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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 10:00:53 +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/2014/Nov/30/t1417341680zb4l4xnupqneb3t.htm/, Retrieved Sun, 19 May 2024 14:41:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261320, Retrieved Sun, 19 May 2024 14:41:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact119
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 10:00:53] [7a6c09eb8232161d54860d64a56e9131] [Current]
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Dataseries X:
324
336
327
302
299
311
315
264
278
278
287
279
324
354
354
360
363
385
412
370
389
395
417
404
456
478
468
437
432
441
449
386
396
394
403
373
409
430
415
392
401
400
447
392
427
444
448
427
480
490
482
490
485
498
544
483
508
529
547
543
608
638
661
650
654
678
725
644
670
662
641
642




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261320&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261320&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261320&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.755095818858233
beta0.0339123890694804
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.755095818858233 \tabularnewline
beta & 0.0339123890694804 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261320&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]0.755095818858233[/C][/ROW]
[ROW][C]beta[/C][C]0.0339123890694804[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261320&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261320&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
alpha0.755095818858233
beta0.0339123890694804
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3327348-21
4302343.605238636906-41.6052386369061
5299322.586158093328-23.5861580933279
6311314.569236743633-3.56923674363281
7315321.575611197889-6.57561119788909
8264326.143502517307-62.1435025173072
9278287.160996356876-9.16099635687556
10278287.950772491747-9.95077249174733
11287287.889381511289-0.889381511288661
12279294.647434489076-15.6474344890757
13324289.86105789916734.1389421008334
14354323.54236552170430.4576344782956
15354355.22386493966-1.22386493965951
16360362.951456976152-2.95145697615197
17363369.298973225836-6.29897322583565
18385372.95749549441412.0425045055861
19412390.77396456525721.2260354347429
20370416.068416722836-46.0684167228358
21389389.369430722872-0.369430722872153
22395397.168097926898-2.16809792689844
23417403.55308033829913.4469196617014
24404422.073233901665-18.0732339016649
25456416.32984813399739.6701518660028
26478455.20408919876222.7959108012379
27468481.920398629402-13.9203986294025
28437480.555915240858-43.5559152408584
29432455.698436353025-23.6984363530246
30441445.228408441235-4.22840844123488
31449449.35183990739-0.351839907390115
32386456.393442464153-70.3934424641527
33396408.744351638823-12.7443516388232
34394404.299502329124-10.2995023291244
35403401.437008091931.56299190806971
36373407.571857349552-34.5718573495524
37409385.53614789891823.4638521010817
38430407.92380128100722.076198718993
39415429.828950894981-14.8289508949815
40392423.487449865282-31.4874498652818
41401403.760883536642-2.7608835366425
42400405.654929103283-5.65492910328339
43447405.21888660986741.7811133901332
44392441.671494748546-49.671494748546
45427407.79667776620919.2033222337911
46444426.42068856596617.5793114340338
47448444.2685708430143.7314291569856
48427451.755526204106-24.755526204106
