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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 Jan 2009 10:49:28 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jan/27/t1233078648w5vm4nqy3bdw0wa.htm/, Retrieved Mon, 06 May 2024 07:28:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36992, Retrieved Mon, 06 May 2024 07:28:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact196
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [2MAR03A_Robbe Ley...] [2009-01-15 22:43:12] [73702d50a449ca9a9e8052b5a190ceb8]
- RMP     [Exponential Smoothing] [Robbe Leys_2MAR03...] [2009-01-27 17:49:28] [d41d8cd98f00b204e9800998ecf8427e] [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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36992&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36992&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.562783761271795
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.562783761271795 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36992&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]0.562783761271795[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36992&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
alpha0.562783761271795
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
343129396903439
43786341625.4133550137-3762.41335501370
53595339507.9882156199-3554.98821561986
62913337507.2985763564-8374.2985763564
72469332794.3793255415-8101.3793255415
82220528235.0545972237-6030.0545972237
92172524841.4377903239-3116.43779032386
102719223087.55720891584104.44279108416
112179025397.4709608071-3607.47096080709
121325323367.2448848053-10114.2448848053
133770217675.112106110620026.8878938894
143036428945.91940160221418.08059839776
153260929743.99213455512865.00786544491
163021231356.3720371435-1144.37203714345
172996530712.3380377856-747.338037785594
182835230291.7483259391-1939.74832593914
192581429200.0894671464-3386.08946714644
202241427294.4533008230-4880.45330082296
212050624547.8134354745-4041.81343547447
222880622273.14646789936532.85353210073
232222825949.7303505327-3721.73035053265
241397123855.2009454205-9884.2009454205
253684518292.533160190518552.4668398095
263533828733.56022916886604.43977083125
273502232450.43168449022571.56831550981
283477733897.6685734602879.331426539822
292688734392.5420210928-7505.54202109276
302397030168.5448520787-6198.54485207866
312278026680.1044658139-3900.10446581391
321735124485.1890051902-7134.18900519023
332138220470.1832832254911.816716774614
342456120983.33892468233577.6610753177
351740922996.7884812053-5587.78848120529
361151419852.0718625614-8338.07186256137
373151415159.540417994616354.4595820054
382707124363.56469512312707.43530487687
392946225887.26531940183574.73468059822
402610527899.0679484976-1794.06794849758
412239726889.3956404649-4492.39564046494
422384324361.1483248031-518.148324803064
432170524069.5428616737-2364.54286167372
441808922738.8165362926-4649.81653629261
452076420121.9752967741642.024703225936
462531620483.29637408504832.70362591503
471770423203.0634977893-5499.06349778927
481554820108.279859031-4560.27985903099
492802917541.828407513510487.1715924865
502938323443.83828143585939.16171856422
513643826786.30205221089651.69794778919
523203432218.1209259269-184.12092592688
532267932114.5006587049-9435.5006587049
542431926804.3541085165-2485.35410851645
551800425405.6371752333-7401.63717523326
561753721240.1159661863-3703.11596618634
572036619156.06243431041209.93756568964
582278219836.99564843322945.00435156679
591916921494.3962743698-2325.39627436977
601380720185.7010126325-6378.70101263253
612974316595.87166471513147.128335285
622559123994.86199916971596.13800083032
632909624893.14254678584202.85745321419
642648227258.4424723949-776.44247239489
652240526821.4732573693-4416.47325736932
662704424335.95382603072708.04617396928
671797025859.9982375148-7889.99823751485
681873021419.6353529784-2689.63535297841
691968419905.9522525796-221.952252579627
701978519781.04112905013.95887094988211
711847919783.2691173337-1304.26911733368
721069819049.24763777-8351.24763776999

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 43129 & 39690 & 3439 \tabularnewline
4 & 37863 & 41625.4133550137 & -3762.41335501370 \tabularnewline
5 & 35953 & 39507.9882156199 & -3554.98821561986 \tabularnewline
6 & 29133 & 37507.2985763564 & -8374.2985763564 \tabularnewline
