Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 13 Dec 2013 11:02:47 -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/2013/Dec/13/t1386950608ffln5jz3l3rps8l.htm/, Retrieved Tue, 19 Nov 2019 08:24:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232301, Retrieved Tue, 19 Nov 2019 08:24:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact44
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-13 16:02:47] [ab12ae47238ac832614ec82c15c6db51] [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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 5 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232301&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232301&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 time5 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.567263099764302
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.567263099764302 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232301&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]0.567263099764302[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232301&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
alpha0.567263099764302
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23969041086-1396
34312940294.1007127292834.89928727096
43786341902.234469946-4039.23446994597
53595339610.9258038496-3657.9258038496
62913337535.9194736501-8402.91947365005
72469332769.2533259575-8076.25332595751
82220528187.8928297931-5982.8928297931
92172524794.018497607-3069.01849760705
102719223053.07755142054138.92244857951
112179025400.9355292858-3610.93552928576
121325323352.5850478941-10099.5850478941
133770217623.463127292520078.5368727075
143036429013.27619243641350.72380756362
153260929779.49196644042829.50803355964
163021231384.5674643654-1172.56746436539
172996530719.4132098467-754.413209846713
182835230291.4624339259-1939.46243392593
192581429191.2769617807-3377.27696178069
202241427275.4723636784-4861.47236367841
212050624517.7384812397-4011.73848123971
222880622242.02727492796563.97272507206
232222825965.5267897207-3737.52678972065
241397123845.3657575316-9874.36575753159
253684518244.002429707718600.9975702923
263533828795.661970146542.33802986002
273502232506.88892066422515.11107933575
283477733933.6186277798843.38137222021
292688734412.0377592689-7525.0377592689
302397030143.3615141026-6173.36151410261
312278026641.4413256471-3861.44132564712
321735124450.9881497026-7099.98814970256
332138220423.4268636125958.573136387527
342456120967.19003231043593.80996768955
351740923005.8258145459-5596.82581454587
361151419830.9530541457-8316.95305414572
373151415113.052484056816400.9475159432
382707124416.70481102242654.29518897762
392946225922.38852761133539.6114723887
402610527930.2795033998-1825.2795033998
412239726894.865794365-4497.86579436498
422384324343.3925015297-500.392501529677
432170524059.5383000131-2354.53830001314
441808922723.8956054339-4634.89560543392
452076420094.6903572115669.309642788467
462531620474.36501988194841.63498011814
471770423220.8458866309-5516.84588663095
481554820091.3427880587-4543.34278805874
492802917514.072074812810514.9279251872
502938323478.80268345275904.19731654731
513643826828.03595485749609.96404514261
523203432279.4139477285-245.413947728477
532267932140.1996710146-9461.19967101463
542431926773.2102181459-2454.21021814588
551800425381.0273223272-7377.02732232722
561753721196.3119364179-3659.31193641793
572036619120.5193043611245.48069563901
582278219827.03454446582954.96545553423
591916921503.2774084686-2334.27740846855
601380720179.1279700309-6372.1279700309
612974316564.454905656413178.5450943436
622559124040.15724625741550.84275374263
632909624919.89311399244176.10688600758
642648227288.8444510961-806.844451096127
652240526831.1513667397-4426.15136673971
662704424320.35902241692723.64097758306
671797025865.3800460058-7895.38004600578
681873021386.6222872913-2656.62228729132
691968419879.6184936995-195.618493699516
701978519768.651340592316.3486594076967
711847919777.9253318049-1298.9253318049
721069819041.0929217229-8343.09292172288

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 39690 & 41086 & -1396 \tabularnewline
3 & 43129 & 40294.100712729 & 2834.89928727096 \tabularnewline
4 & 37863 & 41902.234469946 & -4039.23446994597 \tabularnewline
5 & 35953 & 39610.9258038496 & -3657.9258038496 \tabularnewline
6 & 29133 & 37535.9194736501 & -8402.91947365005 \tabularnewline
