Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 31 May 2010 15:05:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/May/31/t127531836597j092n6j3org1k.htm/, Retrieved Mon, 29 Apr 2024 09:39:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76746, Retrieved Mon, 29 Apr 2024 09:39:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact159
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Het aantal inschr...] [2010-05-27 12:18:36] [e6858d370c345b8be9ebab3064023a2f]
-    D    [Exponential Smoothing] [Opgave 10 oefenin...] [2010-05-31 15:05:24] [8c87877ca0a068b5d9f0f8fa9cf6c0e7] [Current]
-   PD      [Exponential Smoothing] [stap 33 exponenti...] [2010-08-19 13:26:45] [44f4e89d2978fa9cb7cef84cf6986739]
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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
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76746&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76746&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta1
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 1 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76746&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]1[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76746&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
alpha1
beta1
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133770241487.9961256583-3785.99612565827
143036426985.96613032113378.03386967886
153260932727.9358210002-118.935821000206
163021230145.877718237966.1222817621128
172996529887.902049961877.0979500382091
182835228391.3748481016-39.3748481016046
192581422414.01962249313399.9803775069
202241426784.6171673481-4370.61716734807
212050621340.5520439118-834.552043911786
222880623717.11592731045088.88407268965
232222825561.4177256393-3333.41772563932
241397112837.6719600381133.32803996199
253684540601.5340145322-3756.53401453224
263533827298.93724802818039.06275197186
273502244169.1342060279-9147.13420602795
283477729660.53847484215116.4615251579
292688736705.4820559147-9818.4820559147
302397018314.53078484545655.46921515461
312278017792.05318680264987.94681319737
321735124394.9811555839-7043.98115558389
332138213941.3020668187440.69793318201
342456132526.7733061008-7965.77330610083
351740917693.0108338551-284.01083385514
36115149048.620097668362465.37990233164
373151435051.2864794491-3537.28647944907
382707124344.4845598372726.51544016304
392946230993.2773260638-1531.27732606379
402610527597.7751894846-1492.7751894846
412239724647.8615532109-2250.86155321087
422384317930.78679426095912.21320573911
432170520938.1454020331766.854597966936
441808922518.2329109566-4429.23291095655
452076416418.67877605184345.3212239482
462531629981.5307429842-4665.5307429842
471770419578.8057375386-1874.80573753865
48155489031.56311555276516.4368844473
492802957475.3424653159-29446.3424653159
50293839524.3922222938719858.6077777061
513643838979.699162503-2541.69916250305
523203438213.6173641055-6179.61736410549
532267929985.4261796034-7306.42617960342
542431912927.155397327811391.8446026722
551800421479.2311892206-3475.23118922059
561753715397.13943321972139.8605667803
572036618719.1618236321646.83817636797
582278229672.6780384295-6890.67803842952
591916915850.89612447033318.10387552967
601380712106.81668321061700.18331678943
612974345014.8164697156-15271.8164697156
622559116257.92614304529333.07385695475
632909629340.4209292218-244.420929221818
642648228394.0018115126-1912.00181151256
652240525728.3604886563-3323.36048865629
662704417593.86754746049450.13245253962
671797025984.3096810551-8014.30968105509
681873013365.97693473335364.02306526672
691968421153.1133629432-1469.11336294321
701978526373.6035376064-6588.60353760635