7 & 24693 & 32794.3793255415 & -8101.3793255415 \tabularnewline
8 & 22205 & 28235.0545972237 & -6030.0545972237 \tabularnewline
9 & 21725 & 24841.4377903239 & -3116.43779032386 \tabularnewline
10 & 27192 & 23087.5572089158 & 4104.44279108416 \tabularnewline
11 & 21790 & 25397.4709608071 & -3607.47096080709 \tabularnewline
12 & 13253 & 23367.2448848053 & -10114.2448848053 \tabularnewline
13 & 37702 & 17675.1121061106 & 20026.8878938894 \tabularnewline
14 & 30364 & 28945.9194016022 & 1418.08059839776 \tabularnewline
15 & 32609 & 29743.9921345551 & 2865.00786544491 \tabularnewline
16 & 30212 & 31356.3720371435 & -1144.37203714345 \tabularnewline
17 & 29965 & 30712.3380377856 & -747.338037785594 \tabularnewline
18 & 28352 & 30291.7483259391 & -1939.74832593914 \tabularnewline
19 & 25814 & 29200.0894671464 & -3386.08946714644 \tabularnewline
20 & 22414 & 27294.4533008230 & -4880.45330082296 \tabularnewline
21 & 20506 & 24547.8134354745 & -4041.81343547447 \tabularnewline
22 & 28806 & 22273.1464678993 & 6532.85353210073 \tabularnewline
23 & 22228 & 25949.7303505327 & -3721.73035053265 \tabularnewline
24 & 13971 & 23855.2009454205 & -9884.2009454205 \tabularnewline
25 & 36845 & 18292.5331601905 & 18552.4668398095 \tabularnewline
26 & 35338 & 28733.5602291688 & 6604.43977083125 \tabularnewline
27 & 35022 & 32450.4316844902 & 2571.56831550981 \tabularnewline
28 & 34777 & 33897.6685734602 & 879.331426539822 \tabularnewline
29 & 26887 & 34392.5420210928 & -7505.54202109276 \tabularnewline
30 & 23970 & 30168.5448520787 & -6198.54485207866 \tabularnewline
31 & 22780 & 26680.1044658139 & -3900.10446581391 \tabularnewline
32 & 17351 & 24485.1890051902 & -7134.18900519023 \tabularnewline
33 & 21382 & 20470.1832832254 & 911.816716774614 \tabularnewline
34 & 24561 & 20983.3389246823 & 3577.6610753177 \tabularnewline
35 & 17409 & 22996.7884812053 & -5587.78848120529 \tabularnewline
36 & 11514 & 19852.0718625614 & -8338.07186256137 \tabularnewline
37 & 31514 & 15159.5404179946 & 16354.4595820054 \tabularnewline
38 & 27071 & 24363.5646951231 & 2707.43530487687 \tabularnewline
39 & 29462 & 25887.2653194018 & 3574.73468059822 \tabularnewline
40 & 26105 & 27899.0679484976 & -1794.06794849758 \tabularnewline
41 & 22397 & 26889.3956404649 & -4492.39564046494 \tabularnewline
42 & 23843 & 24361.1483248031 & -518.148324803064 \tabularnewline
43 & 21705 & 24069.5428616737 & -2364.54286167372 \tabularnewline
44 & 18089 & 22738.8165362926 & -4649.81653629261 \tabularnewline
45 & 20764 & 20121.9752967741 & 642.024703225936 \tabularnewline
46 & 25316 & 20483.2963740850 & 4832.70362591503 \tabularnewline
47 & 17704 & 23203.0634977893 & -5499.06349778927 \tabularnewline
48 & 15548 & 20108.279859031 & -4560.27985903099 \tabularnewline
49 & 28029 & 17541.8284075135 & 10487.1715924865 \tabularnewline
50 & 29383 & 23443.8382814358 & 5939.16171856422 \tabularnewline
51 & 36438 & 26786.3020522108 & 9651.69794778919 \tabularnewline
52 & 32034 & 32218.1209259269 & -184.12092592688 \tabularnewline
53 & 22679 & 32114.5006587049 & -9435.5006587049 \tabularnewline
54 & 24319 & 26804.3541085165 & -2485.35410851645 \tabularnewline
55 & 18004 & 25405.6371752333 & -7401.63717523326 \tabularnewline
56 & 17537 & 21240.1159661863 & -3703.11596618634 \tabularnewline
57 & 20366 & 19156.0624343104 & 1209.93756568964 \tabularnewline
58 & 22782 & 19836.9956484332 & 2945.00435156679 \tabularnewline
59 & 19169 & 21494.3962743698 & -2325.39627436977 \tabularnewline
60 & 13807 & 20185.7010126325 & -6378.70101263253 \tabularnewline
61 & 29743 & 16595.871664715 & 13147.128335285 \tabularnewline
62 & 25591 & 23994.8619991697 & 1596.13800083032 \tabularnewline
63 & 29096 & 24893.1425467858 & 4202.85745321419 \tabularnewline
64 & 26482 & 27258.4424723949 & -776.44247239489 \tabularnewline
65 & 22405 & 26821.4732573693 & -4416.47325736932 \tabularnewline
66 & 27044 & 24335.9538260307 & 2708.04617396928 \tabularnewline
67 & 17970 & 25859.9982375148 & -7889.99823751485 \tabularnewline
68 & 18730 & 21419.6353529784 & -2689.63535297841 \tabularnewline
69 & 19684 & 19905.9522525796 & -221.952252579627 \tabularnewline
70 & 19785 & 19781.0411290501 & 3.95887094988211 \tabularnewline
71 & 18479 & 19783.2691173337 & -1304.26911733368 \tabularnewline
