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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, 03 Jun 2009 11:20:49 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/03/t12440497091f94b41vyl1ft4m.htm/, Retrieved Sun, 12 May 2024 09:42:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41512, Retrieved Sun, 12 May 2024 09:42:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Datareeks-Werkloo...] [2009-02-15 13:51:16] [74be16979710d4c4e7c6647856088456]
- RMP   [Classical Decomposition] [Robin Bosmans-Dat...] [2009-06-02 11:52:28] [74be16979710d4c4e7c6647856088456]
- RMP       [Exponential Smoothing] [Robin Bosmans- Da...] [2009-06-03 17:20:49] [f565a348fef35d164bc634b6b1fffd89] [Current]
Feedback Forum

Post a new message
Dataseries X:
467
460
448
443
436
431
484
510
513
503
471
471
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
528




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41512&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41512&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41512&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.562952218589531
beta0.0858271961966097
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.562952218589531 \tabularnewline
beta & 0.0858271961966097 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41512&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]0.562952218589531[/C][/ROW]
[ROW][C]beta[/C][C]0.0858271961966097[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41512&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41512&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
alpha0.562952218589531
beta0.0858271961966097
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13476465.26919754111810.7308024588818
14475470.6103181364854.38968186351536
15470469.5149090973490.485090902650995
16461462.154835841513-1.15483584151264
17455455.688271059507-0.688271059506519
18456455.4880906720020.5119093279975
19517506.51866578333410.4813342166659
20525541.980873253753-16.9808732537530
21523536.173392747286-13.1733927472857
22519518.3192040464850.68079595351503
23509485.73864947190523.2613505280948
24512499.64135450028612.3586454997137
25519517.8392629628761.16073703712357
26517515.6349679629871.36503203701307
27510511.431449157141-1.43144915714072
28509502.2059513187386.7940486812617
29501500.867509169280.132490830719860
30507502.7554503746144.24454962538562
31569567.453719067461.54628093254007
32580588.368267814747-8.36826781474736
33578590.940298202399-12.9402982023992
34565580.166219772499-15.1662197724987
35547546.5239363737110.476063626289374
36555541.93034336879313.0696566312072
37562555.5500477804366.44995221956435
38561555.8906989589465.10930104105432
39555551.9314570449033.06854295509697
40544548.462736569939-4.46273656993912
41537536.8388765937120.161123406288198
42543540.3427850304062.65721496959407
43594606.580432142004-12.5804321420038
44611614.784867324054-3.78486732405418
45613617.154246372086-4.15424637208571
46611609.3930344927851.60696550721514
47594590.7918406666053.2081593333952
48595593.5589357124551.44106428754469
49591597.723180425056-6.72318042505606
50589588.9929080030140.00709199698576413
51584579.827643564264.17235643573997
52573572.282853760940.717146239059502
53567564.5023482647832.49765173521746
54569570.03951166734-1.03951166734009
55621629.440004697-8.44000469699927
56629644.140849730675-15.1408497306750
57628638.956021174525-10.9560211745252
