Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Aug 2013 01:48:06 -0400
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/Aug/19/t1376891330whb53b7wsx8srkk.htm/, Retrieved Thu, 02 May 2024 10:14:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211191, Retrieved Thu, 02 May 2024 10:14:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsStefanie Gubbi
Estimated Impact127
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2013-08-19 05:48:06] [3958f9c0a64aeec6b83979b094ee8a96] [Current]
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Dataseries X:
196088
192639
189187
182286
252115
248662
196088
161176
164624
164624
168076
175352
154275
133164
115877
115877
182286
189187
136613
77137
108601
108601
133164
147340
143888
108601
126263
119329
178804
164624
108601
66754
105149
115877
126263
140065
112050
87865
98252
101700
192639
192639
140065
133164
154275
143888
171903
206816
213750
164624
150789
136613
231378
238313
220651
238313
234827
206816
238313
273225
287402
245214
217199
238313
329249
357263
350363
364161
360712
325800
385275
399451
420187
357263
332701
360712
427463
486938
472762
472762
479696
455474
518436
518436
507708
448199
458927
465861
511501
570976
528785
549899
532237
521884
602474
584812
560249
525336
560249
577911
598988
626999
598988
616275
595195
591746
679233
686508
658497
609374
651221
668850
689961
721424
689961
714523
703796
665398
745984
745984




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211191&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211191&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211191&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.653620350905747
beta0.0529315168636585
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.653620350905747 \tabularnewline
beta & 0.0529315168636585 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211191&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]0.653620350905747[/C][/ROW]
[ROW][C]beta[/C][C]0.0529315168636585[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211191&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211191&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
alpha0.653620350905747
beta0.0529315168636585
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13154275186224.175480769-31949.1754807692
14133164143896.492481514-10732.4924815143
15115877118745.31864188-2868.31864188006
16115877114754.7599789831122.24002101674
17182286178940.7129385293345.287061471
18189187184020.3069713515166.69302864908
19136613133357.12002623255.87997380013
207713798455.172507465-21318.172507465
2110860186425.951882246922175.0481177531
22108601100432.8947766978168.10522330253
23133164108874.16596372124289.8340362788
24147340132228.36874901215111.631250988
25143888110255.36941935633632.6305806437
26108601120956.735617432-12355.7356174318
27126263100226.82616680726036.1738331926
28119329120269.351786876-940.351786876126
29178804187564.082748946-8760.08274894566
30164624188630.359517053-24006.3595170533
31108601120496.002312138-11895.0023121383
326675468913.798617986-2159.79861798596
3310514986869.492547294718279.5074527053
3411587795741.181337874720135.8186621253
35126263120265.7512461955997.24875380458
36140065130528.2535485249536.74645147605
37112050113177.666557472-1127.66655747248
388786585877.92819122071987.07180877928
399825288965.53266311389286.4673368862
4010170089281.085194384512418.9148056155
41192639163626.3965391229012.6034608801
42192639186434.78328686204.21671319962
43140065145621.113567835-5556.11356783527
44133164105152.8326622728011.1673377297
45154275154551.091702858-276.091702858306
46143888155937.929551026-12049.9295510263
47171903157414.87031351114488.1296864889
48206816177633.89893788529182.101062115
49213750173290.35628673840459.6437132615
50164624179550.989660275-14926.9896602746
51150789178825.58106896-28036.5810689601
52136613159253.775468615-22640.7754686152
