Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 May 2015 23:26:41 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/May/26/t1432679217dtqacmgb12gpzsx.htm/, Retrieved Tue, 30 Apr 2024 08:30:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279446, Retrieved Tue, 30 Apr 2024 08:30:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-05-26 22:26:41] [d87d05de12b09f00f3ae4d3dfdb2afe6] [Current]
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Dataseries X:
507
233
346
159
225
146
253
169
246
129
318
378
580
336
468
229
189
181
210
270
229
319
377
275
365
269
377
194
337
212
278
197
305
343
588
382
266
305
345
249
253
167
149
286
260
375
339
322
396
421
254
279
347
264
324
243
324
420
295
731
576
391
229
347
262
317
249
211
303
337
383
588
456
375
507
405
363
394
166
217
299
549
395
730




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279446&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279446&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279446&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0
beta0
gamma0.64261433345284

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.64261433345284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279446&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[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.64261433345284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279446&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279446&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
beta0
gamma0.64261433345284







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13580537.2425850209642.7574149790404
14336313.04816548019522.9518345198052
15468436.90473087492431.0952691250757
16229211.56288910577817.4371108942221
17189171.10283413998717.8971658600127
18181167.05824898567813.9417510143221
19210279.429763167664-69.4297631676641
20270183.96389576089786.0361042391033
21229262.138980830778-33.1389808307783
22319135.342306699431183.657693300569
23377336.19712355749540.8028764425054
24275404.684249456457-129.684249456457
25365661.524278115199-296.524278115199
26269383.197552825438-114.197552825438
27377533.031903881767-156.031903881767
28194259.386273447332-65.3862734473317
29337212.214131164843124.785868835157
30212204.1791662440017.82083375599905
31278271.8876215692286.11237843077231
32197276.536605118614-79.5366051186138
33305277.89491304925227.1050869507482
34343291.84760098160451.1523990183962
35588416.778402703406171.221597296594
36382368.95267242326613.0473275767343
37266539.89415698679-273.89415698679
38305354.603254375769-49.6032543757689
39345494.584896742879-149.584896742879
40249248.054381864020.945618135979515
41253333.202469935597-80.2024699355969
42167238.059883315162-71.0598833151625
43149313.42554910449-164.42554910449
44286255.8187127344730.1812872655297
45260334.686891003684-74.6868910036844
46375367.5376344229947.46236557700621
47339595.519857457837-256.519857457837
48322426.024278478255-104.024278478255
49396410.337991143856-14.3379911438558
50421363.49188313074357.5081168692566
51254448.265500169916-194.265500169916
52279279.42348782747-0.423487827469671
53347316.15161274968930.8483872503112
54264215.71583324303648.2841667569639
55324232.69424497429191.3057550257086
56243307.911395381105-64.9113953811049
57324320.4195831130793.5804168869214
58420415.7105012099714.28949879002948
59295480.368643193934-185.368643193934
60731400.224480284655330.775519715345
61576446.533293484538129.466706515462
62391445.356253745564-54.356253745564
63229359.36319656491-130.36319656491