58612628.337375525677-16.3373755256772
59595597.894877543472-2.89487754347158
60597594.0124226396472.98757736035293
61593593.114305172382-0.114305172381705
62590589.0212282297620.978771770238268
63580580.278248995199-0.278248995199078
64574566.7204127572227.27958724277778
65573561.70554645702911.2944535429713
66573569.3304941524713.66950584752942
67620627.152635579839-7.1526355798386
68626638.449907212287-12.4499072122871
69620635.533751599433-15.5337515994333
70588618.647754874405-30.6477548744048
71566584.401715489263-18.4017154892629
72557571.71987540367-14.7198754036706
73561556.284320463144.71567953685974
74549552.413903995036-3.41390399503587
75532537.988317669999-5.98831766999888
76526521.767138980954.23286101904966
77511513.800564988936-2.80056498893566
78499506.211878883097-7.21187888309674
79555541.81789992043613.1821000795644
80565556.523567868278.47643213173
81542560.404248347054-18.4042483470541
82527533.218076268099-6.21807626809903
83510516.741928476132-6.74192847613176
84514510.3271134913833.67288650861724
85517512.5807493861214.41925061387872
86508504.7809098283423.21909017165774
87493493.305087308172-0.305087308171608
88490484.9260023820295.07399761797126
89469474.965392741366-5.96539274136592
90478463.72057222333814.2794277766620
91528518.2126828764119.78731712358876
92534529.09241362054.90758637950012
93518520.117735768265-2.11773576826465
94506508.958853313268-2.95885331326770
95502495.760066304816.23993369518951
96516503.05177489134412.9482251086557
97528513.25406132606314.7459386739371

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 476 & 465.269197541118 & 10.7308024588818 \tabularnewline
14 & 475 & 470.610318136485 & 4.38968186351536 \tabularnewline
15 & 470 & 469.514909097349 & 0.485090902650995 \tabularnewline
16 & 461 & 462.154835841513 & -1.15483584151264 \tabularnewline
17 & 455 & 455.688271059507 & -0.688271059506519 \tabularnewline
18 & 456 & 455.488090672002 & 0.5119093279975 \tabularnewline
19 & 517 & 506.518665783334 & 10.4813342166659 \tabularnewline
20 & 525 & 541.980873253753 & -16.9808732537530 \tabularnewline
21 & 523 & 536.173392747286 & -13.1733927472857 \tabularnewline
22 & 519 & 518.319204046485 & 0.68079595351503 \tabularnewline
23 & 509 & 485.738649471905 & 23.2613505280948 \tabularnewline
24 & 512 & 499.641354500286 & 12.3586454997137 \tabularnewline
25 & 519 & 517.839262962876 & 1.16073703712357 \tabularnewline
26 & 517 & 515.634967962987 & 1.36503203701307 \tabularnewline
27 & 510 & 511.431449157141 & -1.43144915714072 \tabularnewline
28 & 509 & 502.205951318738 & 6.7940486812617 \tabularnewline
29 & 501 & 500.86750916928 & 0.132490830719860 \tabularnewline
30 & 507 & 502.755450374614 & 4.24454962538562 \tabularnewline
31 & 569 & 567.45371906746 & 1.54628093254007 \tabularnewline
32 & 580 & 588.368267814747 & -8.36826781474736 \tabularnewline
33 & 578 & 590.940298202399 & -12.9402982023992 \tabularnewline
34 & 565 & 580.166219772499 & -15.1662197724987 \tabularnewline
35 & 547 & 546.523936373711 & 0.476063626289374 \tabularnewline
36 & 555 & 541.930343368793 & 13.0696566312072 \tabularnewline
37 & 562 & 555.550047780436 & 6.44995221956435 \tabularnewline
38 & 561 & 555.890698958946 & 5.10930104105432 \tabularnewline
39 & 555 & 551.931457044903 & 3.06854295509697 \tabularnewline
40 & 544 & 548.462736569939 & -4.46273656993912 \tabularnewline
41 & 537 & 536.838876593712 & 0.161123406288198 \tabularnewline
42 & 543 & 540.342785030406 & 2.65721496959407 \tabularnewline
