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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 Aug 2010 10:42:04 +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/Aug/19/t1282214511zpbbv5mfk4x9qxm.htm/, Retrieved Fri, 03 May 2024 10:09:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79267, Retrieved Fri, 03 May 2024 10:09:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVanhille Olivier
Estimated Impact141
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks 1 - sta...] [2010-08-19 10:42:04] [ddb1c76c3acba5bf82e5ed3b5a08f68d] [Current]
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Dataseries X:
568
567
566
564
584
583
568
558
559
559
560
562
563
552
552
555
575
567
548
541
544
546
551
550
546
532
523
528
555
543
525
517
519
521
520
516
509
494
484
482
508
500
480
467
471
482
481
477
471
455
441
434
459
448
432
414
415
423
425
427
415
399
386
377
397
379
361
350
348
363
367
365
354
327
312
307
335
317
298
286
288
303
310
301
293
264
255
251
279
253
233
226
232
245
250
242
230
196
188
181
212
186
166
155
157
173
182
182
168
131
114
106
134
103
83
74
83
96
95
100




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79267&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79267&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.159879826158029
beta0.162679015015255
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.159879826158029 \tabularnewline
beta & 0.162679015015255 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79267&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]0.159879826158029[/C][/ROW]
[ROW][C]beta[/C][C]0.162679015015255[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79267&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
alpha0.159879826158029
beta0.162679015015255
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13563569.183250874616-6.18325087461562
14552557.33439358698-5.33439358698047
15552556.374463218462-4.37446321846176
16555558.303105875734-3.30310587573388
17575577.116827516407-2.1168275164066
18567567.905907590769-0.905907590769061
19548554.850008677484-6.8500086774842
20541542.925582471361-1.92558247136083
21544542.8147942048011.18520579519884
22546542.0162316568423.98376834315786
23551542.5347840132678.46521598673348
24550545.2408633109844.75913668901569
25546541.9527071716914.04729282830931
26532532.708499398416-0.708499398415938
27523533.276144824115-10.2761448241147
28528534.876877616726-6.87687761672566
29555553.0767194309471.92328056905274
30543545.669373155249-2.66937315524876
31525527.816738128259-2.81673812825886
32517520.826727169917-3.82672716991749
33519522.764195053015-3.76419505301465
34521523.181445422551-2.18144542255106
35520525.856627034538-5.85662703453795
36516522.412863367555-6.4128633675549
37509515.867723666687-6.86772366668686
38494500.312420258103-6.3124202581027
39484490.873109716892-6.87310971689237
40482494.018407219926-12.0184072199262
41508515.274577405886-7.27457740588579
42500501.478023083515-1.47802308351476
43480483.202757856554-3.2027578565536
44467474.053853723052-7.0538537230521
45471473.343060449829-2.34306044982924
46482473.1521969413028.84780305869788
47481472.8191258745558.18087412544503
48477470.077443089096.92255691090969
49471464.7964807643176.20351923568319
50455452.3309588799982.66904112000202
51441444.170547781539-3.17054778153914
52434443.216200539286-9.2162005392857
53459466.306458446974-7.30645844697403
54448457.692182392112-9.69218239211187
55432437.813469603639-5.81346960363891
56414425.445136318417-11.4451363184170
57415426.804306564024-11.8043065640240
58423432.465801311299-9.46580131129872
59425427.301500995212-2.30150099521234
60427420.5487511174136.4512488825871