72 & 10698 & 19049.24763777 & -8351.24763776999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36992&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]3[/C][C]43129[/C][C]39690[/C][C]3439[/C][/ROW]
[ROW][C]4[/C][C]37863[/C][C]41625.4133550137[/C][C]-3762.41335501370[/C][/ROW]
[ROW][C]5[/C][C]35953[/C][C]39507.9882156199[/C][C]-3554.98821561986[/C][/ROW]
[ROW][C]6[/C][C]29133[/C][C]37507.2985763564[/C][C]-8374.2985763564[/C][/ROW]
[ROW][C]7[/C][C]24693[/C][C]32794.3793255415[/C][C]-8101.3793255415[/C][/ROW]
[ROW][C]8[/C][C]22205[/C][C]28235.0545972237[/C][C]-6030.0545972237[/C][/ROW]
[ROW][C]9[/C][C]21725[/C][C]24841.4377903239[/C][C]-3116.43779032386[/C][/ROW]
[ROW][C]10[/C][C]27192[/C][C]23087.5572089158[/C][C]4104.44279108416[/C][/ROW]
[ROW][C]11[/C][C]21790[/C][C]25397.4709608071[/C][C]-3607.47096080709[/C][/ROW]
[ROW][C]12[/C][C]13253[/C][C]23367.2448848053[/C][C]-10114.2448848053[/C][/ROW]
[ROW][C]13[/C][C]37702[/C][C]17675.1121061106[/C][C]20026.8878938894[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]28945.9194016022[/C][C]1418.08059839776[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]29743.9921345551[/C][C]2865.00786544491[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]31356.3720371435[/C][C]-1144.37203714345[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]30712.3380377856[/C][C]-747.338037785594[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]30291.7483259391[/C][C]-1939.74832593914[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]29200.0894671464[/C][C]-3386.08946714644[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]27294.4533008230[/C][C]-4880.45330082296[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]24547.8134354745[/C][C]-4041.81343547447[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]22273.1464678993[/C][C]6532.85353210073[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]25949.7303505327[/C][C]-3721.73035053265[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]23855.2009454205[/C][C]-9884.2009454205[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]18292.5331601905[/C][C]18552.4668398095[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]28733.5602291688[/C][C]6604.43977083125[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]32450.4316844902[/C][C]2571.56831550981[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]33897.6685734602[/C][C]879.331426539822[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]34392.5420210928[/C][C]-7505.54202109276[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]30168.5448520787[/C][C]-6198.54485207866[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]26680.1044658139[/C][C]-3900.10446581391[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]24485.1890051902[/C][C]-7134.18900519023[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]20470.1832832254[/C][C]911.816716774614[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]20983.3389246823[/C][C]3577.6610753177[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]22996.7884812053[/C][C]-5587.78848120529[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]19852.0718625614[/C][C]-8338.07186256137[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]15159.5404179946[/C][C]16354.4595820054[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]24363.5646951231[/C][C]2707.43530487687[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]25887.2653194018[/C][C]3574.73468059822[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27899.0679484976[/C][C]-1794.06794849758[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]26889.3956404649[/C][C]-4492.39564046494[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]24361.1483248031[/C][C]-518.148324803064[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]24069.5428616737[/C][C]-2364.54286167372[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]22738.8165362926[/C][C]-4649.81653629261[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]20121.9752967741[/C][C]642.024703225936[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]20483.2963740850[/C][C]4832.70362591503[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]23203.0634977893[/C][C]-5499.06349778927[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]20108.279859031[/C][C]-4560.27985903099[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]17541.8284075135[/C][C]10487.1715924865[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