Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 Dec 2013 05:10:53 -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/2013/Dec/18/t13873615050i5plrygghuffx1.htm/, Retrieved Wed, 24 Apr 2024 12:20:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232430, Retrieved Wed, 24 Apr 2024 12:20:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact135
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-18 10:10:53] [2c34efa97876d72ba05657ad219ce09b] [Current]
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Dataseries X:
339
139
186
155
153
222
102
107
188
162
185
24
394
209
248
254
202
258
215
309
240
258
276
48
455
345
311
346
310
297
300
274
292
304
186
14
321
206
160
217
204
246
234
175
364
328
158
40
556
193
221
278
230
253
240
252
228
306
206
48
557
279
399
364
306
471
293
333
316
329
265
61
679
428
394
352
387
590
177
199
203
255
261
115




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232430&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232430&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232430&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.364306851657357
beta0.0175860401361263
gamma0.365175630758897

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.364306851657357 \tabularnewline
beta & 0.0175860401361263 \tabularnewline
gamma & 0.365175630758897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232430&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]0.364306851657357[/C][/ROW]
[ROW][C]beta[/C][C]0.0175860401361263[/C][/ROW]
[ROW][C]gamma[/C][C]0.365175630758897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232430&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232430&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
alpha0.364306851657357
beta0.0175860401361263
gamma0.365175630758897







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13394337.38799388943456.6120061105661
14209185.83675956824623.163240431754
15248228.41592046719119.5840795328086
16254243.68500570492310.3149942950772
17202197.2306306557624.7693693442377
18258257.7893170004460.210682999554194
19215153.56609093790161.4339090620995
20309184.449859395439124.550140604561
21240401.940842324329-161.940842324329
22258292.733884509088-34.733884509088
23276318.064149366133-42.0641493661333
244839.6186478504068.38135214959402
25455722.05544768289-267.05544768289
26345316.46731116962928.5326888303713
27311375.88542548327-64.88542548327
28346356.67098263017-10.67098263017
29310277.01165604686732.9883439531326
30297368.616845922488-71.6168459224876
31300218.41853289839381.5814671016068
32274268.8211629726085.17883702739152
33292372.573040156957-80.5730401569572
34304317.676284506365-13.6762845063647
35186351.7127866458-165.7127866458
361440.970341542691-26.970341542691
37321452.507676090507-131.507676090507
38206231.246509763799-25.2465097637987
39160238.817484525147-78.8174845251469
40217220.039207785348-3.03920778534848
41204177.20532376531426.7946762346862
42246220.43438589266725.565614107333
43234165.21102403811568.7889759618849
44175191.851169961352-16.8511699613521
45364240.005872076321123.994127923679
46328275.50743798932452.4925620106764
47158289.715127918355-131.715127918355
484031.18245303979798.81754696020209
49556575.586209421048-19.5862094210484
50193340.426516057843-147.426516057843
51221287.697275683571-66.697275683571
52278299.550412397761-21.5504123977607
53230243.451461780413-13.4514617804134
54253277.857458185179-24.8574581851793
55240203.29364304852736.7063569514725
56252196.51539852113255.4846014788677
57228313.810877272973-85.8108772729734
