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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 01 Dec 2011 10:57:04 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/01/t1322755035qv9kdtrc7ffl6ct.htm/, Retrieved Thu, 25 Apr 2024 01:45:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=149839, Retrieved Thu, 25 Apr 2024 01:45:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2011-11-27 08:38:06] [ee8c3a74bf3b349877806e9a50913c60]
- R PD      [Exponential Smoothing] [] [2011-12-01 15:57:04] [7dc03dd48c8acabd98b217fada4a6bc0] [Current]
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Dataseries X:
274
291
280
258
252
251
224
225
234
233
229
208
224
226
223
205
201
202
183
188
200
206
211
201
299
244
251
241
244
252
234
246
265
277
287
275
320
338
342
322
323
343
315
334
359
362
378
345
422
430
443
431
425
432
387
396
411
421
424
410
464
486
490
459
454
446
406
412
428
429
425
396
429
439
424
379
370
353
322
322
338
348
350
312
358
378
352
312
310
292
276
269
286
292
288
255
304
299
293
275
272
264
234
231
263
264
264
245
297
317
318
315
312
310
306
313
350
354
371
357
419
425
424
399
393
378
371
364
384
377
383
352




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149839&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149839&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149839&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.81649858807122
beta0.0957373254674197
gamma0.687383866337763

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.81649858807122 \tabularnewline
beta & 0.0957373254674197 \tabularnewline
gamma & 0.687383866337763 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149839&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]0.81649858807122[/C][/ROW]
[ROW][C]beta[/C][C]0.0957373254674197[/C][/ROW]
[ROW][C]gamma[/C][C]0.687383866337763[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149839&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149839&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
alpha0.81649858807122
beta0.0957373254674197
gamma0.687383866337763







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13224250.122596153846-26.1225961538461
14226228.422437451358-2.42243745135764
15223220.5923977393712.40760226062935
16205201.4776127685343.5223872314659
17201196.8817243507184.11827564928205
18202197.2609677511264.73903224887448
19183180.1008386371252.89916136287547
20188183.8317498874884.16825011251211
21200197.2163665498552.78363345014469
22206199.1880405941396.81195940586068
23211201.7313238123059.26867618769518
24201189.83837292107811.1616270789217
25299213.65184724757885.3481527524224
26244296.494566693005-52.4945666930052
27251255.013565724944-4.01356572494396
28241236.9182019024864.08179809751442
29244239.0196447271574.98035527284276
30252246.4138729931815.58612700681928
31234236.012337017494-2.01233701749402
32246241.8081808546534.19181914534727
33265260.9543205086364.0456794913635
34277270.4801520867496.51984791325089
35287279.0875548759027.91244512409753
36275272.2127445483772.7872554516228
37320303.77825388977316.2217461102269
38338312.62098664209425.3790133579059
39342346.754722926158-4.75472292615808
40322334.933259488073-12.9332594880729
41323327.783153564779-4.78315356477918
42343331.04657409825611.9534259017441
43315329.147891262162-14.1478912621625
44334329.1314119473764.86858805262392
45359352.1783744845796.82162551542115
46362367.866513051874-5.8665130518736
47378369.1515613184798.84843868152115
48345365.0831191925-20.0831191925001
49422380.57040962036241.4295903796384
50430414.02169168849915.9783083115014
51443438.8152917620334.18470823796741
52431436.096516421365-5.09651642136521
53425439.820976933461-14.8209769334606
54432439.662817759202-7.6628177592018
55387419.585001674337-32.5850016743366
56396406.601906366029-10.6019063660287
57411415.74285878561-4.74285878560988
58421417.9634722232913.03652777670851
59424426.64515974233-2.64515974233024
60410406.9156899196883.08431008031243
61464448.26188664473215.7381133552684
62486454.70127766536531.2987223346348
