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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 computationFri, 17 Dec 2010 14:30:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/17/t1292596449uj61ofnr2p5d1ps.htm/, Retrieved Sun, 05 May 2024 17:40:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111492, Retrieved Sun, 05 May 2024 17:40:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact147
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
F  MPD  [Exponential Smoothing] [] [2010-11-26 12:44:04] [8a9a6f7c332640af31ddca253a8ded58]
-    D    [Exponential Smoothing] [] [2010-11-30 10:29:51] [fb3a7008aea9486db3846dc25434607b]
- R PD        [Exponential Smoothing] [Tripple exponenti...] [2010-12-17 14:30:56] [7cc6e89f95359dcad314da35cb7f084f] [Current]
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Post a new message
Dataseries X:
300
302
400
392
373
379
303
324
353
392
327
376
329
359
413
338
422
390
370
367
406
418
346
350
330
318
382
337
372
422
428
426
396
458
315
337
386
352
383
439
397
453
363
365
474
373
403
384
364
361
419
352
363
410
361
383
342
369
361
317
386
318
407
393
404
498
438




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111492&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111492&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111492&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.295879428539368
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.295879428539368 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111492&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]0.295879428539368[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111492&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111492&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
alpha0.295879428539368
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
23023002
3400300.59175885707999.4082411429213
4392330.0046124385561.99538756145
5373348.34777228230824.6522277176916
6379355.64185933164123.3581406683587
7303362.553052644337-59.5530526443375
8324344.932529460156-20.9325294601560
9353338.73902460560214.2609753943984
10392342.9585538557149.0414461442898
11327357.468908915627-30.4689089156269
12376348.45378555745327.5462144425468
13329356.604143745137-27.6041437451368
14359348.43664546850710.5633545314928
15413351.56212477074461.437875229256
16338369.740328184249-31.7403281842492
17422360.34901801944261.6509819805584
18390378.5902753367411.4097246632600
19370381.966178149897-11.9661781498969
20367378.425632197105-11.4256321971051
21406375.04502267192530.9549773280754
22418384.20396367420533.7960363257953
23346394.203515589177-48.2035155891767
24350379.941086943063-29.9410869430626
25330371.082135248502-41.0821352485017
26318358.926776547998-40.926776547998
27382346.81738529101835.1826147089820
28337357.227197225632-20.2271972256323
29372351.24238566955920.7576143304408
30422357.38413673549164.6158632645094
31428376.50264143277251.4973585672284
32426391.7396504569334.26034954307
33396401.876583101293-5.87658310129257
34458400.13782305151857.862176948482
35315417.258050901079-102.258050901079
36337387.001997236918-50.0019972369179
37386372.20743486863213.7925651313684
38352376.288371157793-24.2883711577929
39383369.10194177947313.8980582205269
40439373.21409130356965.7859086964306
41397392.6787883746124.32121162538766