53231378218640.84142320912737.1585767908
54238313224557.58732769313755.4126723066
55220651186513.92564372334137.0743562766
56238313186898.14474910951414.855250891
57234827245886.301366195-11059.3013661954
58206816239864.629876179-33048.6298761787
59238313239799.975693951-1486.97569395075
60273225257105.68968277516119.3103172254
61287402250117.06423250637284.9357674937
62245214236994.7173162268219.28268377378
63217199249534.95805259-32335.9580525898
64238313231550.9137109446762.08628905579
65329249325956.6634039153292.33659608522
66357263329272.19887820727990.8011217934
67350363311304.78793511539058.2120648848
68364161324772.40998029439388.5900197059
69360712357726.2798500522985.72014994803
70325800357220.083005854-31420.0830058538
71385275373160.55657401712114.4434259831
72399451409933.825627878-10482.8256278777
73420187396447.41901949423739.5809805056
74357263367493.745975896-10230.7459758962
75332701356378.788794542-23677.7887945416
76360712360347.840996696364.159003303619
77427463451899.748730339-24436.7487303386
78486938447216.51299922839721.4870007716
79472762442726.36870340130035.6312965988
80472762452075.25496951720686.7450304831
81479696461213.14557982318482.8544201774
82455474460472.017729674-4998.01772967377
83518436511229.3888163447206.61118365626
84518436539265.191820044-20829.1918200444
85507708532809.807572521-25101.8075725214
86448199460415.680527241-12216.6805272409
87458927443526.08797924415400.9120207558
88465861482898.619977271-17037.6199772707
89511501555416.993946626-43915.9939466264
90570976560482.06141975210493.938580248
91528785532779.251586627-3994.25158662652
92549899514715.95230758235183.0476924178
93532237531135.7711587591101.22884124133
94521884508869.24137977113014.758620229
95602474574219.63340658928254.3665934112
96584812605621.906390343-20809.9063903426
97560249597020.1078772-36771.1078771998
98525336520379.0378429494956.96215705073
99560249523792.0215735636456.9784264399
100577911565931.02084425411979.9791557461
101598988649349.532749566-50361.5327495662
102626999670068.927518674-43069.9275186744
103598988601504.884475941-2516.88447594084
104616275597196.16819701519078.8318029852
105595195589946.262532095248.73746791005
106591746573322.29207981218423.7079201883
107679233646478.96657638432754.0334236161
108686508662975.31627978123532.6837202187
109658497678510.096032508-20013.096032508
110609374628537.931054604-19163.931054604
111651221627523.23254442323697.7674555768
112668850652830.04539729416019.9546027061
113689961717420.935908334-27459.935908334
114721424756552.87277337-35128.8727733698
115689961708418.679806879-18457.6798068793
116714523701812.21262968912710.7873703107
117703796686030.4050424817765.5949575197
118665398683005.140932357-17607.1409323569
119745984737182.3809133528801.61908664752
120745984733607.50124161512376.4987583853

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 154275 & 186224.175480769 & -31949.1754807692 \tabularnewline
14 & 133164 & 143896.492481514 & -10732.4924815143 \tabularnewline
15 & 115877 & 118745.31864188 & -2868.31864188006 \tabularnewline
16 & 115877 & 114754.759978983 & 1122.24002101674 \tabularnewline
17 & 182286 & 178940.712938529 & 3345.287061471 \tabularnewline
18 & 189187 & 184020.306971351 & 5166.69302864908 \tabularnewline
19 & 136613 & 133357.1200262 & 3255.87997380013 \tabularnewline
20 & 77137 & 98455.172507465 & -21318.172507465 \tabularnewline
21 & 108601 & 86425.9518822469 & 22175.0481177531 \tabularnewline
22 & 108601 & 100432.894776697 & 8168.10522330253 \tabularnewline
23 & 133164 & 108874.165963721 & 24289.8340362788 \tabularnewline
24 & 147340 & 132228.368749012 & 15111.631250988 \tabularnewline
25 & 143888 & 110255.369419356 & 33632.6305806437 \tabularnewline
26 & 108601 & 120956.735617432 & -12355.7356174318 \tabularnewline
27 & 126263 & 100226.826166807 & 26036.1738331926 \tabularnewline