711847911664.16063211776814.83936788228
721069812765.8235286875-2067.82352868753
733195628541.12943222833414.87056777168
742950626919.63865511792586.36134488209
753450635849.4789327642-1343.47893276417
762716534513.3508750869-7348.35087508686
772673622126.41816001864609.58183998139
782369125137.1476304567-1446.14763045668
791815717464.253448161692.746551839035
801732816131.05953140591196.94046859407
811820518157.19326476947.8067352310027
822099524385.0774564696-3390.07745646963
831738215200.51980515262181.48019484744
84936710808.7908846448-1441.79088464483
853112422889.42066342658234.5793365735
862655128623.8134118605-2072.81341186048
873065130211.7736790038439.22632099616
882585930317.5117468502-4458.51174685019
892510023072.99658975362027.00341024635
902577823266.32686679862511.67313320136
912041821977.5195299962-1559.51952999621
921868818763.4129777217-75.4129777216986
932042418811.57586318511612.42413681493
942477628331.3280990513-3555.32809905126
951981419052.9011431531761.098856846937
961273811896.906659231841.093340768961
973156637808.6848699408-6242.68486994076
983011121631.04651343418479.95348656592
993001937488.1358370153-7469.1358370153
1003193425601.5732487666332.426751234
1012582635663.8163727304-9837.81637273038
1022683518965.05919923827869.94080076176
1032020523104.6686210557-2899.6686210557
1041778917609.655864695179.344135304989
1052052017197.44001122263322.55998877743
1062251829742.4407326765-7224.44073267652
1071557215256.8323835081315.167616491928
108115097817.874273777463691.12572622254
1092544738233.1770809934-12786.1770809934
1102409014603.79671776179486.2032822383
1112778629825.2075899902-2039.20758999023
1122619527463.0014345558-1268.00143455579
1132051626360.0760125685-5844.07601256846
1142275914293.63189102838465.3681089717
1151902820629.239528044-1601.23952804403
1161697118399.4112133541-1428.41121335415
1172003616635.1989777213400.80102227902
1182248529556.8562177491-7071.85621774909
1191873015712.12079180913017.87920819086
1201453811716.52702127532821.47297872474

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 37702 & 41487.9961256583 & -3785.99612565827 \tabularnewline
14 & 30364 & 26985.9661303211 & 3378.03386967886 \tabularnewline
15 & 32609 & 32727.9358210002 & -118.935821000206 \tabularnewline
16 & 30212 & 30145.8777182379 & 66.1222817621128 \tabularnewline
17 & 29965 & 29887.9020499618 & 77.0979500382091 \tabularnewline
18 & 28352 & 28391.3748481016 & -39.3748481016046 \tabularnewline
19 & 25814 & 22414.0196224931 & 3399.9803775069 \tabularnewline
20 & 22414 & 26784.6171673481 & -4370.61716734807 \tabularnewline
21 & 20506 & 21340.5520439118 & -834.552043911786 \tabularnewline
22 & 28806 & 23717.1159273104 & 5088.88407268965 \tabularnewline
23 & 22228 & 25561.4177256393 & -3333.41772563932 \tabularnewline
24 & 13971 & 12837.671960038 & 1133.32803996199 \tabularnewline
25 & 36845 & 40601.5340145322 & -3756.53401453224 \tabularnewline
26 & 35338 & 27298.9372480281 & 8039.06275197186 \tabularnewline
27 & 35022 & 44169.1342060279 & -9147.13420602795 \tabularnewline
28 & 34777 & 29660.5384748421 & 5116.4615251579 \tabularnewline
29 & 26887 & 36705.4820559147 & -9818.4820559147 \tabularnewline
30 & 23970 & 18314.5307848454 & 5655.46921515461 \tabularnewline
31 & 22780 & 17792.0531868026 & 4987.94681319737 \tabularnewline
32 & 17351 & 24394.9811555839 & -7043.98115558389 \tabularnewline
33 & 21382 & 13941.302066818 & 7440.69793318201 \tabularnewline
34 & 24561 & 32526.7733061008 & -7965.77330610083 \tabularnewline
35 & 17409 & 17693.0108338551 & -284.01083385514 \tabularnewline
36 & 11514 & 9048.62009766836 & 2465.37990233164 \tabularnewline
37 & 31514 & 35051.2864794491 & -3537.28647944907 \tabularnewline