58306257.27817710858848.7218228914119
59206226.119291357119-20.1192913571195
604834.118669329548813.8813306704512
61557612.083277775202-55.0832777752019
62279313.847077191337-34.8470771913372
63399322.05194587582876.9480541241721
64364414.723685379123-50.723685379123
65306331.239167754688-25.2391677546882
66471370.991741029289100.008258970711
67293326.607180935449-33.6071809354488
68333289.99290777076743.0070922292334
69316387.472271490094-71.4722714900944
70329367.839216061215-38.8392160612147
71265272.684719569595-7.68471956959496
726146.434247523500114.5657524764999
73679729.294269141665-50.2942691416652
74428374.10741434227353.8925856577268
75394454.017712828108-60.0177128281079
76352471.62375057301-119.62375057301
77387361.19193125063525.8080687493654
78590458.635130614346131.364869385654
79177373.90779652733-196.90779652733
80199294.305136045165-95.3051360451646
81203302.811318510877-99.8113185108766
82255275.671042563595-20.6710425635953
83261209.74845212737151.2515478726286
8411541.988073969302873.0119260306972

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 394 & 337.387993889434 & 56.6120061105661 \tabularnewline
14 & 209 & 185.836759568246 & 23.163240431754 \tabularnewline
15 & 248 & 228.415920467191 & 19.5840795328086 \tabularnewline
16 & 254 & 243.685005704923 & 10.3149942950772 \tabularnewline
17 & 202 & 197.230630655762 & 4.7693693442377 \tabularnewline
18 & 258 & 257.789317000446 & 0.210682999554194 \tabularnewline
19 & 215 & 153.566090937901 & 61.4339090620995 \tabularnewline
20 & 309 & 184.449859395439 & 124.550140604561 \tabularnewline
21 & 240 & 401.940842324329 & -161.940842324329 \tabularnewline
22 & 258 & 292.733884509088 & -34.733884509088 \tabularnewline
23 & 276 & 318.064149366133 & -42.0641493661333 \tabularnewline
24 & 48 & 39.618647850406 & 8.38135214959402 \tabularnewline
25 & 455 & 722.05544768289 & -267.05544768289 \tabularnewline
26 & 345 & 316.467311169629 & 28.5326888303713 \tabularnewline
27 & 311 & 375.88542548327 & -64.88542548327 \tabularnewline
28 & 346 & 356.67098263017 & -10.67098263017 \tabularnewline
29 & 310 & 277.011656046867 & 32.9883439531326 \tabularnewline
30 & 297 & 368.616845922488 & -71.6168459224876 \tabularnewline
31 & 300 & 218.418532898393 & 81.5814671016068 \tabularnewline
32 & 274 & 268.821162972608 & 5.17883702739152 \tabularnewline
33 & 292 & 372.573040156957 & -80.5730401569572 \tabularnewline
34 & 304 & 317.676284506365 & -13.6762845063647 \tabularnewline
35 & 186 & 351.7127866458 & -165.7127866458 \tabularnewline
36 & 14 & 40.970341542691 & -26.970341542691 \tabularnewline
37 & 321 & 452.507676090507 & -131.507676090507 \tabularnewline
38 & 206 & 231.246509763799 & -25.2465097637987 \tabularnewline
39 & 160 & 238.817484525147 & -78.8174845251469 \tabularnewline
40 & 217 & 220.039207785348 & -3.03920778534848 \tabularnewline
41 & 204 & 177.205323765314 & 26.7946762346862 \tabularnewline
42 & 246 & 220.434385892667 & 25.565614107333 \tabularnewline
43 & 234 & 165.211024038115 & 68.7889759618849 \tabularnewline
44 & 175 & 191.851169961352 & -16.8511699613521 \tabularnewline
45 & 364 & 240.005872076321 & 123.994127923679 \tabularnewline
46 & 328 & 275.507437989324 & 52.4925620106764 \tabularnewline
47 & 158 & 289.715127918355 & -131.715127918355 \tabularnewline
48 & 40 & 31.1824530397979 & 8.81754696020209 \tabularnewline
49 & 556 & 575.586209421048 & -19.5862094210484 \tabularnewline
50 & 193 & 340.426516057843 & -147.426516057843 \tabularnewline
51 & 221 & 287.697275683571 & -66.697275683571 \tabularnewline