7 & 24693 & 32769.2533259575 & -8076.25332595751 \tabularnewline
8 & 22205 & 28187.8928297931 & -5982.8928297931 \tabularnewline
9 & 21725 & 24794.018497607 & -3069.01849760705 \tabularnewline
10 & 27192 & 23053.0775514205 & 4138.92244857951 \tabularnewline
11 & 21790 & 25400.9355292858 & -3610.93552928576 \tabularnewline
12 & 13253 & 23352.5850478941 & -10099.5850478941 \tabularnewline
13 & 37702 & 17623.4631272925 & 20078.5368727075 \tabularnewline
14 & 30364 & 29013.2761924364 & 1350.72380756362 \tabularnewline
15 & 32609 & 29779.4919664404 & 2829.50803355964 \tabularnewline
16 & 30212 & 31384.5674643654 & -1172.56746436539 \tabularnewline
17 & 29965 & 30719.4132098467 & -754.413209846713 \tabularnewline
18 & 28352 & 30291.4624339259 & -1939.46243392593 \tabularnewline
19 & 25814 & 29191.2769617807 & -3377.27696178069 \tabularnewline
20 & 22414 & 27275.4723636784 & -4861.47236367841 \tabularnewline
21 & 20506 & 24517.7384812397 & -4011.73848123971 \tabularnewline
22 & 28806 & 22242.0272749279 & 6563.97272507206 \tabularnewline
23 & 22228 & 25965.5267897207 & -3737.52678972065 \tabularnewline
24 & 13971 & 23845.3657575316 & -9874.36575753159 \tabularnewline
25 & 36845 & 18244.0024297077 & 18600.9975702923 \tabularnewline
26 & 35338 & 28795.66197014 & 6542.33802986002 \tabularnewline
27 & 35022 & 32506.8889206642 & 2515.11107933575 \tabularnewline
28 & 34777 & 33933.6186277798 & 843.38137222021 \tabularnewline
29 & 26887 & 34412.0377592689 & -7525.0377592689 \tabularnewline
30 & 23970 & 30143.3615141026 & -6173.36151410261 \tabularnewline
31 & 22780 & 26641.4413256471 & -3861.44132564712 \tabularnewline
32 & 17351 & 24450.9881497026 & -7099.98814970256 \tabularnewline
33 & 21382 & 20423.4268636125 & 958.573136387527 \tabularnewline
34 & 24561 & 20967.1900323104 & 3593.80996768955 \tabularnewline
35 & 17409 & 23005.8258145459 & -5596.82581454587 \tabularnewline
36 & 11514 & 19830.9530541457 & -8316.95305414572 \tabularnewline
37 & 31514 & 15113.0524840568 & 16400.9475159432 \tabularnewline
38 & 27071 & 24416.7048110224 & 2654.29518897762 \tabularnewline
39 & 29462 & 25922.3885276113 & 3539.6114723887 \tabularnewline
40 & 26105 & 27930.2795033998 & -1825.2795033998 \tabularnewline
41 & 22397 & 26894.865794365 & -4497.86579436498 \tabularnewline
42 & 23843 & 24343.3925015297 & -500.392501529677 \tabularnewline
43 & 21705 & 24059.5383000131 & -2354.53830001314 \tabularnewline
44 & 18089 & 22723.8956054339 & -4634.89560543392 \tabularnewline
45 & 20764 & 20094.6903572115 & 669.309642788467 \tabularnewline
46 & 25316 & 20474.3650198819 & 4841.63498011814 \tabularnewline
47 & 17704 & 23220.8458866309 & -5516.84588663095 \tabularnewline
48 & 15548 & 20091.3427880587 & -4543.34278805874 \tabularnewline
49 & 28029 & 17514.0720748128 & 10514.9279251872 \tabularnewline
50 & 29383 & 23478.8026834527 & 5904.19731654731 \tabularnewline
51 & 36438 & 26828.0359548574 & 9609.96404514261 \tabularnewline
52 & 32034 & 32279.4139477285 & -245.413947728477 \tabularnewline
53 & 22679 & 32140.1996710146 & -9461.19967101463 \tabularnewline
54 & 24319 & 26773.2102181459 & -2454.21021814588 \tabularnewline
55 & 18004 & 25381.0273223272 & -7377.02732232722 \tabularnewline
56 & 17537 & 21196.3119364179 & -3659.31193641793 \tabularnewline
57 & 20366 & 19120.519304361 & 1245.48069563901 \tabularnewline
58 & 22782 & 19827.0345444658 & 2954.96545553423 \tabularnewline
59 & 19169 & 21503.2774084686 & -2334.27740846855 \tabularnewline
60 & 13807 & 20179.1279700309 & -6372.1279700309 \tabularnewline
61 & 29743 & 16564.4549056564 & 13178.5450943436 \tabularnewline
62 & 25591 & 24040.1572462574 & 1550.84275374263 \tabularnewline
63 & 29096 & 24919.8931139924 & 4176.10688600758 \tabularnewline
64 & 26482 & 27288.8444510961 & -806.844451096127 \tabularnewline
65 & 22405 & 26831.1513667397 & -4426.15136673971 \tabularnewline
66 & 27044 & 24320.3590224169 & 2723.64097758306 \tabularnewline
67 & 17970 & 25865.3800460058 & -7895.38004600578 \tabularnewline
68 & 18730 & 21386.6222872913 & -2656.62228729132 \tabularnewline
69 & 19684 & 19879.6184936995 & -195.618493699516 \tabularnewline
70 & 19785 & 19768.6513405923 & 16.3486594076967 \tabularnewline
71 & 18479 & 19777.9253318049 & -1298.9253318049 \tabularnewline
72 & 10698 & 19041.0929217229 & -8343.09292172288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232301&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]2[/C][C]39690[/C][C]41086[/C][C]-1396[/C][/ROW]
