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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Dec 2011 05:51:29 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/27/t13249833490rl6c7tq4ripsje.htm/, Retrieved Wed, 15 May 2024 18:59:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160836, Retrieved Wed, 15 May 2024 18:59:10 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W101
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Triple exponentia...] [2011-12-27 10:51:29] [a207ad521877ea2910ca3b39cbf26b1e] [Current]
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Dataseries X:
112
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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160836&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160836&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160836&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.25902280888716
beta0.00643275255092282
gamma0.518508624875071

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.25902280888716 \tabularnewline
beta & 0.00643275255092282 \tabularnewline
gamma & 0.518508624875071 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160836&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]0.25902280888716[/C][/ROW]
[ROW][C]beta[/C][C]0.00643275255092282[/C][/ROW]
[ROW][C]gamma[/C][C]0.518508624875071[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160836&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160836&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
alpha0.25902280888716
beta0.00643275255092282
gamma0.518508624875071







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131325314896.890033251-1643.89003325099
143770240729.7276444574-3027.72764445741
153036431766.1329411378-1402.13294113784
163260933411.6681128013-802.668112801308
173021230403.8105452627-191.810545262666
182996529673.2804454557291.719554544325
192835226223.20071690732128.79928309275
202581422135.39479064333678.60520935673
212241420918.11694229631495.88305770367
222050621233.6777040348-727.677704034762
232880626780.18250824972025.81749175026
242222822111.0534198786116.946580121359
251397112879.76560323841091.23439676157
263684537607.8080031076-762.808003107573
273533830122.96947918865215.03052081139
283502233793.69470082411228.30529917585
293477731496.6415844473280.35841555296
302688731878.3013483372-4991.30134833717
312397027714.2188039815-3744.21880398154
322278022774.82698719435.17301280567699
331735119960.729176134-2609.72917613399
342138218440.64723609552941.35276390448
352456125456.6759355639-895.67593556389
361740919879.9980018742-2470.9980018742
371151411505.66033651158.33966348851754
383151431549.5821304599-35.5821304598503
392707127170.638643196-99.6386431959945
402946227701.21162938511760.78837061486
412610526569.6298487773-464.629848777331
422239723437.6468824021-1040.64688240214
432384321130.08555654552712.91444345445
442170519615.85116512982089.14883487021
451808916723.52670386621365.47329613375
462076418233.12435997842530.87564002159
472531623316.62647676211999.37352323794
481770418106.9836227449-402.983622744949
491554811334.90190119194213.09809880808
502802934119.7517749012-6090.75177490119
512938328048.13142272111334.86857727891
