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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 14:53:49 +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/2011/May/19/t130581689658inyx5dcixzoh2.htm/, Retrieved Sat, 11 May 2024 17:36:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122076, Retrieved Sat, 11 May 2024 17:36:20 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-19 14:53:49] [697c881a84403defd656157daf408edb] [Current]
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Dataseries X:
12544
12264
13783
11214
11453
10883
10381
10348
10024
10805
10796
11907
12261
11377
12689
11474
10992
10764
12164
10409
10398
10349
10865
11630
12221
10884
12019
11021
10799
10423
10484
10450
9906
11049
11281
12485
12849
11380
12079
11366
11328
10444
10854
10434
10137
10992
10906
12367
14371
11695
11546
10922
10670
10254
10573
10239
10253
11176
10719
11817
12503
11510
12012
10941
11252
10662
11114
10415
10626
11411
10936
12513




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122076&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122076&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122076&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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.000665490790061819
beta0.502252609509736
gamma0.291292247840986

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.000665490790061819 \tabularnewline
beta & 0.502252609509736 \tabularnewline
gamma & 0.291292247840986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122076&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]0.000665490790061819[/C][/ROW]
[ROW][C]beta[/C][C]0.502252609509736[/C][/ROW]
[ROW][C]gamma[/C][C]0.291292247840986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122076&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122076&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
alpha0.000665490790061819
beta0.502252609509736
gamma0.291292247840986







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131226112392.7409188034-131.740918803423
141137711435.3280356034-58.3280356034284
151268912732.6528455101-43.6528455101361
161147411524.5144975645-50.5144975644507
171099211062.0630323936-70.063032393582
181076410846.1168063372-82.1168063372479
191216410403.9684448491760.03155515101
201040910424.8842969716-15.8842969715643
211039810187.4046508786210.595349121379
221034911007.3544485718-658.354448571823
231086511010.1309168334-145.130916833421
241163012148.9920880866-518.992088086612
251222112398.5814178402-177.581417840202
261088411462.5585402414-578.558540241409
271201912763.6853211715-744.685321171455
281102111552.7249657691-531.724965769115
291079911083.7438094974-284.743809497388
301042310863.5552223976-440.555222397581
311048410956.7042910348-472.704291034797
321045010457.7112784433-7.71127844331022
33990610284.7109203862-378.710920386213
341104910849.6676632752199.332336724841
351128111001.0491529082279.950847091808
361248512030.1405983684454.859401631551
371284912378.8653934484470.13460655163
381138011325.869541234154.1304587658724
391207912578.5893776035-499.589377603535
401136611429.397717153-63.3977171530241
411132811032.393750559295.60624944104
421044410767.198611474-323.198611473972
431085410851.07014605342.9298539466381