64347309.88282713989837.1171728601015
65262372.626150023481-110.626150023481
66317273.41828570319843.5817142968024
67249322.585928585481-73.5859285854808
68211294.466567205437-83.4665672054373
69303356.690155575252-53.6901555752518
70337462.132065497593-125.132065497593
71383398.617697686425-15.6176976864252
72588675.633886624973-87.6338866249727
73456583.600085696887-127.600085696887
74375451.812694467101-76.812694467101
75507303.148296433534203.851703566466
76405366.83176933234938.1682306676508
77363331.19482630026231.8051736997379
78394330.8311289042963.1688710957103
79166301.939757588981-135.939757588981
80217263.94889960409-46.9488996040903
81299352.871998610844-53.8719986108441
82549417.787690982482131.212309017518
83395425.010273550435-30.0102735504352
84730676.92893825909453.0710617409059

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 580 & 537.24258502096 & 42.7574149790404 \tabularnewline
14 & 336 & 313.048165480195 & 22.9518345198052 \tabularnewline
15 & 468 & 436.904730874924 & 31.0952691250757 \tabularnewline
16 & 229 & 211.562889105778 & 17.4371108942221 \tabularnewline
17 & 189 & 171.102834139987 & 17.8971658600127 \tabularnewline
18 & 181 & 167.058248985678 & 13.9417510143221 \tabularnewline
19 & 210 & 279.429763167664 & -69.4297631676641 \tabularnewline
20 & 270 & 183.963895760897 & 86.0361042391033 \tabularnewline
21 & 229 & 262.138980830778 & -33.1389808307783 \tabularnewline
22 & 319 & 135.342306699431 & 183.657693300569 \tabularnewline
23 & 377 & 336.197123557495 & 40.8028764425054 \tabularnewline
24 & 275 & 404.684249456457 & -129.684249456457 \tabularnewline
25 & 365 & 661.524278115199 & -296.524278115199 \tabularnewline
26 & 269 & 383.197552825438 & -114.197552825438 \tabularnewline
27 & 377 & 533.031903881767 & -156.031903881767 \tabularnewline
28 & 194 & 259.386273447332 & -65.3862734473317 \tabularnewline
29 & 337 & 212.214131164843 & 124.785868835157 \tabularnewline
30 & 212 & 204.179166244001 & 7.82083375599905 \tabularnewline
31 & 278 & 271.887621569228 & 6.11237843077231 \tabularnewline
32 & 197 & 276.536605118614 & -79.5366051186138 \tabularnewline
33 & 305 & 277.894913049252 & 27.1050869507482 \tabularnewline
34 & 343 & 291.847600981604 & 51.1523990183962 \tabularnewline
35 & 588 & 416.778402703406 & 171.221597296594 \tabularnewline
36 & 382 & 368.952672423266 & 13.0473275767343 \tabularnewline
37 & 266 & 539.89415698679 & -273.89415698679 \tabularnewline
38 & 305 & 354.603254375769 & -49.6032543757689 \tabularnewline
39 & 345 & 494.584896742879 & -149.584896742879 \tabularnewline
40 & 249 & 248.05438186402 & 0.945618135979515 \tabularnewline
41 & 253 & 333.202469935597 & -80.2024699355969 \tabularnewline
42 & 167 & 238.059883315162 & -71.0598833151625 \tabularnewline
43 & 149 & 313.42554910449 & -164.42554910449 \tabularnewline
44 & 286 & 255.81871273447 & 30.1812872655297 \tabularnewline
45 & 260 & 334.686891003684 & -74.6868910036844 \tabularnewline
46 & 375 & 367.537634422994 & 7.46236557700621 \tabularnewline
47 & 339 & 595.519857457837 & -256.519857457837 \tabularnewline
48 & 322 & 426.024278478255 & -104.024278478255 \tabularnewline
49 & 396 & 410.337991143856 & -14.3379911438558 \tabularnewline
50 & 421 & 363.491883130743 & 57.5081168692566 \tabularnewline
51 & 254 & 448.265500169916 & -194.265500169916 \tabularnewline
52 & 279 & 279.42348782747 & -0.423487827469671 \tabularnewline
53 & 347 & 316.151612749689 & 30.8483872503112 \tabularnewline
54 & 264 & 215.715833243036 & 48.2841667569639 \tabularnewline
