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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 computationWed, 18 May 2011 17:52:00 +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/2011/May/18/t1305740965ufxzk05ni4h71p5.htm/, Retrieved Mon, 13 May 2024 22:26:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121907, Retrieved Mon, 13 May 2024 22:26:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10-Daphné...] [2011-05-18 17:52:00] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
476
475
470
461
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121907&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121907&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121907&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.908493182493487
beta0.125208658779051
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.908493182493487 \tabularnewline
beta & 0.125208658779051 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121907&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]0.908493182493487[/C][/ROW]
[ROW][C]beta[/C][C]0.125208658779051[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121907&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121907&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
alpha0.908493182493487
beta0.125208658779051
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13519495.15261712648823.8473828735125
14517517.093475249971-0.093475249970652
15510512.075431881386-2.07543188138561
16509511.36144411155-2.36144411154982
17501503.739744728424-2.7397447284236
18507509.599514771422-2.59951477142238
19569568.1421080523140.857891947686085
20580579.5646284660760.435371533924354
21578579.7485661572-1.74856615719955
22565575.222868009268-10.2228680092677
23547555.126370653665-8.12637065366516
24555550.0660785558284.93392144417248
25562563.853913698699-1.85391369869876
26561556.6335525837124.36644741628822
27555552.1592753074562.84072469254409
28544553.671275484217-9.67127548421706
29537536.0321355606180.967864439381515
30543543.342096864995-0.342096864995142
31594606.108805718683-12.1088057186828
32611602.3409182403648.65908175963557
33613606.8445633751336.15543662486709
34611606.4567538625074.5432461374935
35594598.731864300194-4.73186430019359
36595598.322465538278-3.32246553827792
37591603.750211721385-12.7502117213853
38589584.941843265244.05815673476013
39584577.6385886605616.36141133943897
40573579.485372333632-6.48537233363197
41567564.125369174172.87463082583042
42569572.439615455722-3.43961545572233
43621632.876389185919-11.876389185919
44629630.297068467522-1.29706846752219
45628622.9773356929035.02266430709665
46612618.743104942904-6.74310494290387
47595596.259424804809-1.25942480480876
48597595.91781998031.08218001969976
49593601.742170238892-8.74217023889207
50590585.8245775097454.1754224902545
51580576.6322402231093.36775977689069
52574572.1454684485621.8545315514383
53573563.6864198566459.3135801433549
54573576.507065028749-3.50706502874903
55620635.67105170788-15.6710517078805
56626629.288303079767-3.28830307976693
57620619.2228278179110.77717218208943
58588608.209040035549-20.2090400355493
59566571.170539247736-5.17053924773575
60557563.598761917183-6.59876191718297
61561556.5535920664124.44640793358781
62549550.91896141542-1.91896141541974
63532533.191940704597-1.19194070459707
64526520.8091272548445.1908727451555
65511513.069113956602-2.06911395660245
66499509.072928369888-10.0729283698878
67555547.0063169083437.99368309165686