441043410487.914270091-53.9142700910488
451013710207.0322073474-70.0322073474053
461099210940.7114554251.2885445799839
471090611115.6624771192-209.662477119176
481236712195.3801732874171.619826712631
491437112548.30487569081822.69512430924
501169511375.5048989919319.495101008126
511154612467.6969727165-921.696972716512
521092211445.5406044865-523.540604486499
531067011152.923603917-482.92360391695
541025410707.0047471266-453.004747126577
551057310885.6094718567-312.609471856727
561023910505.4750087136-266.475008713622
571025310219.467170463933.532829536065
581117610988.2738197706187.72618022936
591071911087.1410226828-368.141022682825
601181712277.4787561014-460.478756101396
611250313110.1317336603-607.131733660295
621151011496.847019295613.1529807043698
631201212226.1352154643-214.135215464286
641094111319.1979131589-378.197913158865
651125211037.3952706309214.604729369104
661066210599.777178851162.2228211489019
671111410818.893069249295.106930751033
681041510452.0952769259-37.0952769258656
691062610253.1511309988372.848869001227
701141111066.7616853704344.238314629611
711093611003.6659644645-67.6659644644733
721251312167.169697048345.830302952012

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 12261 & 12392.7409188034 & -131.740918803423 \tabularnewline
14 & 11377 & 11435.3280356034 & -58.3280356034284 \tabularnewline
15 & 12689 & 12732.6528455101 & -43.6528455101361 \tabularnewline
16 & 11474 & 11524.5144975645 & -50.5144975644507 \tabularnewline
17 & 10992 & 11062.0630323936 & -70.063032393582 \tabularnewline
18 & 10764 & 10846.1168063372 & -82.1168063372479 \tabularnewline
19 & 12164 & 10403.968444849 & 1760.03155515101 \tabularnewline
20 & 10409 & 10424.8842969716 & -15.8842969715643 \tabularnewline
21 & 10398 & 10187.4046508786 & 210.595349121379 \tabularnewline
22 & 10349 & 11007.3544485718 & -658.354448571823 \tabularnewline
23 & 10865 & 11010.1309168334 & -145.130916833421 \tabularnewline
24 & 11630 & 12148.9920880866 & -518.992088086612 \tabularnewline
25 & 12221 & 12398.5814178402 & -177.581417840202 \tabularnewline
26 & 10884 & 11462.5585402414 & -578.558540241409 \tabularnewline
27 & 12019 & 12763.6853211715 & -744.685321171455 \tabularnewline
28 & 11021 & 11552.7249657691 & -531.724965769115 \tabularnewline
29 & 10799 & 11083.7438094974 & -284.743809497388 \tabularnewline
30 & 10423 & 10863.5552223976 & -440.555222397581 \tabularnewline
31 & 10484 & 10956.7042910348 & -472.704291034797 \tabularnewline
32 & 10450 & 10457.7112784433 & -7.71127844331022 \tabularnewline
33 & 9906 & 10284.7109203862 & -378.710920386213 \tabularnewline
34 & 11049 & 10849.6676632752 & 199.332336724841 \tabularnewline
35 & 11281 & 11001.0491529082 & 279.950847091808 \tabularnewline
36 & 12485 & 12030.1405983684 & 454.859401631551 \tabularnewline
37 & 12849 & 12378.8653934484 & 470.13460655163 \tabularnewline
38 & 11380 & 11325.8695412341 & 54.1304587658724 \tabularnewline
39 & 12079 & 12578.5893776035 & -499.589377603535 \tabularnewline
40 & 11366 & 11429.397717153 & -63.3977171530241 \tabularnewline
41 & 11328 & 11032.393750559 & 295.60624944104 \tabularnewline
42 & 10444 & 10767.198611474 & -323.198611473972 \tabularnewline
43 & 10854 & 10851.0701460534 & 2.9298539466381 \tabularnewline