52 & 278 & 299.550412397761 & -21.5504123977607 \tabularnewline
53 & 230 & 243.451461780413 & -13.4514617804134 \tabularnewline
54 & 253 & 277.857458185179 & -24.8574581851793 \tabularnewline
55 & 240 & 203.293643048527 & 36.7063569514725 \tabularnewline
56 & 252 & 196.515398521132 & 55.4846014788677 \tabularnewline
57 & 228 & 313.810877272973 & -85.8108772729734 \tabularnewline
58 & 306 & 257.278177108588 & 48.7218228914119 \tabularnewline
59 & 206 & 226.119291357119 & -20.1192913571195 \tabularnewline
60 & 48 & 34.1186693295488 & 13.8813306704512 \tabularnewline
61 & 557 & 612.083277775202 & -55.0832777752019 \tabularnewline
62 & 279 & 313.847077191337 & -34.8470771913372 \tabularnewline
63 & 399 & 322.051945875828 & 76.9480541241721 \tabularnewline
64 & 364 & 414.723685379123 & -50.723685379123 \tabularnewline
65 & 306 & 331.239167754688 & -25.2391677546882 \tabularnewline
66 & 471 & 370.991741029289 & 100.008258970711 \tabularnewline
67 & 293 & 326.607180935449 & -33.6071809354488 \tabularnewline
68 & 333 & 289.992907770767 & 43.0070922292334 \tabularnewline
69 & 316 & 387.472271490094 & -71.4722714900944 \tabularnewline
70 & 329 & 367.839216061215 & -38.8392160612147 \tabularnewline
71 & 265 & 272.684719569595 & -7.68471956959496 \tabularnewline
72 & 61 & 46.4342475235001 & 14.5657524764999 \tabularnewline
73 & 679 & 729.294269141665 & -50.2942691416652 \tabularnewline
74 & 428 & 374.107414342273 & 53.8925856577268 \tabularnewline
75 & 394 & 454.017712828108 & -60.0177128281079 \tabularnewline
76 & 352 & 471.62375057301 & -119.62375057301 \tabularnewline
77 & 387 & 361.191931250635 & 25.8080687493654 \tabularnewline
78 & 590 & 458.635130614346 & 131.364869385654 \tabularnewline
79 & 177 & 373.90779652733 & -196.90779652733 \tabularnewline
80 & 199 & 294.305136045165 & -95.3051360451646 \tabularnewline
81 & 203 & 302.811318510877 & -99.8113185108766 \tabularnewline
82 & 255 & 275.671042563595 & -20.6710425635953 \tabularnewline
83 & 261 & 209.748452127371 & 51.2515478726286 \tabularnewline
84 & 115 & 41.9880739693028 & 73.0119260306972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232430&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]394[/C][C]337.387993889434[/C][C]56.6120061105661[/C][/ROW]
[ROW][C]14[/C][C]209[/C][C]185.836759568246[/C][C]23.163240431754[/C][/ROW]
[ROW][C]15[/C][C]248[/C][C]228.415920467191[/C][C]19.5840795328086[/C][/ROW]
[ROW][C]16[/C][C]254[/C][C]243.685005704923[/C][C]10.3149942950772[/C][/ROW]
[ROW][C]17[/C][C]202[/C][C]197.230630655762[/C][C]4.7693693442377[/C][/ROW]
[ROW][C]18[/C][C]258[/C][C]257.789317000446[/C][C]0.210682999554194[/C][/ROW]
[ROW][C]19[/C][C]215[/C][C]153.566090937901[/C][C]61.4339090620995[/C][/ROW]
[ROW][C]20[/C][C]309[/C][C]184.449859395439[/C][C]124.550140604561[/C][/ROW]
[ROW][C]21[/C][C]240[/C][C]401.940842324329[/C][C]-161.940842324329[/C][/ROW]
[ROW][C]22[/C][C]258[/C][C]292.733884509088[/C][C]-34.733884509088[/C][/ROW]
[ROW][C]23[/C][C]276[/C][C]318.064149366133[/C][C]-42.0641493661333[/C][/ROW]
[ROW][C]24[/C][C]48[/C][C]39.618647850406[/C][C]8.38135214959402[/C][/ROW]
[ROW][C]25[/C][C]455[/C][C]722.05544768289[/C][C]-267.05544768289[/C][/ROW]
[ROW][C]26[/C][C]345[/C][C]316.467311169629[/C][C]28.5326888303713[/C][/ROW]
[ROW][C]27[/C][C]311[/C][C]375.88542548327[/C][C]-64.88542548327[/C][/ROW]
[ROW][C]28[/C][C]346[/C][C]356.67098263017[/C][C]-10.67098263017[/C][/ROW]
[ROW][C]29[/C][C]310[/C][C]277.011656046867[/C][C]32.9883439531326[/C][/ROW]
[ROW][C]30[/C][C]297[/C][C]368.616845922488[/C][C]-71.6168459224876[/C][/ROW]