42453393.9573460009359.0426539990703
43363411.426852725622-48.4268527256222
44365397.098343215205-32.098343215205
45474387.6011037676386.3988962323704
46373413.164759811295-40.1647598112955
47403401.2808336309081.71916636909157
48384401.789499593759-17.7894995937593
49364396.525952619957-32.5259526199565
50361386.902192346065-25.9021923460652
51419379.23826647679539.7617335232053
52352391.002945469375-39.0029454693753
53363379.462776252544-16.4627762525444
54410374.5917794227735.4082205772299
55361385.068343492757-24.0683434927568
56383377.9470157742315.05298422576931
57342379.44208985937-37.4420898593697
58369368.363745708460.63625429154024
59361368.552000264646-7.55200026464638
60317366.317518742014-49.3175187420136
61386351.72547947964734.2745205203529
62318361.86660502467-43.8666050246699
63407348.88737899800858.1126210019916
64393366.08170809100326.9182919089974
65404374.04627691829329.9537230817074
66498382.908967386335115.091032613665
67438416.96203634607221.0379636539283

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 302 & 300 & 2 \tabularnewline
3 & 400 & 300.591758857079 & 99.4082411429213 \tabularnewline
4 & 392 & 330.00461243855 & 61.99538756145 \tabularnewline
5 & 373 & 348.347772282308 & 24.6522277176916 \tabularnewline
6 & 379 & 355.641859331641 & 23.3581406683587 \tabularnewline
7 & 303 & 362.553052644337 & -59.5530526443375 \tabularnewline
8 & 324 & 344.932529460156 & -20.9325294601560 \tabularnewline
9 & 353 & 338.739024605602 & 14.2609753943984 \tabularnewline
10 & 392 & 342.95855385571 & 49.0414461442898 \tabularnewline
11 & 327 & 357.468908915627 & -30.4689089156269 \tabularnewline
12 & 376 & 348.453785557453 & 27.5462144425468 \tabularnewline
13 & 329 & 356.604143745137 & -27.6041437451368 \tabularnewline
14 & 359 & 348.436645468507 & 10.5633545314928 \tabularnewline
15 & 413 & 351.562124770744 & 61.437875229256 \tabularnewline
16 & 338 & 369.740328184249 & -31.7403281842492 \tabularnewline
17 & 422 & 360.349018019442 & 61.6509819805584 \tabularnewline
18 & 390 & 378.59027533674 & 11.4097246632600 \tabularnewline
19 & 370 & 381.966178149897 & -11.9661781498969 \tabularnewline
20 & 367 & 378.425632197105 & -11.4256321971051 \tabularnewline
21 & 406 & 375.045022671925 & 30.9549773280754 \tabularnewline
22 & 418 & 384.203963674205 & 33.7960363257953 \tabularnewline
23 & 346 & 394.203515589177 & -48.2035155891767 \tabularnewline
24 & 350 & 379.941086943063 & -29.9410869430626 \tabularnewline
25 & 330 & 371.082135248502 & -41.0821352485017 \tabularnewline
26 & 318 & 358.926776547998 & -40.926776547998 \tabularnewline
27 & 382 & 346.817385291018 & 35.1826147089820 \tabularnewline
28 & 337 & 357.227197225632 & -20.2271972256323 \tabularnewline
29 & 372 & 351.242385669559 & 20.7576143304408 \tabularnewline
30 & 422 & 357.384136735491 & 64.6158632645094 \tabularnewline
31 & 428 & 376.502641432772 & 51.4973585672284 \tabularnewline
32 & 426 & 391.73965045693 & 34.26034954307 \tabularnewline
33 & 396 & 401.876583101293 & -5.87658310129257 \tabularnewline
34 & 458 & 400.137823051518 & 57.862176948482 \tabularnewline
35 & 315 & 417.258050901079 & -102.258050901079 \tabularnewline
36 & 337 & 387.001997236918 & -50.0019972369179 \tabularnewline
37 & 386 & 372.207434868632 & 13.7925651313684 \tabularnewline
38 & 352 & 376.288371157793 & -24.2883711577929 \tabularnewline