44 & 10434 & 10487.914270091 & -53.9142700910488 \tabularnewline
45 & 10137 & 10207.0322073474 & -70.0322073474053 \tabularnewline
46 & 10992 & 10940.71145542 & 51.2885445799839 \tabularnewline
47 & 10906 & 11115.6624771192 & -209.662477119176 \tabularnewline
48 & 12367 & 12195.3801732874 & 171.619826712631 \tabularnewline
49 & 14371 & 12548.3048756908 & 1822.69512430924 \tabularnewline
50 & 11695 & 11375.5048989919 & 319.495101008126 \tabularnewline
51 & 11546 & 12467.6969727165 & -921.696972716512 \tabularnewline
52 & 10922 & 11445.5406044865 & -523.540604486499 \tabularnewline
53 & 10670 & 11152.923603917 & -482.92360391695 \tabularnewline
54 & 10254 & 10707.0047471266 & -453.004747126577 \tabularnewline
55 & 10573 & 10885.6094718567 & -312.609471856727 \tabularnewline
56 & 10239 & 10505.4750087136 & -266.475008713622 \tabularnewline
57 & 10253 & 10219.4671704639 & 33.532829536065 \tabularnewline
58 & 11176 & 10988.2738197706 & 187.72618022936 \tabularnewline
59 & 10719 & 11087.1410226828 & -368.141022682825 \tabularnewline
60 & 11817 & 12277.4787561014 & -460.478756101396 \tabularnewline
61 & 12503 & 13110.1317336603 & -607.131733660295 \tabularnewline
62 & 11510 & 11496.8470192956 & 13.1529807043698 \tabularnewline
63 & 12012 & 12226.1352154643 & -214.135215464286 \tabularnewline
64 & 10941 & 11319.1979131589 & -378.197913158865 \tabularnewline
65 & 11252 & 11037.3952706309 & 214.604729369104 \tabularnewline
66 & 10662 & 10599.7771788511 & 62.2228211489019 \tabularnewline
67 & 11114 & 10818.893069249 & 295.106930751033 \tabularnewline
68 & 10415 & 10452.0952769259 & -37.0952769258656 \tabularnewline
69 & 10626 & 10253.1511309988 & 372.848869001227 \tabularnewline
70 & 11411 & 11066.7616853704 & 344.238314629611 \tabularnewline
71 & 10936 & 11003.6659644645 & -67.6659644644733 \tabularnewline
72 & 12513 & 12167.169697048 & 345.830302952012 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122076&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]12261[/C][C]12392.7409188034[/C][C]-131.740918803423[/C][/ROW]
[ROW][C]14[/C][C]11377[/C][C]11435.3280356034[/C][C]-58.3280356034284[/C][/ROW]
[ROW][C]15[/C][C]12689[/C][C]12732.6528455101[/C][C]-43.6528455101361[/C][/ROW]
[ROW][C]16[/C][C]11474[/C][C]11524.5144975645[/C][C]-50.5144975644507[/C][/ROW]
[ROW][C]17[/C][C]10992[/C][C]11062.0630323936[/C][C]-70.063032393582[/C][/ROW]
[ROW][C]18[/C][C]10764[/C][C]10846.1168063372[/C][C]-82.1168063372479[/C][/ROW]
[ROW][C]19[/C][C]12164[/C][C]10403.968444849[/C][C]1760.03155515101[/C][/ROW]
[ROW][C]20[/C][C]10409[/C][C]10424.8842969716[/C][C]-15.8842969715643[/C][/ROW]
[ROW][C]21[/C][C]10398[/C][C]10187.4046508786[/C][C]210.595349121379[/C][/ROW]
[ROW][C]22[/C][C]10349[/C][C]11007.3544485718[/C][C]-658.354448571823[/C][/ROW]
[ROW][C]23[/C][C]10865[/C][C]11010.1309168334[/C][C]-145.130916833421[/C][/ROW]
[ROW][C]24[/C][C]11630[/C][C]12148.9920880866[/C][C]-518.992088086612[/C][/ROW]
[ROW][C]25[/C][C]12221[/C][C]12398.5814178402[/C][C]-177.581417840202[/C][/ROW]
[ROW][C]26[/C][C]10884[/C][C]11462.5585402414[/C][C]-578.558540241409[/C][/ROW]
[ROW][C]27[/C][C]12019[/C][C]12763.6853211715[/C][C]-744.685321171455[/C][/ROW]
[ROW][C]28[/C][C]11021[/C][C]11552.7249657691[/C][C]-531.724965769115[/C][/ROW]