[ROW][C]31[/C][C]300[/C][C]218.418532898393[/C][C]81.5814671016068[/C][/ROW]
[ROW][C]32[/C][C]274[/C][C]268.821162972608[/C][C]5.17883702739152[/C][/ROW]
[ROW][C]33[/C][C]292[/C][C]372.573040156957[/C][C]-80.5730401569572[/C][/ROW]
[ROW][C]34[/C][C]304[/C][C]317.676284506365[/C][C]-13.6762845063647[/C][/ROW]
[ROW][C]35[/C][C]186[/C][C]351.7127866458[/C][C]-165.7127866458[/C][/ROW]
[ROW][C]36[/C][C]14[/C][C]40.970341542691[/C][C]-26.970341542691[/C][/ROW]
[ROW][C]37[/C][C]321[/C][C]452.507676090507[/C][C]-131.507676090507[/C][/ROW]
[ROW][C]38[/C][C]206[/C][C]231.246509763799[/C][C]-25.2465097637987[/C][/ROW]
[ROW][C]39[/C][C]160[/C][C]238.817484525147[/C][C]-78.8174845251469[/C][/ROW]
[ROW][C]40[/C][C]217[/C][C]220.039207785348[/C][C]-3.03920778534848[/C][/ROW]
[ROW][C]41[/C][C]204[/C][C]177.205323765314[/C][C]26.7946762346862[/C][/ROW]
[ROW][C]42[/C][C]246[/C][C]220.434385892667[/C][C]25.565614107333[/C][/ROW]
[ROW][C]43[/C][C]234[/C][C]165.211024038115[/C][C]68.7889759618849[/C][/ROW]
[ROW][C]44[/C][C]175[/C][C]191.851169961352[/C][C]-16.8511699613521[/C][/ROW]
[ROW][C]45[/C][C]364[/C][C]240.005872076321[/C][C]123.994127923679[/C][/ROW]
[ROW][C]46[/C][C]328[/C][C]275.507437989324[/C][C]52.4925620106764[/C][/ROW]
[ROW][C]47[/C][C]158[/C][C]289.715127918355[/C][C]-131.715127918355[/C][/ROW]
[ROW][C]48[/C][C]40[/C][C]31.1824530397979[/C][C]8.81754696020209[/C][/ROW]
[ROW][C]49[/C][C]556[/C][C]575.586209421048[/C][C]-19.5862094210484[/C][/ROW]
[ROW][C]50[/C][C]193[/C][C]340.426516057843[/C][C]-147.426516057843[/C][/ROW]
[ROW][C]51[/C][C]221[/C][C]287.697275683571[/C][C]-66.697275683571[/C][/ROW]
[ROW][C]52[/C][C]278[/C][C]299.550412397761[/C][C]-21.5504123977607[/C][/ROW]
[ROW][C]53[/C][C]230[/C][C]243.451461780413[/C][C]-13.4514617804134[/C][/ROW]
[ROW][C]54[/C][C]253[/C][C]277.857458185179[/C][C]-24.8574581851793[/C][/ROW]
[ROW][C]55[/C][C]240[/C][C]203.293643048527[/C][C]36.7063569514725[/C][/ROW]
[ROW][C]56[/C][C]252[/C][C]196.515398521132[/C][C]55.4846014788677[/C][/ROW]
[ROW][C]57[/C][C]228[/C][C]313.810877272973[/C][C]-85.8108772729734[/C][/ROW]
[ROW][C]58[/C][C]306[/C][C]257.278177108588[/C][C]48.7218228914119[/C][/ROW]
[ROW][C]59[/C][C]206[/C][C]226.119291357119[/C][C]-20.1192913571195[/C][/ROW]
[ROW][C]60[/C][C]48[/C][C]34.1186693295488[/C][C]13.8813306704512[/C][/ROW]
[ROW][C]61[/C][C]557[/C][C]612.083277775202[/C][C]-55.0832777752019[/C][/ROW]
[ROW][C]62[/C][C]279[/C][C]313.847077191337[/C][C]-34.8470771913372[/C][/ROW]
[ROW][C]63[/C][C]399[/C][C]322.051945875828[/C][C]76.9480541241721[/C][/ROW]
[ROW][C]64[/C][C]364[/C][C]414.723685379123[/C][C]-50.723685379123[/C][/ROW]
[ROW][C]65[/C][C]306[/C][C]331.239167754688[/C][C]-25.2391677546882[/C][/ROW]
[ROW][C]66[/C][C]471[/C][C]370.991741029289[/C][C]100.008258970711[/C][/ROW]
[ROW][C]67[/C][C]293[/C][C]326.607180935449[/C][C]-33.6071809354488[/C][/ROW]
[ROW][C]68[/C][C]333[/C][C]289.992907770767[/C][C]43.0070922292334[/C][/ROW]
[ROW][C]69[/C][C]316[/C][C]387.472271490094[/C][C]-71.4722714900944[/C][/ROW]
[ROW][C]70[/C][C]329[/C][C]367.839216061215[/C][C]-38.8392160612147[/C][/ROW]
[ROW][C]71[/C][C]265[/C][C]272.684719569595[/C][C]-7.68471956959496[/C][/ROW]
[ROW][C]72[/C][C]61[/C][C]46.4342475235001[/C][C]14.5657524764999[/C][/ROW]
[ROW][C]73[/C][C]679[/C][C]729.294269141665[/C][C]-50.2942691416652[/C][/ROW]
[ROW][C]74[/C][C]428[/C][C]374.107414342273[/C][C]53.8925856577268[/C][/ROW]
[ROW][C]75[/C][C]394[/C][C]454.017712828108[/C][C]-60.0177128281079[/C][/ROW]
[ROW][C]76[/C][C]352[/C][C]471.62375057301[/C][C]-119.62375057301[/C][/ROW]