39 & 383 & 369.101941779473 & 13.8980582205269 \tabularnewline
40 & 439 & 373.214091303569 & 65.7859086964306 \tabularnewline
41 & 397 & 392.678788374612 & 4.32121162538766 \tabularnewline
42 & 453 & 393.95734600093 & 59.0426539990703 \tabularnewline
43 & 363 & 411.426852725622 & -48.4268527256222 \tabularnewline
44 & 365 & 397.098343215205 & -32.098343215205 \tabularnewline
45 & 474 & 387.60110376763 & 86.3988962323704 \tabularnewline
46 & 373 & 413.164759811295 & -40.1647598112955 \tabularnewline
47 & 403 & 401.280833630908 & 1.71916636909157 \tabularnewline
48 & 384 & 401.789499593759 & -17.7894995937593 \tabularnewline
49 & 364 & 396.525952619957 & -32.5259526199565 \tabularnewline
50 & 361 & 386.902192346065 & -25.9021923460652 \tabularnewline
51 & 419 & 379.238266476795 & 39.7617335232053 \tabularnewline
52 & 352 & 391.002945469375 & -39.0029454693753 \tabularnewline
53 & 363 & 379.462776252544 & -16.4627762525444 \tabularnewline
54 & 410 & 374.59177942277 & 35.4082205772299 \tabularnewline
55 & 361 & 385.068343492757 & -24.0683434927568 \tabularnewline
56 & 383 & 377.947015774231 & 5.05298422576931 \tabularnewline
57 & 342 & 379.44208985937 & -37.4420898593697 \tabularnewline
58 & 369 & 368.36374570846 & 0.63625429154024 \tabularnewline
59 & 361 & 368.552000264646 & -7.55200026464638 \tabularnewline
60 & 317 & 366.317518742014 & -49.3175187420136 \tabularnewline
61 & 386 & 351.725479479647 & 34.2745205203529 \tabularnewline
62 & 318 & 361.86660502467 & -43.8666050246699 \tabularnewline
63 & 407 & 348.887378998008 & 58.1126210019916 \tabularnewline
64 & 393 & 366.081708091003 & 26.9182919089974 \tabularnewline
65 & 404 & 374.046276918293 & 29.9537230817074 \tabularnewline
66 & 498 & 382.908967386335 & 115.091032613665 \tabularnewline
67 & 438 & 416.962036346072 & 21.0379636539283 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111492&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]2[/C][C]302[/C][C]300[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]400[/C][C]300.591758857079[/C][C]99.4082411429213[/C][/ROW]
[ROW][C]4[/C][C]392[/C][C]330.00461243855[/C][C]61.99538756145[/C][/ROW]
[ROW][C]5[/C][C]373[/C][C]348.347772282308[/C][C]24.6522277176916[/C][/ROW]
[ROW][C]6[/C][C]379[/C][C]355.641859331641[/C][C]23.3581406683587[/C][/ROW]
[ROW][C]7[/C][C]303[/C][C]362.553052644337[/C][C]-59.5530526443375[/C][/ROW]
[ROW][C]8[/C][C]324[/C][C]344.932529460156[/C][C]-20.9325294601560[/C][/ROW]
[ROW][C]9[/C][C]353[/C][C]338.739024605602[/C][C]14.2609753943984[/C][/ROW]
[ROW][C]10[/C][C]392[/C][C]342.95855385571[/C][C]49.0414461442898[/C][/ROW]
[ROW][C]11[/C][C]327[/C][C]357.468908915627[/C][C]-30.4689089156269[/C][/ROW]
[ROW][C]12[/C][C]376[/C][C]348.453785557453[/C][C]27.5462144425468[/C][/ROW]
[ROW][C]13[/C][C]329[/C][C]356.604143745137[/C][C]-27.6041437451368[/C][/ROW]
[ROW][C]14[/C][C]359[/C][C]348.436645468507[/C][C]10.5633545314928[/C][/ROW]
[ROW][C]15[/C][C]413[/C][C]351.562124770744[/C][C]61.437875229256[/C][/ROW]
[ROW][C]16[/C][C]338[/C][C]369.740328184249[/C][C]-31.7403281842492[/C][/ROW]
[ROW][C]17[/C][C]422[/C][C]360.349018019442[/C][C]61.6509819805584[/C][/ROW]
[ROW][C]18[/C][C]390[/C][C]378.59027533674[/C][C]11.4097246632600[/C][/ROW]
[ROW][C]19[/C][C]370[/C][C]381.966178149897[/C][C]-11.9661781498969[/C][/ROW]
