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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, 02 Jun 2010 08:51:22 +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/Jun/02/t1275468764urz354lhuhh7pgr.htm/, Retrieved Thu, 28 Mar 2024 15:10:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76921, Retrieved Thu, 28 Mar 2024 15:10:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opgave 10 oefening 1] [2010-01-19 17:45:21] [acb4d9171c10fb50d016574efb6916c7]
-    D    [Exponential Smoothing] [Maandelijkse cijf...] [2010-06-02 08:51:22] [26ddb8a30b965ed6738d4d4bc4c527d5] [Current]
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Dataseries X:
580
575
558
564
581
597
587
536
524
537
536
533
528
516
502
506
518
534
528
478
469
490
493
508
517
514
510
527
542
565
555
499
511
526
532
549
561
557
566
588
620
626
620
573
573
574
580
590
593
597
595
612
628
629
621
569
567
573
584
589
591
595
594
611
613
611
594
543
537
544
555
561
562




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76921&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76921&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76921&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.811699206863691
beta0.698542100789111
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.811699206863691 \tabularnewline
beta & 0.698542100789111 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76921&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]0.811699206863691[/C][/ROW]
[ROW][C]beta[/C][C]0.698542100789111[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76921&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76921&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
alpha0.811699206863691
beta0.698542100789111
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13528557.922684722142-29.9226847221424
14516504.98523942639211.0147605736081
15502489.66392793047412.3360720695259
16506499.8283506643136.17164933568688
17518515.9721879778012.02781202219933
18534532.9705978173961.02940218260392
19528531.104441925337-3.10444192533748
20478482.285441358656-4.28544135865587
21469465.4325945940733.56740540592727
22490479.25900522863510.7409947713649
23493492.8464428830260.153557116974355
24508496.34878055420311.6512194457973
25517508.3768697354638.62313026453728
26514528.589728203554-14.5897282035536
27510511.985660040853-1.98566004085342
28527520.7833929513836.21660704861677
29542548.437020320311-6.43702032031149
30565566.40612780695-1.40612780695005
31555567.485189897755-12.4851898977553
32499508.858460230444-9.85846023044382
33511485.95294761576525.0470523842353
34526529.655536278595-3.65553627859458
35532531.2683300645690.731669935431455
36549539.6184537292429.38154627075812
37561549.3598082010411.6401917989602
38557569.553232218153-12.5532322181531
39566559.723013681916.27698631809051
40588585.85507924792.14492075210023
41620615.323553188124.67644681188051
42626658.955127329477-32.9551273294775
43620626.880318524231-6.88031852423103
44573566.2064582028696.79354179713096
45573570.9923896961452.0076103038549
46574586.461483491403-12.4614834914028
47580571.2483244222978.7516755777026
48590581.9669687994968.0330312005043
49593583.5889580212329.41104197876837
50597588.7592689243868.24073107561446
51595602.668128288203-7.66812828820298
52612612.783174609366-0.783174609365915
53628634.76138608244-6.76138608243957
54629648.972535709871-19.9725357098707
55621626.481679579038-5.48167957903843