68565558.3958870363296.60411296367135
69542555.560954425597-13.5609544255969
70527526.9108333154460.089166684553902
71510509.2819984021580.718001597842317
72514505.6450854642738.3549145357266
73517513.3295233203833.67047667961651
74508507.2992614789860.700738521014387
75493493.578755031763-0.578755031763194
76490483.5471181089786.45288189102206
77469477.816520286092-8.81652028609182
78478466.96663495239811.033365047602
79528526.0761985478611.92380145213906
80534533.4847587826270.515241217373386
81518525.003655631961-7.00365563196101
82506506.05922847729-0.0592284772903895
83502490.85881728650911.1411827134908
84516500.53964122804315.4603587719569

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 519 & 495.152617126488 & 23.8473828735125 \tabularnewline
14 & 517 & 517.093475249971 & -0.093475249970652 \tabularnewline
15 & 510 & 512.075431881386 & -2.07543188138561 \tabularnewline
16 & 509 & 511.36144411155 & -2.36144411154982 \tabularnewline
17 & 501 & 503.739744728424 & -2.7397447284236 \tabularnewline
18 & 507 & 509.599514771422 & -2.59951477142238 \tabularnewline
19 & 569 & 568.142108052314 & 0.857891947686085 \tabularnewline
20 & 580 & 579.564628466076 & 0.435371533924354 \tabularnewline
21 & 578 & 579.7485661572 & -1.74856615719955 \tabularnewline
22 & 565 & 575.222868009268 & -10.2228680092677 \tabularnewline
23 & 547 & 555.126370653665 & -8.12637065366516 \tabularnewline
24 & 555 & 550.066078555828 & 4.93392144417248 \tabularnewline
25 & 562 & 563.853913698699 & -1.85391369869876 \tabularnewline
26 & 561 & 556.633552583712 & 4.36644741628822 \tabularnewline
27 & 555 & 552.159275307456 & 2.84072469254409 \tabularnewline
28 & 544 & 553.671275484217 & -9.67127548421706 \tabularnewline
29 & 537 & 536.032135560618 & 0.967864439381515 \tabularnewline
30 & 543 & 543.342096864995 & -0.342096864995142 \tabularnewline
31 & 594 & 606.108805718683 & -12.1088057186828 \tabularnewline
32 & 611 & 602.340918240364 & 8.65908175963557 \tabularnewline
33 & 613 & 606.844563375133 & 6.15543662486709 \tabularnewline
34 & 611 & 606.456753862507 & 4.5432461374935 \tabularnewline
35 & 594 & 598.731864300194 & -4.73186430019359 \tabularnewline
36 & 595 & 598.322465538278 & -3.32246553827792 \tabularnewline
37 & 591 & 603.750211721385 & -12.7502117213853 \tabularnewline
38 & 589 & 584.94184326524 & 4.05815673476013 \tabularnewline
39 & 584 & 577.638588660561 & 6.36141133943897 \tabularnewline
40 & 573 & 579.485372333632 & -6.48537233363197 \tabularnewline
41 & 567 & 564.12536917417 & 2.87463082583042 \tabularnewline
42 & 569 & 572.439615455722 & -3.43961545572233 \tabularnewline
43 & 621 & 632.876389185919 & -11.876389185919 \tabularnewline
44 & 629 & 630.297068467522 & -1.29706846752219 \tabularnewline
45 & 628 & 622.977335692903 & 5.02266430709665 \tabularnewline
46 & 612 & 618.743104942904 & -6.74310494290387 \tabularnewline
47 & 595 & 596.259424804809 & -1.25942480480876 \tabularnewline
48 & 597 & 595.9178199803 & 1.08218001969976 \tabularnewline
49 & 593 & 601.742170238892 & -8.74217023889207 \tabularnewline
50 & 590 & 585.824577509745 & 4.1754224902545 \tabularnewline
51 & 580 & 576.632240223109 & 3.36775977689069 \tabularnewline
52 & 574 & 572.145468448562 & 1.8545315514383 \tabularnewline
53 & 573 & 563.686419856645 & 9.3135801433549 \tabularnewline
54 & 573 & 576.507065028749 & -3.50706502874903 \tabularnewline
55 & 620 & 635.67105170788 & -15.6710517078805 \tabularnewline
56 & 626 & 629.288303079767 & -3.28830307976693 \tabularnewline