38 & 27071 & 24344.484559837 & 2726.51544016304 \tabularnewline
39 & 29462 & 30993.2773260638 & -1531.27732606379 \tabularnewline
40 & 26105 & 27597.7751894846 & -1492.7751894846 \tabularnewline
41 & 22397 & 24647.8615532109 & -2250.86155321087 \tabularnewline
42 & 23843 & 17930.7867942609 & 5912.21320573911 \tabularnewline
43 & 21705 & 20938.1454020331 & 766.854597966936 \tabularnewline
44 & 18089 & 22518.2329109566 & -4429.23291095655 \tabularnewline
45 & 20764 & 16418.6787760518 & 4345.3212239482 \tabularnewline
46 & 25316 & 29981.5307429842 & -4665.5307429842 \tabularnewline
47 & 17704 & 19578.8057375386 & -1874.80573753865 \tabularnewline
48 & 15548 & 9031.5631155527 & 6516.4368844473 \tabularnewline
49 & 28029 & 57475.3424653159 & -29446.3424653159 \tabularnewline
50 & 29383 & 9524.39222229387 & 19858.6077777061 \tabularnewline
51 & 36438 & 38979.699162503 & -2541.69916250305 \tabularnewline
52 & 32034 & 38213.6173641055 & -6179.61736410549 \tabularnewline
53 & 22679 & 29985.4261796034 & -7306.42617960342 \tabularnewline
54 & 24319 & 12927.1553973278 & 11391.8446026722 \tabularnewline
55 & 18004 & 21479.2311892206 & -3475.23118922059 \tabularnewline
56 & 17537 & 15397.1394332197 & 2139.8605667803 \tabularnewline
57 & 20366 & 18719.161823632 & 1646.83817636797 \tabularnewline
58 & 22782 & 29672.6780384295 & -6890.67803842952 \tabularnewline
59 & 19169 & 15850.8961244703 & 3318.10387552967 \tabularnewline
60 & 13807 & 12106.8166832106 & 1700.18331678943 \tabularnewline
61 & 29743 & 45014.8164697156 & -15271.8164697156 \tabularnewline
62 & 25591 & 16257.9261430452 & 9333.07385695475 \tabularnewline
63 & 29096 & 29340.4209292218 & -244.420929221818 \tabularnewline
64 & 26482 & 28394.0018115126 & -1912.00181151256 \tabularnewline
65 & 22405 & 25728.3604886563 & -3323.36048865629 \tabularnewline
66 & 27044 & 17593.8675474604 & 9450.13245253962 \tabularnewline
67 & 17970 & 25984.3096810551 & -8014.30968105509 \tabularnewline
68 & 18730 & 13365.9769347333 & 5364.02306526672 \tabularnewline
69 & 19684 & 21153.1133629432 & -1469.11336294321 \tabularnewline
70 & 19785 & 26373.6035376064 & -6588.60353760635 \tabularnewline
71 & 18479 & 11664.1606321177 & 6814.83936788228 \tabularnewline
72 & 10698 & 12765.8235286875 & -2067.82352868753 \tabularnewline
73 & 31956 & 28541.1294322283 & 3414.87056777168 \tabularnewline
74 & 29506 & 26919.6386551179 & 2586.36134488209 \tabularnewline
75 & 34506 & 35849.4789327642 & -1343.47893276417 \tabularnewline
76 & 27165 & 34513.3508750869 & -7348.35087508686 \tabularnewline
77 & 26736 & 22126.4181600186 & 4609.58183998139 \tabularnewline
78 & 23691 & 25137.1476304567 & -1446.14763045668 \tabularnewline
79 & 18157 & 17464.253448161 & 692.746551839035 \tabularnewline
80 & 17328 & 16131.0595314059 & 1196.94046859407 \tabularnewline
81 & 18205 & 18157.193264769 & 47.8067352310027 \tabularnewline
82 & 20995 & 24385.0774564696 & -3390.07745646963 \tabularnewline
83 & 17382 & 15200.5198051526 & 2181.48019484744 \tabularnewline
84 & 9367 & 10808.7908846448 & -1441.79088464483 \tabularnewline
85 & 31124 & 22889.4206634265 & 8234.5793365735 \tabularnewline
86 & 26551 & 28623.8134118605 & -2072.81341186048 \tabularnewline
87 & 30651 & 30211.7736790038 & 439.22632099616 \tabularnewline
88 & 25859 & 30317.5117468502 & -4458.51174685019 \tabularnewline
89 & 25100 & 23072.9965897536 & 2027.00341024635 \tabularnewline
90 & 25778 & 23266.3268667986 & 2511.67313320136 \tabularnewline
91 & 20418 & 21977.5195299962 & -1559.51952999621 \tabularnewline
92 & 18688 & 18763.4129777217 & -75.4129777216986 \tabularnewline
93 & 20424 & 18811.5758631851 & 1612.42413681493 \tabularnewline
94 & 24776 & 28331.3280990513 & -3555.32809905126 \tabularnewline