28 & 119329 & 120269.351786876 & -940.351786876126 \tabularnewline
29 & 178804 & 187564.082748946 & -8760.08274894566 \tabularnewline
30 & 164624 & 188630.359517053 & -24006.3595170533 \tabularnewline
31 & 108601 & 120496.002312138 & -11895.0023121383 \tabularnewline
32 & 66754 & 68913.798617986 & -2159.79861798596 \tabularnewline
33 & 105149 & 86869.4925472947 & 18279.5074527053 \tabularnewline
34 & 115877 & 95741.1813378747 & 20135.8186621253 \tabularnewline
35 & 126263 & 120265.751246195 & 5997.24875380458 \tabularnewline
36 & 140065 & 130528.253548524 & 9536.74645147605 \tabularnewline
37 & 112050 & 113177.666557472 & -1127.66655747248 \tabularnewline
38 & 87865 & 85877.9281912207 & 1987.07180877928 \tabularnewline
39 & 98252 & 88965.5326631138 & 9286.4673368862 \tabularnewline
40 & 101700 & 89281.0851943845 & 12418.9148056155 \tabularnewline
41 & 192639 & 163626.39653912 & 29012.6034608801 \tabularnewline
42 & 192639 & 186434.7832868 & 6204.21671319962 \tabularnewline
43 & 140065 & 145621.113567835 & -5556.11356783527 \tabularnewline
44 & 133164 & 105152.83266227 & 28011.1673377297 \tabularnewline
45 & 154275 & 154551.091702858 & -276.091702858306 \tabularnewline
46 & 143888 & 155937.929551026 & -12049.9295510263 \tabularnewline
47 & 171903 & 157414.870313511 & 14488.1296864889 \tabularnewline
48 & 206816 & 177633.898937885 & 29182.101062115 \tabularnewline
49 & 213750 & 173290.356286738 & 40459.6437132615 \tabularnewline
50 & 164624 & 179550.989660275 & -14926.9896602746 \tabularnewline
51 & 150789 & 178825.58106896 & -28036.5810689601 \tabularnewline
52 & 136613 & 159253.775468615 & -22640.7754686152 \tabularnewline
53 & 231378 & 218640.841423209 & 12737.1585767908 \tabularnewline
54 & 238313 & 224557.587327693 & 13755.4126723066 \tabularnewline
55 & 220651 & 186513.925643723 & 34137.0743562766 \tabularnewline
56 & 238313 & 186898.144749109 & 51414.855250891 \tabularnewline
57 & 234827 & 245886.301366195 & -11059.3013661954 \tabularnewline
58 & 206816 & 239864.629876179 & -33048.6298761787 \tabularnewline
59 & 238313 & 239799.975693951 & -1486.97569395075 \tabularnewline
60 & 273225 & 257105.689682775 & 16119.3103172254 \tabularnewline
61 & 287402 & 250117.064232506 & 37284.9357674937 \tabularnewline
62 & 245214 & 236994.717316226 & 8219.28268377378 \tabularnewline
63 & 217199 & 249534.95805259 & -32335.9580525898 \tabularnewline
64 & 238313 & 231550.913710944 & 6762.08628905579 \tabularnewline
65 & 329249 & 325956.663403915 & 3292.33659608522 \tabularnewline
66 & 357263 & 329272.198878207 & 27990.8011217934 \tabularnewline
67 & 350363 & 311304.787935115 & 39058.2120648848 \tabularnewline
68 & 364161 & 324772.409980294 & 39388.5900197059 \tabularnewline
69 & 360712 & 357726.279850052 & 2985.72014994803 \tabularnewline
70 & 325800 & 357220.083005854 & -31420.0830058538 \tabularnewline
71 & 385275 & 373160.556574017 & 12114.4434259831 \tabularnewline
72 & 399451 & 409933.825627878 & -10482.8256278777 \tabularnewline
73 & 420187 & 396447.419019494 & 23739.5809805056 \tabularnewline
74 & 357263 & 367493.745975896 & -10230.7459758962 \tabularnewline
75 & 332701 & 356378.788794542 & -23677.7887945416 \tabularnewline
76 & 360712 & 360347.840996696 & 364.159003303619 \tabularnewline
77 & 427463 & 451899.748730339 & -24436.7487303386 \tabularnewline
78 & 486938 & 447216.512999228 & 39721.4870007716 \tabularnewline
79 & 472762 & 442726.368703401 & 30035.6312965988 \tabularnewline
80 & 472762 & 452075.254969517 & 20686.7450304831 \tabularnewline
81 & 479696 & 461213.145579823 & 18482.8544201774 \tabularnewline
82 & 455474 & 460472.017729674 & -4998.01772967377 \tabularnewline
83 & 518436 & 511229.388816344 & 7206.61118365626 \tabularnewline
84 & 518436 & 539265.191820044 & -20829.1918200444 \tabularnewline
85 & 507708 & 532809.807572521 & -25101.8075725214 \tabularnewline