63490488.8894494079571.11055059204341
64459480.622699668309-21.6226996683089
65454466.467876232734-12.4678762327337
66446466.158786844267-20.1587868442666
67406428.782510467701-22.7825104677007
68412423.390311059742-11.3903110597425
69428429.379257282602-1.37925728260166
70429432.343126107149-3.3431261071492
71425431.616096258158-6.61609625815828
72396405.573574423686-9.57357442368618
73429433.397786347222-4.39778634722171
74439419.00204527956419.9979547204358
75424432.915019598139-8.91501959813877
76379405.570909919017-26.570909919017
77370380.119816377597-10.1198163775972
78353372.530545538146-19.5305455381464
79322327.158121775866-5.1581217758656
80322330.792704263494-8.79270426349376
81338333.5679274614414.432072538559
82348334.88587392713213.1141260728684
83350342.3266309884937.67336901150713
84312323.838694780364-11.8386947803644
85358346.54953040003611.450469599964
86378345.49313398362732.5068660163726
87352364.272553412865-12.2725534128645
88312329.997424974155-17.9974249741551
89310312.329272189258-2.32927218925761
90292309.230549638359-17.2305496383593
91276267.045348155078.95465184493025
92269282.344126052448-13.3441260524476
93286283.3150442170442.68495578295585
94292284.4088251634227.59117483657815
95288286.3293338817651.6706661182352
96255259.685308070644-4.68530807064388
97304290.93993042093913.0600695790611
98299293.7450159282945.25498407170647
99293282.38603448083210.6139655191684
100275265.6256448733779.37435512662313
101272273.972504307895-1.97250430789484
102264271.003060069518-7.00306006951786
103234242.988524260835-8.98852426083533
104231241.938481074341-10.9384810743415
105263248.19792910816214.8020708918381
106264262.0538366643261.94616333567393
107264260.4268144228673.57318557713342
108245236.4915969782428.50840302175757
109297283.74566003010813.2543399698921
110317288.72851633714628.2714836628545
111318301.64127093044216.3587290695581
112315294.66701455497820.3329854450223
113312316.638864479299-4.63886447929895
114310316.757910194026-6.75791019402584
115306294.61236679366611.3876332063344
116313317.465525867514-4.46552586751443
117350340.2749856369469.7250143630539
118354355.98506669209-1.98506669208996
119371358.66729934207712.3327006579232
120357350.5053204239796.49467957602053
121419404.555001353314.4449986467001
122425420.3384900898894.66150991011057
123424418.5597912524935.44020874750731
124399408.407063753993-9.4070637539935
125393405.85678580625-12.8567858062503
126378401.266660018012-23.2666600180124
127371368.9081088208632.09189117913718
128364382.422571010194-18.422571010194
129384394.785962114638-10.7859621146375
130377389.828369846232-12.8283698462321
131383382.1720027307240.827997269275841
132352359.689707315349-7.68970731534904

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 224 & 250.122596153846 & -26.1225961538461 \tabularnewline
14 & 226 & 228.422437451358 & -2.42243745135764 \tabularnewline
15 & 223 & 220.592397739371 & 2.40760226062935 \tabularnewline
16 & 205 & 201.477612768534 & 3.5223872314659 \tabularnewline
17 & 201 & 196.881724350718 & 4.11827564928205 \tabularnewline
18 & 202 & 197.260967751126 & 4.73903224887448 \tabularnewline
19 & 183 & 180.100838637125 & 2.89916136287547 \tabularnewline
20 & 188 & 183.831749887488 & 4.16825011251211 \tabularnewline
21 & 200 & 197.216366549855 & 2.78363345014469 \tabularnewline
22 & 206 & 199.188040594139 & 6.81195940586068 \tabularnewline
23 & 211 & 201.731323812305 & 9.26867618769518 \tabularnewline
24 & 201 & 189.838372921078 & 11.1616270789217 \tabularnewline
25 & 299 & 213.651847247578 & 85.3481527524224 \tabularnewline
26 & 244 & 296.494566693005 & -52.4945666930052 \tabularnewline
27 & 251 & 255.013565724944 & -4.01356572494396 \tabularnewline
28 & 241 & 236.918201902486 & 4.08179809751442 \tabularnewline
29 & 244 & 239.019644727157 & 4.98035527284276 \tabularnewline
30 & 252 & 246.413872993181 & 5.58612700681928 \tabularnewline
31 & 234 & 236.012337017494 & -2.01233701749402 \tabularnewline
32 & 246 & 241.808180854653 & 4.19181914534727 \tabularnewline