[ROW][C]20[/C][C]367[/C][C]378.425632197105[/C][C]-11.4256321971051[/C][/ROW]
[ROW][C]21[/C][C]406[/C][C]375.045022671925[/C][C]30.9549773280754[/C][/ROW]
[ROW][C]22[/C][C]418[/C][C]384.203963674205[/C][C]33.7960363257953[/C][/ROW]
[ROW][C]23[/C][C]346[/C][C]394.203515589177[/C][C]-48.2035155891767[/C][/ROW]
[ROW][C]24[/C][C]350[/C][C]379.941086943063[/C][C]-29.9410869430626[/C][/ROW]
[ROW][C]25[/C][C]330[/C][C]371.082135248502[/C][C]-41.0821352485017[/C][/ROW]
[ROW][C]26[/C][C]318[/C][C]358.926776547998[/C][C]-40.926776547998[/C][/ROW]
[ROW][C]27[/C][C]382[/C][C]346.817385291018[/C][C]35.1826147089820[/C][/ROW]
[ROW][C]28[/C][C]337[/C][C]357.227197225632[/C][C]-20.2271972256323[/C][/ROW]
[ROW][C]29[/C][C]372[/C][C]351.242385669559[/C][C]20.7576143304408[/C][/ROW]
[ROW][C]30[/C][C]422[/C][C]357.384136735491[/C][C]64.6158632645094[/C][/ROW]
[ROW][C]31[/C][C]428[/C][C]376.502641432772[/C][C]51.4973585672284[/C][/ROW]
[ROW][C]32[/C][C]426[/C][C]391.73965045693[/C][C]34.26034954307[/C][/ROW]
[ROW][C]33[/C][C]396[/C][C]401.876583101293[/C][C]-5.87658310129257[/C][/ROW]
[ROW][C]34[/C][C]458[/C][C]400.137823051518[/C][C]57.862176948482[/C][/ROW]
[ROW][C]35[/C][C]315[/C][C]417.258050901079[/C][C]-102.258050901079[/C][/ROW]
[ROW][C]36[/C][C]337[/C][C]387.001997236918[/C][C]-50.0019972369179[/C][/ROW]
[ROW][C]37[/C][C]386[/C][C]372.207434868632[/C][C]13.7925651313684[/C][/ROW]
[ROW][C]38[/C][C]352[/C][C]376.288371157793[/C][C]-24.2883711577929[/C][/ROW]
[ROW][C]39[/C][C]383[/C][C]369.101941779473[/C][C]13.8980582205269[/C][/ROW]
[ROW][C]40[/C][C]439[/C][C]373.214091303569[/C][C]65.7859086964306[/C][/ROW]
[ROW][C]41[/C][C]397[/C][C]392.678788374612[/C][C]4.32121162538766[/C][/ROW]
[ROW][C]42[/C][C]453[/C][C]393.95734600093[/C][C]59.0426539990703[/C][/ROW]
[ROW][C]43[/C][C]363[/C][C]411.426852725622[/C][C]-48.4268527256222[/C][/ROW]
[ROW][C]44[/C][C]365[/C][C]397.098343215205[/C][C]-32.098343215205[/C][/ROW]
[ROW][C]45[/C][C]474[/C][C]387.60110376763[/C][C]86.3988962323704[/C][/ROW]
[ROW][C]46[/C][C]373[/C][C]413.164759811295[/C][C]-40.1647598112955[/C][/ROW]
[ROW][C]47[/C][C]403[/C][C]401.280833630908[/C][C]1.71916636909157[/C][/ROW]
[ROW][C]48[/C][C]384[/C][C]401.789499593759[/C][C]-17.7894995937593[/C][/ROW]
[ROW][C]49[/C][C]364[/C][C]396.525952619957[/C][C]-32.5259526199565[/C][/ROW]
[ROW][C]50[/C][C]361[/C][C]386.902192346065[/C][C]-25.9021923460652[/C][/ROW]
[ROW][C]51[/C][C]419[/C][C]379.238266476795[/C][C]39.7617335232053[/C][/ROW]
[ROW][C]52[/C][C]352[/C][C]391.002945469375[/C][C]-39.0029454693753[/C][/ROW]
[ROW][C]53[/C][C]363[/C][C]379.462776252544[/C][C]-16.4627762525444[/C][/ROW]
[ROW][C]54[/C][C]410[/C][C]374.59177942277[/C][C]35.4082205772299[/C][/ROW]
[ROW][C]55[/C][C]361[/C][C]385.068343492757[/C][C]-24.0683434927568[/C][/ROW]
[ROW][C]56[/C][C]383[/C][C]377.947015774231[/C][C]5.05298422576931[/C][/ROW]
[ROW][C]57[/C][C]342[/C][C]379.44208985937[/C][C]-37.4420898593697[/C][/ROW]
[ROW][C]58[/C][C]369[/C][C]368.36374570846[/C][C]0.63625429154024[/C][/ROW]
[ROW][C]59[/C][C]361[/C][C]368.552000264646[/C][C]-7.55200026464638[/C][/ROW]
[ROW][C]60[/C][C]317[/C][C]366.317518742014[/C][C]-49.3175187420136[/C][/ROW]
[ROW][C]61[/C][C]386[/C][C]351.725479479647[/C][C]34.2745205203529[/C][/ROW]
[ROW][C]62[/C][C]318[/C][C]361.86660502467[/C][C]-43.8666050246699[/C][/ROW]