86 & 448199 & 460415.680527241 & -12216.6805272409 \tabularnewline
87 & 458927 & 443526.087979244 & 15400.9120207558 \tabularnewline
88 & 465861 & 482898.619977271 & -17037.6199772707 \tabularnewline
89 & 511501 & 555416.993946626 & -43915.9939466264 \tabularnewline
90 & 570976 & 560482.061419752 & 10493.938580248 \tabularnewline
91 & 528785 & 532779.251586627 & -3994.25158662652 \tabularnewline
92 & 549899 & 514715.952307582 & 35183.0476924178 \tabularnewline
93 & 532237 & 531135.771158759 & 1101.22884124133 \tabularnewline
94 & 521884 & 508869.241379771 & 13014.758620229 \tabularnewline
95 & 602474 & 574219.633406589 & 28254.3665934112 \tabularnewline
96 & 584812 & 605621.906390343 & -20809.9063903426 \tabularnewline
97 & 560249 & 597020.1078772 & -36771.1078771998 \tabularnewline
98 & 525336 & 520379.037842949 & 4956.96215705073 \tabularnewline
99 & 560249 & 523792.02157356 & 36456.9784264399 \tabularnewline
100 & 577911 & 565931.020844254 & 11979.9791557461 \tabularnewline
101 & 598988 & 649349.532749566 & -50361.5327495662 \tabularnewline
102 & 626999 & 670068.927518674 & -43069.9275186744 \tabularnewline
103 & 598988 & 601504.884475941 & -2516.88447594084 \tabularnewline
104 & 616275 & 597196.168197015 & 19078.8318029852 \tabularnewline
105 & 595195 & 589946.26253209 & 5248.73746791005 \tabularnewline
106 & 591746 & 573322.292079812 & 18423.7079201883 \tabularnewline
107 & 679233 & 646478.966576384 & 32754.0334236161 \tabularnewline
108 & 686508 & 662975.316279781 & 23532.6837202187 \tabularnewline
109 & 658497 & 678510.096032508 & -20013.096032508 \tabularnewline
110 & 609374 & 628537.931054604 & -19163.931054604 \tabularnewline
111 & 651221 & 627523.232544423 & 23697.7674555768 \tabularnewline
112 & 668850 & 652830.045397294 & 16019.9546027061 \tabularnewline
113 & 689961 & 717420.935908334 & -27459.935908334 \tabularnewline
114 & 721424 & 756552.87277337 & -35128.8727733698 \tabularnewline
115 & 689961 & 708418.679806879 & -18457.6798068793 \tabularnewline
116 & 714523 & 701812.212629689 & 12710.7873703107 \tabularnewline
117 & 703796 & 686030.40504248 & 17765.5949575197 \tabularnewline
118 & 665398 & 683005.140932357 & -17607.1409323569 \tabularnewline
119 & 745984 & 737182.380913352 & 8801.61908664752 \tabularnewline
120 & 745984 & 733607.501241615 & 12376.4987583853 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211191&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]154275[/C][C]186224.175480769[/C][C]-31949.1754807692[/C][/ROW]
[ROW][C]14[/C][C]133164[/C][C]143896.492481514[/C][C]-10732.4924815143[/C][/ROW]
[ROW][C]15[/C][C]115877[/C][C]118745.31864188[/C][C]-2868.31864188006[/C][/ROW]
[ROW][C]16[/C][C]115877[/C][C]114754.759978983[/C][C]1122.24002101674[/C][/ROW]
[ROW][C]17[/C][C]182286[/C][C]178940.712938529[/C][C]3345.287061471[/C][/ROW]
[ROW][C]18[/C][C]189187[/C][C]184020.306971351[/C][C]5166.69302864908[/C][/ROW]
[ROW][C]19[/C][C]136613[/C][C]133357.1200262[/C][C]3255.87997380013[/C][/ROW]
[ROW][C]20[/C][C]77137[/C][C]98455.172507465[/C][C]-21318.172507465[/C][/ROW]
[ROW][C]21[/C][C]108601[/C][C]86425.9518822469[/C][C]22175.0481177531[/C][/ROW]
[ROW][C]22[/C][C]108601[/C][C]100432.894776697[/C][C]8168.10522330253[/C][/ROW]
[ROW][C]23[/C][C]133164[/C][C]108874.165963721[/C][C]24289.8340362788[/C][/ROW]
[ROW][C]24[/C][C]147340[/C][C]132228.368749012[/C][C]15111.631250988[/C][/ROW]
[ROW][C]25[/C][C]143888[/C][C]110255.369419356[/C][C]33632.6305806437[/C][/ROW]
[ROW][C]26[/C][C]108601[/C][C]120956.735617432[/C][C]-12355.7356174318[/C][/ROW]
[ROW][C]27[/C][C]126263[/C][C]100226.826166807[/C][C]26036.1738331926[/C][/ROW]
[ROW][C]28[/C][C]119329[/C][C]120269.351786876[/C][C]-940.351786876126[/C][/ROW]
[ROW][C]29[/C][C]178804[/C][C]187564.082748946[/C][C]-8760.08274894566[/C][/ROW]
[ROW][C]30[/C][C]164624[/C][C]188630.359517053[/C][C]-24006.3595170533[/C][/ROW]