33 & 265 & 260.954320508636 & 4.0456794913635 \tabularnewline
34 & 277 & 270.480152086749 & 6.51984791325089 \tabularnewline
35 & 287 & 279.087554875902 & 7.91244512409753 \tabularnewline
36 & 275 & 272.212744548377 & 2.7872554516228 \tabularnewline
37 & 320 & 303.778253889773 & 16.2217461102269 \tabularnewline
38 & 338 & 312.620986642094 & 25.3790133579059 \tabularnewline
39 & 342 & 346.754722926158 & -4.75472292615808 \tabularnewline
40 & 322 & 334.933259488073 & -12.9332594880729 \tabularnewline
41 & 323 & 327.783153564779 & -4.78315356477918 \tabularnewline
42 & 343 & 331.046574098256 & 11.9534259017441 \tabularnewline
43 & 315 & 329.147891262162 & -14.1478912621625 \tabularnewline
44 & 334 & 329.131411947376 & 4.86858805262392 \tabularnewline
45 & 359 & 352.178374484579 & 6.82162551542115 \tabularnewline
46 & 362 & 367.866513051874 & -5.8665130518736 \tabularnewline
47 & 378 & 369.151561318479 & 8.84843868152115 \tabularnewline
48 & 345 & 365.0831191925 & -20.0831191925001 \tabularnewline
49 & 422 & 380.570409620362 & 41.4295903796384 \tabularnewline
50 & 430 & 414.021691688499 & 15.9783083115014 \tabularnewline
51 & 443 & 438.815291762033 & 4.18470823796741 \tabularnewline
52 & 431 & 436.096516421365 & -5.09651642136521 \tabularnewline
53 & 425 & 439.820976933461 & -14.8209769334606 \tabularnewline
54 & 432 & 439.662817759202 & -7.6628177592018 \tabularnewline
55 & 387 & 419.585001674337 & -32.5850016743366 \tabularnewline
56 & 396 & 406.601906366029 & -10.6019063660287 \tabularnewline
57 & 411 & 415.74285878561 & -4.74285878560988 \tabularnewline
58 & 421 & 417.963472223291 & 3.03652777670851 \tabularnewline
59 & 424 & 426.64515974233 & -2.64515974233024 \tabularnewline
60 & 410 & 406.915689919688 & 3.08431008031243 \tabularnewline
61 & 464 & 448.261886644732 & 15.7381133552684 \tabularnewline
62 & 486 & 454.701277665365 & 31.2987223346348 \tabularnewline
63 & 490 & 488.889449407957 & 1.11055059204341 \tabularnewline
64 & 459 & 480.622699668309 & -21.6226996683089 \tabularnewline
65 & 454 & 466.467876232734 & -12.4678762327337 \tabularnewline
66 & 446 & 466.158786844267 & -20.1587868442666 \tabularnewline
67 & 406 & 428.782510467701 & -22.7825104677007 \tabularnewline
68 & 412 & 423.390311059742 & -11.3903110597425 \tabularnewline
69 & 428 & 429.379257282602 & -1.37925728260166 \tabularnewline
70 & 429 & 432.343126107149 & -3.3431261071492 \tabularnewline
71 & 425 & 431.616096258158 & -6.61609625815828 \tabularnewline
72 & 396 & 405.573574423686 & -9.57357442368618 \tabularnewline
73 & 429 & 433.397786347222 & -4.39778634722171 \tabularnewline
74 & 439 & 419.002045279564 & 19.9979547204358 \tabularnewline
75 & 424 & 432.915019598139 & -8.91501959813877 \tabularnewline
76 & 379 & 405.570909919017 & -26.570909919017 \tabularnewline
77 & 370 & 380.119816377597 & -10.1198163775972 \tabularnewline
78 & 353 & 372.530545538146 & -19.5305455381464 \tabularnewline
79 & 322 & 327.158121775866 & -5.1581217758656 \tabularnewline
80 & 322 & 330.792704263494 & -8.79270426349376 \tabularnewline
81 & 338 & 333.567927461441 & 4.432072538559 \tabularnewline
82 & 348 & 334.885873927132 & 13.1141260728684 \tabularnewline
83 & 350 & 342.326630988493 & 7.67336901150713 \tabularnewline
84 & 312 & 323.838694780364 & -11.8386947803644 \tabularnewline
85 & 358 & 346.549530400036 & 11.450469599964 \tabularnewline
86 & 378 & 345.493133983627 & 32.5068660163726 \tabularnewline
87 & 352 & 364.272553412865 & -12.2725534128645 \tabularnewline
88 & 312 & 329.997424974155 & -17.9974249741551 \tabularnewline
89 & 310 & 312.329272189258 & -2.32927218925761 \tabularnewline
90 & 292 & 309.230549638359 & -17.2305496383593 \tabularnewline
91 & 276 & 267.04534815507 & 8.95465184493025 \tabularnewline
92 & 269 & 282.344126052448 & -13.3441260524476 \tabularnewline
93 & 286 & 283.315044217044 & 2.68495578295585 \tabularnewline
94 & 292 & 284.408825163422 & 7.59117483657815 \tabularnewline
95 & 288 & 286.329333881765 & 1.6706661182352 \tabularnewline
96 & 255 & 259.685308070644 & -4.68530807064388 \tabularnewline