57 & 620 & 619.222827817911 & 0.77717218208943 \tabularnewline
58 & 588 & 608.209040035549 & -20.2090400355493 \tabularnewline
59 & 566 & 571.170539247736 & -5.17053924773575 \tabularnewline
60 & 557 & 563.598761917183 & -6.59876191718297 \tabularnewline
61 & 561 & 556.553592066412 & 4.44640793358781 \tabularnewline
62 & 549 & 550.91896141542 & -1.91896141541974 \tabularnewline
63 & 532 & 533.191940704597 & -1.19194070459707 \tabularnewline
64 & 526 & 520.809127254844 & 5.1908727451555 \tabularnewline
65 & 511 & 513.069113956602 & -2.06911395660245 \tabularnewline
66 & 499 & 509.072928369888 & -10.0729283698878 \tabularnewline
67 & 555 & 547.006316908343 & 7.99368309165686 \tabularnewline
68 & 565 & 558.395887036329 & 6.60411296367135 \tabularnewline
69 & 542 & 555.560954425597 & -13.5609544255969 \tabularnewline
70 & 527 & 526.910833315446 & 0.089166684553902 \tabularnewline
71 & 510 & 509.281998402158 & 0.718001597842317 \tabularnewline
72 & 514 & 505.645085464273 & 8.3549145357266 \tabularnewline
73 & 517 & 513.329523320383 & 3.67047667961651 \tabularnewline
74 & 508 & 507.299261478986 & 0.700738521014387 \tabularnewline
75 & 493 & 493.578755031763 & -0.578755031763194 \tabularnewline
76 & 490 & 483.547118108978 & 6.45288189102206 \tabularnewline
77 & 469 & 477.816520286092 & -8.81652028609182 \tabularnewline
78 & 478 & 466.966634952398 & 11.033365047602 \tabularnewline
79 & 528 & 526.076198547861 & 1.92380145213906 \tabularnewline
80 & 534 & 533.484758782627 & 0.515241217373386 \tabularnewline
81 & 518 & 525.003655631961 & -7.00365563196101 \tabularnewline
82 & 506 & 506.05922847729 & -0.0592284772903895 \tabularnewline
83 & 502 & 490.858817286509 & 11.1411827134908 \tabularnewline
84 & 516 & 500.539641228043 & 15.4603587719569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121907&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]519[/C][C]495.152617126488[/C][C]23.8473828735125[/C][/ROW]
[ROW][C]14[/C][C]517[/C][C]517.093475249971[/C][C]-0.093475249970652[/C][/ROW]
[ROW][C]15[/C][C]510[/C][C]512.075431881386[/C][C]-2.07543188138561[/C][/ROW]
[ROW][C]16[/C][C]509[/C][C]511.36144411155[/C][C]-2.36144411154982[/C][/ROW]
[ROW][C]17[/C][C]501[/C][C]503.739744728424[/C][C]-2.7397447284236[/C][/ROW]
[ROW][C]18[/C][C]507[/C][C]509.599514771422[/C][C]-2.59951477142238[/C][/ROW]
[ROW][C]19[/C][C]569[/C][C]568.142108052314[/C][C]0.857891947686085[/C][/ROW]
[ROW][C]20[/C][C]580[/C][C]579.564628466076[/C][C]0.435371533924354[/C][/ROW]
[ROW][C]21[/C][C]578[/C][C]579.7485661572[/C][C]-1.74856615719955[/C][/ROW]
[ROW][C]22[/C][C]565[/C][C]575.222868009268[/C][C]-10.2228680092677[/C][/ROW]
[ROW][C]23[/C][C]547[/C][C]555.126370653665[/C][C]-8.12637065366516[/C][/ROW]
[ROW][C]24[/C][C]555[/C][C]550.066078555828[/C][C]4.93392144417248[/C][/ROW]
[ROW][C]25[/C][C]562[/C][C]563.853913698699[/C][C]-1.85391369869876[/C][/ROW]
[ROW][C]26[/C][C]561[/C][C]556.633552583712[/C][C]4.36644741628822[/C][/ROW]
[ROW][C]27[/C][C]555[/C][C]552.159275307456[/C][C]2.84072469254409[/C][/ROW]
[ROW][C]28[/C][C]544[/C][C]553.671275484217[/C][C]-9.67127548421706[/C][/ROW]
[ROW][C]29[/C][C]537[/C][C]536.032135560618[/C][C]0.967864439381515[/C][/ROW]
[ROW][C]30[/C][C]543[/C][C]543.342096864995[/C][C]-0.342096864995142[/C][/ROW]
[ROW][C]31[/C][C]594[/C][C]606.108805718683[/C][C]-12.1088057186828[/C][/ROW]
[ROW][C]32[/C][C]611[/C][C]602.340918240364[/C][C]8.65908175963557[/C][/ROW]
[ROW][C]33[/C][C]613[/C][C]606.844563375133[/C][C]6.15543662486709[/C][/ROW]