61415413.5587974423191.44120255768121
62399397.4561669503201.54383304968047
63386384.0172640085121.98273599148757
64377377.73218555922-0.732185559219772
65397398.680810987198-1.68081098719796
66379388.62806665606-9.62806665606001
67361372.49138231528-11.4913823152800
68350355.035453869911-5.03545386991073
69348355.036203170460-7.03620317045954
70363360.3815987496552.61840125034513
71367361.4516391559315.54836084406901
72365361.9629472853333.03705271466686
73354350.8145304025183.18546959748193
74327336.391564304689-9.39156430468944
75312322.255834734169-10.2558347341690
76307311.454649951764-4.45464995176371
77335325.4110061232399.58899387676075
78317311.6592298173825.34077018261831
79298297.8310463463520.168953653647634
80286288.385916173362-2.38591617336215
81288286.237972790251.76202720975016
82303297.6400037907335.35999620926719
83310300.2225209761979.77747902380327
84301299.0426435182591.95735648174099
85293289.2027005633753.79729943662483
86264268.258173423532-4.25817342353236
87255256.057995209247-1.05799520924688
88251252.00795861768-1.00795861767980
89279273.2089231975245.7910768024758
90253258.322202851802-5.32220285180227
91233241.385436755265-8.3854367552646
92226229.815310740906-3.81531074090634
93232229.6195837208472.38041627915322
94245240.2685683945664.73143160543427
95250244.2558972974185.7441027025823
96242236.6796484944765.32035150552414
97230229.7058157318060.294184268194044
98196206.5070530395-10.5070530394999
99188196.735807264228-8.73580726422759
100181190.901480569547-9.90148056954718
101212207.7059977227444.29400227725611
102186187.684545379428-1.6845453794281
103166171.783155564777-5.78315556477665
104155164.367775272895-9.36777527289519
105157164.786971595525-7.78697159552459
106173169.5171736957623.48282630423765
107182170.08587171443711.9141282855631
108182163.28884935081618.7111506491844
109168155.84973409014412.1502659098561
110131133.946072823694-2.94607282369441
111114127.413737722008-13.4137377220083
112106119.818643675952-13.8186436759520
113134134.805710996569-0.805710996569218
114103115.910168634481-12.910168634481
1158399.5139545307705-16.5139545307705
1167488.240643099221-14.2406430992211
1178384.105161574591-1.10516157459108
1189687.99446751860258.00553248139747
1199588.39410008299226.60589991700779
12010083.100509050091216.8994909499088

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 563 & 569.183250874616 & -6.18325087461562 \tabularnewline
14 & 552 & 557.33439358698 & -5.33439358698047 \tabularnewline
15 & 552 & 556.374463218462 & -4.37446321846176 \tabularnewline
16 & 555 & 558.303105875734 & -3.30310587573388 \tabularnewline
17 & 575 & 577.116827516407 & -2.1168275164066 \tabularnewline
18 & 567 & 567.905907590769 & -0.905907590769061 \tabularnewline
19 & 548 & 554.850008677484 & -6.8500086774842 \tabularnewline
20 & 541 & 542.925582471361 & -1.92558247136083 \tabularnewline
21 & 544 & 542.814794204801 & 1.18520579519884 \tabularnewline
22 & 546 & 542.016231656842 & 3.98376834315786 \tabularnewline
23 & 551 & 542.534784013267 & 8.46521598673348 \tabularnewline
24 & 550 & 545.240863310984 & 4.75913668901569 \tabularnewline
25 & 546 & 541.952707171691 & 4.04729282830931 \tabularnewline
26 & 532 & 532.708499398416 & -0.708499398415938 \tabularnewline
27 & 523 & 533.276144824115 & -10.2761448241147 \tabularnewline
28 & 528 & 534.876877616726 & -6.87687761672566 \tabularnewline
29 & 555 & 553.076719430947 & 1.92328056905274 \tabularnewline
30 & 543 & 545.669373155249 & -2.66937315524876 \tabularnewline
31 & 525 & 527.816738128259 & -2.81673812825886 \tabularnewline
32 & 517 & 520.826727169917 & -3.82672716991749 \tabularnewline