49480437.09818336590942.9018166340906
50490474.62720846564615.3727915343538
51482491.762834474526-9.76283447452624
52490489.6686564698630.331343530137019
53485495.205034819301-10.2050348193005
54498492.5241165514555.47588344854535
55544501.82401561606142.1759843839387
56483539.916012233081-56.9160122330807
57508501.7266023236396.2733976763609
58529511.41189517461117.5881048253895
59547530.09125650066716.908743499333
60543548.69061886959-5.69061886959003
61608550.07957694024757.9204230597531
62638600.98414105528937.0158589447105
63661637.05162513181623.9483748681841
64650663.865155125736-13.8651551257356
65654661.770800266873-7.77080026687258
66678664.07927959624313.9207204037573
67725683.12340481259441.8765951874059
68644724.349232484974-80.3492324849743
69670671.225337637663-1.2253376376633
70662677.816187614-15.8161876140002
71641672.984541031252-31.9845410312524
72642655.12520694252-13.1252069425198

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 327 & 348 & -21 \tabularnewline
4 & 302 & 343.605238636906 & -41.6052386369061 \tabularnewline
5 & 299 & 322.586158093328 & -23.5861580933279 \tabularnewline
6 & 311 & 314.569236743633 & -3.56923674363281 \tabularnewline
7 & 315 & 321.575611197889 & -6.57561119788909 \tabularnewline
8 & 264 & 326.143502517307 & -62.1435025173072 \tabularnewline
9 & 278 & 287.160996356876 & -9.16099635687556 \tabularnewline
10 & 278 & 287.950772491747 & -9.95077249174733 \tabularnewline
11 & 287 & 287.889381511289 & -0.889381511288661 \tabularnewline
12 & 279 & 294.647434489076 & -15.6474344890757 \tabularnewline
13 & 324 & 289.861057899167 & 34.1389421008334 \tabularnewline
14 & 354 & 323.542365521704 & 30.4576344782956 \tabularnewline
15 & 354 & 355.22386493966 & -1.22386493965951 \tabularnewline
16 & 360 & 362.951456976152 & -2.95145697615197 \tabularnewline
17 & 363 & 369.298973225836 & -6.29897322583565 \tabularnewline
18 & 385 & 372.957495494414 & 12.0425045055861 \tabularnewline
19 & 412 & 390.773964565257 & 21.2260354347429 \tabularnewline
20 & 370 & 416.068416722836 & -46.0684167228358 \tabularnewline
21 & 389 & 389.369430722872 & -0.369430722872153 \tabularnewline
22 & 395 & 397.168097926898 & -2.16809792689844 \tabularnewline
23 & 417 & 403.553080338299 & 13.4469196617014 \tabularnewline
24 & 404 & 422.073233901665 & -18.0732339016649 \tabularnewline
25 & 456 & 416.329848133997 & 39.6701518660028 \tabularnewline
26 & 478 & 455.204089198762 & 22.7959108012379 \tabularnewline
27 & 468 & 481.920398629402 & -13.9203986294025 \tabularnewline
28 & 437 & 480.555915240858 & -43.5559152408584 \tabularnewline
29 & 432 & 455.698436353025 & -23.6984363530246 \tabularnewline
30 & 441 & 445.228408441235 & -4.22840844123488 \tabularnewline
31 & 449 & 449.35183990739 & -0.351839907390115 \tabularnewline
32 & 386 & 456.393442464153 & -70.3934424641527 \tabularnewline
33 & 396 & 408.744351638823 & -12.7443516388232 \tabularnewline
34 & 394 & 404.299502329124 & -10.2995023291244 \tabularnewline
35 & 403 & 401.43700809193 & 1.56299190806971 \tabularnewline
36 & 373 & 407.571857349552 & -34.5718573495524 \tabularnewline
37 & 409 & 385.536147898918 & 23.4638521010817 \tabularnewline
38 & 430 & 407.923801281007 & 22.076198718993 \tabularnewline
39 & 415 & 429.828950894981 & -14.8289508949815 \tabularnewline
40 & 392 & 423.487449865282 & -31.4874498652818 \tabularnewline
41 & 401 & 403.760883536642 & -2.7608835366425 \tabularnewline
42 & 400 & 405.654929103283 & -5.65492910328339 \tabularnewline