[ROW][C]34[/C][C]611[/C][C]606.456753862507[/C][C]4.5432461374935[/C][/ROW]
[ROW][C]35[/C][C]594[/C][C]598.731864300194[/C][C]-4.73186430019359[/C][/ROW]
[ROW][C]36[/C][C]595[/C][C]598.322465538278[/C][C]-3.32246553827792[/C][/ROW]
[ROW][C]37[/C][C]591[/C][C]603.750211721385[/C][C]-12.7502117213853[/C][/ROW]
[ROW][C]38[/C][C]589[/C][C]584.94184326524[/C][C]4.05815673476013[/C][/ROW]
[ROW][C]39[/C][C]584[/C][C]577.638588660561[/C][C]6.36141133943897[/C][/ROW]
[ROW][C]40[/C][C]573[/C][C]579.485372333632[/C][C]-6.48537233363197[/C][/ROW]
[ROW][C]41[/C][C]567[/C][C]564.12536917417[/C][C]2.87463082583042[/C][/ROW]
[ROW][C]42[/C][C]569[/C][C]572.439615455722[/C][C]-3.43961545572233[/C][/ROW]
[ROW][C]43[/C][C]621[/C][C]632.876389185919[/C][C]-11.876389185919[/C][/ROW]
[ROW][C]44[/C][C]629[/C][C]630.297068467522[/C][C]-1.29706846752219[/C][/ROW]
[ROW][C]45[/C][C]628[/C][C]622.977335692903[/C][C]5.02266430709665[/C][/ROW]
[ROW][C]46[/C][C]612[/C][C]618.743104942904[/C][C]-6.74310494290387[/C][/ROW]
[ROW][C]47[/C][C]595[/C][C]596.259424804809[/C][C]-1.25942480480876[/C][/ROW]
[ROW][C]48[/C][C]597[/C][C]595.9178199803[/C][C]1.08218001969976[/C][/ROW]
[ROW][C]49[/C][C]593[/C][C]601.742170238892[/C][C]-8.74217023889207[/C][/ROW]
[ROW][C]50[/C][C]590[/C][C]585.824577509745[/C][C]4.1754224902545[/C][/ROW]
[ROW][C]51[/C][C]580[/C][C]576.632240223109[/C][C]3.36775977689069[/C][/ROW]
[ROW][C]52[/C][C]574[/C][C]572.145468448562[/C][C]1.8545315514383[/C][/ROW]
[ROW][C]53[/C][C]573[/C][C]563.686419856645[/C][C]9.3135801433549[/C][/ROW]
[ROW][C]54[/C][C]573[/C][C]576.507065028749[/C][C]-3.50706502874903[/C][/ROW]
[ROW][C]55[/C][C]620[/C][C]635.67105170788[/C][C]-15.6710517078805[/C][/ROW]
[ROW][C]56[/C][C]626[/C][C]629.288303079767[/C][C]-3.28830307976693[/C][/ROW]
[ROW][C]57[/C][C]620[/C][C]619.222827817911[/C][C]0.77717218208943[/C][/ROW]
[ROW][C]58[/C][C]588[/C][C]608.209040035549[/C][C]-20.2090400355493[/C][/ROW]
[ROW][C]59[/C][C]566[/C][C]571.170539247736[/C][C]-5.17053924773575[/C][/ROW]
[ROW][C]60[/C][C]557[/C][C]563.598761917183[/C][C]-6.59876191718297[/C][/ROW]
[ROW][C]61[/C][C]561[/C][C]556.553592066412[/C][C]4.44640793358781[/C][/ROW]
[ROW][C]62[/C][C]549[/C][C]550.91896141542[/C][C]-1.91896141541974[/C][/ROW]
[ROW][C]63[/C][C]532[/C][C]533.191940704597[/C][C]-1.19194070459707[/C][/ROW]
[ROW][C]64[/C][C]526[/C][C]520.809127254844[/C][C]5.1908727451555[/C][/ROW]
[ROW][C]65[/C][C]511[/C][C]513.069113956602[/C][C]-2.06911395660245[/C][/ROW]
[ROW][C]66[/C][C]499[/C][C]509.072928369888[/C][C]-10.0729283698878[/C][/ROW]
[ROW][C]67[/C][C]555[/C][C]547.006316908343[/C][C]7.99368309165686[/C][/ROW]
[ROW][C]68[/C][C]565[/C][C]558.395887036329[/C][C]6.60411296367135[/C][/ROW]
[ROW][C]69[/C][C]542[/C][C]555.560954425597[/C][C]-13.5609544255969[/C][/ROW]
[ROW][C]70[/C][C]527[/C][C]526.910833315446[/C][C]0.089166684553902[/C][/ROW]
[ROW][C]71[/C][C]510[/C][C]509.281998402158[/C][C]0.718001597842317[/C][/ROW]
[ROW][C]72[/C][C]514[/C][C]505.645085464273[/C][C]8.3549145357266[/C][/ROW]
[ROW][C]73[/C][C]517[/C][C]513.329523320383[/C][C]3.67047667961651[/C][/ROW]
[ROW][C]74[/C][C]508[/C][C]507.299261478986[/C][C]0.700738521014387[/C][/ROW]
[ROW][C]75[/C][C]493[/C][C]493.578755031763[/C][C]-0.578755031763194[/C][/ROW]
[ROW][C]76[/C][C]490[/C][C]483.547118108978[/C][C]6.45288189102206[/C][/ROW]
[ROW][C]77[/C][C]469[/C][C]477.816520286092[/C][C]-8.81652028609182[/C][/ROW]
[ROW][C]78[/C][C]478[/C][C]466.966634952398[/C][C]11.033365047602[/C][/ROW]