523643829766.4261812886671.57381871197
533203428896.37887225413137.62112774588
542267926127.4166978422-3448.41669784225
552431924604.7222863251-285.722286325145
561800421920.2462249163-3916.24622491633
571753717207.5863200489329.413679951089
582036618845.86079972361520.13920027636
592278223321.9415223941-539.94152239407
601916916911.33181547922257.66818452077
611380712565.3606654111241.639334589
622974329037.0014467255705.998553274469
632559127633.4894690157-2042.48946901567
642909630173.5382312881-1077.53823128811
652648226355.8170054716126.182994528368
662240521091.56280773891313.43719226111
672704421933.28981104465110.7101889554
681797019373.1494182699-1403.14941826993
691873016992.33916464081737.66083535922
701968419460.7114608472223.288539152847
711978522770.7482653044-2985.74826530437
721847916996.31890748761482.68109251244
731069812331.482585119-1633.482585119

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13253 & 14896.890033251 & -1643.89003325099 \tabularnewline
14 & 37702 & 40729.7276444574 & -3027.72764445741 \tabularnewline
15 & 30364 & 31766.1329411378 & -1402.13294113784 \tabularnewline
16 & 32609 & 33411.6681128013 & -802.668112801308 \tabularnewline
17 & 30212 & 30403.8105452627 & -191.810545262666 \tabularnewline
18 & 29965 & 29673.2804454557 & 291.719554544325 \tabularnewline
19 & 28352 & 26223.2007169073 & 2128.79928309275 \tabularnewline
20 & 25814 & 22135.3947906433 & 3678.60520935673 \tabularnewline
21 & 22414 & 20918.1169422963 & 1495.88305770367 \tabularnewline
22 & 20506 & 21233.6777040348 & -727.677704034762 \tabularnewline
23 & 28806 & 26780.1825082497 & 2025.81749175026 \tabularnewline
24 & 22228 & 22111.0534198786 & 116.946580121359 \tabularnewline
25 & 13971 & 12879.7656032384 & 1091.23439676157 \tabularnewline
26 & 36845 & 37607.8080031076 & -762.808003107573 \tabularnewline
27 & 35338 & 30122.9694791886 & 5215.03052081139 \tabularnewline
28 & 35022 & 33793.6947008241 & 1228.30529917585 \tabularnewline
29 & 34777 & 31496.641584447 & 3280.35841555296 \tabularnewline
30 & 26887 & 31878.3013483372 & -4991.30134833717 \tabularnewline
31 & 23970 & 27714.2188039815 & -3744.21880398154 \tabularnewline
32 & 22780 & 22774.8269871943 & 5.17301280567699 \tabularnewline
33 & 17351 & 19960.729176134 & -2609.72917613399 \tabularnewline
34 & 21382 & 18440.6472360955 & 2941.35276390448 \tabularnewline
35 & 24561 & 25456.6759355639 & -895.67593556389 \tabularnewline
36 & 17409 & 19879.9980018742 & -2470.9980018742 \tabularnewline
37 & 11514 & 11505.6603365115 & 8.33966348851754 \tabularnewline
38 & 31514 & 31549.5821304599 & -35.5821304598503 \tabularnewline
39 & 27071 & 27170.638643196 & -99.6386431959945 \tabularnewline
40 & 29462 & 27701.2116293851 & 1760.78837061486 \tabularnewline
41 & 26105 & 26569.6298487773 & -464.629848777331 \tabularnewline
42 & 22397 & 23437.6468824021 & -1040.64688240214 \tabularnewline
43 & 23843 & 21130.0855565455 & 2712.91444345445 \tabularnewline
44 & 21705 & 19615.8511651298 & 2089.14883487021 \tabularnewline
45 & 18089 & 16723.5267038662 & 1365.47329613375 \tabularnewline
46 & 20764 & 18233.1243599784 & 2530.87564002159 \tabularnewline
47 & 25316 & 23316.6264767621 & 1999.37352323794 \tabularnewline