43 & 447 & 405.218886609867 & 41.7811133901332 \tabularnewline
44 & 392 & 441.671494748546 & -49.671494748546 \tabularnewline
45 & 427 & 407.796677766209 & 19.2033222337911 \tabularnewline
46 & 444 & 426.420688565966 & 17.5793114340338 \tabularnewline
47 & 448 & 444.268570843014 & 3.7314291569856 \tabularnewline
48 & 427 & 451.755526204106 & -24.755526204106 \tabularnewline
49 & 480 & 437.098183365909 & 42.9018166340906 \tabularnewline
50 & 490 & 474.627208465646 & 15.3727915343538 \tabularnewline
51 & 482 & 491.762834474526 & -9.76283447452624 \tabularnewline
52 & 490 & 489.668656469863 & 0.331343530137019 \tabularnewline
53 & 485 & 495.205034819301 & -10.2050348193005 \tabularnewline
54 & 498 & 492.524116551455 & 5.47588344854535 \tabularnewline
55 & 544 & 501.824015616061 & 42.1759843839387 \tabularnewline
56 & 483 & 539.916012233081 & -56.9160122330807 \tabularnewline
57 & 508 & 501.726602323639 & 6.2733976763609 \tabularnewline
58 & 529 & 511.411895174611 & 17.5881048253895 \tabularnewline
59 & 547 & 530.091256500667 & 16.908743499333 \tabularnewline
60 & 543 & 548.69061886959 & -5.69061886959003 \tabularnewline
61 & 608 & 550.079576940247 & 57.9204230597531 \tabularnewline
62 & 638 & 600.984141055289 & 37.0158589447105 \tabularnewline
63 & 661 & 637.051625131816 & 23.9483748681841 \tabularnewline
64 & 650 & 663.865155125736 & -13.8651551257356 \tabularnewline
65 & 654 & 661.770800266873 & -7.77080026687258 \tabularnewline
66 & 678 & 664.079279596243 & 13.9207204037573 \tabularnewline
67 & 725 & 683.123404812594 & 41.8765951874059 \tabularnewline
68 & 644 & 724.349232484974 & -80.3492324849743 \tabularnewline
69 & 670 & 671.225337637663 & -1.2253376376633 \tabularnewline
70 & 662 & 677.816187614 & -15.8161876140002 \tabularnewline
71 & 641 & 672.984541031252 & -31.9845410312524 \tabularnewline
72 & 642 & 655.12520694252 & -13.1252069425198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261320&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]3[/C][C]327[/C][C]348[/C][C]-21[/C][/ROW]
[ROW][C]4[/C][C]302[/C][C]343.605238636906[/C][C]-41.6052386369061[/C][/ROW]
[ROW][C]5[/C][C]299[/C][C]322.586158093328[/C][C]-23.5861580933279[/C][/ROW]
[ROW][C]6[/C][C]311[/C][C]314.569236743633[/C][C]-3.56923674363281[/C][/ROW]
[ROW][C]7[/C][C]315[/C][C]321.575611197889[/C][C]-6.57561119788909[/C][/ROW]
[ROW][C]8[/C][C]264[/C][C]326.143502517307[/C][C]-62.1435025173072[/C][/ROW]
[ROW][C]9[/C][C]278[/C][C]287.160996356876[/C][C]-9.16099635687556[/C][/ROW]
[ROW][C]10[/C][C]278[/C][C]287.950772491747[/C][C]-9.95077249174733[/C][/ROW]
[ROW][C]11[/C][C]287[/C][C]287.889381511289[/C][C]-0.889381511288661[/C][/ROW]
[ROW][C]12[/C][C]279[/C][C]294.647434489076[/C][C]-15.6474344890757[/C][/ROW]
[ROW][C]13[/C][C]324[/C][C]289.861057899167[/C][C]34.1389421008334[/C][/ROW]
[ROW][C]14[/C][C]354[/C][C]323.542365521704[/C][C]30.4576344782956[/C][/ROW]
[ROW][C]15[/C][C]354[/C][C]355.22386493966[/C][C]-1.22386493965951[/C][/ROW]
[ROW][C]16[/C][C]360[/C][C]362.951456976152[/C][C]-2.95145697615197[/C][/ROW]
[ROW][C]17[/C][C]363[/C][C]369.298973225836[/C][C]-6.29897322583565[/C][/ROW]
[ROW][C]18[/C][C]385[/C][C]372.957495494414[/C][C]12.0425045055861[/C][/ROW]
[ROW][C]19[/C][C]412[/C][C]390.773964565257[/C][C]21.2260354347429[/C][/ROW]
[ROW][C]20[/C][C]370[/C][C]416.068416722836[/C][C]-46.0684167228358[/C][/ROW]
[ROW][C]21[/C][C]389[/C][C]389.369430722872[/C][C]-0.369430722872153[/C][/ROW]