[ROW][C]31[/C][C]108601[/C][C]120496.002312138[/C][C]-11895.0023121383[/C][/ROW]
[ROW][C]32[/C][C]66754[/C][C]68913.798617986[/C][C]-2159.79861798596[/C][/ROW]
[ROW][C]33[/C][C]105149[/C][C]86869.4925472947[/C][C]18279.5074527053[/C][/ROW]
[ROW][C]34[/C][C]115877[/C][C]95741.1813378747[/C][C]20135.8186621253[/C][/ROW]
[ROW][C]35[/C][C]126263[/C][C]120265.751246195[/C][C]5997.24875380458[/C][/ROW]
[ROW][C]36[/C][C]140065[/C][C]130528.253548524[/C][C]9536.74645147605[/C][/ROW]
[ROW][C]37[/C][C]112050[/C][C]113177.666557472[/C][C]-1127.66655747248[/C][/ROW]
[ROW][C]38[/C][C]87865[/C][C]85877.9281912207[/C][C]1987.07180877928[/C][/ROW]
[ROW][C]39[/C][C]98252[/C][C]88965.5326631138[/C][C]9286.4673368862[/C][/ROW]
[ROW][C]40[/C][C]101700[/C][C]89281.0851943845[/C][C]12418.9148056155[/C][/ROW]
[ROW][C]41[/C][C]192639[/C][C]163626.39653912[/C][C]29012.6034608801[/C][/ROW]
[ROW][C]42[/C][C]192639[/C][C]186434.7832868[/C][C]6204.21671319962[/C][/ROW]
[ROW][C]43[/C][C]140065[/C][C]145621.113567835[/C][C]-5556.11356783527[/C][/ROW]
[ROW][C]44[/C][C]133164[/C][C]105152.83266227[/C][C]28011.1673377297[/C][/ROW]
[ROW][C]45[/C][C]154275[/C][C]154551.091702858[/C][C]-276.091702858306[/C][/ROW]
[ROW][C]46[/C][C]143888[/C][C]155937.929551026[/C][C]-12049.9295510263[/C][/ROW]
[ROW][C]47[/C][C]171903[/C][C]157414.870313511[/C][C]14488.1296864889[/C][/ROW]
[ROW][C]48[/C][C]206816[/C][C]177633.898937885[/C][C]29182.101062115[/C][/ROW]
[ROW][C]49[/C][C]213750[/C][C]173290.356286738[/C][C]40459.6437132615[/C][/ROW]
[ROW][C]50[/C][C]164624[/C][C]179550.989660275[/C][C]-14926.9896602746[/C][/ROW]
[ROW][C]51[/C][C]150789[/C][C]178825.58106896[/C][C]-28036.5810689601[/C][/ROW]
[ROW][C]52[/C][C]136613[/C][C]159253.775468615[/C][C]-22640.7754686152[/C][/ROW]
[ROW][C]53[/C][C]231378[/C][C]218640.841423209[/C][C]12737.1585767908[/C][/ROW]
[ROW][C]54[/C][C]238313[/C][C]224557.587327693[/C][C]13755.4126723066[/C][/ROW]
[ROW][C]55[/C][C]220651[/C][C]186513.925643723[/C][C]34137.0743562766[/C][/ROW]
[ROW][C]56[/C][C]238313[/C][C]186898.144749109[/C][C]51414.855250891[/C][/ROW]
[ROW][C]57[/C][C]234827[/C][C]245886.301366195[/C][C]-11059.3013661954[/C][/ROW]
[ROW][C]58[/C][C]206816[/C][C]239864.629876179[/C][C]-33048.6298761787[/C][/ROW]
[ROW][C]59[/C][C]238313[/C][C]239799.975693951[/C][C]-1486.97569395075[/C][/ROW]
[ROW][C]60[/C][C]273225[/C][C]257105.689682775[/C][C]16119.3103172254[/C][/ROW]
[ROW][C]61[/C][C]287402[/C][C]250117.064232506[/C][C]37284.9357674937[/C][/ROW]
[ROW][C]62[/C][C]245214[/C][C]236994.717316226[/C][C]8219.28268377378[/C][/ROW]
[ROW][C]63[/C][C]217199[/C][C]249534.95805259[/C][C]-32335.9580525898[/C][/ROW]
[ROW][C]64[/C][C]238313[/C][C]231550.913710944[/C][C]6762.08628905579[/C][/ROW]
[ROW][C]65[/C][C]329249[/C][C]325956.663403915[/C][C]3292.33659608522[/C][/ROW]
[ROW][C]66[/C][C]357263[/C][C]329272.198878207[/C][C]27990.8011217934[/C][/ROW]
[ROW][C]67[/C][C]350363[/C][C]311304.787935115[/C][C]39058.2120648848[/C][/ROW]
[ROW][C]68[/C][C]364161[/C][C]324772.409980294[/C][C]39388.5900197059[/C][/ROW]
[ROW][C]69[/C][C]360712[/C][C]357726.279850052[/C][C]2985.72014994803[/C][/ROW]
[ROW][C]70[/C][C]325800[/C][C]357220.083005854[/C][C]-31420.0830058538[/C][/ROW]
[ROW][C]71[/C][C]385275[/C][C]373160.556574017[/C][C]12114.4434259831[/C][/ROW]
[ROW][C]72[/C][C]399451[/C][C]409933.825627878[/C][C]-10482.8256278777[/C][/ROW]
[ROW][C]73[/C][C]420187[/C][C]396447.419019494[/C][C]23739.5809805056[/C][/ROW]
[ROW][C]74[/C][C]357263[/C][C]367493.745975896[/C][C]-10230.7459758962[/C][/ROW]
[ROW][C]75[/C][C]332701[/C][C]356378.788794542[/C][C]-23677.7887945416[/C][/ROW]
[ROW][C]76[/C][C]360712[/C][C]360347.840996696[/C][C]364.159003303619[/C][/ROW]
[ROW][C]77[/C][C]427463[/C][C]451899.748730339[/C][C]-24436.7487303386[/C][/ROW]
[ROW][C]78[/C][C]486938[/C][C]447216.512999228[/C][C]39721.4870007716[/C][/ROW]
[ROW][C]79[/C][C]472762[/C][C]442726.368703401[/C][C]30035.6312965988[/C][/ROW]