[ROW][C]77[/C][C]387[/C][C]361.191931250635[/C][C]25.8080687493654[/C][/ROW]
[ROW][C]78[/C][C]590[/C][C]458.635130614346[/C][C]131.364869385654[/C][/ROW]
[ROW][C]79[/C][C]177[/C][C]373.90779652733[/C][C]-196.90779652733[/C][/ROW]
[ROW][C]80[/C][C]199[/C][C]294.305136045165[/C][C]-95.3051360451646[/C][/ROW]
[ROW][C]81[/C][C]203[/C][C]302.811318510877[/C][C]-99.8113185108766[/C][/ROW]
[ROW][C]82[/C][C]255[/C][C]275.671042563595[/C][C]-20.6710425635953[/C][/ROW]
[ROW][C]83[/C][C]261[/C][C]209.748452127371[/C][C]51.2515478726286[/C][/ROW]
[ROW][C]84[/C][C]115[/C][C]41.9880739693028[/C][C]73.0119260306972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232430&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232430&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
13394337.38799388943456.6120061105661
14209185.83675956824623.163240431754
15248228.41592046719119.5840795328086
16254243.68500570492310.3149942950772
17202197.2306306557624.7693693442377
18258257.7893170004460.210682999554194
19215153.56609093790161.4339090620995
20309184.449859395439124.550140604561
21240401.940842324329-161.940842324329
22258292.733884509088-34.733884509088
23276318.064149366133-42.0641493661333
244839.6186478504068.38135214959402
25455722.05544768289-267.05544768289
26345316.46731116962928.5326888303713
27311375.88542548327-64.88542548327
28346356.67098263017-10.67098263017
29310277.01165604686732.9883439531326
30297368.616845922488-71.6168459224876
31300218.41853289839381.5814671016068
32274268.8211629726085.17883702739152
33292372.573040156957-80.5730401569572
34304317.676284506365-13.6762845063647
35186351.7127866458-165.7127866458
361440.970341542691-26.970341542691
37321452.507676090507-131.507676090507
38206231.246509763799-25.2465097637987
39160238.817484525147-78.8174845251469
40217220.039207785348-3.03920778534848
41204177.20532376531426.7946762346862
42246220.43438589266725.565614107333
43234165.21102403811568.7889759618849
44175191.851169961352-16.8511699613521
45364240.005872076321123.994127923679
46328275.50743798932452.4925620106764
47158289.715127918355-131.715127918355
484031.18245303979798.81754696020209
49556575.586209421048-19.5862094210484
50193340.426516057843-147.426516057843
51221287.697275683571-66.697275683571
52278299.550412397761-21.5504123977607
53230243.451461780413-13.4514617804134
54253277.857458185179-24.8574581851793
55240203.29364304852736.7063569514725
56252196.51539852113255.4846014788677
57228313.810877272973-85.8108772729734
58306257.27817710858848.7218228914119
59206226.119291357119-20.1192913571195
604834.118669329548813.8813306704512
61557612.083277775202-55.0832777752019
62279313.847077191337-34.8470771913372
63399322.05194587582876.9480541241721
64364414.723685379123-50.723685379123
65306331.239167754688-25.2391677546882
66471370.991741029289100.008258970711
67293326.607180935449-33.6071809354488
68333289.99290777076743.0070922292334
69316387.472271490094-71.4722714900944
70329367.839216061215-38.8392160612147
71265272.684719569595-7.68471956959496
726146.434247523500114.5657524764999
73679729.294269141665-50.2942691416652
74428374.10741434227353.8925856577268
75394454.017712828108-60.0177128281079
76352471.62375057301-119.62375057301
77387361.19193125063525.8080687493654
78590458.635130614346131.364869385654
79177373.90779652733-196.90779652733
80199294.305136045165-95.3051360451646
81203302.811318510877-99.8113185108766
82255275.671042563595-20.6710425635953
83261209.74845212737151.2515478726286
8411541.988073969302873.0119260306972







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85891.786725917621803.332122495702980.24132933954