43 & 594 & 606.580432142004 & -12.5804321420038 \tabularnewline
44 & 611 & 614.784867324054 & -3.78486732405418 \tabularnewline
45 & 613 & 617.154246372086 & -4.15424637208571 \tabularnewline
46 & 611 & 609.393034492785 & 1.60696550721514 \tabularnewline
47 & 594 & 590.791840666605 & 3.2081593333952 \tabularnewline
48 & 595 & 593.558935712455 & 1.44106428754469 \tabularnewline
49 & 591 & 597.723180425056 & -6.72318042505606 \tabularnewline
50 & 589 & 588.992908003014 & 0.00709199698576413 \tabularnewline
51 & 584 & 579.82764356426 & 4.17235643573997 \tabularnewline
52 & 573 & 572.28285376094 & 0.717146239059502 \tabularnewline
53 & 567 & 564.502348264783 & 2.49765173521746 \tabularnewline
54 & 569 & 570.03951166734 & -1.03951166734009 \tabularnewline
55 & 621 & 629.440004697 & -8.44000469699927 \tabularnewline
56 & 629 & 644.140849730675 & -15.1408497306750 \tabularnewline
57 & 628 & 638.956021174525 & -10.9560211745252 \tabularnewline
58 & 612 & 628.337375525677 & -16.3373755256772 \tabularnewline
59 & 595 & 597.894877543472 & -2.89487754347158 \tabularnewline
60 & 597 & 594.012422639647 & 2.98757736035293 \tabularnewline
61 & 593 & 593.114305172382 & -0.114305172381705 \tabularnewline
62 & 590 & 589.021228229762 & 0.978771770238268 \tabularnewline
63 & 580 & 580.278248995199 & -0.278248995199078 \tabularnewline
64 & 574 & 566.720412757222 & 7.27958724277778 \tabularnewline
65 & 573 & 561.705546457029 & 11.2944535429713 \tabularnewline
66 & 573 & 569.330494152471 & 3.66950584752942 \tabularnewline
67 & 620 & 627.152635579839 & -7.1526355798386 \tabularnewline
68 & 626 & 638.449907212287 & -12.4499072122871 \tabularnewline
69 & 620 & 635.533751599433 & -15.5337515994333 \tabularnewline
70 & 588 & 618.647754874405 & -30.6477548744048 \tabularnewline
71 & 566 & 584.401715489263 & -18.4017154892629 \tabularnewline
72 & 557 & 571.71987540367 & -14.7198754036706 \tabularnewline
73 & 561 & 556.28432046314 & 4.71567953685974 \tabularnewline
74 & 549 & 552.413903995036 & -3.41390399503587 \tabularnewline
75 & 532 & 537.988317669999 & -5.98831766999888 \tabularnewline
76 & 526 & 521.76713898095 & 4.23286101904966 \tabularnewline
77 & 511 & 513.800564988936 & -2.80056498893566 \tabularnewline
78 & 499 & 506.211878883097 & -7.21187888309674 \tabularnewline
79 & 555 & 541.817899920436 & 13.1821000795644 \tabularnewline
80 & 565 & 556.52356786827 & 8.47643213173 \tabularnewline
81 & 542 & 560.404248347054 & -18.4042483470541 \tabularnewline
82 & 527 & 533.218076268099 & -6.21807626809903 \tabularnewline
83 & 510 & 516.741928476132 & -6.74192847613176 \tabularnewline
84 & 514 & 510.327113491383 & 3.67288650861724 \tabularnewline
85 & 517 & 512.580749386121 & 4.41925061387872 \tabularnewline
86 & 508 & 504.780909828342 & 3.21909017165774 \tabularnewline
87 & 493 & 493.305087308172 & -0.305087308171608 \tabularnewline
88 & 490 & 484.926002382029 & 5.07399761797126 \tabularnewline
89 & 469 & 474.965392741366 & -5.96539274136592 \tabularnewline
90 & 478 & 463.720572223338 & 14.2794277766620 \tabularnewline
91 & 528 & 518.212682876411 & 9.78731712358876 \tabularnewline
92 & 534 & 529.0924136205 & 4.90758637950012 \tabularnewline
93 & 518 & 520.117735768265 & -2.11773576826465 \tabularnewline
94 & 506 & 508.958853313268 & -2.95885331326770 \tabularnewline
95 & 502 & 495.76006630481 & 6.23993369518951 \tabularnewline
96 & 516 & 503.051774891344 & 12.9482251086557 \tabularnewline
