641.871478024910774.394610096824509.3483459531
8411158.52607673704143.5934102811618173.4587431928

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 28491.7795305358 & 23325.3667810814 & 33658.1922799902 \tabularnewline
74 & 26187.1159822807 & 20826.2520144948 & 31547.9799500666 \tabularnewline
75 & 30287.8727757260 & 24739.3680884714 & 35836.3774629805 \tabularnewline
76 & 27279.9275516323 & 21549.9235334953 & 33009.9315697693 \tabularnewline
77 & 22066.1965187291 & 16160.2683248509 & 27972.1247126074 \tabularnewline
78 & 24483.2344568724 & 18406.4730155596 & 30559.9958981853 \tabularnewline
79 & 17821.7875338443 & 11578.8658301860 & 24064.7092375025 \tabularnewline
80 & 17171.4525626484 & 10766.6798749266 & 23576.2252503703 \tabularnewline
81 & 18695.2944595905 & 12132.6612255321 & 25257.9276936489 \tabularnewline
82 & 20861.1384970406 & 14144.3537939146 & 27577.9232001667 \tabularnewline
83 & 17641.8714780249 & 10774.3946100968 & 24509.3483459531 \tabularnewline
84 & 11158.5260767370 & 4143.59341028116 & 18173.4587431928 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76501&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]28491.7795305358[/C][C]23325.3667810814[/C][C]33658.1922799902[/C][/ROW]
[ROW][C]74[/C][C]26187.1159822807[/C][C]20826.2520144948[/C][C]31547.9799500666[/C][/ROW]
[ROW][C]75[/C][C]30287.8727757260[/C][C]24739.3680884714[/C][C]35836.3774629805[/C][/ROW]
[ROW][C]76[/C][C]27279.9275516323[/C][C]21549.9235334953[/C][C]33009.9315697693[/C][/ROW]
[ROW][C]77[/C][C]22066.1965187291[/C][C]16160.2683248509[/C][C]27972.1247126074[/C][/ROW]
[ROW][C]78[/C][C]24483.2344568724[/C][C]18406.4730155596[/C][C]30559.9958981853[/C][/ROW]
[ROW][C]79[/C][C]17821.7875338443[/C][C]11578.8658301860[/C][C]24064.7092375025[/C][/ROW]
[ROW][C]80[/C][C]17171.4525626484[/C][C]10766.6798749266[/C][C]23576.2252503703[/C][/ROW]
[ROW][C]81[/C][C]18695.2944595905[/C][C]12132.6612255321[/C][C]25257.9276936489[/C][/ROW]
[ROW][C]82[/C][C]20861.1384970406[/C][C]14144.3537939146[/C][C]27577.9232001667[/C][/ROW]
[ROW][C]83[/C][C]17641.8714780249[/C][C]10774.3946100968[/C][C]24509.3483459531[/C][/ROW]
[ROW][C]84[/C][C]11158.5260767370[/C][C]4143.59341028116[/C][C]18173.4587431928[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76501&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76501&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
7328491.779530535823325.366781081433658.1922799902
7426187.115982280720826.252014494831547.9799500666
7530287.872775726024739.368088471435836.3774629805
7627279.927551632321549.923533495333009.9315697693
7722066.196518729116160.268324850927972.1247126074
7824483.234456872418406.473015559630559.9958981853
7917821.787533844311578.865830186024064.7092375025
8017171.452562648410766.679874926623576.2252503703
8118695.294459590512132.661225532125257.9276936489
8220861.138497040614144.353793914627577.9232001667
8317641.871478024910774.394610096824509.3483459531
8411158.52607673704143.5934102811618173.4587431928



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')