97 & 304 & 290.939930420939 & 13.0600695790611 \tabularnewline
98 & 299 & 293.745015928294 & 5.25498407170647 \tabularnewline
99 & 293 & 282.386034480832 & 10.6139655191684 \tabularnewline
100 & 275 & 265.625644873377 & 9.37435512662313 \tabularnewline
101 & 272 & 273.972504307895 & -1.97250430789484 \tabularnewline
102 & 264 & 271.003060069518 & -7.00306006951786 \tabularnewline
103 & 234 & 242.988524260835 & -8.98852426083533 \tabularnewline
104 & 231 & 241.938481074341 & -10.9384810743415 \tabularnewline
105 & 263 & 248.197929108162 & 14.8020708918381 \tabularnewline
106 & 264 & 262.053836664326 & 1.94616333567393 \tabularnewline
107 & 264 & 260.426814422867 & 3.57318557713342 \tabularnewline
108 & 245 & 236.491596978242 & 8.50840302175757 \tabularnewline
109 & 297 & 283.745660030108 & 13.2543399698921 \tabularnewline
110 & 317 & 288.728516337146 & 28.2714836628545 \tabularnewline
111 & 318 & 301.641270930442 & 16.3587290695581 \tabularnewline
112 & 315 & 294.667014554978 & 20.3329854450223 \tabularnewline
113 & 312 & 316.638864479299 & -4.63886447929895 \tabularnewline
114 & 310 & 316.757910194026 & -6.75791019402584 \tabularnewline
115 & 306 & 294.612366793666 & 11.3876332063344 \tabularnewline
116 & 313 & 317.465525867514 & -4.46552586751443 \tabularnewline
117 & 350 & 340.274985636946 & 9.7250143630539 \tabularnewline
118 & 354 & 355.98506669209 & -1.98506669208996 \tabularnewline
119 & 371 & 358.667299342077 & 12.3327006579232 \tabularnewline
120 & 357 & 350.505320423979 & 6.49467957602053 \tabularnewline
121 & 419 & 404.5550013533 & 14.4449986467001 \tabularnewline
122 & 425 & 420.338490089889 & 4.66150991011057 \tabularnewline
123 & 424 & 418.559791252493 & 5.44020874750731 \tabularnewline
124 & 399 & 408.407063753993 & -9.4070637539935 \tabularnewline
125 & 393 & 405.85678580625 & -12.8567858062503 \tabularnewline
126 & 378 & 401.266660018012 & -23.2666600180124 \tabularnewline
127 & 371 & 368.908108820863 & 2.09189117913718 \tabularnewline
128 & 364 & 382.422571010194 & -18.422571010194 \tabularnewline
129 & 384 & 394.785962114638 & -10.7859621146375 \tabularnewline
130 & 377 & 389.828369846232 & -12.8283698462321 \tabularnewline
131 & 383 & 382.172002730724 & 0.827997269275841 \tabularnewline
132 & 352 & 359.689707315349 & -7.68970731534904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149839&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]224[/C][C]250.122596153846[/C][C]-26.1225961538461[/C][/ROW]
[ROW][C]14[/C][C]226[/C][C]228.422437451358[/C][C]-2.42243745135764[/C][/ROW]
[ROW][C]15[/C][C]223[/C][C]220.592397739371[/C][C]2.40760226062935[/C][/ROW]
[ROW][C]16[/C][C]205[/C][C]201.477612768534[/C][C]3.5223872314659[/C][/ROW]
[ROW][C]17[/C][C]201[/C][C]196.881724350718[/C][C]4.11827564928205[/C][/ROW]
[ROW][C]18[/C][C]202[/C][C]197.260967751126[/C][C]4.73903224887448[/C][/ROW]
[ROW][C]19[/C][C]183[/C][C]180.100838637125[/C][C]2.89916136287547[/C][/ROW]
[ROW][C]20[/C][C]188[/C][C]183.831749887488[/C][C]4.16825011251211[/C][/ROW]
[ROW][C]21[/C][C]200[/C][C]197.216366549855[/C][C]2.78363345014469[/C][/ROW]
[ROW][C]22[/C][C]206[/C][C]199.188040594139[/C][C]6.81195940586068[/C][/ROW]
[ROW][C]23[/C][C]211[/C][C]201.731323812305[/C][C]9.26867618769518[/C][/ROW]
[ROW][C]24[/C][C]201[/C][C]189.838372921078[/C][C]11.1616270789217[/C][/ROW]
[ROW][C]25[/C][C]299[/C][C]213.651847247578[/C][C]85.3481527524224[/C][/ROW]
[ROW][C]26[/C][C]244[/C][C]296.494566693005[/C][C]-52.4945666930052[/C][/ROW]
[ROW][C]27[/C][C]251[/C][C]255.013565724944[/C][C]-4.01356572494396[/C][/ROW]
[ROW][C]28[/C][C]241[/C][C]236.918201902486[/C][C]4.08179809751442[/C][/ROW]
[ROW][C]29[/C][C]244[/C][C]239.019644727157[/C][C]4.98035527284276[/C][/ROW]
[ROW][C]30[/C][C]252[/C][C]246.413872993181[/C][C]5.58612700681928[/C][/ROW]
[ROW][C]31[/C][C]234[/C][C]236.012337017494[/C][C]-2.01233701749402[/C][/ROW]
[ROW][C]32[/C][C]246[/C][C]241.808180854653[/C][C]4.19181914534727[/C][/ROW]
[ROW][C]33[/C][C]265[/C][C]260.954320508636[/C][C]4.0456794913635[/C][/ROW]