97 & 528 & 513.254061326063 & 14.7459386739371 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41512&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]476[/C][C]465.269197541118[/C][C]10.7308024588818[/C][/ROW]
[ROW][C]14[/C][C]475[/C][C]470.610318136485[/C][C]4.38968186351536[/C][/ROW]
[ROW][C]15[/C][C]470[/C][C]469.514909097349[/C][C]0.485090902650995[/C][/ROW]
[ROW][C]16[/C][C]461[/C][C]462.154835841513[/C][C]-1.15483584151264[/C][/ROW]
[ROW][C]17[/C][C]455[/C][C]455.688271059507[/C][C]-0.688271059506519[/C][/ROW]
[ROW][C]18[/C][C]456[/C][C]455.488090672002[/C][C]0.5119093279975[/C][/ROW]
[ROW][C]19[/C][C]517[/C][C]506.518665783334[/C][C]10.4813342166659[/C][/ROW]
[ROW][C]20[/C][C]525[/C][C]541.980873253753[/C][C]-16.9808732537530[/C][/ROW]
[ROW][C]21[/C][C]523[/C][C]536.173392747286[/C][C]-13.1733927472857[/C][/ROW]
[ROW][C]22[/C][C]519[/C][C]518.319204046485[/C][C]0.68079595351503[/C][/ROW]
[ROW][C]23[/C][C]509[/C][C]485.738649471905[/C][C]23.2613505280948[/C][/ROW]
[ROW][C]24[/C][C]512[/C][C]499.641354500286[/C][C]12.3586454997137[/C][/ROW]
[ROW][C]25[/C][C]519[/C][C]517.839262962876[/C][C]1.16073703712357[/C][/ROW]
[ROW][C]26[/C][C]517[/C][C]515.634967962987[/C][C]1.36503203701307[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]511.431449157141[/C][C]-1.43144915714072[/C][/ROW]
[ROW][C]28[/C][C]509[/C][C]502.205951318738[/C][C]6.7940486812617[/C][/ROW]
[ROW][C]29[/C][C]501[/C][C]500.86750916928[/C][C]0.132490830719860[/C][/ROW]
[ROW][C]30[/C][C]507[/C][C]502.755450374614[/C][C]4.24454962538562[/C][/ROW]
[ROW][C]31[/C][C]569[/C][C]567.45371906746[/C][C]1.54628093254007[/C][/ROW]
[ROW][C]32[/C][C]580[/C][C]588.368267814747[/C][C]-8.36826781474736[/C][/ROW]
[ROW][C]33[/C][C]578[/C][C]590.940298202399[/C][C]-12.9402982023992[/C][/ROW]
[ROW][C]34[/C][C]565[/C][C]580.166219772499[/C][C]-15.1662197724987[/C][/ROW]
[ROW][C]35[/C][C]547[/C][C]546.523936373711[/C][C]0.476063626289374[/C][/ROW]
[ROW][C]36[/C][C]555[/C][C]541.930343368793[/C][C]13.0696566312072[/C][/ROW]
[ROW][C]37[/C][C]562[/C][C]555.550047780436[/C][C]6.44995221956435[/C][/ROW]
[ROW][C]38[/C][C]561[/C][C]555.890698958946[/C][C]5.10930104105432[/C][/ROW]
[ROW][C]39[/C][C]555[/C][C]551.931457044903[/C][C]3.06854295509697[/C][/ROW]
[ROW][C]40[/C][C]544[/C][C]548.462736569939[/C][C]-4.46273656993912[/C][/ROW]
[ROW][C]41[/C][C]537[/C][C]536.838876593712[/C][C]0.161123406288198[/C][/ROW]
[ROW][C]42[/C][C]543[/C][C]540.342785030406[/C][C]2.65721496959407[/C][/ROW]
[ROW][C]43[/C][C]594[/C][C]606.580432142004[/C][C]-12.5804321420038[/C][/ROW]
[ROW][C]44[/C][C]611[/C][C]614.784867324054[/C][C]-3.78486732405418[/C][/ROW]
[ROW][C]45[/C][C]613[/C][C]617.154246372086[/C][C]-4.15424637208571[/C][/ROW]
[ROW][C]46[/C][C]611[/C][C]609.393034492785[/C][C]1.60696550721514[/C][/ROW]
[ROW][C]47[/C][C]594[/C][C]590.791840666605[/C][C]3.2081593333952[/C][/ROW]
[ROW][C]48[/C][C]595[/C][C]593.558935712455[/C][C]1.44106428754469[/C][/ROW]
[ROW][C]49[/C][C]591[/C][C]597.723180425056[/C][C]-6.72318042505606[/C][/ROW]
[ROW][C]50[/C][C]589[/C][C]588.992908003014[/C][C]0.00709199698576413[/C][/ROW]
[ROW][C]51[/C][C]584[/C][C]579.82764356426[/C][C]4.17235643573997[/C][/ROW]
[ROW][C]52[/C][C]573[/C][C]572.28285376094[/C][C]0.717146239059502[/C][/ROW]
[ROW][C]53[/C][C]567[/C][C]564.502348264783[/C][C]2.49765173521746[/C][/ROW]
[ROW][C]54[/C][C]569[/C][C]570.03951166734[/C][C]-1.03951166734009[/C][/ROW]
[ROW][C]55[/C][C]621[/C][C]629.440004697[/C][C]-8.44000469699927[/C][/ROW]