55 & 324 & 232.694244974291 & 91.3057550257086 \tabularnewline
56 & 243 & 307.911395381105 & -64.9113953811049 \tabularnewline
57 & 324 & 320.419583113079 & 3.5804168869214 \tabularnewline
58 & 420 & 415.710501209971 & 4.28949879002948 \tabularnewline
59 & 295 & 480.368643193934 & -185.368643193934 \tabularnewline
60 & 731 & 400.224480284655 & 330.775519715345 \tabularnewline
61 & 576 & 446.533293484538 & 129.466706515462 \tabularnewline
62 & 391 & 445.356253745564 & -54.356253745564 \tabularnewline
63 & 229 & 359.36319656491 & -130.36319656491 \tabularnewline
64 & 347 & 309.882827139898 & 37.1171728601015 \tabularnewline
65 & 262 & 372.626150023481 & -110.626150023481 \tabularnewline
66 & 317 & 273.418285703198 & 43.5817142968024 \tabularnewline
67 & 249 & 322.585928585481 & -73.5859285854808 \tabularnewline
68 & 211 & 294.466567205437 & -83.4665672054373 \tabularnewline
69 & 303 & 356.690155575252 & -53.6901555752518 \tabularnewline
70 & 337 & 462.132065497593 & -125.132065497593 \tabularnewline
71 & 383 & 398.617697686425 & -15.6176976864252 \tabularnewline
72 & 588 & 675.633886624973 & -87.6338866249727 \tabularnewline
73 & 456 & 583.600085696887 & -127.600085696887 \tabularnewline
74 & 375 & 451.812694467101 & -76.812694467101 \tabularnewline
75 & 507 & 303.148296433534 & 203.851703566466 \tabularnewline
76 & 405 & 366.831769332349 & 38.1682306676508 \tabularnewline
77 & 363 & 331.194826300262 & 31.8051736997379 \tabularnewline
78 & 394 & 330.83112890429 & 63.1688710957103 \tabularnewline
79 & 166 & 301.939757588981 & -135.939757588981 \tabularnewline
80 & 217 & 263.94889960409 & -46.9488996040903 \tabularnewline
81 & 299 & 352.871998610844 & -53.8719986108441 \tabularnewline
82 & 549 & 417.787690982482 & 131.212309017518 \tabularnewline
83 & 395 & 425.010273550435 & -30.0102735504352 \tabularnewline
84 & 730 & 676.928938259094 & 53.0710617409059 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279446&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]580[/C][C]537.24258502096[/C][C]42.7574149790404[/C][/ROW]
[ROW][C]14[/C][C]336[/C][C]313.048165480195[/C][C]22.9518345198052[/C][/ROW]
[ROW][C]15[/C][C]468[/C][C]436.904730874924[/C][C]31.0952691250757[/C][/ROW]
[ROW][C]16[/C][C]229[/C][C]211.562889105778[/C][C]17.4371108942221[/C][/ROW]
[ROW][C]17[/C][C]189[/C][C]171.102834139987[/C][C]17.8971658600127[/C][/ROW]
[ROW][C]18[/C][C]181[/C][C]167.058248985678[/C][C]13.9417510143221[/C][/ROW]
[ROW][C]19[/C][C]210[/C][C]279.429763167664[/C][C]-69.4297631676641[/C][/ROW]
[ROW][C]20[/C][C]270[/C][C]183.963895760897[/C][C]86.0361042391033[/C][/ROW]
[ROW][C]21[/C][C]229[/C][C]262.138980830778[/C][C]-33.1389808307783[/C][/ROW]
[ROW][C]22[/C][C]319[/C][C]135.342306699431[/C][C]183.657693300569[/C][/ROW]
[ROW][C]23[/C][C]377[/C][C]336.197123557495[/C][C]40.8028764425054[/C][/ROW]
[ROW][C]24[/C][C]275[/C][C]404.684249456457[/C][C]-129.684249456457[/C][/ROW]
[ROW][C]25[/C][C]365[/C][C]661.524278115199[/C][C]-296.524278115199[/C][/ROW]
[ROW][C]26[/C][C]269[/C][C]383.197552825438[/C][C]-114.197552825438[/C][/ROW]
[ROW][C]27[/C][C]377[/C][C]533.031903881767[/C][C]-156.031903881767[/C][/ROW]
[ROW][C]28[/C][C]194[/C][C]259.386273447332[/C][C]-65.3862734473317[/C][/ROW]
[ROW][C]29[/C][C]337[/C][C]212.214131164843[/C][C]124.785868835157[/C][/ROW]
[ROW][C]30[/C][C]212[/C][C]204.179166244001[/C][C]7.82083375599905[/C][/ROW]
[ROW][C]31[/C][C]278[/C][C]271.887621569228[/C][C]6.11237843077231[/C][/ROW]
[ROW][C]32[/C][C]197[/C][C]276.536605118614[/C][C]-79.5366051186138[/C][/ROW]