95 & 19814 & 19052.9011431531 & 761.098856846937 \tabularnewline
96 & 12738 & 11896.906659231 & 841.093340768961 \tabularnewline
97 & 31566 & 37808.6848699408 & -6242.68486994076 \tabularnewline
98 & 30111 & 21631.0465134341 & 8479.95348656592 \tabularnewline
99 & 30019 & 37488.1358370153 & -7469.1358370153 \tabularnewline
100 & 31934 & 25601.573248766 & 6332.426751234 \tabularnewline
101 & 25826 & 35663.8163727304 & -9837.81637273038 \tabularnewline
102 & 26835 & 18965.0591992382 & 7869.94080076176 \tabularnewline
103 & 20205 & 23104.6686210557 & -2899.6686210557 \tabularnewline
104 & 17789 & 17609.655864695 & 179.344135304989 \tabularnewline
105 & 20520 & 17197.4400112226 & 3322.55998877743 \tabularnewline
106 & 22518 & 29742.4407326765 & -7224.44073267652 \tabularnewline
107 & 15572 & 15256.8323835081 & 315.167616491928 \tabularnewline
108 & 11509 & 7817.87427377746 & 3691.12572622254 \tabularnewline
109 & 25447 & 38233.1770809934 & -12786.1770809934 \tabularnewline
110 & 24090 & 14603.7967177617 & 9486.2032822383 \tabularnewline
111 & 27786 & 29825.2075899902 & -2039.20758999023 \tabularnewline
112 & 26195 & 27463.0014345558 & -1268.00143455579 \tabularnewline
113 & 20516 & 26360.0760125685 & -5844.07601256846 \tabularnewline
114 & 22759 & 14293.6318910283 & 8465.3681089717 \tabularnewline
115 & 19028 & 20629.239528044 & -1601.23952804403 \tabularnewline
116 & 16971 & 18399.4112133541 & -1428.41121335415 \tabularnewline
117 & 20036 & 16635.198977721 & 3400.80102227902 \tabularnewline
118 & 22485 & 29556.8562177491 & -7071.85621774909 \tabularnewline
119 & 18730 & 15712.1207918091 & 3017.87920819086 \tabularnewline
120 & 14538 & 11716.5270212753 & 2821.47297872474 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76746&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]37702[/C][C]41487.9961256583[/C][C]-3785.99612565827[/C][/ROW]
[ROW][C]14[/C][C]30364[/C][C]26985.9661303211[/C][C]3378.03386967886[/C][/ROW]
[ROW][C]15[/C][C]32609[/C][C]32727.9358210002[/C][C]-118.935821000206[/C][/ROW]
[ROW][C]16[/C][C]30212[/C][C]30145.8777182379[/C][C]66.1222817621128[/C][/ROW]
[ROW][C]17[/C][C]29965[/C][C]29887.9020499618[/C][C]77.0979500382091[/C][/ROW]
[ROW][C]18[/C][C]28352[/C][C]28391.3748481016[/C][C]-39.3748481016046[/C][/ROW]
[ROW][C]19[/C][C]25814[/C][C]22414.0196224931[/C][C]3399.9803775069[/C][/ROW]
[ROW][C]20[/C][C]22414[/C][C]26784.6171673481[/C][C]-4370.61716734807[/C][/ROW]
[ROW][C]21[/C][C]20506[/C][C]21340.5520439118[/C][C]-834.552043911786[/C][/ROW]
[ROW][C]22[/C][C]28806[/C][C]23717.1159273104[/C][C]5088.88407268965[/C][/ROW]
[ROW][C]23[/C][C]22228[/C][C]25561.4177256393[/C][C]-3333.41772563932[/C][/ROW]
[ROW][C]24[/C][C]13971[/C][C]12837.671960038[/C][C]1133.32803996199[/C][/ROW]
[ROW][C]25[/C][C]36845[/C][C]40601.5340145322[/C][C]-3756.53401453224[/C][/ROW]
[ROW][C]26[/C][C]35338[/C][C]27298.9372480281[/C][C]8039.06275197186[/C][/ROW]
[ROW][C]27[/C][C]35022[/C][C]44169.1342060279[/C][C]-9147.13420602795[/C][/ROW]
[ROW][C]28[/C][C]34777[/C][C]29660.5384748421[/C][C]5116.4615251579[/C][/ROW]
[ROW][C]29[/C][C]26887[/C][C]36705.4820559147[/C][C]-9818.4820559147[/C][/ROW]
[ROW][C]30[/C][C]23970[/C][C]18314.5307848454[/C][C]5655.46921515461[/C][/ROW]
[ROW][C]31[/C][C]22780[/C][C]17792.0531868026[/C][C]4987.94681319737[/C][/ROW]
[ROW][C]32[/C][C]17351[/C][C]24394.9811555839[/C][C]-7043.98115558389[/C][/ROW]
[ROW][C]33[/C][C]21382[/C][C]13941.302066818[/C][C]7440.69793318201[/C][/ROW]
[ROW][C]34[/C][C]24561[/C][C]32526.7733061008[/C][C]-7965.77330610083[/C][/ROW]
[ROW][C]35[/C][C]17409[/C][C]17693.0108338551[/C][C]-284.01083385514[/C][/ROW]
[ROW][C]36[/C][C]11514[/C][C]9048.62009766836[/C][C]2465.37990233164[/C][/ROW]