[ROW][C]3[/C][C]43129[/C][C]40294.100712729[/C][C]2834.89928727096[/C][/ROW]
[ROW][C]4[/C][C]37863[/C][C]41902.234469946[/C][C]-4039.23446994597[/C][/ROW]
[ROW][C]5[/C][C]35953[/C][C]39610.9258038496[/C][C]-3657.9258038496[/C][/ROW]
[ROW][C]6[/C][C]29133[/C][C]37535.9194736501[/C][C]-8402.91947365005[/C][/ROW]
[ROW][C]7[/C][C]24693[/C][C]32769.2533259575[/C][C]-8076.25332595751[/C][/ROW]
[ROW][C]8[/C][C]22205[/C][C]28187.8928297931[/C][C]-5982.8928297931[/C][/ROW]
[ROW][C]9[/C][C]21725[/C][C]24794.018497607[/C][C]-3069.01849760705[/C][/ROW]
[ROW][C]10[/C][C]27192[/C][C]23053.0775514205[/C][C]4138.92244857951[/C][/ROW]
[ROW][C]11[/C][C]21790[/C][C]25400.9355292858[/C][C]-3610.93552928576[/C][/ROW]
[ROW][C]12[/C][C]13253[/C][C]23352.5850478941[/C][C]-10099.5850478941[/C][/ROW]
[ROW][C]13[/C][C]37702[/C][C]17623.4631272925[/C][C]20078.5368727075[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]29013.2761924364[/C][C]1350.72380756362[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]29779.4919664404[/C][C]2829.50803355964[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]31384.5674643654[/C][C]-1172.56746436539[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30719.4132098467[/C][C]-754.413209846713[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]30291.4624339259[/C][C]-1939.46243392593[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]29191.2769617807[/C][C]-3377.27696178069[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]27275.4723636784[/C][C]-4861.47236367841[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]24517.7384812397[/C][C]-4011.73848123971[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]22242.0272749279[/C][C]6563.97272507206[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]25965.5267897207[/C][C]-3737.52678972065[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]23845.3657575316[/C][C]-9874.36575753159[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]18244.0024297077[/C][C]18600.9975702923[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]28795.66197014[/C][C]6542.33802986002[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]32506.8889206642[/C][C]2515.11107933575[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]33933.6186277798[/C][C]843.38137222021[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]34412.0377592689[/C][C]-7525.0377592689[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]30143.3615141026[/C][C]-6173.36151410261[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]26641.4413256471[/C][C]-3861.44132564712[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]24450.9881497026[/C][C]-7099.98814970256[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]20423.4268636125[/C][C]958.573136387527[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]20967.1900323104[/C][C]3593.80996768955[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]23005.8258145459[/C][C]-5596.82581454587[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]19830.9530541457[/C][C]-8316.95305414572[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]15113.0524840568[/C][C]16400.9475159432[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]24416.7048110224[/C][C]2654.29518897762[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]25922.3885276113[/C][C]3539.6114723887[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27930.2795033998[/C][C]-1825.2795033998[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]26894.865794365[/C][C]-4497.86579436498[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]24343.3925015297[/C][C]-500.392501529677[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]24059.5383000131[/C][C]-2354.53830001314[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]22723.8956054339[/C][C]-4634.89560543392[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]20094.6903572115[/C][C]669.309642788467[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]20474.3650198819[/C][C]4841.63498011814[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]23220.8458866309[/C][C]-5516.84588663095[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]20091.3427880587[/C][C]-4543.34278805874[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]17514.0720748128[/C][C]10514.9279251872[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