[ROW][C]33[/C][C]305[/C][C]277.894913049252[/C][C]27.1050869507482[/C][/ROW]
[ROW][C]34[/C][C]343[/C][C]291.847600981604[/C][C]51.1523990183962[/C][/ROW]
[ROW][C]35[/C][C]588[/C][C]416.778402703406[/C][C]171.221597296594[/C][/ROW]
[ROW][C]36[/C][C]382[/C][C]368.952672423266[/C][C]13.0473275767343[/C][/ROW]
[ROW][C]37[/C][C]266[/C][C]539.89415698679[/C][C]-273.89415698679[/C][/ROW]
[ROW][C]38[/C][C]305[/C][C]354.603254375769[/C][C]-49.6032543757689[/C][/ROW]
[ROW][C]39[/C][C]345[/C][C]494.584896742879[/C][C]-149.584896742879[/C][/ROW]
[ROW][C]40[/C][C]249[/C][C]248.05438186402[/C][C]0.945618135979515[/C][/ROW]
[ROW][C]41[/C][C]253[/C][C]333.202469935597[/C][C]-80.2024699355969[/C][/ROW]
[ROW][C]42[/C][C]167[/C][C]238.059883315162[/C][C]-71.0598833151625[/C][/ROW]
[ROW][C]43[/C][C]149[/C][C]313.42554910449[/C][C]-164.42554910449[/C][/ROW]
[ROW][C]44[/C][C]286[/C][C]255.81871273447[/C][C]30.1812872655297[/C][/ROW]
[ROW][C]45[/C][C]260[/C][C]334.686891003684[/C][C]-74.6868910036844[/C][/ROW]
[ROW][C]46[/C][C]375[/C][C]367.537634422994[/C][C]7.46236557700621[/C][/ROW]
[ROW][C]47[/C][C]339[/C][C]595.519857457837[/C][C]-256.519857457837[/C][/ROW]
[ROW][C]48[/C][C]322[/C][C]426.024278478255[/C][C]-104.024278478255[/C][/ROW]
[ROW][C]49[/C][C]396[/C][C]410.337991143856[/C][C]-14.3379911438558[/C][/ROW]
[ROW][C]50[/C][C]421[/C][C]363.491883130743[/C][C]57.5081168692566[/C][/ROW]
[ROW][C]51[/C][C]254[/C][C]448.265500169916[/C][C]-194.265500169916[/C][/ROW]
[ROW][C]52[/C][C]279[/C][C]279.42348782747[/C][C]-0.423487827469671[/C][/ROW]
[ROW][C]53[/C][C]347[/C][C]316.151612749689[/C][C]30.8483872503112[/C][/ROW]
[ROW][C]54[/C][C]264[/C][C]215.715833243036[/C][C]48.2841667569639[/C][/ROW]
[ROW][C]55[/C][C]324[/C][C]232.694244974291[/C][C]91.3057550257086[/C][/ROW]
[ROW][C]56[/C][C]243[/C][C]307.911395381105[/C][C]-64.9113953811049[/C][/ROW]
[ROW][C]57[/C][C]324[/C][C]320.419583113079[/C][C]3.5804168869214[/C][/ROW]
[ROW][C]58[/C][C]420[/C][C]415.710501209971[/C][C]4.28949879002948[/C][/ROW]
[ROW][C]59[/C][C]295[/C][C]480.368643193934[/C][C]-185.368643193934[/C][/ROW]
[ROW][C]60[/C][C]731[/C][C]400.224480284655[/C][C]330.775519715345[/C][/ROW]
[ROW][C]61[/C][C]576[/C][C]446.533293484538[/C][C]129.466706515462[/C][/ROW]
[ROW][C]62[/C][C]391[/C][C]445.356253745564[/C][C]-54.356253745564[/C][/ROW]
[ROW][C]63[/C][C]229[/C][C]359.36319656491[/C][C]-130.36319656491[/C][/ROW]
[ROW][C]64[/C][C]347[/C][C]309.882827139898[/C][C]37.1171728601015[/C][/ROW]
[ROW][C]65[/C][C]262[/C][C]372.626150023481[/C][C]-110.626150023481[/C][/ROW]
[ROW][C]66[/C][C]317[/C][C]273.418285703198[/C][C]43.5817142968024[/C][/ROW]
[ROW][C]67[/C][C]249[/C][C]322.585928585481[/C][C]-73.5859285854808[/C][/ROW]
[ROW][C]68[/C][C]211[/C][C]294.466567205437[/C][C]-83.4665672054373[/C][/ROW]
[ROW][C]69[/C][C]303[/C][C]356.690155575252[/C][C]-53.6901555752518[/C][/ROW]
[ROW][C]70[/C][C]337[/C][C]462.132065497593[/C][C]-125.132065497593[/C][/ROW]
[ROW][C]71[/C][C]383[/C][C]398.617697686425[/C][C]-15.6176976864252[/C][/ROW]
[ROW][C]72[/C][C]588[/C][C]675.633886624973[/C][C]-87.6338866249727[/C][/ROW]
[ROW][C]73[/C][C]456[/C][C]583.600085696887[/C][C]-127.600085696887[/C][/ROW]
[ROW][C]74[/C][C]375[/C][C]451.812694467101[/C][C]-76.812694467101[/C][/ROW]
[ROW][C]75[/C][C]507[/C][C]303.148296433534[/C][C]203.851703566466[/C][/ROW]
[ROW][C]76[/C][C]405[/C][C]366.831769332349[/C][C]38.1682306676508[/C][/ROW]
[ROW][C]77[/C][C]363[/C][C]331.194826300262[/C][C]31.8051736997379[/C][/ROW]
[ROW][C]78[/C][C]394[/C][C]330.83112890429[/C][C]63.1688710957103[/C][/ROW]