[ROW][C]34[/C][C]277[/C][C]270.480152086749[/C][C]6.51984791325089[/C][/ROW]
[ROW][C]35[/C][C]287[/C][C]279.087554875902[/C][C]7.91244512409753[/C][/ROW]
[ROW][C]36[/C][C]275[/C][C]272.212744548377[/C][C]2.7872554516228[/C][/ROW]
[ROW][C]37[/C][C]320[/C][C]303.778253889773[/C][C]16.2217461102269[/C][/ROW]
[ROW][C]38[/C][C]338[/C][C]312.620986642094[/C][C]25.3790133579059[/C][/ROW]
[ROW][C]39[/C][C]342[/C][C]346.754722926158[/C][C]-4.75472292615808[/C][/ROW]
[ROW][C]40[/C][C]322[/C][C]334.933259488073[/C][C]-12.9332594880729[/C][/ROW]
[ROW][C]41[/C][C]323[/C][C]327.783153564779[/C][C]-4.78315356477918[/C][/ROW]
[ROW][C]42[/C][C]343[/C][C]331.046574098256[/C][C]11.9534259017441[/C][/ROW]
[ROW][C]43[/C][C]315[/C][C]329.147891262162[/C][C]-14.1478912621625[/C][/ROW]
[ROW][C]44[/C][C]334[/C][C]329.131411947376[/C][C]4.86858805262392[/C][/ROW]
[ROW][C]45[/C][C]359[/C][C]352.178374484579[/C][C]6.82162551542115[/C][/ROW]
[ROW][C]46[/C][C]362[/C][C]367.866513051874[/C][C]-5.8665130518736[/C][/ROW]
[ROW][C]47[/C][C]378[/C][C]369.151561318479[/C][C]8.84843868152115[/C][/ROW]
[ROW][C]48[/C][C]345[/C][C]365.0831191925[/C][C]-20.0831191925001[/C][/ROW]
[ROW][C]49[/C][C]422[/C][C]380.570409620362[/C][C]41.4295903796384[/C][/ROW]
[ROW][C]50[/C][C]430[/C][C]414.021691688499[/C][C]15.9783083115014[/C][/ROW]
[ROW][C]51[/C][C]443[/C][C]438.815291762033[/C][C]4.18470823796741[/C][/ROW]
[ROW][C]52[/C][C]431[/C][C]436.096516421365[/C][C]-5.09651642136521[/C][/ROW]
[ROW][C]53[/C][C]425[/C][C]439.820976933461[/C][C]-14.8209769334606[/C][/ROW]
[ROW][C]54[/C][C]432[/C][C]439.662817759202[/C][C]-7.6628177592018[/C][/ROW]
[ROW][C]55[/C][C]387[/C][C]419.585001674337[/C][C]-32.5850016743366[/C][/ROW]
[ROW][C]56[/C][C]396[/C][C]406.601906366029[/C][C]-10.6019063660287[/C][/ROW]
[ROW][C]57[/C][C]411[/C][C]415.74285878561[/C][C]-4.74285878560988[/C][/ROW]
[ROW][C]58[/C][C]421[/C][C]417.963472223291[/C][C]3.03652777670851[/C][/ROW]
[ROW][C]59[/C][C]424[/C][C]426.64515974233[/C][C]-2.64515974233024[/C][/ROW]
[ROW][C]60[/C][C]410[/C][C]406.915689919688[/C][C]3.08431008031243[/C][/ROW]
[ROW][C]61[/C][C]464[/C][C]448.261886644732[/C][C]15.7381133552684[/C][/ROW]
[ROW][C]62[/C][C]486[/C][C]454.701277665365[/C][C]31.2987223346348[/C][/ROW]
[ROW][C]63[/C][C]490[/C][C]488.889449407957[/C][C]1.11055059204341[/C][/ROW]
[ROW][C]64[/C][C]459[/C][C]480.622699668309[/C][C]-21.6226996683089[/C][/ROW]
[ROW][C]65[/C][C]454[/C][C]466.467876232734[/C][C]-12.4678762327337[/C][/ROW]
[ROW][C]66[/C][C]446[/C][C]466.158786844267[/C][C]-20.1587868442666[/C][/ROW]
[ROW][C]67[/C][C]406[/C][C]428.782510467701[/C][C]-22.7825104677007[/C][/ROW]
[ROW][C]68[/C][C]412[/C][C]423.390311059742[/C][C]-11.3903110597425[/C][/ROW]
[ROW][C]69[/C][C]428[/C][C]429.379257282602[/C][C]-1.37925728260166[/C][/ROW]
[ROW][C]70[/C][C]429[/C][C]432.343126107149[/C][C]-3.3431261071492[/C][/ROW]
[ROW][C]71[/C][C]425[/C][C]431.616096258158[/C][C]-6.61609625815828[/C][/ROW]
[ROW][C]72[/C][C]396[/C][C]405.573574423686[/C][C]-9.57357442368618[/C][/ROW]
[ROW][C]73[/C][C]429[/C][C]433.397786347222[/C][C]-4.39778634722171[/C][/ROW]
[ROW][C]74[/C][C]439[/C][C]419.002045279564[/C][C]19.9979547204358[/C][/ROW]
[ROW][C]75[/C][C]424[/C][C]432.915019598139[/C][C]-8.91501959813877[/C][/ROW]
[ROW][C]76[/C][C]379[/C][C]405.570909919017[/C][C]-26.570909919017[/C][/ROW]
[ROW][C]77[/C][C]370[/C][C]380.119816377597[/C][C]-10.1198163775972[/C][/ROW]
[ROW][C]78[/C][C]353[/C][C]372.530545538146[/C][C]-19.5305455381464[/C][/ROW]
[ROW][C]79[/C][C]322[/C][C]327.158121775866[/C][C]-5.1581217758656[/C][/ROW]
[ROW][C]80[/C][C]322[/C][C]330.792704263494[/C][C]-8.79270426349376[/C][/ROW]
[ROW][C]81[/C][C]338[/C][C]333.567927461441[/C][C]4.432072538559[/C][/ROW]
[ROW][C]82[/C][C]348[/C][C]334.885873927132[/C][C]13.1141260728684[/C][/ROW]
[ROW][C]83[/C][C]350[/C][C]342.326630988493[/C][C]7.67336901150713[/C][/ROW]
[ROW][C]84[/C][C]312[/C][C]323.838694780364[/C][C]-11.8386947803644[/C][/ROW]
[ROW][C]85[/C][C]358[/C][C]346.549530400036[/C][C]11.450469599964[/C][/ROW]
[ROW][C]86[/C][C]378[/C][C]345.493133983627[/C][C]32.5068660163726[/C][/ROW]