48 & 17704 & 18106.9836227449 & -402.983622744949 \tabularnewline
49 & 15548 & 11334.9019011919 & 4213.09809880808 \tabularnewline
50 & 28029 & 34119.7517749012 & -6090.75177490119 \tabularnewline
51 & 29383 & 28048.1314227211 & 1334.86857727891 \tabularnewline
52 & 36438 & 29766.426181288 & 6671.57381871197 \tabularnewline
53 & 32034 & 28896.3788722541 & 3137.62112774588 \tabularnewline
54 & 22679 & 26127.4166978422 & -3448.41669784225 \tabularnewline
55 & 24319 & 24604.7222863251 & -285.722286325145 \tabularnewline
56 & 18004 & 21920.2462249163 & -3916.24622491633 \tabularnewline
57 & 17537 & 17207.5863200489 & 329.413679951089 \tabularnewline
58 & 20366 & 18845.8607997236 & 1520.13920027636 \tabularnewline
59 & 22782 & 23321.9415223941 & -539.94152239407 \tabularnewline
60 & 19169 & 16911.3318154792 & 2257.66818452077 \tabularnewline
61 & 13807 & 12565.360665411 & 1241.639334589 \tabularnewline
62 & 29743 & 29037.0014467255 & 705.998553274469 \tabularnewline
63 & 25591 & 27633.4894690157 & -2042.48946901567 \tabularnewline
64 & 29096 & 30173.5382312881 & -1077.53823128811 \tabularnewline
65 & 26482 & 26355.8170054716 & 126.182994528368 \tabularnewline
66 & 22405 & 21091.5628077389 & 1313.43719226111 \tabularnewline
67 & 27044 & 21933.2898110446 & 5110.7101889554 \tabularnewline
68 & 17970 & 19373.1494182699 & -1403.14941826993 \tabularnewline
69 & 18730 & 16992.3391646408 & 1737.66083535922 \tabularnewline
70 & 19684 & 19460.7114608472 & 223.288539152847 \tabularnewline
71 & 19785 & 22770.7482653044 & -2985.74826530437 \tabularnewline
72 & 18479 & 16996.3189074876 & 1482.68109251244 \tabularnewline
73 & 10698 & 12331.482585119 & -1633.482585119 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160836&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]13253[/C][C]14896.890033251[/C][C]-1643.89003325099[/C][/ROW]
[ROW][C]14[/C][C]37702[/C][C]40729.7276444574[/C][C]-3027.72764445741[/C][/ROW]
[ROW][C]15[/C][C]30364[/C][C]31766.1329411378[/C][C]-1402.13294113784[/C][/ROW]
[ROW][C]16[/C][C]32609[/C][C]33411.6681128013[/C][C]-802.668112801308[/C][/ROW]
[ROW][C]17[/C][C]30212[/C][C]30403.8105452627[/C][C]-191.810545262666[/C][/ROW]
[ROW][C]18[/C][C]29965[/C][C]29673.2804454557[/C][C]291.719554544325[/C][/ROW]
[ROW][C]19[/C][C]28352[/C][C]26223.2007169073[/C][C]2128.79928309275[/C][/ROW]
[ROW][C]20[/C][C]25814[/C][C]22135.3947906433[/C][C]3678.60520935673[/C][/ROW]
[ROW][C]21[/C][C]22414[/C][C]20918.1169422963[/C][C]1495.88305770367[/C][/ROW]
[ROW][C]22[/C][C]20506[/C][C]21233.6777040348[/C][C]-727.677704034762[/C][/ROW]
[ROW][C]23[/C][C]28806[/C][C]26780.1825082497[/C][C]2025.81749175026[/C][/ROW]
[ROW][C]24[/C][C]22228[/C][C]22111.0534198786[/C][C]116.946580121359[/C][/ROW]
[ROW][C]25[/C][C]13971[/C][C]12879.7656032384[/C][C]1091.23439676157[/C][/ROW]
[ROW][C]26[/C][C]36845[/C][C]37607.8080031076[/C][C]-762.808003107573[/C][/ROW]
[ROW][C]27[/C][C]35338[/C][C]30122.9694791886[/C][C]5215.03052081139[/C][/ROW]
[ROW][C]28[/C][C]35022[/C][C]33793.6947008241[/C][C]1228.30529917585[/C][/ROW]
[ROW][C]29[/C][C]34777[/C][C]31496.641584447[/C][C]3280.35841555296[/C][/ROW]
[ROW][C]30[/C][C]26887[/C][C]31878.3013483372[/C][C]-4991.30134833717[/C][/ROW]