56569564.6468711905174.35312880948345
57567560.4450697441886.55493025581222
58573573.091463343326-0.0914633433263816
59584575.3096847238728.69031527612822
60589589.270115136402-0.270115136401614
61591583.1100895414347.88991045856551
62595584.73069131110610.2693086888941
63594596.339202920928-2.33920292092773
64611614.130133911347-3.13013391134746
65613633.807436630685-20.8074366306846
66611626.402002233322-15.402002233322
67594605.333710089779-11.3337100897794
68543534.7734958421948.22650415780572
69537528.6438466707088.3561533292924
70544536.4077671255817.59223287441876
71555545.8930274767159.10697252328453
72561558.3201508564242.67984914357612
73562558.0290405143683.97095948563231

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 528 & 557.922684722142 & -29.9226847221424 \tabularnewline
14 & 516 & 504.985239426392 & 11.0147605736081 \tabularnewline
15 & 502 & 489.663927930474 & 12.3360720695259 \tabularnewline
16 & 506 & 499.828350664313 & 6.17164933568688 \tabularnewline
17 & 518 & 515.972187977801 & 2.02781202219933 \tabularnewline
18 & 534 & 532.970597817396 & 1.02940218260392 \tabularnewline
19 & 528 & 531.104441925337 & -3.10444192533748 \tabularnewline
20 & 478 & 482.285441358656 & -4.28544135865587 \tabularnewline
21 & 469 & 465.432594594073 & 3.56740540592727 \tabularnewline
22 & 490 & 479.259005228635 & 10.7409947713649 \tabularnewline
23 & 493 & 492.846442883026 & 0.153557116974355 \tabularnewline
24 & 508 & 496.348780554203 & 11.6512194457973 \tabularnewline
25 & 517 & 508.376869735463 & 8.62313026453728 \tabularnewline
26 & 514 & 528.589728203554 & -14.5897282035536 \tabularnewline
27 & 510 & 511.985660040853 & -1.98566004085342 \tabularnewline
28 & 527 & 520.783392951383 & 6.21660704861677 \tabularnewline
29 & 542 & 548.437020320311 & -6.43702032031149 \tabularnewline
30 & 565 & 566.40612780695 & -1.40612780695005 \tabularnewline
31 & 555 & 567.485189897755 & -12.4851898977553 \tabularnewline
32 & 499 & 508.858460230444 & -9.85846023044382 \tabularnewline
33 & 511 & 485.952947615765 & 25.0470523842353 \tabularnewline
34 & 526 & 529.655536278595 & -3.65553627859458 \tabularnewline
35 & 532 & 531.268330064569 & 0.731669935431455 \tabularnewline
36 & 549 & 539.618453729242 & 9.38154627075812 \tabularnewline
37 & 561 & 549.35980820104 & 11.6401917989602 \tabularnewline
38 & 557 & 569.553232218153 & -12.5532322181531 \tabularnewline
39 & 566 & 559.72301368191 & 6.27698631809051 \tabularnewline
40 & 588 & 585.8550792479 & 2.14492075210023 \tabularnewline
41 & 620 & 615.32355318812 & 4.67644681188051 \tabularnewline
42 & 626 & 658.955127329477 & -32.9551273294775 \tabularnewline
43 & 620 & 626.880318524231 & -6.88031852423103 \tabularnewline
44 & 573 & 566.206458202869 & 6.79354179713096 \tabularnewline
45 & 573 & 570.992389696145 & 2.0076103038549 \tabularnewline
46 & 574 & 586.461483491403 & -12.4614834914028 \tabularnewline
47 & 580 & 571.248324422297 & 8.7516755777026 \tabularnewline
48 & 590 & 581.966968799496 & 8.0330312005043 \tabularnewline
49 & 593 & 583.588958021232 & 9.41104197876837 \tabularnewline
50 & 597 & 588.759268924386 & 8.24073107561446 \tabularnewline
51 & 595 & 602.668128288203 & -7.66812828820298 \tabularnewline
52 & 612 & 612.783174609366 & -0.783174609365915 \tabularnewline
53 & 628 & 634.76138608244 & -6.76138608243957 \tabularnewline
54 & 629 & 648.972535709871 & -19.9725357098707 \tabularnewline