33 & 519 & 522.764195053015 & -3.76419505301465 \tabularnewline
34 & 521 & 523.181445422551 & -2.18144542255106 \tabularnewline
35 & 520 & 525.856627034538 & -5.85662703453795 \tabularnewline
36 & 516 & 522.412863367555 & -6.4128633675549 \tabularnewline
37 & 509 & 515.867723666687 & -6.86772366668686 \tabularnewline
38 & 494 & 500.312420258103 & -6.3124202581027 \tabularnewline
39 & 484 & 490.873109716892 & -6.87310971689237 \tabularnewline
40 & 482 & 494.018407219926 & -12.0184072199262 \tabularnewline
41 & 508 & 515.274577405886 & -7.27457740588579 \tabularnewline
42 & 500 & 501.478023083515 & -1.47802308351476 \tabularnewline
43 & 480 & 483.202757856554 & -3.2027578565536 \tabularnewline
44 & 467 & 474.053853723052 & -7.0538537230521 \tabularnewline
45 & 471 & 473.343060449829 & -2.34306044982924 \tabularnewline
46 & 482 & 473.152196941302 & 8.84780305869788 \tabularnewline
47 & 481 & 472.819125874555 & 8.18087412544503 \tabularnewline
48 & 477 & 470.07744308909 & 6.92255691090969 \tabularnewline
49 & 471 & 464.796480764317 & 6.20351923568319 \tabularnewline
50 & 455 & 452.330958879998 & 2.66904112000202 \tabularnewline
51 & 441 & 444.170547781539 & -3.17054778153914 \tabularnewline
52 & 434 & 443.216200539286 & -9.2162005392857 \tabularnewline
53 & 459 & 466.306458446974 & -7.30645844697403 \tabularnewline
54 & 448 & 457.692182392112 & -9.69218239211187 \tabularnewline
55 & 432 & 437.813469603639 & -5.81346960363891 \tabularnewline
56 & 414 & 425.445136318417 & -11.4451363184170 \tabularnewline
57 & 415 & 426.804306564024 & -11.8043065640240 \tabularnewline
58 & 423 & 432.465801311299 & -9.46580131129872 \tabularnewline
59 & 425 & 427.301500995212 & -2.30150099521234 \tabularnewline
60 & 427 & 420.548751117413 & 6.4512488825871 \tabularnewline
61 & 415 & 413.558797442319 & 1.44120255768121 \tabularnewline
62 & 399 & 397.456166950320 & 1.54383304968047 \tabularnewline
63 & 386 & 384.017264008512 & 1.98273599148757 \tabularnewline
64 & 377 & 377.73218555922 & -0.732185559219772 \tabularnewline
65 & 397 & 398.680810987198 & -1.68081098719796 \tabularnewline
66 & 379 & 388.62806665606 & -9.62806665606001 \tabularnewline
67 & 361 & 372.49138231528 & -11.4913823152800 \tabularnewline
68 & 350 & 355.035453869911 & -5.03545386991073 \tabularnewline
69 & 348 & 355.036203170460 & -7.03620317045954 \tabularnewline
70 & 363 & 360.381598749655 & 2.61840125034513 \tabularnewline
71 & 367 & 361.451639155931 & 5.54836084406901 \tabularnewline
72 & 365 & 361.962947285333 & 3.03705271466686 \tabularnewline
73 & 354 & 350.814530402518 & 3.18546959748193 \tabularnewline
74 & 327 & 336.391564304689 & -9.39156430468944 \tabularnewline
75 & 312 & 322.255834734169 & -10.2558347341690 \tabularnewline
76 & 307 & 311.454649951764 & -4.45464995176371 \tabularnewline
77 & 335 & 325.411006123239 & 9.58899387676075 \tabularnewline
78 & 317 & 311.659229817382 & 5.34077018261831 \tabularnewline
79 & 298 & 297.831046346352 & 0.168953653647634 \tabularnewline
80 & 286 & 288.385916173362 & -2.38591617336215 \tabularnewline
81 & 288 & 286.23797279025 & 1.76202720975016 \tabularnewline
82 & 303 & 297.640003790733 & 5.35999620926719 \tabularnewline
83 & 310 & 300.222520976197 & 9.77747902380327 \tabularnewline
84 & 301 & 299.042643518259 & 1.95735648174099 \tabularnewline
85 & 293 & 289.202700563375 & 3.79729943662483 \tabularnewline
86 & 264 & 268.258173423532 & -4.25817342353236 \tabularnewline
87 & 255 & 256.057995209247 & -1.05799520924688 \tabularnewline
88 & 251 & 252.00795861768 & -1.00795861767980 \tabularnewline
89 & 279 & 273.208923197524 & 5.7910768024758 \tabularnewline
90 & 253 & 258.322202851802 & -5.32220285180227 \tabularnewline