[ROW][C]31[/C][C]23970[/C][C]27714.2188039815[/C][C]-3744.21880398154[/C][/ROW]
[ROW][C]32[/C][C]22780[/C][C]22774.8269871943[/C][C]5.17301280567699[/C][/ROW]
[ROW][C]33[/C][C]17351[/C][C]19960.729176134[/C][C]-2609.72917613399[/C][/ROW]
[ROW][C]34[/C][C]21382[/C][C]18440.6472360955[/C][C]2941.35276390448[/C][/ROW]
[ROW][C]35[/C][C]24561[/C][C]25456.6759355639[/C][C]-895.67593556389[/C][/ROW]
[ROW][C]36[/C][C]17409[/C][C]19879.9980018742[/C][C]-2470.9980018742[/C][/ROW]
[ROW][C]37[/C][C]11514[/C][C]11505.6603365115[/C][C]8.33966348851754[/C][/ROW]
[ROW][C]38[/C][C]31514[/C][C]31549.5821304599[/C][C]-35.5821304598503[/C][/ROW]
[ROW][C]39[/C][C]27071[/C][C]27170.638643196[/C][C]-99.6386431959945[/C][/ROW]
[ROW][C]40[/C][C]29462[/C][C]27701.2116293851[/C][C]1760.78837061486[/C][/ROW]
[ROW][C]41[/C][C]26105[/C][C]26569.6298487773[/C][C]-464.629848777331[/C][/ROW]
[ROW][C]42[/C][C]22397[/C][C]23437.6468824021[/C][C]-1040.64688240214[/C][/ROW]
[ROW][C]43[/C][C]23843[/C][C]21130.0855565455[/C][C]2712.91444345445[/C][/ROW]
[ROW][C]44[/C][C]21705[/C][C]19615.8511651298[/C][C]2089.14883487021[/C][/ROW]
[ROW][C]45[/C][C]18089[/C][C]16723.5267038662[/C][C]1365.47329613375[/C][/ROW]
[ROW][C]46[/C][C]20764[/C][C]18233.1243599784[/C][C]2530.87564002159[/C][/ROW]
[ROW][C]47[/C][C]25316[/C][C]23316.6264767621[/C][C]1999.37352323794[/C][/ROW]
[ROW][C]48[/C][C]17704[/C][C]18106.9836227449[/C][C]-402.983622744949[/C][/ROW]
[ROW][C]49[/C][C]15548[/C][C]11334.9019011919[/C][C]4213.09809880808[/C][/ROW]
[ROW][C]50[/C][C]28029[/C][C]34119.7517749012[/C][C]-6090.75177490119[/C][/ROW]
[ROW][C]51[/C][C]29383[/C][C]28048.1314227211[/C][C]1334.86857727891[/C][/ROW]
[ROW][C]52[/C][C]36438[/C][C]29766.426181288[/C][C]6671.57381871197[/C][/ROW]
[ROW][C]53[/C][C]32034[/C][C]28896.3788722541[/C][C]3137.62112774588[/C][/ROW]
[ROW][C]54[/C][C]22679[/C][C]26127.4166978422[/C][C]-3448.41669784225[/C][/ROW]
[ROW][C]55[/C][C]24319[/C][C]24604.7222863251[/C][C]-285.722286325145[/C][/ROW]
[ROW][C]56[/C][C]18004[/C][C]21920.2462249163[/C][C]-3916.24622491633[/C][/ROW]
[ROW][C]57[/C][C]17537[/C][C]17207.5863200489[/C][C]329.413679951089[/C][/ROW]
[ROW][C]58[/C][C]20366[/C][C]18845.8607997236[/C][C]1520.13920027636[/C][/ROW]
[ROW][C]59[/C][C]22782[/C][C]23321.9415223941[/C][C]-539.94152239407[/C][/ROW]
[ROW][C]60[/C][C]19169[/C][C]16911.3318154792[/C][C]2257.66818452077[/C][/ROW]
[ROW][C]61[/C][C]13807[/C][C]12565.360665411[/C][C]1241.639334589[/C][/ROW]
[ROW][C]62[/C][C]29743[/C][C]29037.0014467255[/C][C]705.998553274469[/C][/ROW]
[ROW][C]63[/C][C]25591[/C][C]27633.4894690157[/C][C]-2042.48946901567[/C][/ROW]
[ROW][C]64[/C][C]29096[/C][C]30173.5382312881[/C][C]-1077.53823128811[/C][/ROW]
[ROW][C]65[/C][C]26482[/C][C]26355.8170054716[/C][C]126.182994528368[/C][/ROW]
[ROW][C]66[/C][C]22405[/C][C]21091.5628077389[/C][C]1313.43719226111[/C][/ROW]
[ROW][C]67[/C][C]27044[/C][C]21933.2898110446[/C][C]5110.7101889554[/C][/ROW]
[ROW][C]68[/C][C]17970[/C][C]19373.1494182699[/C][C]-1403.14941826993[/C][/ROW]
[ROW][C]69[/C][C]18730[/C][C]16992.3391646408[/C][C]1737.66083535922[/C][/ROW]
[ROW][C]70[/C][C]19684[/C][C]19460.7114608472[/C][C]223.288539152847[/C][/ROW]
[ROW][C]71[/C][C]19785[/C][C]22770.7482653044[/C][C]-2985.74826530437[/C][/ROW]