[ROW][C]37[/C][C]31514[/C][C]35051.2864794491[/C][C]-3537.28647944907[/C][/ROW]
[ROW][C]38[/C][C]27071[/C][C]24344.484559837[/C][C]2726.51544016304[/C][/ROW]
[ROW][C]39[/C][C]29462[/C][C]30993.2773260638[/C][C]-1531.27732606379[/C][/ROW]
[ROW][C]40[/C][C]26105[/C][C]27597.7751894846[/C][C]-1492.7751894846[/C][/ROW]
[ROW][C]41[/C][C]22397[/C][C]24647.8615532109[/C][C]-2250.86155321087[/C][/ROW]
[ROW][C]42[/C][C]23843[/C][C]17930.7867942609[/C][C]5912.21320573911[/C][/ROW]
[ROW][C]43[/C][C]21705[/C][C]20938.1454020331[/C][C]766.854597966936[/C][/ROW]
[ROW][C]44[/C][C]18089[/C][C]22518.2329109566[/C][C]-4429.23291095655[/C][/ROW]
[ROW][C]45[/C][C]20764[/C][C]16418.6787760518[/C][C]4345.3212239482[/C][/ROW]
[ROW][C]46[/C][C]25316[/C][C]29981.5307429842[/C][C]-4665.5307429842[/C][/ROW]
[ROW][C]47[/C][C]17704[/C][C]19578.8057375386[/C][C]-1874.80573753865[/C][/ROW]
[ROW][C]48[/C][C]15548[/C][C]9031.5631155527[/C][C]6516.4368844473[/C][/ROW]
[ROW][C]49[/C][C]28029[/C][C]57475.3424653159[/C][C]-29446.3424653159[/C][/ROW]
[ROW][C]50[/C][C]29383[/C][C]9524.39222229387[/C][C]19858.6077777061[/C][/ROW]
[ROW][C]51[/C][C]36438[/C][C]38979.699162503[/C][C]-2541.69916250305[/C][/ROW]
[ROW][C]52[/C][C]32034[/C][C]38213.6173641055[/C][C]-6179.61736410549[/C][/ROW]
[ROW][C]53[/C][C]22679[/C][C]29985.4261796034[/C][C]-7306.42617960342[/C][/ROW]
[ROW][C]54[/C][C]24319[/C][C]12927.1553973278[/C][C]11391.8446026722[/C][/ROW]
[ROW][C]55[/C][C]18004[/C][C]21479.2311892206[/C][C]-3475.23118922059[/C][/ROW]
[ROW][C]56[/C][C]17537[/C][C]15397.1394332197[/C][C]2139.8605667803[/C][/ROW]
[ROW][C]57[/C][C]20366[/C][C]18719.161823632[/C][C]1646.83817636797[/C][/ROW]
[ROW][C]58[/C][C]22782[/C][C]29672.6780384295[/C][C]-6890.67803842952[/C][/ROW]
[ROW][C]59[/C][C]19169[/C][C]15850.8961244703[/C][C]3318.10387552967[/C][/ROW]
[ROW][C]60[/C][C]13807[/C][C]12106.8166832106[/C][C]1700.18331678943[/C][/ROW]
[ROW][C]61[/C][C]29743[/C][C]45014.8164697156[/C][C]-15271.8164697156[/C][/ROW]
[ROW][C]62[/C][C]25591[/C][C]16257.9261430452[/C][C]9333.07385695475[/C][/ROW]
[ROW][C]63[/C][C]29096[/C][C]29340.4209292218[/C][C]-244.420929221818[/C][/ROW]
[ROW][C]64[/C][C]26482[/C][C]28394.0018115126[/C][C]-1912.00181151256[/C][/ROW]
[ROW][C]65[/C][C]22405[/C][C]25728.3604886563[/C][C]-3323.36048865629[/C][/ROW]
[ROW][C]66[/C][C]27044[/C][C]17593.8675474604[/C][C]9450.13245253962[/C][/ROW]
[ROW][C]67[/C][C]17970[/C][C]25984.3096810551[/C][C]-8014.30968105509[/C][/ROW]
[ROW][C]68[/C][C]18730[/C][C]13365.9769347333[/C][C]5364.02306526672[/C][/ROW]
[ROW][C]69[/C][C]19684[/C][C]21153.1133629432[/C][C]-1469.11336294321[/C][/ROW]
[ROW][C]70[/C][C]19785[/C][C]26373.6035376064[/C][C]-6588.60353760635[/C][/ROW]
[ROW][C]71[/C][C]18479[/C][C]11664.1606321177[/C][C]6814.83936788228[/C][/ROW]
[ROW][C]72[/C][C]10698[/C][C]12765.8235286875[/C][C]-2067.82352868753[/C][/ROW]
[ROW][C]73[/C][C]31956[/C][C]28541.1294322283[/C][C]3414.87056777168[/C][/ROW]
[ROW][C]74[/C][C]29506[/C][C]26919.6386551179[/C][C]2586.36134488209[/C][/ROW]
[ROW][C]75[/C][C]34506[/C][C]35849.4789327642[/C][C]-1343.47893276417[/C][/ROW]
[ROW][C]76[/C][C]27165[/C][C]34513.3508750869[/C][C]-7348.35087508686[/C][/ROW]
[ROW][C]77[/C][C]26736[/C][C]22126.4181600186[/C][C]4609.58183998139[/C][/ROW]
[ROW][C]78[/C][C]23691[/C][C]25137.1476304567[/C][C]-1446.14763045668[/C][/ROW]
[ROW][C]79[/C][C]18157[/C][C]17464.253448161[/C][C]692.746551839035[/C][/ROW]
[ROW][C]80[/C][C]17328[/C][C]16131.0595314059[/C][C]1196.94046859407[/C][/ROW]
[ROW][C]81[/C][C]18205[/C][C]18157.193264769[/C][C]47.8067352310027[/C][/ROW]
[ROW][C]82[/C][C]20995[/C][C]24385.0774564696[/C][C]-3390.07745646963[/C][/ROW]
[ROW][C]83[/C][C]17382[/C][C]15200.5198051526[/C][C]2181.48019484744[/C][/ROW]