91 & 233 & 241.385436755265 & -8.3854367552646 \tabularnewline
92 & 226 & 229.815310740906 & -3.81531074090634 \tabularnewline
93 & 232 & 229.619583720847 & 2.38041627915322 \tabularnewline
94 & 245 & 240.268568394566 & 4.73143160543427 \tabularnewline
95 & 250 & 244.255897297418 & 5.7441027025823 \tabularnewline
96 & 242 & 236.679648494476 & 5.32035150552414 \tabularnewline
97 & 230 & 229.705815731806 & 0.294184268194044 \tabularnewline
98 & 196 & 206.5070530395 & -10.5070530394999 \tabularnewline
99 & 188 & 196.735807264228 & -8.73580726422759 \tabularnewline
100 & 181 & 190.901480569547 & -9.90148056954718 \tabularnewline
101 & 212 & 207.705997722744 & 4.29400227725611 \tabularnewline
102 & 186 & 187.684545379428 & -1.6845453794281 \tabularnewline
103 & 166 & 171.783155564777 & -5.78315556477665 \tabularnewline
104 & 155 & 164.367775272895 & -9.36777527289519 \tabularnewline
105 & 157 & 164.786971595525 & -7.78697159552459 \tabularnewline
106 & 173 & 169.517173695762 & 3.48282630423765 \tabularnewline
107 & 182 & 170.085871714437 & 11.9141282855631 \tabularnewline
108 & 182 & 163.288849350816 & 18.7111506491844 \tabularnewline
109 & 168 & 155.849734090144 & 12.1502659098561 \tabularnewline
110 & 131 & 133.946072823694 & -2.94607282369441 \tabularnewline
111 & 114 & 127.413737722008 & -13.4137377220083 \tabularnewline
112 & 106 & 119.818643675952 & -13.8186436759520 \tabularnewline
113 & 134 & 134.805710996569 & -0.805710996569218 \tabularnewline
114 & 103 & 115.910168634481 & -12.910168634481 \tabularnewline
115 & 83 & 99.5139545307705 & -16.5139545307705 \tabularnewline
116 & 74 & 88.240643099221 & -14.2406430992211 \tabularnewline
117 & 83 & 84.105161574591 & -1.10516157459108 \tabularnewline
118 & 96 & 87.9944675186025 & 8.00553248139747 \tabularnewline
119 & 95 & 88.3941000829922 & 6.60589991700779 \tabularnewline
120 & 100 & 83.1005090500912 & 16.8994909499088 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79267&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]563[/C][C]569.183250874616[/C][C]-6.18325087461562[/C][/ROW]
[ROW][C]14[/C][C]552[/C][C]557.33439358698[/C][C]-5.33439358698047[/C][/ROW]
[ROW][C]15[/C][C]552[/C][C]556.374463218462[/C][C]-4.37446321846176[/C][/ROW]
[ROW][C]16[/C][C]555[/C][C]558.303105875734[/C][C]-3.30310587573388[/C][/ROW]
[ROW][C]17[/C][C]575[/C][C]577.116827516407[/C][C]-2.1168275164066[/C][/ROW]
[ROW][C]18[/C][C]567[/C][C]567.905907590769[/C][C]-0.905907590769061[/C][/ROW]
[ROW][C]19[/C][C]548[/C][C]554.850008677484[/C][C]-6.8500086774842[/C][/ROW]
[ROW][C]20[/C][C]541[/C][C]542.925582471361[/C][C]-1.92558247136083[/C][/ROW]
[ROW][C]21[/C][C]544[/C][C]542.814794204801[/C][C]1.18520579519884[/C][/ROW]
[ROW][C]22[/C][C]546[/C][C]542.016231656842[/C][C]3.98376834315786[/C][/ROW]
[ROW][C]23[/C][C]551[/C][C]542.534784013267[/C][C]8.46521598673348[/C][/ROW]
[ROW][C]24[/C][C]550[/C][C]545.240863310984[/C][C]4.75913668901569[/C][/ROW]
[ROW][C]25[/C][C]546[/C][C]541.952707171691[/C][C]4.04729282830931[/C][/ROW]
[ROW][C]26[/C][C]532[/C][C]532.708499398416[/C][C]-0.708499398415938[/C][/ROW]
[ROW][C]27[/C][C]523[/C][C]533.276144824115[/C][C]-10.2761448241147[/C][/ROW]
[ROW][C]28[/C][C]528[/C][C]534.876877616726[/C][C]-6.87687761672566[/C][/ROW]
[ROW][C]29[/C][C]555[/C][C]553.076719430947[/C][C]1.92328056905274[/C][/ROW]
[ROW][C]30[/C][C]543[/C][C]545.669373155249[/C][C]-2.66937315524876[/C][/ROW]
[ROW][C]31[/C][C]525[/C][C]527.816738128259[/C][C]-2.81673812825886[/C][/ROW]
[ROW][C]32[/C][C]517[/C][C]520.826727169917[/C][C]-3.82672716991749[/C][/ROW]
[ROW][C]33[/C][C]519[/C][C]522.764195053015[/C][C]-3.76419505301465[/C][/ROW]
[ROW][C]34[/C][C]521[/C][C]523.181445422551[/C][C]-2.18144542255106[/C][/ROW]