[ROW][C]22[/C][C]395[/C][C]397.168097926898[/C][C]-2.16809792689844[/C][/ROW]
[ROW][C]23[/C][C]417[/C][C]403.553080338299[/C][C]13.4469196617014[/C][/ROW]
[ROW][C]24[/C][C]404[/C][C]422.073233901665[/C][C]-18.0732339016649[/C][/ROW]
[ROW][C]25[/C][C]456[/C][C]416.329848133997[/C][C]39.6701518660028[/C][/ROW]
[ROW][C]26[/C][C]478[/C][C]455.204089198762[/C][C]22.7959108012379[/C][/ROW]
[ROW][C]27[/C][C]468[/C][C]481.920398629402[/C][C]-13.9203986294025[/C][/ROW]
[ROW][C]28[/C][C]437[/C][C]480.555915240858[/C][C]-43.5559152408584[/C][/ROW]
[ROW][C]29[/C][C]432[/C][C]455.698436353025[/C][C]-23.6984363530246[/C][/ROW]
[ROW][C]30[/C][C]441[/C][C]445.228408441235[/C][C]-4.22840844123488[/C][/ROW]
[ROW][C]31[/C][C]449[/C][C]449.35183990739[/C][C]-0.351839907390115[/C][/ROW]
[ROW][C]32[/C][C]386[/C][C]456.393442464153[/C][C]-70.3934424641527[/C][/ROW]
[ROW][C]33[/C][C]396[/C][C]408.744351638823[/C][C]-12.7443516388232[/C][/ROW]
[ROW][C]34[/C][C]394[/C][C]404.299502329124[/C][C]-10.2995023291244[/C][/ROW]
[ROW][C]35[/C][C]403[/C][C]401.43700809193[/C][C]1.56299190806971[/C][/ROW]
[ROW][C]36[/C][C]373[/C][C]407.571857349552[/C][C]-34.5718573495524[/C][/ROW]
[ROW][C]37[/C][C]409[/C][C]385.536147898918[/C][C]23.4638521010817[/C][/ROW]
[ROW][C]38[/C][C]430[/C][C]407.923801281007[/C][C]22.076198718993[/C][/ROW]
[ROW][C]39[/C][C]415[/C][C]429.828950894981[/C][C]-14.8289508949815[/C][/ROW]
[ROW][C]40[/C][C]392[/C][C]423.487449865282[/C][C]-31.4874498652818[/C][/ROW]
[ROW][C]41[/C][C]401[/C][C]403.760883536642[/C][C]-2.7608835366425[/C][/ROW]
[ROW][C]42[/C][C]400[/C][C]405.654929103283[/C][C]-5.65492910328339[/C][/ROW]
[ROW][C]43[/C][C]447[/C][C]405.218886609867[/C][C]41.7811133901332[/C][/ROW]
[ROW][C]44[/C][C]392[/C][C]441.671494748546[/C][C]-49.671494748546[/C][/ROW]
[ROW][C]45[/C][C]427[/C][C]407.796677766209[/C][C]19.2033222337911[/C][/ROW]
[ROW][C]46[/C][C]444[/C][C]426.420688565966[/C][C]17.5793114340338[/C][/ROW]
[ROW][C]47[/C][C]448[/C][C]444.268570843014[/C][C]3.7314291569856[/C][/ROW]
[ROW][C]48[/C][C]427[/C][C]451.755526204106[/C][C]-24.755526204106[/C][/ROW]
[ROW][C]49[/C][C]480[/C][C]437.098183365909[/C][C]42.9018166340906[/C][/ROW]
[ROW][C]50[/C][C]490[/C][C]474.627208465646[/C][C]15.3727915343538[/C][/ROW]
[ROW][C]51[/C][C]482[/C][C]491.762834474526[/C][C]-9.76283447452624[/C][/ROW]
[ROW][C]52[/C][C]490[/C][C]489.668656469863[/C][C]0.331343530137019[/C][/ROW]
[ROW][C]53[/C][C]485[/C][C]495.205034819301[/C][C]-10.2050348193005[/C][/ROW]
[ROW][C]54[/C][C]498[/C][C]492.524116551455[/C][C]5.47588344854535[/C][/ROW]
[ROW][C]55[/C][C]544[/C][C]501.824015616061[/C][C]42.1759843839387[/C][/ROW]
[ROW][C]56[/C][C]483[/C][C]539.916012233081[/C][C]-56.9160122330807[/C][/ROW]
[ROW][C]57[/C][C]508[/C][C]501.726602323639[/C][C]6.2733976763609[/C][/ROW]
[ROW][C]58[/C][C]529[/C][C]511.411895174611[/C][C]17.5881048253895[/C][/ROW]
[ROW][C]59[/C][C]547[/C][C]530.091256500667[/C][C]16.908743499333[/C][/ROW]
[ROW][C]60[/C][C]543[/C][C]548.69061886959[/C][C]-5.69061886959003[/C][/ROW]
[ROW][C]61[/C][C]608[/C][C]550.079576940247[/C][C]57.9204230597531[/C][/ROW]
[ROW][C]62[/C][C]638[/C][C]600.984141055289[/C][C]37.0158589447105[/C][/ROW]
[ROW][C]63[/C][C]661[/C][C]637.051625131816[/C][C]23.9483748681841[/C][/ROW]
[ROW][C]64[/C][C]650[/C][C]663.865155125736[/C][C]-13.8651551257356[/C][/ROW]
[ROW][C]65[/C][C]654[/C][C]661.770800266873[/C][C]-7.77080026687258[/C][/ROW]
[ROW][C]66[/C][C]678[/C][C]664.079279596243[/C][C]13.9207204037573[/C][/ROW]