[ROW][C]63[/C][C]407[/C][C]348.887378998008[/C][C]58.1126210019916[/C][/ROW]
[ROW][C]64[/C][C]393[/C][C]366.081708091003[/C][C]26.9182919089974[/C][/ROW]
[ROW][C]65[/C][C]404[/C][C]374.046276918293[/C][C]29.9537230817074[/C][/ROW]
[ROW][C]66[/C][C]498[/C][C]382.908967386335[/C][C]115.091032613665[/C][/ROW]
[ROW][C]67[/C][C]438[/C][C]416.962036346072[/C][C]21.0379636539283[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111492&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111492&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
23023002
3400300.59175885707999.4082411429213
4392330.0046124385561.99538756145
5373348.34777228230824.6522277176916
6379355.64185933164123.3581406683587
7303362.553052644337-59.5530526443375
8324344.932529460156-20.9325294601560
9353338.73902460560214.2609753943984
10392342.9585538557149.0414461442898
11327357.468908915627-30.4689089156269
12376348.45378555745327.5462144425468
13329356.604143745137-27.6041437451368
14359348.43664546850710.5633545314928
15413351.56212477074461.437875229256
16338369.740328184249-31.7403281842492
17422360.34901801944261.6509819805584
18390378.5902753367411.4097246632600
19370381.966178149897-11.9661781498969
20367378.425632197105-11.4256321971051
21406375.04502267192530.9549773280754
22418384.20396367420533.7960363257953
23346394.203515589177-48.2035155891767
24350379.941086943063-29.9410869430626
25330371.082135248502-41.0821352485017
26318358.926776547998-40.926776547998
27382346.81738529101835.1826147089820
28337357.227197225632-20.2271972256323
29372351.24238566955920.7576143304408
30422357.38413673549164.6158632645094
31428376.50264143277251.4973585672284
32426391.7396504569334.26034954307
33396401.876583101293-5.87658310129257
34458400.13782305151857.862176948482
35315417.258050901079-102.258050901079
36337387.001997236918-50.0019972369179
37386372.20743486863213.7925651313684
38352376.288371157793-24.2883711577929
39383369.10194177947313.8980582205269
40439373.21409130356965.7859086964306
41397392.6787883746124.32121162538766
42453393.9573460009359.0426539990703
43363411.426852725622-48.4268527256222
44365397.098343215205-32.098343215205
45474387.6011037676386.3988962323704
46373413.164759811295-40.1647598112955
47403401.2808336309081.71916636909157
48384401.789499593759-17.7894995937593
49364396.525952619957-32.5259526199565
50361386.902192346065-25.9021923460652
51419379.23826647679539.7617335232053
52352391.002945469375-39.0029454693753
53363379.462776252544-16.4627762525444
54410374.5917794227735.4082205772299
55361385.068343492757-24.0683434927568
56383377.9470157742315.05298422576931
57342379.44208985937-37.4420898593697
58369368.363745708460.63625429154024
59361368.552000264646-7.55200026464638
60317366.317518742014-49.3175187420136
61386351.72547947964734.2745205203529
62318361.86660502467-43.8666050246699
63407348.88737899800858.1126210019916
64393366.08170809100326.9182919089974
65404374.04627691829329.9537230817074
66498382.908967386335115.091032613665
67438416.96203634607221.0379636539283







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
68423.186737009628339.072912714504507.300561304752
69423.186737009628335.468291995314510.905182023942
70423.186737009628332.006060581411514.367413437845
71423.186737009628328.670569545615517.702904473641
72423.186737009628325.44884225911520.924631760146