[ROW][C]80[/C][C]472762[/C][C]452075.254969517[/C][C]20686.7450304831[/C][/ROW]
[ROW][C]81[/C][C]479696[/C][C]461213.145579823[/C][C]18482.8544201774[/C][/ROW]
[ROW][C]82[/C][C]455474[/C][C]460472.017729674[/C][C]-4998.01772967377[/C][/ROW]
[ROW][C]83[/C][C]518436[/C][C]511229.388816344[/C][C]7206.61118365626[/C][/ROW]
[ROW][C]84[/C][C]518436[/C][C]539265.191820044[/C][C]-20829.1918200444[/C][/ROW]
[ROW][C]85[/C][C]507708[/C][C]532809.807572521[/C][C]-25101.8075725214[/C][/ROW]
[ROW][C]86[/C][C]448199[/C][C]460415.680527241[/C][C]-12216.6805272409[/C][/ROW]
[ROW][C]87[/C][C]458927[/C][C]443526.087979244[/C][C]15400.9120207558[/C][/ROW]
[ROW][C]88[/C][C]465861[/C][C]482898.619977271[/C][C]-17037.6199772707[/C][/ROW]
[ROW][C]89[/C][C]511501[/C][C]555416.993946626[/C][C]-43915.9939466264[/C][/ROW]
[ROW][C]90[/C][C]570976[/C][C]560482.061419752[/C][C]10493.938580248[/C][/ROW]
[ROW][C]91[/C][C]528785[/C][C]532779.251586627[/C][C]-3994.25158662652[/C][/ROW]
[ROW][C]92[/C][C]549899[/C][C]514715.952307582[/C][C]35183.0476924178[/C][/ROW]
[ROW][C]93[/C][C]532237[/C][C]531135.771158759[/C][C]1101.22884124133[/C][/ROW]
[ROW][C]94[/C][C]521884[/C][C]508869.241379771[/C][C]13014.758620229[/C][/ROW]
[ROW][C]95[/C][C]602474[/C][C]574219.633406589[/C][C]28254.3665934112[/C][/ROW]
[ROW][C]96[/C][C]584812[/C][C]605621.906390343[/C][C]-20809.9063903426[/C][/ROW]
[ROW][C]97[/C][C]560249[/C][C]597020.1078772[/C][C]-36771.1078771998[/C][/ROW]
[ROW][C]98[/C][C]525336[/C][C]520379.037842949[/C][C]4956.96215705073[/C][/ROW]
[ROW][C]99[/C][C]560249[/C][C]523792.02157356[/C][C]36456.9784264399[/C][/ROW]
[ROW][C]100[/C][C]577911[/C][C]565931.020844254[/C][C]11979.9791557461[/C][/ROW]
[ROW][C]101[/C][C]598988[/C][C]649349.532749566[/C][C]-50361.5327495662[/C][/ROW]
[ROW][C]102[/C][C]626999[/C][C]670068.927518674[/C][C]-43069.9275186744[/C][/ROW]
[ROW][C]103[/C][C]598988[/C][C]601504.884475941[/C][C]-2516.88447594084[/C][/ROW]
[ROW][C]104[/C][C]616275[/C][C]597196.168197015[/C][C]19078.8318029852[/C][/ROW]
[ROW][C]105[/C][C]595195[/C][C]589946.26253209[/C][C]5248.73746791005[/C][/ROW]
[ROW][C]106[/C][C]591746[/C][C]573322.292079812[/C][C]18423.7079201883[/C][/ROW]
[ROW][C]107[/C][C]679233[/C][C]646478.966576384[/C][C]32754.0334236161[/C][/ROW]
[ROW][C]108[/C][C]686508[/C][C]662975.316279781[/C][C]23532.6837202187[/C][/ROW]
[ROW][C]109[/C][C]658497[/C][C]678510.096032508[/C][C]-20013.096032508[/C][/ROW]
[ROW][C]110[/C][C]609374[/C][C]628537.931054604[/C][C]-19163.931054604[/C][/ROW]
[ROW][C]111[/C][C]651221[/C][C]627523.232544423[/C][C]23697.7674555768[/C][/ROW]
[ROW][C]112[/C][C]668850[/C][C]652830.045397294[/C][C]16019.9546027061[/C][/ROW]
[ROW][C]113[/C][C]689961[/C][C]717420.935908334[/C][C]-27459.935908334[/C][/ROW]
[ROW][C]114[/C][C]721424[/C][C]756552.87277337[/C][C]-35128.8727733698[/C][/ROW]
[ROW][C]115[/C][C]689961[/C][C]708418.679806879[/C][C]-18457.6798068793[/C][/ROW]
[ROW][C]116[/C][C]714523[/C][C]701812.212629689[/C][C]12710.7873703107[/C][/ROW]
[ROW][C]117[/C][C]703796[/C][C]686030.40504248[/C][C]17765.5949575197[/C][/ROW]
[ROW][C]118[/C][C]665398[/C][C]683005.140932357[/C][C]-17607.1409323569[/C][/ROW]
[ROW][C]119[/C][C]745984[/C][C]737182.380913352[/C][C]8801.61908664752[/C][/ROW]
[ROW][C]120[/C][C]745984[/C][C]733607.501241615[/C][C]12376.4987583853[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211191&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211191&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
13154275186224.175480769-31949.1754807692
14133164143896.492481514-10732.4924815143
15115877118745.31864188-2868.31864188006
16115877114754.7599789831122.24002101674
17182286178940.7129385293345.287061471
18189187184020.3069713515166.69302864908
19136613133357.12002623255.87997380013
207713798455.172507465-21318.172507465
2110860186425.951882246922175.0481177531