[ROW][C]87[/C][C]352[/C][C]364.272553412865[/C][C]-12.2725534128645[/C][/ROW]
[ROW][C]88[/C][C]312[/C][C]329.997424974155[/C][C]-17.9974249741551[/C][/ROW]
[ROW][C]89[/C][C]310[/C][C]312.329272189258[/C][C]-2.32927218925761[/C][/ROW]
[ROW][C]90[/C][C]292[/C][C]309.230549638359[/C][C]-17.2305496383593[/C][/ROW]
[ROW][C]91[/C][C]276[/C][C]267.04534815507[/C][C]8.95465184493025[/C][/ROW]
[ROW][C]92[/C][C]269[/C][C]282.344126052448[/C][C]-13.3441260524476[/C][/ROW]
[ROW][C]93[/C][C]286[/C][C]283.315044217044[/C][C]2.68495578295585[/C][/ROW]
[ROW][C]94[/C][C]292[/C][C]284.408825163422[/C][C]7.59117483657815[/C][/ROW]
[ROW][C]95[/C][C]288[/C][C]286.329333881765[/C][C]1.6706661182352[/C][/ROW]
[ROW][C]96[/C][C]255[/C][C]259.685308070644[/C][C]-4.68530807064388[/C][/ROW]
[ROW][C]97[/C][C]304[/C][C]290.939930420939[/C][C]13.0600695790611[/C][/ROW]
[ROW][C]98[/C][C]299[/C][C]293.745015928294[/C][C]5.25498407170647[/C][/ROW]
[ROW][C]99[/C][C]293[/C][C]282.386034480832[/C][C]10.6139655191684[/C][/ROW]
[ROW][C]100[/C][C]275[/C][C]265.625644873377[/C][C]9.37435512662313[/C][/ROW]
[ROW][C]101[/C][C]272[/C][C]273.972504307895[/C][C]-1.97250430789484[/C][/ROW]
[ROW][C]102[/C][C]264[/C][C]271.003060069518[/C][C]-7.00306006951786[/C][/ROW]
[ROW][C]103[/C][C]234[/C][C]242.988524260835[/C][C]-8.98852426083533[/C][/ROW]
[ROW][C]104[/C][C]231[/C][C]241.938481074341[/C][C]-10.9384810743415[/C][/ROW]
[ROW][C]105[/C][C]263[/C][C]248.197929108162[/C][C]14.8020708918381[/C][/ROW]
[ROW][C]106[/C][C]264[/C][C]262.053836664326[/C][C]1.94616333567393[/C][/ROW]
[ROW][C]107[/C][C]264[/C][C]260.426814422867[/C][C]3.57318557713342[/C][/ROW]
[ROW][C]108[/C][C]245[/C][C]236.491596978242[/C][C]8.50840302175757[/C][/ROW]
[ROW][C]109[/C][C]297[/C][C]283.745660030108[/C][C]13.2543399698921[/C][/ROW]
[ROW][C]110[/C][C]317[/C][C]288.728516337146[/C][C]28.2714836628545[/C][/ROW]
[ROW][C]111[/C][C]318[/C][C]301.641270930442[/C][C]16.3587290695581[/C][/ROW]
[ROW][C]112[/C][C]315[/C][C]294.667014554978[/C][C]20.3329854450223[/C][/ROW]
[ROW][C]113[/C][C]312[/C][C]316.638864479299[/C][C]-4.63886447929895[/C][/ROW]
[ROW][C]114[/C][C]310[/C][C]316.757910194026[/C][C]-6.75791019402584[/C][/ROW]
[ROW][C]115[/C][C]306[/C][C]294.612366793666[/C][C]11.3876332063344[/C][/ROW]
[ROW][C]116[/C][C]313[/C][C]317.465525867514[/C][C]-4.46552586751443[/C][/ROW]
[ROW][C]117[/C][C]350[/C][C]340.274985636946[/C][C]9.7250143630539[/C][/ROW]
[ROW][C]118[/C][C]354[/C][C]355.98506669209[/C][C]-1.98506669208996[/C][/ROW]
[ROW][C]119[/C][C]371[/C][C]358.667299342077[/C][C]12.3327006579232[/C][/ROW]
[ROW][C]120[/C][C]357[/C][C]350.505320423979[/C][C]6.49467957602053[/C][/ROW]
[ROW][C]121[/C][C]419[/C][C]404.5550013533[/C][C]14.4449986467001[/C][/ROW]
[ROW][C]122[/C][C]425[/C][C]420.338490089889[/C][C]4.66150991011057[/C][/ROW]
[ROW][C]123[/C][C]424[/C][C]418.559791252493[/C][C]5.44020874750731[/C][/ROW]
[ROW][C]124[/C][C]399[/C][C]408.407063753993[/C][C]-9.4070637539935[/C][/ROW]
[ROW][C]125[/C][C]393[/C][C]405.85678580625[/C][C]-12.8567858062503[/C][/ROW]
[ROW][C]126[/C][C]378[/C][C]401.266660018012[/C][C]-23.2666600180124[/C][/ROW]
[ROW][C]127[/C][C]371[/C][C]368.908108820863[/C][C]2.09189117913718[/C][/ROW]
[ROW][C]128[/C][C]364[/C][C]382.422571010194[/C][C]-18.422571010194[/C][/ROW]
[ROW][C]129[/C][C]384[/C][C]394.785962114638[/C][C]-10.7859621146375[/C][/ROW]
[ROW][C]130[/C][C]377[/C][C]389.828369846232[/C][C]-12.8283698462321[/C][/ROW]
[ROW][C]131[/C][C]383[/C][C]382.172002730724[/C][C]0.827997269275841[/C][/ROW]
[ROW][C]132[/C][C]352[/C][C]359.689707315349[/C][C]-7.68970731534904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149839&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149839&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
13224250.122596153846-26.1225961538461
14226228.422437451358-2.42243745135764
15223220.5923977393712.40760226062935
16205201.4776127685343.5223872314659
17201196.8817243507184.11827564928205
18202197.2609677511264.73903224887448
19183180.1008386371252.89916136287547