[ROW][C]79[/C][C]166[/C][C]301.939757588981[/C][C]-135.939757588981[/C][/ROW]
[ROW][C]80[/C][C]217[/C][C]263.94889960409[/C][C]-46.9488996040903[/C][/ROW]
[ROW][C]81[/C][C]299[/C][C]352.871998610844[/C][C]-53.8719986108441[/C][/ROW]
[ROW][C]82[/C][C]549[/C][C]417.787690982482[/C][C]131.212309017518[/C][/ROW]
[ROW][C]83[/C][C]395[/C][C]425.010273550435[/C][C]-30.0102735504352[/C][/ROW]
[ROW][C]84[/C][C]730[/C][C]676.928938259094[/C][C]53.0710617409059[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279446&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279446&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
13580537.2425850209642.7574149790404
14336313.04816548019522.9518345198052
15468436.90473087492431.0952691250757
16229211.56288910577817.4371108942221
17189171.10283413998717.8971658600127
18181167.05824898567813.9417510143221
19210279.429763167664-69.4297631676641
20270183.96389576089786.0361042391033
21229262.138980830778-33.1389808307783
22319135.342306699431183.657693300569
23377336.19712355749540.8028764425054
24275404.684249456457-129.684249456457
25365661.524278115199-296.524278115199
26269383.197552825438-114.197552825438
27377533.031903881767-156.031903881767
28194259.386273447332-65.3862734473317
29337212.214131164843124.785868835157
30212204.1791662440017.82083375599905
31278271.8876215692286.11237843077231
32197276.536605118614-79.5366051186138
33305277.89491304925227.1050869507482
34343291.84760098160451.1523990183962
35588416.778402703406171.221597296594
36382368.95267242326613.0473275767343
37266539.89415698679-273.89415698679
38305354.603254375769-49.6032543757689
39345494.584896742879-149.584896742879
40249248.054381864020.945618135979515
41253333.202469935597-80.2024699355969
42167238.059883315162-71.0598833151625
43149313.42554910449-164.42554910449
44286255.8187127344730.1812872655297
45260334.686891003684-74.6868910036844
46375367.5376344229947.46236557700621
47339595.519857457837-256.519857457837
48322426.024278478255-104.024278478255
49396410.337991143856-14.3379911438558
50421363.49188313074357.5081168692566
51254448.265500169916-194.265500169916
52279279.42348782747-0.423487827469671
53347316.15161274968930.8483872503112
54264215.71583324303648.2841667569639
55324232.69424497429191.3057550257086
56243307.911395381105-64.9113953811049
57324320.4195831130793.5804168869214
58420415.7105012099714.28949879002948
59295480.368643193934-185.368643193934
60731400.224480284655330.775519715345
61576446.533293484538129.466706515462
62391445.356253745564-54.356253745564
63229359.36319656491-130.36319656491
64347309.88282713989837.1171728601015
65262372.626150023481-110.626150023481
66317273.41828570319843.5817142968024
67249322.585928585481-73.5859285854808
68211294.466567205437-83.4665672054373
69303356.690155575252-53.6901555752518
70337462.132065497593-125.132065497593
71383398.617697686425-15.6176976864252
72588675.633886624973-87.6338866249727
73456583.600085696887-127.600085696887
74375451.812694467101-76.812694467101
75507303.148296433534203.851703566466
76405366.83176933234938.1682306676508
77363331.19482630026231.8051736997379
78394330.8311289042963.1688710957103
79166301.939757588981-135.939757588981
80217263.94889960409-46.9488996040903
81299352.871998610844-53.8719986108441
82549417.787690982482131.212309017518
83395425.010273550435-30.0102735504352
84730676.92893825909453.0710617409059







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85547.903220335223410.49712042491685.309320245535