22108601100432.8947766978168.10522330253
23133164108874.16596372124289.8340362788
24147340132228.36874901215111.631250988
25143888110255.36941935633632.6305806437
26108601120956.735617432-12355.7356174318
27126263100226.82616680726036.1738331926
28119329120269.351786876-940.351786876126
29178804187564.082748946-8760.08274894566
30164624188630.359517053-24006.3595170533
31108601120496.002312138-11895.0023121383
326675468913.798617986-2159.79861798596
3310514986869.492547294718279.5074527053
3411587795741.181337874720135.8186621253
35126263120265.7512461955997.24875380458
36140065130528.2535485249536.74645147605
37112050113177.666557472-1127.66655747248
388786585877.92819122071987.07180877928
399825288965.53266311389286.4673368862
4010170089281.085194384512418.9148056155
41192639163626.3965391229012.6034608801
42192639186434.78328686204.21671319962
43140065145621.113567835-5556.11356783527
44133164105152.8326622728011.1673377297
45154275154551.091702858-276.091702858306
46143888155937.929551026-12049.9295510263
47171903157414.87031351114488.1296864889
48206816177633.89893788529182.101062115
49213750173290.35628673840459.6437132615
50164624179550.989660275-14926.9896602746
51150789178825.58106896-28036.5810689601
52136613159253.775468615-22640.7754686152
53231378218640.84142320912737.1585767908
54238313224557.58732769313755.4126723066
55220651186513.92564372334137.0743562766
56238313186898.14474910951414.855250891
57234827245886.301366195-11059.3013661954
58206816239864.629876179-33048.6298761787
59238313239799.975693951-1486.97569395075
60273225257105.68968277516119.3103172254
61287402250117.06423250637284.9357674937
62245214236994.7173162268219.28268377378
63217199249534.95805259-32335.9580525898
64238313231550.9137109446762.08628905579
65329249325956.6634039153292.33659608522
66357263329272.19887820727990.8011217934
67350363311304.78793511539058.2120648848
68364161324772.40998029439388.5900197059
69360712357726.2798500522985.72014994803
70325800357220.083005854-31420.0830058538
71385275373160.55657401712114.4434259831
72399451409933.825627878-10482.8256278777
73420187396447.41901949423739.5809805056
74357263367493.745975896-10230.7459758962
75332701356378.788794542-23677.7887945416
76360712360347.840996696364.159003303619
77427463451899.748730339-24436.7487303386
78486938447216.51299922839721.4870007716
79472762442726.36870340130035.6312965988
80472762452075.25496951720686.7450304831
81479696461213.14557982318482.8544201774
82455474460472.017729674-4998.01772967377
83518436511229.3888163447206.61118365626
84518436539265.191820044-20829.1918200444
85507708532809.807572521-25101.8075725214
86448199460415.680527241-12216.6805272409
87458927443526.08797924415400.9120207558
88465861482898.619977271-17037.6199772707
89511501555416.993946626-43915.9939466264
90570976560482.06141975210493.938580248
91528785532779.251586627-3994.25158662652
92549899514715.95230758235183.0476924178
93532237531135.7711587591101.22884124133
94521884508869.24137977113014.758620229
95602474574219.63340658928254.3665934112
96584812605621.906390343-20809.9063903426
97560249597020.1078772-36771.1078771998
98525336520379.0378429494956.96215705073
99560249523792.0215735636456.9784264399
100577911565931.02084425411979.9791557461
101598988649349.532749566-50361.5327495662
102626999670068.927518674-43069.9275186744
103598988601504.884475941-2516.88447594084
104616275597196.16819701519078.8318029852
105595195589946.262532095248.73746791005
106591746573322.29207981218423.7079201883
107679233646478.96657638432754.0334236161
108686508662975.31627978123532.6837202187
109658497678510.096032508-20013.096032508
110609374628537.931054604-19163.931054604
111651221627523.23254442323697.7674555768
112668850652830.04539729416019.9546027061
113689961717420.935908334-27459.935908334
114721424756552.87277337-35128.8727733698
115689961708418.679806879-18457.6798068793