[ROW][C]67[/C][C]725[/C][C]683.123404812594[/C][C]41.8765951874059[/C][/ROW]
[ROW][C]68[/C][C]644[/C][C]724.349232484974[/C][C]-80.3492324849743[/C][/ROW]
[ROW][C]69[/C][C]670[/C][C]671.225337637663[/C][C]-1.2253376376633[/C][/ROW]
[ROW][C]70[/C][C]662[/C][C]677.816187614[/C][C]-15.8161876140002[/C][/ROW]
[ROW][C]71[/C][C]641[/C][C]672.984541031252[/C][C]-31.9845410312524[/C][/ROW]
[ROW][C]72[/C][C]642[/C][C]655.12520694252[/C][C]-13.1252069425198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261320&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261320&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
3327348-21
4302343.605238636906-41.6052386369061
5299322.586158093328-23.5861580933279
6311314.569236743633-3.56923674363281
7315321.575611197889-6.57561119788909
8264326.143502517307-62.1435025173072
9278287.160996356876-9.16099635687556
10278287.950772491747-9.95077249174733
11287287.889381511289-0.889381511288661
12279294.647434489076-15.6474344890757
13324289.86105789916734.1389421008334
14354323.54236552170430.4576344782956
15354355.22386493966-1.22386493965951
16360362.951456976152-2.95145697615197
17363369.298973225836-6.29897322583565
18385372.95749549441412.0425045055861
19412390.77396456525721.2260354347429
20370416.068416722836-46.0684167228358
21389389.369430722872-0.369430722872153
22395397.168097926898-2.16809792689844
23417403.55308033829913.4469196617014
24404422.073233901665-18.0732339016649
25456416.32984813399739.6701518660028
26478455.20408919876222.7959108012379
27468481.920398629402-13.9203986294025
28437480.555915240858-43.5559152408584
29432455.698436353025-23.6984363530246
30441445.228408441235-4.22840844123488
31449449.35183990739-0.351839907390115
32386456.393442464153-70.3934424641527
33396408.744351638823-12.7443516388232
34394404.299502329124-10.2995023291244
35403401.437008091931.56299190806971
36373407.571857349552-34.5718573495524
37409385.53614789891823.4638521010817
38430407.92380128100722.076198718993
39415429.828950894981-14.8289508949815
40392423.487449865282-31.4874498652818
41401403.760883536642-2.7608835366425
42400405.654929103283-5.65492910328339
43447405.21888660986741.7811133901332
44392441.671494748546-49.671494748546
45427407.79667776620919.2033222337911
46444426.42068856596617.5793114340338
47448444.2685708430143.7314291569856
48427451.755526204106-24.755526204106
49480437.09818336590942.9018166340906
50490474.62720846564615.3727915343538
51482491.762834474526-9.76283447452624
52490489.6686564698630.331343530137019
53485495.205034819301-10.2050348193005
54498492.5241165514555.47588344854535
55544501.82401561606142.1759843839387
56483539.916012233081-56.9160122330807
57508501.7266023236396.2733976763609
58529511.41189517461117.5881048253895
59547530.09125650066716.908743499333
60543548.69061886959-5.69061886959003
61608550.07957694024757.9204230597531
62638600.98414105528937.0158589447105
63661637.05162513181623.9483748681841
64650663.865155125736-13.8651551257356
65654661.770800266873-7.77080026687258
66678664.07927959624313.9207204037573
67725683.12340481259441.8765951874059
68644724.349232484974-80.3492324849743
69670671.225337637663-1.2253376376633
70662677.816187614-15.8161876140002
71641672.984541031252-31.9845410312524
72642655.12520694252-13.1252069425198







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73651.170378642022596.321440117449706.019317166594
74657.126339225469587.541709587129726.71096886381