73423.186737009628322.329976064010524.043497955246
74423.186737009628319.304705904054527.068768115202
75423.186737009628316.365079351653530.008394667603
76423.186737009628313.504210128745532.869263890511
77423.186737009628310.716088122224535.657385897032
78423.186737009628307.995430830160538.378043189096
79423.186737009628305.337565703632541.035908315624

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
68 & 423.186737009628 & 339.072912714504 & 507.300561304752 \tabularnewline
69 & 423.186737009628 & 335.468291995314 & 510.905182023942 \tabularnewline
70 & 423.186737009628 & 332.006060581411 & 514.367413437845 \tabularnewline
71 & 423.186737009628 & 328.670569545615 & 517.702904473641 \tabularnewline
72 & 423.186737009628 & 325.44884225911 & 520.924631760146 \tabularnewline
73 & 423.186737009628 & 322.329976064010 & 524.043497955246 \tabularnewline
74 & 423.186737009628 & 319.304705904054 & 527.068768115202 \tabularnewline
75 & 423.186737009628 & 316.365079351653 & 530.008394667603 \tabularnewline
76 & 423.186737009628 & 313.504210128745 & 532.869263890511 \tabularnewline
77 & 423.186737009628 & 310.716088122224 & 535.657385897032 \tabularnewline
78 & 423.186737009628 & 307.995430830160 & 538.378043189096 \tabularnewline
79 & 423.186737009628 & 305.337565703632 & 541.035908315624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111492&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]68[/C][C]423.186737009628[/C][C]339.072912714504[/C][C]507.300561304752[/C][/ROW]
[ROW][C]69[/C][C]423.186737009628[/C][C]335.468291995314[/C][C]510.905182023942[/C][/ROW]
[ROW][C]70[/C][C]423.186737009628[/C][C]332.006060581411[/C][C]514.367413437845[/C][/ROW]
[ROW][C]71[/C][C]423.186737009628[/C][C]328.670569545615[/C][C]517.702904473641[/C][/ROW]
[ROW][C]72[/C][C]423.186737009628[/C][C]325.44884225911[/C][C]520.924631760146[/C][/ROW]
[ROW][C]73[/C][C]423.186737009628[/C][C]322.329976064010[/C][C]524.043497955246[/C][/ROW]
[ROW][C]74[/C][C]423.186737009628[/C][C]319.304705904054[/C][C]527.068768115202[/C][/ROW]
[ROW][C]75[/C][C]423.186737009628[/C][C]316.365079351653[/C][C]530.008394667603[/C][/ROW]
[ROW][C]76[/C][C]423.186737009628[/C][C]313.504210128745[/C][C]532.869263890511[/C][/ROW]
[ROW][C]77[/C][C]423.186737009628[/C][C]310.716088122224[/C][C]535.657385897032[/C][/ROW]
[ROW][C]78[/C][C]423.186737009628[/C][C]307.995430830160[/C][C]538.378043189096[/C][/ROW]
[ROW][C]79[/C][C]423.186737009628[/C][C]305.337565703632[/C][C]541.035908315624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111492&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111492&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
68423.186737009628339.072912714504507.300561304752
69423.186737009628335.468291995314510.905182023942
70423.186737009628332.006060581411514.367413437845
71423.186737009628328.670569545615517.702904473641
72423.186737009628325.44884225911520.924631760146
73423.186737009628322.329976064010524.043497955246
74423.186737009628319.304705904054527.068768115202
75423.186737009628316.365079351653530.008394667603
76423.186737009628313.504210128745532.869263890511
77423.186737009628310.716088122224535.657385897032
78423.186737009628307.995430830160538.378043189096
79423.186737009628305.337565703632541.035908315624



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')