[ROW][C]79[/C][C]528[/C][C]526.076198547861[/C][C]1.92380145213906[/C][/ROW]
[ROW][C]80[/C][C]534[/C][C]533.484758782627[/C][C]0.515241217373386[/C][/ROW]
[ROW][C]81[/C][C]518[/C][C]525.003655631961[/C][C]-7.00365563196101[/C][/ROW]
[ROW][C]82[/C][C]506[/C][C]506.05922847729[/C][C]-0.0592284772903895[/C][/ROW]
[ROW][C]83[/C][C]502[/C][C]490.858817286509[/C][C]11.1411827134908[/C][/ROW]
[ROW][C]84[/C][C]516[/C][C]500.539641228043[/C][C]15.4603587719569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121907&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121907&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
13519495.15261712648823.8473828735125
14517517.093475249971-0.093475249970652
15510512.075431881386-2.07543188138561
16509511.36144411155-2.36144411154982
17501503.739744728424-2.7397447284236
18507509.599514771422-2.59951477142238
19569568.1421080523140.857891947686085
20580579.5646284660760.435371533924354
21578579.7485661572-1.74856615719955
22565575.222868009268-10.2228680092677
23547555.126370653665-8.12637065366516
24555550.0660785558284.93392144417248
25562563.853913698699-1.85391369869876
26561556.6335525837124.36644741628822
27555552.1592753074562.84072469254409
28544553.671275484217-9.67127548421706
29537536.0321355606180.967864439381515
30543543.342096864995-0.342096864995142
31594606.108805718683-12.1088057186828
32611602.3409182403648.65908175963557
33613606.8445633751336.15543662486709
34611606.4567538625074.5432461374935
35594598.731864300194-4.73186430019359
36595598.322465538278-3.32246553827792
37591603.750211721385-12.7502117213853
38589584.941843265244.05815673476013
39584577.6385886605616.36141133943897
40573579.485372333632-6.48537233363197
41567564.125369174172.87463082583042
42569572.439615455722-3.43961545572233
43621632.876389185919-11.876389185919
44629630.297068467522-1.29706846752219
45628622.9773356929035.02266430709665
46612618.743104942904-6.74310494290387
47595596.259424804809-1.25942480480876
48597595.91781998031.08218001969976
49593601.742170238892-8.74217023889207
50590585.8245775097454.1754224902545
51580576.6322402231093.36775977689069
52574572.1454684485621.8545315514383
53573563.6864198566459.3135801433549
54573576.507065028749-3.50706502874903
55620635.67105170788-15.6710517078805
56626629.288303079767-3.28830307976693
57620619.2228278179110.77717218208943
58588608.209040035549-20.2090400355493
59566571.170539247736-5.17053924773575
60557563.598761917183-6.59876191718297
61561556.5535920664124.44640793358781
62549550.91896141542-1.91896141541974
63532533.191940704597-1.19194070459707
64526520.8091272548445.1908727451555
65511513.069113956602-2.06911395660245
66499509.072928369888-10.0729283698878
67555547.0063169083437.99368309165686
68565558.3958870363296.60411296367135
69542555.560954425597-13.5609544255969
70527526.9108333154460.089166684553902
71510509.2819984021580.718001597842317
72514505.6450854642738.3549145357266
73517513.3295233203833.67047667961651
74508507.2992614789860.700738521014387
75493493.578755031763-0.578755031763194
76490483.5471181089786.45288189102206
77469477.816520286092-8.81652028609182
78478466.96663495239811.033365047602
79528526.0761985478611.92380145213906
80534533.4847587826270.515241217373386
81518525.003655631961-7.00365563196101
82506506.05922847729-0.0592284772903895
83502490.85881728650911.1411827134908
84516500.53964122804315.4603587719569







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85518.261494818009503.834489756166532.688499879853