[ROW][C]35[/C][C]520[/C][C]525.856627034538[/C][C]-5.85662703453795[/C][/ROW]
[ROW][C]36[/C][C]516[/C][C]522.412863367555[/C][C]-6.4128633675549[/C][/ROW]
[ROW][C]37[/C][C]509[/C][C]515.867723666687[/C][C]-6.86772366668686[/C][/ROW]
[ROW][C]38[/C][C]494[/C][C]500.312420258103[/C][C]-6.3124202581027[/C][/ROW]
[ROW][C]39[/C][C]484[/C][C]490.873109716892[/C][C]-6.87310971689237[/C][/ROW]
[ROW][C]40[/C][C]482[/C][C]494.018407219926[/C][C]-12.0184072199262[/C][/ROW]
[ROW][C]41[/C][C]508[/C][C]515.274577405886[/C][C]-7.27457740588579[/C][/ROW]
[ROW][C]42[/C][C]500[/C][C]501.478023083515[/C][C]-1.47802308351476[/C][/ROW]
[ROW][C]43[/C][C]480[/C][C]483.202757856554[/C][C]-3.2027578565536[/C][/ROW]
[ROW][C]44[/C][C]467[/C][C]474.053853723052[/C][C]-7.0538537230521[/C][/ROW]
[ROW][C]45[/C][C]471[/C][C]473.343060449829[/C][C]-2.34306044982924[/C][/ROW]
[ROW][C]46[/C][C]482[/C][C]473.152196941302[/C][C]8.84780305869788[/C][/ROW]
[ROW][C]47[/C][C]481[/C][C]472.819125874555[/C][C]8.18087412544503[/C][/ROW]
[ROW][C]48[/C][C]477[/C][C]470.07744308909[/C][C]6.92255691090969[/C][/ROW]
[ROW][C]49[/C][C]471[/C][C]464.796480764317[/C][C]6.20351923568319[/C][/ROW]
[ROW][C]50[/C][C]455[/C][C]452.330958879998[/C][C]2.66904112000202[/C][/ROW]
[ROW][C]51[/C][C]441[/C][C]444.170547781539[/C][C]-3.17054778153914[/C][/ROW]
[ROW][C]52[/C][C]434[/C][C]443.216200539286[/C][C]-9.2162005392857[/C][/ROW]
[ROW][C]53[/C][C]459[/C][C]466.306458446974[/C][C]-7.30645844697403[/C][/ROW]
[ROW][C]54[/C][C]448[/C][C]457.692182392112[/C][C]-9.69218239211187[/C][/ROW]
[ROW][C]55[/C][C]432[/C][C]437.813469603639[/C][C]-5.81346960363891[/C][/ROW]
[ROW][C]56[/C][C]414[/C][C]425.445136318417[/C][C]-11.4451363184170[/C][/ROW]
[ROW][C]57[/C][C]415[/C][C]426.804306564024[/C][C]-11.8043065640240[/C][/ROW]
[ROW][C]58[/C][C]423[/C][C]432.465801311299[/C][C]-9.46580131129872[/C][/ROW]
[ROW][C]59[/C][C]425[/C][C]427.301500995212[/C][C]-2.30150099521234[/C][/ROW]
[ROW][C]60[/C][C]427[/C][C]420.548751117413[/C][C]6.4512488825871[/C][/ROW]
[ROW][C]61[/C][C]415[/C][C]413.558797442319[/C][C]1.44120255768121[/C][/ROW]
[ROW][C]62[/C][C]399[/C][C]397.456166950320[/C][C]1.54383304968047[/C][/ROW]
[ROW][C]63[/C][C]386[/C][C]384.017264008512[/C][C]1.98273599148757[/C][/ROW]
[ROW][C]64[/C][C]377[/C][C]377.73218555922[/C][C]-0.732185559219772[/C][/ROW]
[ROW][C]65[/C][C]397[/C][C]398.680810987198[/C][C]-1.68081098719796[/C][/ROW]
[ROW][C]66[/C][C]379[/C][C]388.62806665606[/C][C]-9.62806665606001[/C][/ROW]
[ROW][C]67[/C][C]361[/C][C]372.49138231528[/C][C]-11.4913823152800[/C][/ROW]
[ROW][C]68[/C][C]350[/C][C]355.035453869911[/C][C]-5.03545386991073[/C][/ROW]
[ROW][C]69[/C][C]348[/C][C]355.036203170460[/C][C]-7.03620317045954[/C][/ROW]
[ROW][C]70[/C][C]363[/C][C]360.381598749655[/C][C]2.61840125034513[/C][/ROW]
[ROW][C]71[/C][C]367[/C][C]361.451639155931[/C][C]5.54836084406901[/C][/ROW]
[ROW][C]72[/C][C]365[/C][C]361.962947285333[/C][C]3.03705271466686[/C][/ROW]
[ROW][C]73[/C][C]354[/C][C]350.814530402518[/C][C]3.18546959748193[/C][/ROW]
[ROW][C]74[/C][C]327[/C][C]336.391564304689[/C][C]-9.39156430468944[/C][/ROW]
[ROW][C]75[/C][C]312[/C][C]322.255834734169[/C][C]-10.2558347341690[/C][/ROW]
[ROW][C]76[/C][C]307[/C][C]311.454649951764[/C][C]-4.45464995176371[/C][/ROW]
[ROW][C]77[/C][C]335[/C][C]325.411006123239[/C][C]9.58899387676075[/C][/ROW]
[ROW][C]78[/C][C]317[/C][C]311.659229817382[/C][C]5.34077018261831[/C][/ROW]
[ROW][C]79[/C][C]298[/C][C]297.831046346352[/C][C]0.168953653647634[/C][/ROW]
[ROW][C]80[/C][C]286[/C][C]288.385916173362[/C][C]-2.38591617336215[/C][/ROW]
[ROW][C]81[/C][C]288[/C][C]286.23797279025[/C][C]1.76202720975016[/C][/ROW]