]23443.8382814358[/C][C]5939.16171856422[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]26786.3020522108[/C][C]9651.69794778919[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]32218.1209259269[/C][C]-184.12092592688[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]32114.5006587049[/C][C]-9435.5006587049[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]26804.3541085165[/C][C]-2485.35410851645[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]25405.6371752333[/C][C]-7401.63717523326[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]21240.1159661863[/C][C]-3703.11596618634[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]19156.0624343104[/C][C]1209.93756568964[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]19836.9956484332[/C][C]2945.00435156679[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]21494.3962743698[/C][C]-2325.39627436977[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]20185.7010126325[/C][C]-6378.70101263253[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]16595.871664715[/C][C]13147.128335285[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]23994.8619991697[/C][C]1596.13800083032[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]24893.1425467858[/C][C]4202.85745321419[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]27258.4424723949[/C][C]-776.44247239489[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]26821.4732573693[/C][C]-4416.47325736932[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]24335.9538260307[/C][C]2708.04617396928[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]25859.9982375148[/C][C]-7889.99823751485[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]21419.6353529784[/C][C]-2689.63535297841[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]19905.9522525796[/C][C]-221.952252579627[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]19781.0411290501[/C][C]3.95887094988211[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]19783.2691173337[/C][C]-1304.26911733368[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]19049.24763777[/C][C]-8351.24763776999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36992&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
343129396903439
43786341625.4133550137-3762.41335501370
53595339507.9882156199-3554.98821561986
62913337507.2985763564-8374.2985763564
72469332794.3793255415-8101.3793255415
82220528235.0545972237-6030.0545972237
92172524841.4377903239-3116.43779032386
102719223087.55720891584104.44279108416
112179025397.4709608071-3607.47096080709
121325323367.2448848053-10114.2448848053
133770217675.112106110620026.8878938894
143036428945.91940160221418.08059839776
153260929743.99213455512865.00786544491
163021231356.3720371435-1144.37203714345
172996530712.3380377856-747.338037785594
182835230291.7483259391-1939.74832593914
192581429200.0894671464-3386.08946714644
202241427294.4533008230-4880.45330082296
212050624547.8134354745-4041.81343547447
222880622273.14646789936532.85353210073
232222825949.7303505327-3721.73035053265
241397123855.2009454205-9884.2009454205
253684518292.533160190518552.4668398095
263533828733.56022916886604.43977083125
273502232450.43168449022571.56831550981
283477733897.6685734602879.331426539822
292688734392.5420210928-7505.54202109276
302397030168.5448520787-6198.54485207866
312278026680.1044658139-3900.10446581391
321735124485.1890051902-7134.18900519023
332138220470.1832832254911.816716774614
342456120983.33892468233577.6610753177
351740922996.7884812053-5587.78848120529
361151419852.0718625614-8338.07186256137
373151415159.540417994616354.4595820054
382707124363.56469512312707.43530487687
392946225887.26531940183574.73468059822
402610527899.0679484976-1794.06794849758
412239726889.3956404649-4492.39564046494
422384324361.1483248031-518.148324803064
432170524069.5428616737-2364.54286167372
441808922738.8165362926-4649.81653629261
452076420121.9752967741642.024703225936
462531620483.29637408504832.70362591503
471770423203.0634977893-5499.06349778927
481554820108.279859031-4560.27985903099
492802917541.828407513510487.1715924865
502938323443.83828143585939.16171856422
513643826786.30205221089651.69794778919
523203432218.1209259269-184.12092592688
532267932114.5006587049-9435.5006587049
542431926804.3541085165-2485.35410851645
551800425405.6371752333-7401.63717523326