[ROW][C]56[/C][C]629[/C][C]644.140849730675[/C][C]-15.1408497306750[/C][/ROW]
[ROW][C]57[/C][C]628[/C][C]638.956021174525[/C][C]-10.9560211745252[/C][/ROW]
[ROW][C]58[/C][C]612[/C][C]628.337375525677[/C][C]-16.3373755256772[/C][/ROW]
[ROW][C]59[/C][C]595[/C][C]597.894877543472[/C][C]-2.89487754347158[/C][/ROW]
[ROW][C]60[/C][C]597[/C][C]594.012422639647[/C][C]2.98757736035293[/C][/ROW]
[ROW][C]61[/C][C]593[/C][C]593.114305172382[/C][C]-0.114305172381705[/C][/ROW]
[ROW][C]62[/C][C]590[/C][C]589.021228229762[/C][C]0.978771770238268[/C][/ROW]
[ROW][C]63[/C][C]580[/C][C]580.278248995199[/C][C]-0.278248995199078[/C][/ROW]
[ROW][C]64[/C][C]574[/C][C]566.720412757222[/C][C]7.27958724277778[/C][/ROW]
[ROW][C]65[/C][C]573[/C][C]561.705546457029[/C][C]11.2944535429713[/C][/ROW]
[ROW][C]66[/C][C]573[/C][C]569.330494152471[/C][C]3.66950584752942[/C][/ROW]
[ROW][C]67[/C][C]620[/C][C]627.152635579839[/C][C]-7.1526355798386[/C][/ROW]
[ROW][C]68[/C][C]626[/C][C]638.449907212287[/C][C]-12.4499072122871[/C][/ROW]
[ROW][C]69[/C][C]620[/C][C]635.533751599433[/C][C]-15.5337515994333[/C][/ROW]
[ROW][C]70[/C][C]588[/C][C]618.647754874405[/C][C]-30.6477548744048[/C][/ROW]
[ROW][C]71[/C][C]566[/C][C]584.401715489263[/C][C]-18.4017154892629[/C][/ROW]
[ROW][C]72[/C][C]557[/C][C]571.71987540367[/C][C]-14.7198754036706[/C][/ROW]
[ROW][C]73[/C][C]561[/C][C]556.28432046314[/C][C]4.71567953685974[/C][/ROW]
[ROW][C]74[/C][C]549[/C][C]552.413903995036[/C][C]-3.41390399503587[/C][/ROW]
[ROW][C]75[/C][C]532[/C][C]537.988317669999[/C][C]-5.98831766999888[/C][/ROW]
[ROW][C]76[/C][C]526[/C][C]521.76713898095[/C][C]4.23286101904966[/C][/ROW]
[ROW][C]77[/C][C]511[/C][C]513.800564988936[/C][C]-2.80056498893566[/C][/ROW]
[ROW][C]78[/C][C]499[/C][C]506.211878883097[/C][C]-7.21187888309674[/C][/ROW]
[ROW][C]79[/C][C]555[/C][C]541.817899920436[/C][C]13.1821000795644[/C][/ROW]
[ROW][C]80[/C][C]565[/C][C]556.52356786827[/C][C]8.47643213173[/C][/ROW]
[ROW][C]81[/C][C]542[/C][C]560.404248347054[/C][C]-18.4042483470541[/C][/ROW]
[ROW][C]82[/C][C]527[/C][C]533.218076268099[/C][C]-6.21807626809903[/C][/ROW]
[ROW][C]83[/C][C]510[/C][C]516.741928476132[/C][C]-6.74192847613176[/C][/ROW]
[ROW][C]84[/C][C]514[/C][C]510.327113491383[/C][C]3.67288650861724[/C][/ROW]
[ROW][C]85[/C][C]517[/C][C]512.580749386121[/C][C]4.41925061387872[/C][/ROW]
[ROW][C]86[/C][C]508[/C][C]504.780909828342[/C][C]3.21909017165774[/C][/ROW]
[ROW][C]87[/C][C]493[/C][C]493.305087308172[/C][C]-0.305087308171608[/C][/ROW]
[ROW][C]88[/C][C]490[/C][C]484.926002382029[/C][C]5.07399761797126[/C][/ROW]
[ROW][C]89[/C][C]469[/C][C]474.965392741366[/C][C]-5.96539274136592[/C][/ROW]
[ROW][C]90[/C][C]478[/C][C]463.720572223338[/C][C]14.2794277766620[/C][/ROW]
[ROW][C]91[/C][C]528[/C][C]518.212682876411[/C][C]9.78731712358876[/C][/ROW]
[ROW][C]92[/C][C]534[/C][C]529.0924136205[/C][C]4.90758637950012[/C][/ROW]
[ROW][C]93[/C][C]518[/C][C]520.117735768265[/C][C]-2.11773576826465[/C][/ROW]
[ROW][C]94[/C][C]506[/C][C]508.958853313268[/C][C]-2.95885331326770[/C][/ROW]
[ROW][C]95[/C][C]502[/C][C]495.76006630481[/C][C]6.23993369518951[/C][/ROW]
[ROW][C]96[/C][C]516[/C][C]503.051774891344[/C][C]12.9482251086557[/C][/ROW]
[ROW][C]97[/C][C]528[/C][C]513.254061326063[/C][C]14.7459386739371[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41512&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41512&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