[ROW][C]72[/C][C]18479[/C][C]16996.3189074876[/C][C]1482.68109251244[/C][/ROW]
[ROW][C]73[/C][C]10698[/C][C]12331.482585119[/C][C]-1633.482585119[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160836&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160836&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
131325314896.890033251-1643.89003325099
143770240729.7276444574-3027.72764445741
153036431766.1329411378-1402.13294113784
163260933411.6681128013-802.668112801308
173021230403.8105452627-191.810545262666
182996529673.2804454557291.719554544325
192835226223.20071690732128.79928309275
202581422135.39479064333678.60520935673
212241420918.11694229631495.88305770367
222050621233.6777040348-727.677704034762
232880626780.18250824972025.81749175026
242222822111.0534198786116.946580121359
251397112879.76560323841091.23439676157
263684537607.8080031076-762.808003107573
273533830122.96947918865215.03052081139
283502233793.69470082411228.30529917585
293477731496.6415844473280.35841555296
302688731878.3013483372-4991.30134833717
312397027714.2188039815-3744.21880398154
322278022774.82698719435.17301280567699
331735119960.729176134-2609.72917613399
342138218440.64723609552941.35276390448
352456125456.6759355639-895.67593556389
361740919879.9980018742-2470.9980018742
371151411505.66033651158.33966348851754
383151431549.5821304599-35.5821304598503
392707127170.638643196-99.6386431959945
402946227701.21162938511760.78837061486
412610526569.6298487773-464.629848777331
422239723437.6468824021-1040.64688240214
432384321130.08555654552712.91444345445
442170519615.85116512982089.14883487021
451808916723.52670386621365.47329613375
462076418233.12435997842530.87564002159
472531623316.62647676211999.37352323794
481770418106.9836227449-402.983622744949
491554811334.90190119194213.09809880808
502802934119.7517749012-6090.75177490119
512938328048.13142272111334.86857727891
523643829766.4261812886671.57381871197
533203428896.37887225413137.62112774588
542267926127.4166978422-3448.41669784225
552431924604.7222863251-285.722286325145
561800421920.2462249163-3916.24622491633
571753717207.5863200489329.413679951089
582036618845.86079972361520.13920027636
592278223321.9415223941-539.94152239407
601916916911.33181547922257.66818452077
611380712565.3606654111241.639334589
622974329037.0014467255705.998553274469
632559127633.4894690157-2042.48946901567
642909630173.5382312881-1077.53823128811
652648226355.8170054716126.182994528368
662240521091.56280773891313.43719226111
672704421933.28981104465110.7101889554
681797019373.1494182699-1403.14941826993
691873016992.33916464081737.66083535922
701968419460.7114608472223.288539152847
711978522770.7482653044-2985.74826530437
721847916996.31890748761482.68109251244
731069812331.482585119-1633.482585119







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7426083.406022474422973.459253106829193.352791842
7523701.432956641820382.493921111627020.3719921721
7626768.400564773123090.572880959430446.2282485867
7723954.270122334820188.680670761627719.8595739081
7819542.90020680215818.511981353423267.2884322507
7921163.849986121217077.645031773825250.0549404686
8015759.833344671811935.896790719819583.7698986239