116714523701812.21262968912710.7873703107
117703796686030.4050424817765.5949575197
118665398683005.140932357-17607.1409323569
119745984737182.3809133528801.61908664752
120745984733607.50124161512376.4987583853







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121725159.671685575682262.74159622768056.601774931
122687647.674574753635573.499665653739721.849483853
123713753.415801007653147.109285245774359.722316769
124719839.657333896651073.634708726788605.679959067
125757272.995922216680571.957515881833974.034328551
126811020.942320508726520.174100369895521.710540648
127792161.61543032699938.176735083884385.054125557
128809593.526587514709684.553501565909502.499673463
129787992.756042731680406.949496164895578.562589298
130761226.687182103645951.900641978876501.473722228
131836792.471639162713800.927241125959784.0160372
132829131.131348692698383.123025652959879.139671733

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 725159.671685575 & 682262.74159622 & 768056.601774931 \tabularnewline
122 & 687647.674574753 & 635573.499665653 & 739721.849483853 \tabularnewline
123 & 713753.415801007 & 653147.109285245 & 774359.722316769 \tabularnewline
124 & 719839.657333896 & 651073.634708726 & 788605.679959067 \tabularnewline
125 & 757272.995922216 & 680571.957515881 & 833974.034328551 \tabularnewline
126 & 811020.942320508 & 726520.174100369 & 895521.710540648 \tabularnewline
127 & 792161.61543032 & 699938.176735083 & 884385.054125557 \tabularnewline
128 & 809593.526587514 & 709684.553501565 & 909502.499673463 \tabularnewline
129 & 787992.756042731 & 680406.949496164 & 895578.562589298 \tabularnewline
130 & 761226.687182103 & 645951.900641978 & 876501.473722228 \tabularnewline
131 & 836792.471639162 & 713800.927241125 & 959784.0160372 \tabularnewline
132 & 829131.131348692 & 698383.123025652 & 959879.139671733 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211191&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]725159.671685575[/C][C]682262.74159622[/C][C]768056.601774931[/C][/ROW]
[ROW][C]122[/C][C]687647.674574753[/C][C]635573.499665653[/C][C]739721.849483853[/C][/ROW]
[ROW][C]123[/C][C]713753.415801007[/C][C]653147.109285245[/C][C]774359.722316769[/C][/ROW]
[ROW][C]124[/C][C]719839.657333896[/C][C]651073.634708726[/C][C]788605.679959067[/C][/ROW]
[ROW][C]125[/C][C]757272.995922216[/C][C]680571.957515881[/C][C]833974.034328551[/C][/ROW]
[ROW][C]126[/C][C]811020.942320508[/C][C]726520.174100369[/C][C]895521.710540648[/C][/ROW]
[ROW][C]127[/C][C]792161.61543032[/C][C]699938.176735083[/C][C]884385.054125557[/C][/ROW]
[ROW][C]128[/C][C]809593.526587514[/C][C]709684.553501565[/C][C]909502.499673463[/C][/ROW]
[ROW][C]129[/C][C]787992.756042731[/C][C]680406.949496164[/C][C]895578.562589298[/C][/ROW]
[ROW][C]130[/C][C]761226.687182103[/C][C]645951.900641978[/C][C]876501.473722228[/C][/ROW]
[ROW][C]131[/C][C]836792.471639162[/C][C]713800.927241125[/C][C]959784.0160372[/C][/ROW]
[ROW][C]132[/C][C]829131.131348692[/C][C]698383.123025652[/C][C]959879.139671733[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211191&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211191&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
121725159.671685575682262.74159622768056.601774931
122687647.674574753635573.499665653739721.849483853
123713753.415801007653147.109285245774359.722316769
124719839.657333896651073.634708726788605.679959067
125757272.995922216680571.957515881833974.034328551
126811020.942320508726520.174100369895521.710540648
127792161.61543032699938.176735083884385.054125557
128809593.526587514709684.553501565909502.499673463
129787992.756042731680406.949496164895578.562589298
130761226.687182103645951.900641978876501.473722228
131836792.471639162713800.927241125959784.0160372
132829131.131348692698383.123025652959879.139671733



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')