86512.155297010596491.656341035812532.65425298538
87500.9753663982475.166427439476526.784305356925
88495.424374409046464.332533030446526.516215787647
89484.920491026349448.952230550487520.888751502211
90487.587968155072445.864114796691529.311821513452
91539.482715176359487.517508683408591.447921669309
92547.625260089619488.845066984406606.405453194832
93540.136685567944476.044819437564604.228551698324
94530.886999145872461.720459962608600.053538329137
95519.206889045054445.351424820548593.06235326956
96520.929590304987434.237970543672607.621210066301

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 518.261494818009 & 503.834489756166 & 532.688499879853 \tabularnewline
86 & 512.155297010596 & 491.656341035812 & 532.65425298538 \tabularnewline
87 & 500.9753663982 & 475.166427439476 & 526.784305356925 \tabularnewline
88 & 495.424374409046 & 464.332533030446 & 526.516215787647 \tabularnewline
89 & 484.920491026349 & 448.952230550487 & 520.888751502211 \tabularnewline
90 & 487.587968155072 & 445.864114796691 & 529.311821513452 \tabularnewline
91 & 539.482715176359 & 487.517508683408 & 591.447921669309 \tabularnewline
92 & 547.625260089619 & 488.845066984406 & 606.405453194832 \tabularnewline
93 & 540.136685567944 & 476.044819437564 & 604.228551698324 \tabularnewline
94 & 530.886999145872 & 461.720459962608 & 600.053538329137 \tabularnewline
95 & 519.206889045054 & 445.351424820548 & 593.06235326956 \tabularnewline
96 & 520.929590304987 & 434.237970543672 & 607.621210066301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121907&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]518.261494818009[/C][C]503.834489756166[/C][C]532.688499879853[/C][/ROW]
[ROW][C]86[/C][C]512.155297010596[/C][C]491.656341035812[/C][C]532.65425298538[/C][/ROW]
[ROW][C]87[/C][C]500.9753663982[/C][C]475.166427439476[/C][C]526.784305356925[/C][/ROW]
[ROW][C]88[/C][C]495.424374409046[/C][C]464.332533030446[/C][C]526.516215787647[/C][/ROW]
[ROW][C]89[/C][C]484.920491026349[/C][C]448.952230550487[/C][C]520.888751502211[/C][/ROW]
[ROW][C]90[/C][C]487.587968155072[/C][C]445.864114796691[/C][C]529.311821513452[/C][/ROW]
[ROW][C]91[/C][C]539.482715176359[/C][C]487.517508683408[/C][C]591.447921669309[/C][/ROW]
[ROW][C]92[/C][C]547.625260089619[/C][C]488.845066984406[/C][C]606.405453194832[/C][/ROW]
[ROW][C]93[/C][C]540.136685567944[/C][C]476.044819437564[/C][C]604.228551698324[/C][/ROW]
[ROW][C]94[/C][C]530.886999145872[/C][C]461.720459962608[/C][C]600.053538329137[/C][/ROW]
[ROW][C]95[/C][C]519.206889045054[/C][C]445.351424820548[/C][C]593.06235326956[/C][/ROW]
[ROW][C]96[/C][C]520.929590304987[/C][C]434.237970543672[/C][C]607.621210066301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121907&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121907&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
85518.261494818009503.834489756166532.688499879853
86512.155297010596491.656341035812532.65425298538
87500.9753663982475.166427439476526.784305356925
88495.424374409046464.332533030446526.516215787647
89484.920491026349448.952230550487520.888751502211
90487.587968155072445.864114796691529.311821513452
91539.482715176359487.517508683408591.447921669309
92547.625260089619488.845066984406606.405453194832
93540.136685567944476.044819437564604.228551698324
94530.886999145872461.720459962608600.053538329137
95519.206889045054445.351424820548593.06235326956
96520.929590304987434.237970543672607.621210066301



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')