561753721240.1159661863-3703.11596618634
572036619156.06243431041209.93756568964
582278219836.99564843322945.00435156679
591916921494.3962743698-2325.39627436977
601380720185.7010126325-6378.70101263253
612974316595.87166471513147.128335285
622559123994.86199916971596.13800083032
632909624893.14254678584202.85745321419
642648227258.4424723949-776.44247239489
652240526821.4732573693-4416.47325736932
662704424335.95382603072708.04617396928
671797025859.9982375148-7889.99823751485
681873021419.6353529784-2689.63535297841
691968419905.9522525796-221.952252579627
701978519781.04112905013.95887094988211
711847919783.2691173337-1304.26911733368
721069819049.24763777-8351.24763776999







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7314349.30108087361752.9524469122626945.6497148349
7414349.3010808736-104.84054103560128803.4427027828
7514349.3010808736-1749.6560637403430448.2582254875
7614349.3010808736-3241.3393924583631939.9415542056
7714349.3010808736-4616.0579555362533314.6601172834
7814349.3010808736-5897.6506526057134596.2528143529
7914349.3010808736-7102.8145634107435801.4167251579
8014349.3010808736-8243.7836295783436942.3857913255
8114349.3010808736-9329.839272010138028.4414337573
8214349.3010808736-10368.221023283139066.8231850303
8314349.3010808736-11364.705026448240063.3071881954
8414349.3010808736-12323.987452887941022.5896146351

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 14349.3010808736 & 1752.95244691226 & 26945.6497148349 \tabularnewline
74 & 14349.3010808736 & -104.840541035601 & 28803.4427027828 \tabularnewline
75 & 14349.3010808736 & -1749.65606374034 & 30448.2582254875 \tabularnewline
76 & 14349.3010808736 & -3241.33939245836 & 31939.9415542056 \tabularnewline
77 & 14349.3010808736 & -4616.05795553625 & 33314.6601172834 \tabularnewline
78 & 14349.3010808736 & -5897.65065260571 & 34596.2528143529 \tabularnewline
79 & 14349.3010808736 & -7102.81456341074 & 35801.4167251579 \tabularnewline
80 & 14349.3010808736 & -8243.78362957834 & 36942.3857913255 \tabularnewline
81 & 14349.3010808736 & -9329.8392720101 & 38028.4414337573 \tabularnewline
82 & 14349.3010808736 & -10368.2210232831 & 39066.8231850303 \tabularnewline
83 & 14349.3010808736 & -11364.7050264482 & 40063.3071881954 \tabularnewline
84 & 14349.3010808736 & -12323.9874528879 & 41022.5896146351 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36992&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]14349.3010808736[/C][C]1752.95244691226[/C][C]26945.6497148349[/C][/ROW]
[ROW][C]74[/C][C]14349.3010808736[/C][C]-104.840541035601[/C][C]28803.4427027828[/C][/ROW]
[ROW][C]75[/C][C]14349.3010808736[/C][C]-1749.65606374034[/C][C]30448.2582254875[/C][/ROW]
[ROW][C]76[/C][C]14349.3010808736[/C][C]-3241.33939245836[/C][C]31939.9415542056[/C][/ROW]
[ROW][C]77[/C][C]14349.3010808736[/C][C]-4616.05795553625[/C][C]33314.6601172834[/C][/ROW]
[ROW][C]78[/C][C]14349.3010808736[/C][C]-5897.65065260571[/C][C]34596.2528143529[/C][/ROW]
[ROW][C]79[/C][C]14349.3010808736[/C][C]-7102.81456341074[/C][C]35801.4167251579[/C][/ROW]
[ROW][C]80[/C][C]14349.3010808736[/C][C]-8243.78362957834[/C][C]36942.3857913255[/C][/ROW]
[ROW][C]81[/C][C]14349.3010808736[/C][C]-9329.8392720101[/C][C]38028.4414337573[/C][/ROW]
[ROW][C]82[/C][C]14349.3010808736[/C][C]-10368.2210232831[/C][C]39066.8231850303[/C][/ROW]
[ROW][C]83[/C][C]14349.3010808736[/C][C]-11364.7050264482[/C][C]40063.3071881954[/C][/ROW]
[ROW][C]84[/C][C]14349.3010808736[/C][C]-12323.9874528879[/C][C]41022.5896146351[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36992&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36992&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
7314349.30108087361752.9524469122626945.6497148349
7414349.3010808736-104.84054103560128803.4427027828
7514349.3010808736-1749.6560637403430448.2582254875
7614349.3010808736-3241.3393924583631939.9415542056
7714349.3010808736-4616.0579555362533314.6601172834
7814349.3010808736-5897.6506526057134596.2528143529
7914349.3010808736-7102.8145634107435801.4167251579
8014349.3010808736-8243.7836295783436942.3857913255
8114349.3010808736-9329.839272010138028.4414337573
8214349.3010808736-10368.221023283139066.8231850303
8314349.3010808736-11364.705026448240063.3071881954
8414349.3010808736-12323.987452887941022.5896146351



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')