8115023.178093690511044.726594366419001.6295930145
8216173.827955593111817.309337368520530.3465738177
8317759.752089183312931.907855219222587.5963231474
8414920.456512932910355.922227521919484.9907983439
859685.421679130197322.69710310112048.1462551594

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 26083.4060224744 & 22973.4592531068 & 29193.352791842 \tabularnewline
75 & 23701.4329566418 & 20382.4939211116 & 27020.3719921721 \tabularnewline
76 & 26768.4005647731 & 23090.5728809594 & 30446.2282485867 \tabularnewline
77 & 23954.2701223348 & 20188.6806707616 & 27719.8595739081 \tabularnewline
78 & 19542.900206802 & 15818.5119813534 & 23267.2884322507 \tabularnewline
79 & 21163.8499861212 & 17077.6450317738 & 25250.0549404686 \tabularnewline
80 & 15759.8333446718 & 11935.8967907198 & 19583.7698986239 \tabularnewline
81 & 15023.1780936905 & 11044.7265943664 & 19001.6295930145 \tabularnewline
82 & 16173.8279555931 & 11817.3093373685 & 20530.3465738177 \tabularnewline
83 & 17759.7520891833 & 12931.9078552192 & 22587.5963231474 \tabularnewline
84 & 14920.4565129329 & 10355.9222275219 & 19484.9907983439 \tabularnewline
85 & 9685.42167913019 & 7322.697103101 & 12048.1462551594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160836&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]26083.4060224744[/C][C]22973.4592531068[/C][C]29193.352791842[/C][/ROW]
[ROW][C]75[/C][C]23701.4329566418[/C][C]20382.4939211116[/C][C]27020.3719921721[/C][/ROW]
[ROW][C]76[/C][C]26768.4005647731[/C][C]23090.5728809594[/C][C]30446.2282485867[/C][/ROW]
[ROW][C]77[/C][C]23954.2701223348[/C][C]20188.6806707616[/C][C]27719.8595739081[/C][/ROW]
[ROW][C]78[/C][C]19542.900206802[/C][C]15818.5119813534[/C][C]23267.2884322507[/C][/ROW]
[ROW][C]79[/C][C]21163.8499861212[/C][C]17077.6450317738[/C][C]25250.0549404686[/C][/ROW]
[ROW][C]80[/C][C]15759.8333446718[/C][C]11935.8967907198[/C][C]19583.7698986239[/C][/ROW]
[ROW][C]81[/C][C]15023.1780936905[/C][C]11044.7265943664[/C][C]19001.6295930145[/C][/ROW]
[ROW][C]82[/C][C]16173.8279555931[/C][C]11817.3093373685[/C][C]20530.3465738177[/C][/ROW]
[ROW][C]83[/C][C]17759.7520891833[/C][C]12931.9078552192[/C][C]22587.5963231474[/C][/ROW]
[ROW][C]84[/C][C]14920.4565129329[/C][C]10355.9222275219[/C][C]19484.9907983439[/C][/ROW]
[ROW][C]85[/C][C]9685.42167913019[/C][C]7322.697103101[/C][C]12048.1462551594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160836&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160836&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
7426083.406022474422973.459253106829193.352791842
7523701.432956641820382.493921111627020.3719921721
7626768.400564773123090.572880959430446.2282485867
7723954.270122334820188.680670761627719.8595739081
7819542.90020680215818.511981353423267.2884322507
7921163.849986121217077.645031773825250.0549404686
8015759.833344671811935.896790719819583.7698986239
8115023.178093690511044.726594366419001.6295930145
8216173.827955593111817.309337368520530.3465738177
8317759.752089183312931.907855219222587.5963231474
8414920.456512932910355.922227521919484.9907983439
859685.421679130197322.69710310112048.1462551594



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')