20188183.8317498874884.16825011251211
21200197.2163665498552.78363345014469
22206199.1880405941396.81195940586068
23211201.7313238123059.26867618769518
24201189.83837292107811.1616270789217
25299213.65184724757885.3481527524224
26244296.494566693005-52.4945666930052
27251255.013565724944-4.01356572494396
28241236.9182019024864.08179809751442
29244239.0196447271574.98035527284276
30252246.4138729931815.58612700681928
31234236.012337017494-2.01233701749402
32246241.8081808546534.19181914534727
33265260.9543205086364.0456794913635
34277270.4801520867496.51984791325089
35287279.0875548759027.91244512409753
36275272.2127445483772.7872554516228
37320303.77825388977316.2217461102269
38338312.62098664209425.3790133579059
39342346.754722926158-4.75472292615808
40322334.933259488073-12.9332594880729
41323327.783153564779-4.78315356477918
42343331.04657409825611.9534259017441
43315329.147891262162-14.1478912621625
44334329.1314119473764.86858805262392
45359352.1783744845796.82162551542115
46362367.866513051874-5.8665130518736
47378369.1515613184798.84843868152115
48345365.0831191925-20.0831191925001
49422380.57040962036241.4295903796384
50430414.02169168849915.9783083115014
51443438.8152917620334.18470823796741
52431436.096516421365-5.09651642136521
53425439.820976933461-14.8209769334606
54432439.662817759202-7.6628177592018
55387419.585001674337-32.5850016743366
56396406.601906366029-10.6019063660287
57411415.74285878561-4.74285878560988
58421417.9634722232913.03652777670851
59424426.64515974233-2.64515974233024
60410406.9156899196883.08431008031243
61464448.26188664473215.7381133552684
62486454.70127766536531.2987223346348
63490488.8894494079571.11055059204341
64459480.622699668309-21.6226996683089
65454466.467876232734-12.4678762327337
66446466.158786844267-20.1587868442666
67406428.782510467701-22.7825104677007
68412423.390311059742-11.3903110597425
69428429.379257282602-1.37925728260166
70429432.343126107149-3.3431261071492
71425431.616096258158-6.61609625815828
72396405.573574423686-9.57357442368618
73429433.397786347222-4.39778634722171
74439419.00204527956419.9979547204358
75424432.915019598139-8.91501959813877
76379405.570909919017-26.570909919017
77370380.119816377597-10.1198163775972
78353372.530545538146-19.5305455381464
79322327.158121775866-5.1581217758656
80322330.792704263494-8.79270426349376
81338333.5679274614414.432072538559
82348334.88587392713213.1141260728684
83350342.3266309884937.67336901150713
84312323.838694780364-11.8386947803644
85358346.54953040003611.450469599964
86378345.49313398362732.5068660163726
87352364.272553412865-12.2725534128645
88312329.997424974155-17.9974249741551
89310312.329272189258-2.32927218925761
90292309.230549638359-17.2305496383593
91276267.045348155078.95465184493025
92269282.344126052448-13.3441260524476
93286283.3150442170442.68495578295585
94292284.4088251634227.59117483657815
95288286.3293338817651.6706661182352
96255259.685308070644-4.68530807064388
97304290.93993042093913.0600695790611
98299293.7450159282945.25498407170647
99293282.38603448083210.6139655191684
100275265.6256448733779.37435512662313
101272273.972504307895-1.97250430789484
102264271.003060069518-7.00306006951786
103234242.988524260835-8.98852426083533
104231241.938481074341-10.9384810743415
105263248.19792910816214.8020708918381
106264262.0538366643261.94616333567393
107264260.4268144228673.57318557713342
108245236.4915969782428.50840302175757
109297283.74566003010813.2543399698921
110317288.72851633714628.2714836628545
111318301.64127093044216.3587290695581
112315294.66701455497820.3329854450223
113312316.638864479299-4.63886447929895
114310316.757910194026-6.75791019402584
115306294.61236679366611.3876332063344
116313317.465525867514-4.46552586751443
117350340.2749856369469.7250143630539
118354355.98506669209-1.98506669208996
119371358.66729934207712.3327006579232
120357350.5053204239796.49467957602053
121419404.555001353314.4449986467001
122425420.3384900898894.66150991011057
123424418.5597912524935.44020874750731
124399408.407063753993-9.4070637539935