13476465.26919754111810.7308024588818
14475470.6103181364854.38968186351536
15470469.5149090973490.485090902650995
16461462.154835841513-1.15483584151264
17455455.688271059507-0.688271059506519
18456455.4880906720020.5119093279975
19517506.51866578333410.4813342166659
20525541.980873253753-16.9808732537530
21523536.173392747286-13.1733927472857
22519518.3192040464850.68079595351503
23509485.73864947190523.2613505280948
24512499.64135450028612.3586454997137
25519517.8392629628761.16073703712357
26517515.6349679629871.36503203701307
27510511.431449157141-1.43144915714072
28509502.2059513187386.7940486812617
29501500.867509169280.132490830719860
30507502.7554503746144.24454962538562
31569567.453719067461.54628093254007
32580588.368267814747-8.36826781474736
33578590.940298202399-12.9402982023992
34565580.166219772499-15.1662197724987
35547546.5239363737110.476063626289374
36555541.93034336879313.0696566312072
37562555.5500477804366.44995221956435
38561555.8906989589465.10930104105432
39555551.9314570449033.06854295509697
40544548.462736569939-4.46273656993912
41537536.8388765937120.161123406288198
42543540.3427850304062.65721496959407
43594606.580432142004-12.5804321420038
44611614.784867324054-3.78486732405418
45613617.154246372086-4.15424637208571
46611609.3930344927851.60696550721514
47594590.7918406666053.2081593333952
48595593.5589357124551.44106428754469
49591597.723180425056-6.72318042505606
50589588.9929080030140.00709199698576413
51584579.827643564264.17235643573997
52573572.282853760940.717146239059502
53567564.5023482647832.49765173521746
54569570.03951166734-1.03951166734009
55621629.440004697-8.44000469699927
56629644.140849730675-15.1408497306750
57628638.956021174525-10.9560211745252
58612628.337375525677-16.3373755256772
59595597.894877543472-2.89487754347158
60597594.0124226396472.98757736035293
61593593.114305172382-0.114305172381705
62590589.0212282297620.978771770238268
63580580.278248995199-0.278248995199078
64574566.7204127572227.27958724277778
65573561.70554645702911.2944535429713
66573569.3304941524713.66950584752942
67620627.152635579839-7.1526355798386
68626638.449907212287-12.4499072122871
69620635.533751599433-15.5337515994333
70588618.647754874405-30.6477548744048
71566584.401715489263-18.4017154892629
72557571.71987540367-14.7198754036706
73561556.284320463144.71567953685974
74549552.413903995036-3.41390399503587
75532537.988317669999-5.98831766999888
76526521.767138980954.23286101904966
77511513.800564988936-2.80056498893566
78499506.211878883097-7.21187888309674
79555541.81789992043613.1821000795644
80565556.523567868278.47643213173
81542560.404248347054-18.4042483470541
82527533.218076268099-6.21807626809903
83510516.741928476132-6.74192847613176
84514510.3271134913833.67288650861724
85517512.5807493861214.41925061387872
86508504.7809098283423.21909017165774
87493493.305087308172-0.305087308171608
88490484.9260023820295.07399761797126
89469474.965392741366-5.96539274136592
90478463.72057222333814.2794277766620
91528518.2126828764119.78731712358876
92534529.09241362054.90758637950012
93518520.117735768265-2.11773576826465
94506508.958853313268-2.95885331326770
95502495.760066304816.23993369518951
96516503.05177489134412.9482251086557
97528513.25406132606314.7459386739371







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
98513.567323657776495.706964982874531.427682332679
99501.286574407515480.48396057643522.0891882386
100498.046386059857474.217344626514521.875427493201