[ROW][C]29[/C][C]10799[/C][C]11083.7438094974[/C][C]-284.743809497388[/C][/ROW]
[ROW][C]30[/C][C]10423[/C][C]10863.5552223976[/C][C]-440.555222397581[/C][/ROW]
[ROW][C]31[/C][C]10484[/C][C]10956.7042910348[/C][C]-472.704291034797[/C][/ROW]
[ROW][C]32[/C][C]10450[/C][C]10457.7112784433[/C][C]-7.71127844331022[/C][/ROW]
[ROW][C]33[/C][C]9906[/C][C]10284.7109203862[/C][C]-378.710920386213[/C][/ROW]
[ROW][C]34[/C][C]11049[/C][C]10849.6676632752[/C][C]199.332336724841[/C][/ROW]
[ROW][C]35[/C][C]11281[/C][C]11001.0491529082[/C][C]279.950847091808[/C][/ROW]
[ROW][C]36[/C][C]12485[/C][C]12030.1405983684[/C][C]454.859401631551[/C][/ROW]
[ROW][C]37[/C][C]12849[/C][C]12378.8653934484[/C][C]470.13460655163[/C][/ROW]
[ROW][C]38[/C][C]11380[/C][C]11325.8695412341[/C][C]54.1304587658724[/C][/ROW]
[ROW][C]39[/C][C]12079[/C][C]12578.5893776035[/C][C]-499.589377603535[/C][/ROW]
[ROW][C]40[/C][C]11366[/C][C]11429.397717153[/C][C]-63.3977171530241[/C][/ROW]
[ROW][C]41[/C][C]11328[/C][C]11032.393750559[/C][C]295.60624944104[/C][/ROW]
[ROW][C]42[/C][C]10444[/C][C]10767.198611474[/C][C]-323.198611473972[/C][/ROW]
[ROW][C]43[/C][C]10854[/C][C]10851.0701460534[/C][C]2.9298539466381[/C][/ROW]
[ROW][C]44[/C][C]10434[/C][C]10487.914270091[/C][C]-53.9142700910488[/C][/ROW]
[ROW][C]45[/C][C]10137[/C][C]10207.0322073474[/C][C]-70.0322073474053[/C][/ROW]
[ROW][C]46[/C][C]10992[/C][C]10940.71145542[/C][C]51.2885445799839[/C][/ROW]
[ROW][C]47[/C][C]10906[/C][C]11115.6624771192[/C][C]-209.662477119176[/C][/ROW]
[ROW][C]48[/C][C]12367[/C][C]12195.3801732874[/C][C]171.619826712631[/C][/ROW]
[ROW][C]49[/C][C]14371[/C][C]12548.3048756908[/C][C]1822.69512430924[/C][/ROW]
[ROW][C]50[/C][C]11695[/C][C]11375.5048989919[/C][C]319.495101008126[/C][/ROW]
[ROW][C]51[/C][C]11546[/C][C]12467.6969727165[/C][C]-921.696972716512[/C][/ROW]
[ROW][C]52[/C][C]10922[/C][C]11445.5406044865[/C][C]-523.540604486499[/C][/ROW]
[ROW][C]53[/C][C]10670[/C][C]11152.923603917[/C][C]-482.92360391695[/C][/ROW]
[ROW][C]54[/C][C]10254[/C][C]10707.0047471266[/C][C]-453.004747126577[/C][/ROW]
[ROW][C]55[/C][C]10573[/C][C]10885.6094718567[/C][C]-312.609471856727[/C][/ROW]
[ROW][C]56[/C][C]10239[/C][C]10505.4750087136[/C][C]-266.475008713622[/C][/ROW]
[ROW][C]57[/C][C]10253[/C][C]10219.4671704639[/C][C]33.532829536065[/C][/ROW]
[ROW][C]58[/C][C]11176[/C][C]10988.2738197706[/C][C]187.72618022936[/C][/ROW]
[ROW][C]59[/C][C]10719[/C][C]11087.1410226828[/C][C]-368.141022682825[/C][/ROW]
[ROW][C]60[/C][C]11817[/C][C]12277.4787561014[/C][C]-460.478756101396[/C][/ROW]
[ROW][C]61[/C][C]12503[/C][C]13110.1317336603[/C][C]-607.131733660295[/C][/ROW]
[ROW][C]62[/C][C]11510[/C][C]11496.8470192956[/C][C]13.1529807043698[/C][/ROW]
[ROW][C]63[/C][C]12012[/C][C]12226.1352154643[/C][C]-214.135215464286[/C][/ROW]
[ROW][C]64[/C][C]10941[/C][C]11319.1979131589[/C][C]-378.197913158865[/C][/ROW]
[ROW][C]65[/C][C]11252[/C][C]11037.3952706309[/C][C]214.604729369104[/C][/ROW]
[ROW][C]66[/C][C]10662[/C][C]10599.7771788511[/C][C]62.2228211489019[/C][/ROW]
[ROW][C]67[/C][C]11114[/C][C]10818.893069249[/C][C]295.106930751033[/C][/ROW]
[ROW][C]68[/C][C]10415[/C][C]10452.0952769259[/C][C]-37.0952769258656[/C][/ROW]
[ROW][C]69[/C][C]10626[/C][C]10253.1511309988[/C][C]372.848869001227[/C][/ROW]