[ROW][C]82[/C][C]303[/C][C]297.640003790733[/C][C]5.35999620926719[/C][/ROW]
[ROW][C]83[/C][C]310[/C][C]300.222520976197[/C][C]9.77747902380327[/C][/ROW]
[ROW][C]84[/C][C]301[/C][C]299.042643518259[/C][C]1.95735648174099[/C][/ROW]
[ROW][C]85[/C][C]293[/C][C]289.202700563375[/C][C]3.79729943662483[/C][/ROW]
[ROW][C]86[/C][C]264[/C][C]268.258173423532[/C][C]-4.25817342353236[/C][/ROW]
[ROW][C]87[/C][C]255[/C][C]256.057995209247[/C][C]-1.05799520924688[/C][/ROW]
[ROW][C]88[/C][C]251[/C][C]252.00795861768[/C][C]-1.00795861767980[/C][/ROW]
[ROW][C]89[/C][C]279[/C][C]273.208923197524[/C][C]5.7910768024758[/C][/ROW]
[ROW][C]90[/C][C]253[/C][C]258.322202851802[/C][C]-5.32220285180227[/C][/ROW]
[ROW][C]91[/C][C]233[/C][C]241.385436755265[/C][C]-8.3854367552646[/C][/ROW]
[ROW][C]92[/C][C]226[/C][C]229.815310740906[/C][C]-3.81531074090634[/C][/ROW]
[ROW][C]93[/C][C]232[/C][C]229.619583720847[/C][C]2.38041627915322[/C][/ROW]
[ROW][C]94[/C][C]245[/C][C]240.268568394566[/C][C]4.73143160543427[/C][/ROW]
[ROW][C]95[/C][C]250[/C][C]244.255897297418[/C][C]5.7441027025823[/C][/ROW]
[ROW][C]96[/C][C]242[/C][C]236.679648494476[/C][C]5.32035150552414[/C][/ROW]
[ROW][C]97[/C][C]230[/C][C]229.705815731806[/C][C]0.294184268194044[/C][/ROW]
[ROW][C]98[/C][C]196[/C][C]206.5070530395[/C][C]-10.5070530394999[/C][/ROW]
[ROW][C]99[/C][C]188[/C][C]196.735807264228[/C][C]-8.73580726422759[/C][/ROW]
[ROW][C]100[/C][C]181[/C][C]190.901480569547[/C][C]-9.90148056954718[/C][/ROW]
[ROW][C]101[/C][C]212[/C][C]207.705997722744[/C][C]4.29400227725611[/C][/ROW]
[ROW][C]102[/C][C]186[/C][C]187.684545379428[/C][C]-1.6845453794281[/C][/ROW]
[ROW][C]103[/C][C]166[/C][C]171.783155564777[/C][C]-5.78315556477665[/C][/ROW]
[ROW][C]104[/C][C]155[/C][C]164.367775272895[/C][C]-9.36777527289519[/C][/ROW]
[ROW][C]105[/C][C]157[/C][C]164.786971595525[/C][C]-7.78697159552459[/C][/ROW]
[ROW][C]106[/C][C]173[/C][C]169.517173695762[/C][C]3.48282630423765[/C][/ROW]
[ROW][C]107[/C][C]182[/C][C]170.085871714437[/C][C]11.9141282855631[/C][/ROW]
[ROW][C]108[/C][C]182[/C][C]163.288849350816[/C][C]18.7111506491844[/C][/ROW]
[ROW][C]109[/C][C]168[/C][C]155.849734090144[/C][C]12.1502659098561[/C][/ROW]
[ROW][C]110[/C][C]131[/C][C]133.946072823694[/C][C]-2.94607282369441[/C][/ROW]
[ROW][C]111[/C][C]114[/C][C]127.413737722008[/C][C]-13.4137377220083[/C][/ROW]
[ROW][C]112[/C][C]106[/C][C]119.818643675952[/C][C]-13.8186436759520[/C][/ROW]
[ROW][C]113[/C][C]134[/C][C]134.805710996569[/C][C]-0.805710996569218[/C][/ROW]
[ROW][C]114[/C][C]103[/C][C]115.910168634481[/C][C]-12.910168634481[/C][/ROW]
[ROW][C]115[/C][C]83[/C][C]99.5139545307705[/C][C]-16.5139545307705[/C][/ROW]
[ROW][C]116[/C][C]74[/C][C]88.240643099221[/C][C]-14.2406430992211[/C][/ROW]
[ROW][C]117[/C][C]83[/C][C]84.105161574591[/C][C]-1.10516157459108[/C][/ROW]
[ROW][C]118[/C][C]96[/C][C]87.9944675186025[/C][C]8.00553248139747[/C][/ROW]
[ROW][C]119[/C][C]95[/C][C]88.3941000829922[/C][C]6.60589991700779[/C][/ROW]
[ROW][C]120[/C][C]100[/C][C]83.1005090500912[/C][C]16.8994909499088[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79267&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79267&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
13563569.183250874616-6.18325087461562
14552557.33439358698-5.33439358698047
15552556.374463218462-4.37446321846176
16555558.303105875734-3.30310587573388
17575577.116827516407-2.1168275164066
18567567.905907590769-0.905907590769061
19548554.850008677484-6.8500086774842
20541542.925582471361-1.92558247136083
21544542.8147942048011.18520579519884
22546542.0162316568423.98376834315786
23551542.5347840132678.46521598673348
24550545.2408633109844.75913668901569
25546541.9527071716914.04729282830931