86439.316787294327301.910687384014576.722887204639
87473.613343536334336.207243626022611.019443446647
88426.669093509784289.262993599472564.075193420097
89383.122184847441245.716084937128520.528284757754
90404.439172283249267.033072372937541.845272193562
91233.51632291996196.1102230096488370.922422830274
92254.255431108301116.849331197989391.661531018614
93345.926706307699208.520606397386483.332806218011
94545.453071375446408.046971465134682.859171285759
95440.50100379139303.094903881077577.907103701702
96771.545436791992724.240916630758818.849956953226

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 547.903220335223 & 410.49712042491 & 685.309320245535 \tabularnewline
86 & 439.316787294327 & 301.910687384014 & 576.722887204639 \tabularnewline
87 & 473.613343536334 & 336.207243626022 & 611.019443446647 \tabularnewline
88 & 426.669093509784 & 289.262993599472 & 564.075193420097 \tabularnewline
89 & 383.122184847441 & 245.716084937128 & 520.528284757754 \tabularnewline
90 & 404.439172283249 & 267.033072372937 & 541.845272193562 \tabularnewline
91 & 233.516322919961 & 96.1102230096488 & 370.922422830274 \tabularnewline
92 & 254.255431108301 & 116.849331197989 & 391.661531018614 \tabularnewline
93 & 345.926706307699 & 208.520606397386 & 483.332806218011 \tabularnewline
94 & 545.453071375446 & 408.046971465134 & 682.859171285759 \tabularnewline
95 & 440.50100379139 & 303.094903881077 & 577.907103701702 \tabularnewline
96 & 771.545436791992 & 724.240916630758 & 818.849956953226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279446&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]85[/C][C]547.903220335223[/C][C]410.49712042491[/C][C]685.309320245535[/C][/ROW]
[ROW][C]86[/C][C]439.316787294327[/C][C]301.910687384014[/C][C]576.722887204639[/C][/ROW]
[ROW][C]87[/C][C]473.613343536334[/C][C]336.207243626022[/C][C]611.019443446647[/C][/ROW]
[ROW][C]88[/C][C]426.669093509784[/C][C]289.262993599472[/C][C]564.075193420097[/C][/ROW]
[ROW][C]89[/C][C]383.122184847441[/C][C]245.716084937128[/C][C]520.528284757754[/C][/ROW]
[ROW][C]90[/C][C]404.439172283249[/C][C]267.033072372937[/C][C]541.845272193562[/C][/ROW]
[ROW][C]91[/C][C]233.516322919961[/C][C]96.1102230096488[/C][C]370.922422830274[/C][/ROW]
[ROW][C]92[/C][C]254.255431108301[/C][C]116.849331197989[/C][C]391.661531018614[/C][/ROW]
[ROW][C]93[/C][C]345.926706307699[/C][C]208.520606397386[/C][C]483.332806218011[/C][/ROW]
[ROW][C]94[/C][C]545.453071375446[/C][C]408.046971465134[/C][C]682.859171285759[/C][/ROW]
[ROW][C]95[/C][C]440.50100379139[/C][C]303.094903881077[/C][C]577.907103701702[/C][/ROW]
[ROW][C]96[/C][C]771.545436791992[/C][C]724.240916630758[/C][C]818.849956953226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279446&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279446&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
85547.903220335223410.49712042491685.309320245535
86439.316787294327301.910687384014576.722887204639
87473.613343536334336.207243626022611.019443446647
88426.669093509784289.262993599472564.075193420097
89383.122184847441245.716084937128520.528284757754
90404.439172283249267.033072372937541.845272193562
91233.51632291996196.1102230096488370.922422830274
92254.255431108301116.849331197989391.661531018614
93345.926706307699208.520606397386483.332806218011
94545.453071375446408.046971465134682.859171285759
95440.50100379139303.094903881077577.907103701702
96771.545436791992724.240916630758818.849956953226



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')