[ROW][C]84[/C][C]9367[/C][C]10808.7908846448[/C][C]-1441.79088464483[/C][/ROW]
[ROW][C]85[/C][C]31124[/C][C]22889.4206634265[/C][C]8234.5793365735[/C][/ROW]
[ROW][C]86[/C][C]26551[/C][C]28623.8134118605[/C][C]-2072.81341186048[/C][/ROW]
[ROW][C]87[/C][C]30651[/C][C]30211.7736790038[/C][C]439.22632099616[/C][/ROW]
[ROW][C]88[/C][C]25859[/C][C]30317.5117468502[/C][C]-4458.51174685019[/C][/ROW]
[ROW][C]89[/C][C]25100[/C][C]23072.9965897536[/C][C]2027.00341024635[/C][/ROW]
[ROW][C]90[/C][C]25778[/C][C]23266.3268667986[/C][C]2511.67313320136[/C][/ROW]
[ROW][C]91[/C][C]20418[/C][C]21977.5195299962[/C][C]-1559.51952999621[/C][/ROW]
[ROW][C]92[/C][C]18688[/C][C]18763.4129777217[/C][C]-75.4129777216986[/C][/ROW]
[ROW][C]93[/C][C]20424[/C][C]18811.5758631851[/C][C]1612.42413681493[/C][/ROW]
[ROW][C]94[/C][C]24776[/C][C]28331.3280990513[/C][C]-3555.32809905126[/C][/ROW]
[ROW][C]95[/C][C]19814[/C][C]19052.9011431531[/C][C]761.098856846937[/C][/ROW]
[ROW][C]96[/C][C]12738[/C][C]11896.906659231[/C][C]841.093340768961[/C][/ROW]
[ROW][C]97[/C][C]31566[/C][C]37808.6848699408[/C][C]-6242.68486994076[/C][/ROW]
[ROW][C]98[/C][C]30111[/C][C]21631.0465134341[/C][C]8479.95348656592[/C][/ROW]
[ROW][C]99[/C][C]30019[/C][C]37488.1358370153[/C][C]-7469.1358370153[/C][/ROW]
[ROW][C]100[/C][C]31934[/C][C]25601.573248766[/C][C]6332.426751234[/C][/ROW]
[ROW][C]101[/C][C]25826[/C][C]35663.8163727304[/C][C]-9837.81637273038[/C][/ROW]
[ROW][C]102[/C][C]26835[/C][C]18965.0591992382[/C][C]7869.94080076176[/C][/ROW]
[ROW][C]103[/C][C]20205[/C][C]23104.6686210557[/C][C]-2899.6686210557[/C][/ROW]
[ROW][C]104[/C][C]17789[/C][C]17609.655864695[/C][C]179.344135304989[/C][/ROW]
[ROW][C]105[/C][C]20520[/C][C]17197.4400112226[/C][C]3322.55998877743[/C][/ROW]
[ROW][C]106[/C][C]22518[/C][C]29742.4407326765[/C][C]-7224.44073267652[/C][/ROW]
[ROW][C]107[/C][C]15572[/C][C]15256.8323835081[/C][C]315.167616491928[/C][/ROW]
[ROW][C]108[/C][C]11509[/C][C]7817.87427377746[/C][C]3691.12572622254[/C][/ROW]
[ROW][C]109[/C][C]25447[/C][C]38233.1770809934[/C][C]-12786.1770809934[/C][/ROW]
[ROW][C]110[/C][C]24090[/C][C]14603.7967177617[/C][C]9486.2032822383[/C][/ROW]
[ROW][C]111[/C][C]27786[/C][C]29825.2075899902[/C][C]-2039.20758999023[/C][/ROW]
[ROW][C]112[/C][C]26195[/C][C]27463.0014345558[/C][C]-1268.00143455579[/C][/ROW]
[ROW][C]113[/C][C]20516[/C][C]26360.0760125685[/C][C]-5844.07601256846[/C][/ROW]
[ROW][C]114[/C][C]22759[/C][C]14293.6318910283[/C][C]8465.3681089717[/C][/ROW]
[ROW][C]115[/C][C]19028[/C][C]20629.239528044[/C][C]-1601.23952804403[/C][/ROW]
[ROW][C]116[/C][C]16971[/C][C]18399.4112133541[/C][C]-1428.41121335415[/C][/ROW]
[ROW][C]117[/C][C]20036[/C][C]16635.198977721[/C][C]3400.80102227902[/C][/ROW]
[ROW][C]118[/C][C]22485[/C][C]29556.8562177491[/C][C]-7071.85621774909[/C][/ROW]
[ROW][C]119[/C][C]18730[/C][C]15712.1207918091[/C][C]3017.87920819086[/C][/ROW]
[ROW][C]120[/C][C]14538[/C][C]11716.5270212753[/C][C]2821.47297872474[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76746&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
133770241487.9961256583-3785.99612565827
143036426985.96613032113378.03386967886
153260932727.9358210002-118.935821000206
163021230145.877718237966.1222817621128
172996529887.902049961877.0979500382091
182835228391.3748481016-39.3748481016046
192581422414.01962249313399.9803775069
202241426784.6171673481-4370.61716734807
212050621340.5520439118-834.552043911786
222880623717.11592731045088.88407268965
232222825561.4177256393-3333.41772563932
241397112837.6719600381133.32803996199
253684540601.5340145322-3756.53401453224
263533827298.93724802818039.06275197186
273502244169.1342060279-9147.13420602795
283477729660.53847484215116.4615251579