125393405.85678580625-12.8567858062503
126378401.266660018012-23.2666600180124
127371368.9081088208632.09189117913718
128364382.422571010194-18.422571010194
129384394.785962114638-10.7859621146375
130377389.828369846232-12.8283698462321
131383382.1720027307240.827997269275841
132352359.689707315349-7.68970731534904







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
133397.861533897617367.118398677093428.604669118142
134394.188352422962352.937172882302435.439531963622
135381.909071864359330.956618403624432.861525325094
136358.223702223678297.889889675784418.557514771571
137356.436544011142286.828645357021426.044442665264
138355.553313134161276.667478905436434.439147362885
139341.731727978587253.499844454652429.963611502522
140347.128178813426249.44255391109444.813803715762
141373.114530102864265.842103813735480.386956391993
142375.166878158915258.157937768746492.175818549085
143379.171039507658252.264822744097506.077256271218
144354.337197333667217.365626995715491.308767671619

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
133 & 397.861533897617 & 367.118398677093 & 428.604669118142 \tabularnewline
134 & 394.188352422962 & 352.937172882302 & 435.439531963622 \tabularnewline
135 & 381.909071864359 & 330.956618403624 & 432.861525325094 \tabularnewline
136 & 358.223702223678 & 297.889889675784 & 418.557514771571 \tabularnewline
137 & 356.436544011142 & 286.828645357021 & 426.044442665264 \tabularnewline
138 & 355.553313134161 & 276.667478905436 & 434.439147362885 \tabularnewline
139 & 341.731727978587 & 253.499844454652 & 429.963611502522 \tabularnewline
140 & 347.128178813426 & 249.44255391109 & 444.813803715762 \tabularnewline
141 & 373.114530102864 & 265.842103813735 & 480.386956391993 \tabularnewline
142 & 375.166878158915 & 258.157937768746 & 492.175818549085 \tabularnewline
143 & 379.171039507658 & 252.264822744097 & 506.077256271218 \tabularnewline
144 & 354.337197333667 & 217.365626995715 & 491.308767671619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=149839&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]133[/C][C]397.861533897617[/C][C]367.118398677093[/C][C]428.604669118142[/C][/ROW]
[ROW][C]134[/C][C]394.188352422962[/C][C]352.937172882302[/C][C]435.439531963622[/C][/ROW]
[ROW][C]135[/C][C]381.909071864359[/C][C]330.956618403624[/C][C]432.861525325094[/C][/ROW]
[ROW][C]136[/C][C]358.223702223678[/C][C]297.889889675784[/C][C]418.557514771571[/C][/ROW]
[ROW][C]137[/C][C]356.436544011142[/C][C]286.828645357021[/C][C]426.044442665264[/C][/ROW]
[ROW][C]138[/C][C]355.553313134161[/C][C]276.667478905436[/C][C]434.439147362885[/C][/ROW]
[ROW][C]139[/C][C]341.731727978587[/C][C]253.499844454652[/C][C]429.963611502522[/C][/ROW]
[ROW][C]140[/C][C]347.128178813426[/C][C]249.44255391109[/C][C]444.813803715762[/C][/ROW]
[ROW][C]141[/C][C]373.114530102864[/C][C]265.842103813735[/C][C]480.386956391993[/C][/ROW]
[ROW][C]142[/C][C]375.166878158915[/C][C]258.157937768746[/C][C]492.175818549085[/C][/ROW]
[ROW][C]143[/C][C]379.171039507658[/C][C]252.264822744097[/C][C]506.077256271218[/C][/ROW]
[ROW][C]144[/C][C]354.337197333667[/C][C]217.365626995715[/C][C]491.308767671619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=149839&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=149839&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
133397.861533897617367.118398677093428.604669118142
134394.188352422962352.937172882302435.439531963622
135381.909071864359330.956618403624432.861525325094
136358.223702223678297.889889675784418.557514771571
137356.436544011142286.828645357021426.044442665264
138355.553313134161276.667478905436434.439147362885
139341.731727978587253.499844454652429.963611502522
140347.128178813426249.44255391109444.813803715762
141373.114530102864265.842103813735480.386956391993
142375.166878158915258.157937768746492.175818549085
143379.171039507658252.264822744097506.077256271218
144354.337197333667217.365626995715491.308767671619



Parameters (Session):
par1 = 12 ;
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')