[ROW][C]70[/C][C]11411[/C][C]11066.7616853704[/C][C]344.238314629611[/C][/ROW]
[ROW][C]71[/C][C]10936[/C][C]11003.6659644645[/C][C]-67.6659644644733[/C][/ROW]
[ROW][C]72[/C][C]12513[/C][C]12167.169697048[/C][C]345.830302952012[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122076&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122076&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
131226112392.7409188034-131.740918803423
141137711435.3280356034-58.3280356034284
151268912732.6528455101-43.6528455101361
161147411524.5144975645-50.5144975644507
171099211062.0630323936-70.063032393582
181076410846.1168063372-82.1168063372479
191216410403.9684448491760.03155515101
201040910424.8842969716-15.8842969715643
211039810187.4046508786210.595349121379
221034911007.3544485718-658.354448571823
231086511010.1309168334-145.130916833421
241163012148.9920880866-518.992088086612
251222112398.5814178402-177.581417840202
261088411462.5585402414-578.558540241409
271201912763.6853211715-744.685321171455
281102111552.7249657691-531.724965769115
291079911083.7438094974-284.743809497388
301042310863.5552223976-440.555222397581
311048410956.7042910348-472.704291034797
321045010457.7112784433-7.71127844331022
33990610284.7109203862-378.710920386213
341104910849.6676632752199.332336724841
351128111001.0491529082279.950847091808
361248512030.1405983684454.859401631551
371284912378.8653934484470.13460655163
381138011325.869541234154.1304587658724
391207912578.5893776035-499.589377603535
401136611429.397717153-63.3977171530241
411132811032.393750559295.60624944104
421044410767.198611474-323.198611473972
431085410851.07014605342.9298539466381
441043410487.914270091-53.9142700910488
451013710207.0322073474-70.0322073474053
461099210940.7114554251.2885445799839
471090611115.6624771192-209.662477119176
481236712195.3801732874171.619826712631
491437112548.30487569081822.69512430924
501169511375.5048989919319.495101008126
511154612467.6969727165-921.696972716512
521092211445.5406044865-523.540604486499
531067011152.923603917-482.92360391695
541025410707.0047471266-453.004747126577
551057310885.6094718567-312.609471856727
561023910505.4750087136-266.475008713622
571025310219.467170463933.532829536065
581117610988.2738197706187.72618022936
591071911087.1410226828-368.141022682825
601181712277.4787561014-460.478756101396
611250313110.1317336603-607.131733660295
621151011496.847019295613.1529807043698
631201212226.1352154643-214.135215464286
641094111319.1979131589-378.197913158865
651125211037.3952706309214.604729369104
661066210599.777178851162.2228211489019
671111410818.893069249295.106930751033
681041510452.0952769259-37.0952769258656
691062610253.1511309988372.848869001227
701141111066.7616853704344.238314629611
711093611003.6659644645-67.6659644644733
721251312167.169697048345.830302952012







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7312957.783725575412030.361283479513885.2061676713
7411525.784773530410598.361867968912453.2076790919
7512189.214427589511261.790696853713116.6381583253
7611235.046256053310307.621234824812162.4712772818
7711126.570623249210199.143742600912053.9975038974
7810644.89127894829717.4618663461411572.3206915502