292688736705.4820559147-9818.4820559147
302397018314.53078484545655.46921515461
312278017792.05318680264987.94681319737
321735124394.9811555839-7043.98115558389
332138213941.3020668187440.69793318201
342456132526.7733061008-7965.77330610083
351740917693.0108338551-284.01083385514
36115149048.620097668362465.37990233164
373151435051.2864794491-3537.28647944907
382707124344.4845598372726.51544016304
392946230993.2773260638-1531.27732606379
402610527597.7751894846-1492.7751894846
412239724647.8615532109-2250.86155321087
422384317930.78679426095912.21320573911
432170520938.1454020331766.854597966936
441808922518.2329109566-4429.23291095655
452076416418.67877605184345.3212239482
462531629981.5307429842-4665.5307429842
471770419578.8057375386-1874.80573753865
48155489031.56311555276516.4368844473
492802957475.3424653159-29446.3424653159
50293839524.3922222938719858.6077777061
513643838979.699162503-2541.69916250305
523203438213.6173641055-6179.61736410549
532267929985.4261796034-7306.42617960342
542431912927.155397327811391.8446026722
551800421479.2311892206-3475.23118922059
561753715397.13943321972139.8605667803
572036618719.1618236321646.83817636797
582278229672.6780384295-6890.67803842952
591916915850.89612447033318.10387552967
601380712106.81668321061700.18331678943
612974345014.8164697156-15271.8164697156
622559116257.92614304529333.07385695475
632909629340.4209292218-244.420929221818
642648228394.0018115126-1912.00181151256
652240525728.3604886563-3323.36048865629
662704417593.86754746049450.13245253962
671797025984.3096810551-8014.30968105509
681873013365.97693473335364.02306526672
691968421153.1133629432-1469.11336294321
701978526373.6035376064-6588.60353760635
711847911664.16063211776814.83936788228
721069812765.8235286875-2067.82352868753
733195628541.12943222833414.87056777168
742950626919.63865511792586.36134488209
753450635849.4789327642-1343.47893276417
762716534513.3508750869-7348.35087508686
772673622126.41816001864609.58183998139
782369125137.1476304567-1446.14763045668
791815717464.253448161692.746551839035
801732816131.05953140591196.94046859407
811820518157.19326476947.8067352310027
822099524385.0774564696-3390.07745646963
831738215200.51980515262181.48019484744
84936710808.7908846448-1441.79088464483
853112422889.42066342658234.5793365735
862655128623.8134118605-2072.81341186048
873065130211.7736790038439.22632099616
882585930317.5117468502-4458.51174685019
892510023072.99658975362027.00341024635
902577823266.32686679862511.67313320136
912041821977.5195299962-1559.51952999621
921868818763.4129777217-75.4129777216986
932042418811.57586318511612.42413681493
942477628331.3280990513-3555.32809905126
951981419052.9011431531761.098856846937
961273811896.906659231841.093340768961
973156637808.6848699408-6242.68486994076
983011121631.04651343418479.95348656592
993001937488.1358370153-7469.1358370153
1003193425601.5732487666332.426751234
1012582635663.8163727304-9837.81637273038
1022683518965.05919923827869.94080076176
1032020523104.6686210557-2899.6686210557
1041778917609.655864695179.344135304989
1052052017197.44001122263322.55998877743
1062251829742.4407326765-7224.44073267652
1071557215256.8323835081315.167616491928
108115097817.874273777463691.12572622254
1092544738233.1770809934-12786.1770809934
1102409014603.79671776179486.2032822383
1112778629825.2075899902-2039.20758999023
1122619527463.0014345558-1268.00143455579
1132051626360.0760125685-5844.07601256846
1142275914293.63189102838465.3681089717
1151902820629.239528044-1601.23952804403
1161697118399.4112133541-1428.41121335415
1172003616635.1989777213400.80102227902
1182248529556.8562177491-7071.85621774909
1191873015712.12079180913017.87920819086
1201453811716.52702127532821.47297872474