26532532.708499398416-0.708499398415938
27523533.276144824115-10.2761448241147
28528534.876877616726-6.87687761672566
29555553.0767194309471.92328056905274
30543545.669373155249-2.66937315524876
31525527.816738128259-2.81673812825886
32517520.826727169917-3.82672716991749
33519522.764195053015-3.76419505301465
34521523.181445422551-2.18144542255106
35520525.856627034538-5.85662703453795
36516522.412863367555-6.4128633675549
37509515.867723666687-6.86772366668686
38494500.312420258103-6.3124202581027
39484490.873109716892-6.87310971689237
40482494.018407219926-12.0184072199262
41508515.274577405886-7.27457740588579
42500501.478023083515-1.47802308351476
43480483.202757856554-3.2027578565536
44467474.053853723052-7.0538537230521
45471473.343060449829-2.34306044982924
46482473.1521969413028.84780305869788
47481472.8191258745558.18087412544503
48477470.077443089096.92255691090969
49471464.7964807643176.20351923568319
50455452.3309588799982.66904112000202
51441444.170547781539-3.17054778153914
52434443.216200539286-9.2162005392857
53459466.306458446974-7.30645844697403
54448457.692182392112-9.69218239211187
55432437.813469603639-5.81346960363891
56414425.445136318417-11.4451363184170
57415426.804306564024-11.8043065640240
58423432.465801311299-9.46580131129872
59425427.301500995212-2.30150099521234
60427420.5487511174136.4512488825871
61415413.5587974423191.44120255768121
62399397.4561669503201.54383304968047
63386384.0172640085121.98273599148757
64377377.73218555922-0.732185559219772
65397398.680810987198-1.68081098719796
66379388.62806665606-9.62806665606001
67361372.49138231528-11.4913823152800
68350355.035453869911-5.03545386991073
69348355.036203170460-7.03620317045954
70363360.3815987496552.61840125034513
71367361.4516391559315.54836084406901
72365361.9629472853333.03705271466686
73354350.8145304025183.18546959748193
74327336.391564304689-9.39156430468944
75312322.255834734169-10.2558347341690
76307311.454649951764-4.45464995176371
77335325.4110061232399.58899387676075
78317311.6592298173825.34077018261831
79298297.8310463463520.168953653647634
80286288.385916173362-2.38591617336215
81288286.237972790251.76202720975016
82303297.6400037907335.35999620926719
83310300.2225209761979.77747902380327
84301299.0426435182591.95735648174099
85293289.2027005633753.79729943662483
86264268.258173423532-4.25817342353236
87255256.057995209247-1.05799520924688
88251252.00795861768-1.00795861767980
89279273.2089231975245.7910768024758
90253258.322202851802-5.32220285180227
91233241.385436755265-8.3854367552646
92226229.815310740906-3.81531074090634
93232229.6195837208472.38041627915322
94245240.2685683945664.73143160543427
95250244.2558972974185.7441027025823
96242236.6796484944765.32035150552414
97230229.7058157318060.294184268194044
98196206.5070530395-10.5070530394999
99188196.735807264228-8.73580726422759
100181190.901480569547-9.90148056954718
101212207.7059977227444.29400227725611
102186187.684545379428-1.6845453794281
103166171.783155564777-5.78315556477665
104155164.367775272895-9.36777527289519
105157164.786971595525-7.78697159552459
106173169.5171736957623.48282630423765
107182170.08587171443711.9141282855631
108182163.28884935081618.7111506491844
109168155.84973409014412.1502659098561
110131133.946072823694-2.94607282369441
111114127.413737722008-13.4137377220083
112106119.818643675952-13.8186436759520
113134134.805710996569-0.805710996569218
114103115.910168634481-12.910168634481
1158399.5139545307705-16.5139545307705
1167488.240643099221-14.2406430992211
1178384.105161574591-1.10516157459108
1189687.99446751860258.00553248139747
1199588.39410008299226.60589991700779
12010083.100509050091216.8994909499088