86491.897031143415398.505377246997585.288685039833
87531.514468075691420.474700067001642.554236084381
88560.126248197082433.001779106576687.250717287588
89513.545041210723381.676313852823645.413768568623
90662.915623187982493.046595136087832.784651239877
91391.448027036838263.909227079194518.986826994483
92411.128046803908267.966941729587554.289151878228
93479.357322539207308.318114284168650.396530794246
94534.773752214929338.647511412387730.89999301747
95449.321420097673271.059111672924627.583728522421
9698.086207696036862.0274373643868134.144978027687

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 891.786725917621 & 803.332122495702 & 980.24132933954 \tabularnewline
86 & 491.897031143415 & 398.505377246997 & 585.288685039833 \tabularnewline
87 & 531.514468075691 & 420.474700067001 & 642.554236084381 \tabularnewline
88 & 560.126248197082 & 433.001779106576 & 687.250717287588 \tabularnewline
89 & 513.545041210723 & 381.676313852823 & 645.413768568623 \tabularnewline
90 & 662.915623187982 & 493.046595136087 & 832.784651239877 \tabularnewline
91 & 391.448027036838 & 263.909227079194 & 518.986826994483 \tabularnewline
92 & 411.128046803908 & 267.966941729587 & 554.289151878228 \tabularnewline
93 & 479.357322539207 & 308.318114284168 & 650.396530794246 \tabularnewline
94 & 534.773752214929 & 338.647511412387 & 730.89999301747 \tabularnewline
95 & 449.321420097673 & 271.059111672924 & 627.583728522421 \tabularnewline
96 & 98.0862076960368 & 62.0274373643868 & 134.144978027687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232430&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]891.786725917621[/C][C]803.332122495702[/C][C]980.24132933954[/C][/ROW]
[ROW][C]86[/C][C]491.897031143415[/C][C]398.505377246997[/C][C]585.288685039833[/C][/ROW]
[ROW][C]87[/C][C]531.514468075691[/C][C]420.474700067001[/C][C]642.554236084381[/C][/ROW]
[ROW][C]88[/C][C]560.126248197082[/C][C]433.001779106576[/C][C]687.250717287588[/C][/ROW]
[ROW][C]89[/C][C]513.545041210723[/C][C]381.676313852823[/C][C]645.413768568623[/C][/ROW]
[ROW][C]90[/C][C]662.915623187982[/C][C]493.046595136087[/C][C]832.784651239877[/C][/ROW]
[ROW][C]91[/C][C]391.448027036838[/C][C]263.909227079194[/C][C]518.986826994483[/C][/ROW]
[ROW][C]92[/C][C]411.128046803908[/C][C]267.966941729587[/C][C]554.289151878228[/C][/ROW]
[ROW][C]93[/C][C]479.357322539207[/C][C]308.318114284168[/C][C]650.396530794246[/C][/ROW]
[ROW][C]94[/C][C]534.773752214929[/C][C]338.647511412387[/C][C]730.89999301747[/C][/ROW]
[ROW][C]95[/C][C]449.321420097673[/C][C]271.059111672924[/C][C]627.583728522421[/C][/ROW]
[ROW][C]96[/C][C]98.0862076960368[/C][C]62.0274373643868[/C][C]134.144978027687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232430&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232430&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
85891.786725917621803.332122495702980.24132933954
86491.897031143415398.505377246997585.288685039833
87531.514468075691420.474700067001642.554236084381
88560.126248197082433.001779106576687.250717287588
89513.545041210723381.676313852823645.413768568623
90662.915623187982493.046595136087832.784651239877
91391.448027036838263.909227079194518.986826994483
92411.128046803908267.966941729587554.289151878228
93479.357322539207308.318114284168650.396530794246
94534.773752214929338.647511412387730.89999301747
95449.321420097673271.059111672924627.583728522421
9698.086207696036862.0274373643868134.144978027687



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')