]23478.8026834527[/C][C]5904.19731654731[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]26828.0359548574[/C][C]9609.96404514261[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]32279.4139477285[/C][C]-245.413947728477[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]32140.1996710146[/C][C]-9461.19967101463[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]26773.2102181459[/C][C]-2454.21021814588[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]25381.0273223272[/C][C]-7377.02732232722[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]21196.3119364179[/C][C]-3659.31193641793[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]19120.519304361[/C][C]1245.48069563901[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]19827.0345444658[/C][C]2954.96545553423[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]21503.2774084686[/C][C]-2334.27740846855[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]20179.1279700309[/C][C]-6372.1279700309[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]16564.4549056564[/C][C]13178.5450943436[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]24040.1572462574[/C][C]1550.84275374263[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]24919.8931139924[/C][C]4176.10688600758[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]27288.8444510961[/C][C]-806.844451096127[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]26831.1513667397[/C][C]-4426.15136673971[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]24320.3590224169[/C][C]2723.64097758306[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]25865.3800460058[/C][C]-7895.38004600578[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]21386.6222872913[/C][C]-2656.62228729132[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19879.6184936995[/C][C]-195.618493699516[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]19768.6513405923[/C][C]16.3486594076967[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]19777.9253318049[/C][C]-1298.9253318049[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]19041.0929217229[/C][C]-8343.09292172288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232301&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
23969041086-1396
34312940294.1007127292834.89928727096
43786341902.234469946-4039.23446994597
53595339610.9258038496-3657.9258038496
62913337535.9194736501-8402.91947365005
72469332769.2533259575-8076.25332595751
82220528187.8928297931-5982.8928297931
92172524794.018497607-3069.01849760705
102719223053.07755142054138.92244857951
112179025400.9355292858-3610.93552928576
121325323352.5850478941-10099.5850478941
133770217623.463127292520078.5368727075
143036429013.27619243641350.72380756362
153260929779.49196644042829.50803355964
163021231384.5674643654-1172.56746436539
172996530719.4132098467-754.413209846713
182835230291.4624339259-1939.46243392593
192581429191.2769617807-3377.27696178069
202241427275.4723636784-4861.47236367841
212050624517.7384812397-4011.73848123971
222880622242.02727492796563.97272507206
232222825965.5267897207-3737.52678972065
241397123845.3657575316-9874.36575753159
253684518244.002429707718600.9975702923
263533828795.661970146542.33802986002
273502232506.88892066422515.11107933575
283477733933.6186277798843.38137222021
292688734412.0377592689-7525.0377592689
302397030143.3615141026-6173.36151410261
312278026641.4413256471-3861.44132564712
321735124450.9881497026-7099.98814970256
332138220423.4268636125958.573136387527
342456120967.19003231043593.80996768955
351740923005.8258145459-5596.82581454587
361151419830.9530541457-8316.95305414572
373151415113.052484056816400.9475159432
382707124416.70481102242654.29518897762
392946225922.38852761133539.6114723887
402610527930.2795033998-1825.2795033998
412239726894.865794365-4497.86579436498
422384324343.3925015297-500.392501529677
432170524059.5383000131-2354.53830001314
441808922723.8956054339-4634.89560543392
452076420094.6903572115669.309642788467
462531620474.36501988194841.63498011814
471770423220.8458866309-5516.84588663095
481554820091.3427880587-4543.34278805874
492802917514.072074812810514.9279251872
502938323478.80268345275904.19731654731
513643826828.03595485749609.96404514261
523203432279.4139477285-245.413947728477
532267932140.1996710146-9461.19967101463
542431926773.2102181459-2454.21021814588