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12173.79597979265560.10552734069687.486432244614
12253.881206276340340.036477955376167.7259345973045
12344.054430169739329.999704392910658.109155946568
12438.157553001027623.79223261532252.5228733867332
12543.5367074332428.014558727583059.058856138897
12629.987432585165814.593767844117845.3810973262138
12721.16668071182705.7059045294770936.6274568941770
12815.7140742154541-0.20755986403336031.6357082949415
12913.0351101467714-4.6916506035795530.7618708971223
1308.66861068109625-12.075677030974429.4128983931669
1311.24913105866199-21.607833730788324.1060958481123
132-7.5657434885315-30.084662511677414.9531755346144

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 73.795979792655 & 60.105527340696 & 87.486432244614 \tabularnewline
122 & 53.8812062763403 & 40.0364779553761 & 67.7259345973045 \tabularnewline
123 & 44.0544301697393 & 29.9997043929106 & 58.109155946568 \tabularnewline
124 & 38.1575530010276 & 23.792232615322 & 52.5228733867332 \tabularnewline
125 & 43.53670743324 & 28.0145587275830 & 59.058856138897 \tabularnewline
126 & 29.9874325851658 & 14.5937678441178 & 45.3810973262138 \tabularnewline
127 & 21.1666807118270 & 5.70590452947709 & 36.6274568941770 \tabularnewline
128 & 15.7140742154541 & -0.207559864033360 & 31.6357082949415 \tabularnewline
129 & 13.0351101467714 & -4.69165060357955 & 30.7618708971223 \tabularnewline
130 & 8.66861068109625 & -12.0756770309744 & 29.4128983931669 \tabularnewline
131 & 1.24913105866199 & -21.6078337307883 & 24.1060958481123 \tabularnewline
132 & -7.5657434885315 & -30.0846625116774 & 14.9531755346144 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79267&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]73.795979792655[/C][C]60.105527340696[/C][C]87.486432244614[/C][/ROW]
[ROW][C]122[/C][C]53.8812062763403[/C][C]40.0364779553761[/C][C]67.7259345973045[/C][/ROW]
[ROW][C]123[/C][C]44.0544301697393[/C][C]29.9997043929106[/C][C]58.109155946568[/C][/ROW]
[ROW][C]124[/C][C]38.1575530010276[/C][C]23.792232615322[/C][C]52.5228733867332[/C][/ROW]
[ROW][C]125[/C][C]43.53670743324[/C][C]28.0145587275830[/C][C]59.058856138897[/C][/ROW]
[ROW][C]126[/C][C]29.9874325851658[/C][C]14.5937678441178[/C][C]45.3810973262138[/C][/ROW]
[ROW][C]127[/C][C]21.1666807118270[/C][C]5.70590452947709[/C][C]36.6274568941770[/C][/ROW]
[ROW][C]128[/C][C]15.7140742154541[/C][C]-0.207559864033360[/C][C]31.6357082949415[/C][/ROW]
[ROW][C]129[/C][C]13.0351101467714[/C][C]-4.69165060357955[/C][C]30.7618708971223[/C][/ROW]
[ROW][C]130[/C][C]8.66861068109625[/C][C]-12.0756770309744[/C][C]29.4128983931669[/C][/ROW]
[ROW][C]131[/C][C]1.24913105866199[/C][C]-21.6078337307883[/C][C]24.1060958481123[/C][/ROW]
[ROW][C]132[/C][C]-7.5657434885315[/C][C]-30.0846625116774[/C][C]14.9531755346144[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79267&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79267&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
12173.79597979265560.10552734069687.486432244614
12253.881206276340340.036477955376167.7259345973045
12344.054430169739329.999704392910658.109155946568
12438.157553001027623.79223261532252.5228733867332
12543.5367074332428.014558727583059.058856138897
12629.987432585165814.593767844117845.3810973262138
12721.16668071182705.7059045294770936.6274568941770
12815.7140742154541-0.20755986403336031.6357082949415
12913.0351101467714-4.6916506035795530.7618708971223
1308.66861068109625-12.075677030974429.4128983931669
1311.24913105866199-21.607833730788324.1060958481123
132-7.5657434885315-30.084662511677414.9531755346144



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')