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12149938.886170718137811.372079811462066.4002616249
12247050.408501113624092.078789834670008.7382123925
12358046.056746841515420.1830365067100671.930457176
12460632.58662136851707.4597081531119557.713534584
12566753.6356380269-13344.3217216522146851.592997706
12669477.4872993832-29128.3404435172168083.315042284
12759902.5221855174-38063.2768795174157868.321250552
12859492.040879766-50808.9184176144169793.000177146
12964584.5287470717-69499.3606420824198668.418136226
13089074.7858480441-115565.007657598293714.579353686
13177805.1252187176-117880.470648379273490.721085814
13250847.8472650804-87718.127610297189413.822140458

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 49938.8861707181 & 37811.3720798114 & 62066.4002616249 \tabularnewline
122 & 47050.4085011136 & 24092.0787898346 & 70008.7382123925 \tabularnewline
123 & 58046.0567468415 & 15420.1830365067 & 100671.930457176 \tabularnewline
124 & 60632.5866213685 & 1707.4597081531 & 119557.713534584 \tabularnewline
125 & 66753.6356380269 & -13344.3217216522 & 146851.592997706 \tabularnewline
126 & 69477.4872993832 & -29128.3404435172 & 168083.315042284 \tabularnewline
127 & 59902.5221855174 & -38063.2768795174 & 157868.321250552 \tabularnewline
128 & 59492.040879766 & -50808.9184176144 & 169793.000177146 \tabularnewline
129 & 64584.5287470717 & -69499.3606420824 & 198668.418136226 \tabularnewline
130 & 89074.7858480441 & -115565.007657598 & 293714.579353686 \tabularnewline
131 & 77805.1252187176 & -117880.470648379 & 273490.721085814 \tabularnewline
132 & 50847.8472650804 & -87718.127610297 & 189413.822140458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76746&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]121[/C][C]49938.8861707181[/C][C]37811.3720798114[/C][C]62066.4002616249[/C][/ROW]
[ROW][C]122[/C][C]47050.4085011136[/C][C]24092.0787898346[/C][C]70008.7382123925[/C][/ROW]
[ROW][C]123[/C][C]58046.0567468415[/C][C]15420.1830365067[/C][C]100671.930457176[/C][/ROW]
[ROW][C]124[/C][C]60632.5866213685[/C][C]1707.4597081531[/C][C]119557.713534584[/C][/ROW]
[ROW][C]125[/C][C]66753.6356380269[/C][C]-13344.3217216522[/C][C]146851.592997706[/C][/ROW]
[ROW][C]126[/C][C]69477.4872993832[/C][C]-29128.3404435172[/C][C]168083.315042284[/C][/ROW]
[ROW][C]127[/C][C]59902.5221855174[/C][C]-38063.2768795174[/C][C]157868.321250552[/C][/ROW]
[ROW][C]128[/C][C]59492.040879766[/C][C]-50808.9184176144[/C][C]169793.000177146[/C][/ROW]
[ROW][C]129[/C][C]64584.5287470717[/C][C]-69499.3606420824[/C][C]198668.418136226[/C][/ROW]
[ROW][C]130[/C][C]89074.7858480441[/C][C]-115565.007657598[/C][C]293714.579353686[/C][/ROW]
[ROW][C]131[/C][C]77805.1252187176[/C][C]-117880.470648379[/C][C]273490.721085814[/C][/ROW]
[ROW][C]132[/C][C]50847.8472650804[/C][C]-87718.127610297[/C][C]189413.822140458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76746&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76746&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
12149938.886170718137811.372079811462066.4002616249
12247050.408501113624092.078789834670008.7382123925
12358046.056746841515420.1830365067100671.930457176
12460632.58662136851707.4597081531119557.713534584
12566753.6356380269-13344.3217216522146851.592997706
12669477.4872993832-29128.3404435172168083.315042284
12759902.5221855174-38063.2768795174157868.321250552
12859492.040879766-50808.9184176144169793.000177146
12964584.5287470717-69499.3606420824198668.418136226
13089074.7858480441-115565.007657598293714.579353686
13177805.1252187176-117880.470648379273490.721085814
13250847.8472650804-87718.127610297189413.822140458



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')