101482.49717156837456.003689453227508.990653683512
102486.130049200579456.32092534526515.939173055897
103533.534687009506498.173975110009568.895398909003
104538.516658372643499.470365020603577.562951724683
105525.023239660407483.370200731166566.676278589647
106516.074263852053471.554149860144560.594377843962
107510.061725604094462.463442070661557.660009137526
108518.174265982155466.245980490147570.102551474164
109522.511828362385455.514249522678589.509407202092

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
98 & 513.567323657776 & 495.706964982874 & 531.427682332679 \tabularnewline
99 & 501.286574407515 & 480.48396057643 & 522.0891882386 \tabularnewline
100 & 498.046386059857 & 474.217344626514 & 521.875427493201 \tabularnewline
101 & 482.49717156837 & 456.003689453227 & 508.990653683512 \tabularnewline
102 & 486.130049200579 & 456.32092534526 & 515.939173055897 \tabularnewline
103 & 533.534687009506 & 498.173975110009 & 568.895398909003 \tabularnewline
104 & 538.516658372643 & 499.470365020603 & 577.562951724683 \tabularnewline
105 & 525.023239660407 & 483.370200731166 & 566.676278589647 \tabularnewline
106 & 516.074263852053 & 471.554149860144 & 560.594377843962 \tabularnewline
107 & 510.061725604094 & 462.463442070661 & 557.660009137526 \tabularnewline
108 & 518.174265982155 & 466.245980490147 & 570.102551474164 \tabularnewline
109 & 522.511828362385 & 455.514249522678 & 589.509407202092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41512&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]98[/C][C]513.567323657776[/C][C]495.706964982874[/C][C]531.427682332679[/C][/ROW]
[ROW][C]99[/C][C]501.286574407515[/C][C]480.48396057643[/C][C]522.0891882386[/C][/ROW]
[ROW][C]100[/C][C]498.046386059857[/C][C]474.217344626514[/C][C]521.875427493201[/C][/ROW]
[ROW][C]101[/C][C]482.49717156837[/C][C]456.003689453227[/C][C]508.990653683512[/C][/ROW]
[ROW][C]102[/C][C]486.130049200579[/C][C]456.32092534526[/C][C]515.939173055897[/C][/ROW]
[ROW][C]103[/C][C]533.534687009506[/C][C]498.173975110009[/C][C]568.895398909003[/C][/ROW]
[ROW][C]104[/C][C]538.516658372643[/C][C]499.470365020603[/C][C]577.562951724683[/C][/ROW]
[ROW][C]105[/C][C]525.023239660407[/C][C]483.370200731166[/C][C]566.676278589647[/C][/ROW]
[ROW][C]106[/C][C]516.074263852053[/C][C]471.554149860144[/C][C]560.594377843962[/C][/ROW]
[ROW][C]107[/C][C]510.061725604094[/C][C]462.463442070661[/C][C]557.660009137526[/C][/ROW]
[ROW][C]108[/C][C]518.174265982155[/C][C]466.245980490147[/C][C]570.102551474164[/C][/ROW]
[ROW][C]109[/C][C]522.511828362385[/C][C]455.514249522678[/C][C]589.509407202092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41512&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41512&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
98513.567323657776495.706964982874531.427682332679
99501.286574407515480.48396057643522.0891882386
100498.046386059857474.217344626514521.875427493201
101482.49717156837456.003689453227508.990653683512
102486.130049200579456.32092534526515.939173055897
103533.534687009506498.173975110009568.895398909003
104538.516658372643499.470365020603577.562951724683
105525.023239660407483.370200731166566.676278589647
106516.074263852053471.554149860144560.594377843962
107510.061725604094462.463442070661557.660009137526
108518.174265982155466.245980490147570.102551474164
109522.511828362385455.514249522678589.509407202092



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')