7910932.176847587810004.744126893811859.6095682819
8010468.79939311469541.36248458911396.2363016403
8110389.54667422359462.1045945298711316.9887539171
8211194.788649288710267.340311498912122.2369870784
8311011.652141093710084.196354694311939.1079274931
8412295.684596628911368.220067528713223.1491257292

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 12957.7837255754 & 12030.3612834795 & 13885.2061676713 \tabularnewline
74 & 11525.7847735304 & 10598.3618679689 & 12453.2076790919 \tabularnewline
75 & 12189.2144275895 & 11261.7906968537 & 13116.6381583253 \tabularnewline
76 & 11235.0462560533 & 10307.6212348248 & 12162.4712772818 \tabularnewline
77 & 11126.5706232492 & 10199.1437426009 & 12053.9975038974 \tabularnewline
78 & 10644.8912789482 & 9717.46186634614 & 11572.3206915502 \tabularnewline
79 & 10932.1768475878 & 10004.7441268938 & 11859.6095682819 \tabularnewline
80 & 10468.7993931146 & 9541.362484589 & 11396.2363016403 \tabularnewline
81 & 10389.5466742235 & 9462.10459452987 & 11316.9887539171 \tabularnewline
82 & 11194.7886492887 & 10267.3403114989 & 12122.2369870784 \tabularnewline
83 & 11011.6521410937 & 10084.1963546943 & 11939.1079274931 \tabularnewline
84 & 12295.6845966289 & 11368.2200675287 & 13223.1491257292 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122076&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]12957.7837255754[/C][C]12030.3612834795[/C][C]13885.2061676713[/C][/ROW]
[ROW][C]74[/C][C]11525.7847735304[/C][C]10598.3618679689[/C][C]12453.2076790919[/C][/ROW]
[ROW][C]75[/C][C]12189.2144275895[/C][C]11261.7906968537[/C][C]13116.6381583253[/C][/ROW]
[ROW][C]76[/C][C]11235.0462560533[/C][C]10307.6212348248[/C][C]12162.4712772818[/C][/ROW]
[ROW][C]77[/C][C]11126.5706232492[/C][C]10199.1437426009[/C][C]12053.9975038974[/C][/ROW]
[ROW][C]78[/C][C]10644.8912789482[/C][C]9717.46186634614[/C][C]11572.3206915502[/C][/ROW]
[ROW][C]79[/C][C]10932.1768475878[/C][C]10004.7441268938[/C][C]11859.6095682819[/C][/ROW]
[ROW][C]80[/C][C]10468.7993931146[/C][C]9541.362484589[/C][C]11396.2363016403[/C][/ROW]
[ROW][C]81[/C][C]10389.5466742235[/C][C]9462.10459452987[/C][C]11316.9887539171[/C][/ROW]
[ROW][C]82[/C][C]11194.7886492887[/C][C]10267.3403114989[/C][C]12122.2369870784[/C][/ROW]
[ROW][C]83[/C][C]11011.6521410937[/C][C]10084.1963546943[/C][C]11939.1079274931[/C][/ROW]
[ROW][C]84[/C][C]12295.6845966289[/C][C]11368.2200675287[/C][C]13223.1491257292[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122076&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122076&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
7312957.783725575412030.361283479513885.2061676713
7411525.784773530410598.361867968912453.2076790919
7512189.214427589511261.790696853713116.6381583253
7611235.046256053310307.621234824812162.4712772818
7711126.570623249210199.143742600912053.9975038974
7810644.89127894829717.4618663461411572.3206915502
7910932.176847587810004.744126893811859.6095682819
8010468.79939311469541.36248458911396.2363016403
8110389.54667422359462.1045945298711316.9887539171
8211194.788649288710267.340311498912122.2369870784
8311011.652141093710084.196354694311939.1079274931
8412295.684596628911368.220067528713223.1491257292



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')