551800425381.0273223272-7377.02732232722
561753721196.3119364179-3659.31193641793
572036619120.5193043611245.48069563901
582278219827.03454446582954.96545553423
591916921503.2774084686-2334.27740846855
601380720179.1279700309-6372.1279700309
612974316564.454905656413178.5450943436
622559124040.15724625741550.84275374263
632909624919.89311399244176.10688600758
642648227288.8444510961-806.844451096127
652240526831.1513667397-4426.15136673971
662704424320.35902241692723.64097758306
671797025865.3800460058-7895.38004600578
681873021386.6222872913-2656.62228729132
691968419879.6184936995-195.618493699516
701978519768.651340592316.3486594076967
711847919777.9253318049-1298.9253318049
721069819041.0929217229-8343.09292172288







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7314308.36416932481802.4654353410626814.2629033084
7414308.3641693248-69.544331462215328686.2726701117
7514308.3641693248-1724.446020075930341.1743587254
7614308.3641693248-3223.8277153682831840.5560540178
7714308.3641693248-4604.7133696175433221.441708267
7814308.3641693248-5891.4192875935634508.1476262431
7914308.3641693248-7100.9329097186835717.6612483682
8014308.3641693248-8245.6765136900136862.4048523395
8114308.3641693248-9335.0598814220437951.7882200715
8214308.3641693248-10376.413539939338993.1418785888
8314308.3641693248-11375.580237018439992.3085756679
8414308.3641693248-12337.306210316240954.0345489657

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 14308.3641693248 & 1802.46543534106 & 26814.2629033084 \tabularnewline
74 & 14308.3641693248 & -69.5443314622153 & 28686.2726701117 \tabularnewline
75 & 14308.3641693248 & -1724.4460200759 & 30341.1743587254 \tabularnewline
76 & 14308.3641693248 & -3223.82771536828 & 31840.5560540178 \tabularnewline
77 & 14308.3641693248 & -4604.71336961754 & 33221.441708267 \tabularnewline
78 & 14308.3641693248 & -5891.41928759356 & 34508.1476262431 \tabularnewline
79 & 14308.3641693248 & -7100.93290971868 & 35717.6612483682 \tabularnewline
80 & 14308.3641693248 & -8245.67651369001 & 36862.4048523395 \tabularnewline
81 & 14308.3641693248 & -9335.05988142204 & 37951.7882200715 \tabularnewline
82 & 14308.3641693248 & -10376.4135399393 & 38993.1418785888 \tabularnewline
83 & 14308.3641693248 & -11375.5802370184 & 39992.3085756679 \tabularnewline
84 & 14308.3641693248 & -12337.3062103162 & 40954.0345489657 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232301&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]14308.3641693248[/C][C]1802.46543534106[/C][C]26814.2629033084[/C][/ROW]
[ROW][C]74[/C][C]14308.3641693248[/C][C]-69.5443314622153[/C][C]28686.2726701117[/C][/ROW]
[ROW][C]75[/C][C]14308.3641693248[/C][C]-1724.4460200759[/C][C]30341.1743587254[/C][/ROW]
[ROW][C]76[/C][C]14308.3641693248[/C][C]-3223.82771536828[/C][C]31840.5560540178[/C][/ROW]
[ROW][C]77[/C][C]14308.3641693248[/C][C]-4604.71336961754[/C][C]33221.441708267[/C][/ROW]
[ROW][C]78[/C][C]14308.3641693248[/C][C]-5891.41928759356[/C][C]34508.1476262431[/C][/ROW]
[ROW][C]79[/C][C]14308.3641693248[/C][C]-7100.93290971868[/C][C]35717.6612483682[/C][/ROW]
[ROW][C]80[/C][C]14308.3641693248[/C][C]-8245.67651369001[/C][C]36862.4048523395[/C][/ROW]
[ROW][C]81[/C][C]14308.3641693248[/C][C]-9335.05988142204[/C][C]37951.7882200715[/C][/ROW]
[ROW][C]82[/C][C]14308.3641693248[/C][C]-10376.4135399393[/C][C]38993.1418785888[/C][/ROW]
[ROW][C]83[/C][C]14308.3641693248[/C][C]-11375.5802370184[/C][C]39992.3085756679[/C][/ROW]
[ROW][C]84[/C][C]14308.3641693248[/C][C]-12337.3062103162[/C][C]40954.0345489657[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232301&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232301&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
7314308.36416932481802.4654353410626814.2629033084
7414308.3641693248-69.544331462215328686.2726701117
7514308.3641693248-1724.446020075930341.1743587254
7614308.3641693248-3223.8277153682831840.5560540178
7714308.3641693248-4604.7133696175433221.441708267
7814308.3641693248-5891.4192875935634508.1476262431
7914308.3641693248-7100.9329097186835717.6612483682
8014308.3641693248-8245.6765136900136862.4048523395
8114308.3641693248-9335.0598814220437951.7882200715
8214308.3641693248-10376.413539939338993.1418785888
8314308.3641693248-11375.580237018439992.3085756679
8414308.3641693248-12337.306210316240954.0345489657



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')