75663.082299808917580.63296183954745.531637778294
76669.038260392365574.804670983761763.271849800969
77674.994220975813569.674734781976780.31370716965
78680.95018155926565.02558064984796.874782468681
79686.906142142708560.720281163914813.092003121503
80692.862102726156556.66660065838829.057604793932
81698.818063309604552.799269039424844.836857579783
82704.774023893052549.070339391572860.477708394531
83710.729984476499545.443543981045876.016424971954
84716.685945059947541.890797016338891.481093103556

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 651.170378642022 & 596.321440117449 & 706.019317166594 \tabularnewline
74 & 657.126339225469 & 587.541709587129 & 726.71096886381 \tabularnewline
75 & 663.082299808917 & 580.63296183954 & 745.531637778294 \tabularnewline
76 & 669.038260392365 & 574.804670983761 & 763.271849800969 \tabularnewline
77 & 674.994220975813 & 569.674734781976 & 780.31370716965 \tabularnewline
78 & 680.95018155926 & 565.02558064984 & 796.874782468681 \tabularnewline
79 & 686.906142142708 & 560.720281163914 & 813.092003121503 \tabularnewline
80 & 692.862102726156 & 556.66660065838 & 829.057604793932 \tabularnewline
81 & 698.818063309604 & 552.799269039424 & 844.836857579783 \tabularnewline
82 & 704.774023893052 & 549.070339391572 & 860.477708394531 \tabularnewline
83 & 710.729984476499 & 545.443543981045 & 876.016424971954 \tabularnewline
84 & 716.685945059947 & 541.890797016338 & 891.481093103556 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261320&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]73[/C][C]651.170378642022[/C][C]596.321440117449[/C][C]706.019317166594[/C][/ROW]
[ROW][C]74[/C][C]657.126339225469[/C][C]587.541709587129[/C][C]726.71096886381[/C][/ROW]
[ROW][C]75[/C][C]663.082299808917[/C][C]580.63296183954[/C][C]745.531637778294[/C][/ROW]
[ROW][C]76[/C][C]669.038260392365[/C][C]574.804670983761[/C][C]763.271849800969[/C][/ROW]
[ROW][C]77[/C][C]674.994220975813[/C][C]569.674734781976[/C][C]780.31370716965[/C][/ROW]
[ROW][C]78[/C][C]680.95018155926[/C][C]565.02558064984[/C][C]796.874782468681[/C][/ROW]
[ROW][C]79[/C][C]686.906142142708[/C][C]560.720281163914[/C][C]813.092003121503[/C][/ROW]
[ROW][C]80[/C][C]692.862102726156[/C][C]556.66660065838[/C][C]829.057604793932[/C][/ROW]
[ROW][C]81[/C][C]698.818063309604[/C][C]552.799269039424[/C][C]844.836857579783[/C][/ROW]
[ROW][C]82[/C][C]704.774023893052[/C][C]549.070339391572[/C][C]860.477708394531[/C][/ROW]
[ROW][C]83[/C][C]710.729984476499[/C][C]545.443543981045[/C][C]876.016424971954[/C][/ROW]
[ROW][C]84[/C][C]716.685945059947[/C][C]541.890797016338[/C][C]891.481093103556[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261320&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261320&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
73651.170378642022596.321440117449706.019317166594
74657.126339225469587.541709587129726.71096886381
75663.082299808917580.63296183954745.531637778294
76669.038260392365574.804670983761763.271849800969
77674.994220975813569.674734781976780.31370716965
78680.95018155926565.02558064984796.874782468681
79686.906142142708560.720281163914813.092003121503
80692.862102726156556.66660065838829.057604793932
81698.818063309604552.799269039424844.836857579783
82704.774023893052549.070339391572860.477708394531
83710.729984476499545.443543981045876.016424971954
84716.685945059947541.890797016338891.481093103556



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')