55 & 621 & 626.481679579038 & -5.48167957903843 \tabularnewline
56 & 569 & 564.646871190517 & 4.35312880948345 \tabularnewline
57 & 567 & 560.445069744188 & 6.55493025581222 \tabularnewline
58 & 573 & 573.091463343326 & -0.0914633433263816 \tabularnewline
59 & 584 & 575.309684723872 & 8.69031527612822 \tabularnewline
60 & 589 & 589.270115136402 & -0.270115136401614 \tabularnewline
61 & 591 & 583.110089541434 & 7.88991045856551 \tabularnewline
62 & 595 & 584.730691311106 & 10.2693086888941 \tabularnewline
63 & 594 & 596.339202920928 & -2.33920292092773 \tabularnewline
64 & 611 & 614.130133911347 & -3.13013391134746 \tabularnewline
65 & 613 & 633.807436630685 & -20.8074366306846 \tabularnewline
66 & 611 & 626.402002233322 & -15.402002233322 \tabularnewline
67 & 594 & 605.333710089779 & -11.3337100897794 \tabularnewline
68 & 543 & 534.773495842194 & 8.22650415780572 \tabularnewline
69 & 537 & 528.643846670708 & 8.3561533292924 \tabularnewline
70 & 544 & 536.407767125581 & 7.59223287441876 \tabularnewline
71 & 555 & 545.893027476715 & 9.10697252328453 \tabularnewline
72 & 561 & 558.320150856424 & 2.67984914357612 \tabularnewline
73 & 562 & 558.029040514368 & 3.97095948563231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76921&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]528[/C][C]557.922684722142[/C][C]-29.9226847221424[/C][/ROW]
[ROW][C]14[/C][C]516[/C][C]504.985239426392[/C][C]11.0147605736081[/C][/ROW]
[ROW][C]15[/C][C]502[/C][C]489.663927930474[/C][C]12.3360720695259[/C][/ROW]
[ROW][C]16[/C][C]506[/C][C]499.828350664313[/C][C]6.17164933568688[/C][/ROW]
[ROW][C]17[/C][C]518[/C][C]515.972187977801[/C][C]2.02781202219933[/C][/ROW]
[ROW][C]18[/C][C]534[/C][C]532.970597817396[/C][C]1.02940218260392[/C][/ROW]
[ROW][C]19[/C][C]528[/C][C]531.104441925337[/C][C]-3.10444192533748[/C][/ROW]
[ROW][C]20[/C][C]478[/C][C]482.285441358656[/C][C]-4.28544135865587[/C][/ROW]
[ROW][C]21[/C][C]469[/C][C]465.432594594073[/C][C]3.56740540592727[/C][/ROW]
[ROW][C]22[/C][C]490[/C][C]479.259005228635[/C][C]10.7409947713649[/C][/ROW]
[ROW][C]23[/C][C]493[/C][C]492.846442883026[/C][C]0.153557116974355[/C][/ROW]
[ROW][C]24[/C][C]508[/C][C]496.348780554203[/C][C]11.6512194457973[/C][/ROW]
[ROW][C]25[/C][C]517[/C][C]508.376869735463[/C][C]8.62313026453728[/C][/ROW]
[ROW][C]26[/C][C]514[/C][C]528.589728203554[/C][C]-14.5897282035536[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]511.985660040853[/C][C]-1.98566004085342[/C][/ROW]
[ROW][C]28[/C][C]527[/C][C]520.783392951383[/C][C]6.21660704861677[/C][/ROW]
[ROW][C]29[/C][C]542[/C][C]548.437020320311[/C][C]-6.43702032031149[/C][/ROW]
[ROW][C]30[/C][C]565[/C][C]566.40612780695[/C][C]-1.40612780695005[/C][/ROW]
[ROW][C]31[/C][C]555[/C][C]567.485189897755[/C][C]-12.4851898977553[/C][/ROW]
[ROW][C]32[/C][C]499[/C][C]508.858460230444[/C][C]-9.85846023044382[/C][/ROW]
[ROW][C]33[/C][C]511[/C][C]485.952947615765[/C][C]25.0470523842353[/C][/ROW]
[ROW][C]34[/C][C]526[/C][C]529.655536278595[/C][C]-3.65553627859458[/C][/ROW]
[ROW][C]35[/C][C]532[/C][C]531.268330064569[/C][C]0.731669935431455[/C][/ROW]
[ROW][C]36[/C][C]549[/C][C]539.618453729242[/C][C]9.38154627075812[/C][/ROW]
[ROW][C]37[/C][C]561[/C][C]549.35980820104[/C][C]11.6401917989602[/C][/ROW]
[ROW][C]38[/C][C]557[/C][C]569.553232218153[/C][C]-12.5532322181531[/C][/ROW]
[ROW][C]39[/C][C]566[/C][C]559.72301368191[/C][C]6.27698631809051[/C][/ROW]
[ROW][C]40[/C][C]588[/C][C]585.8550792479[/C][C]2.14492075210023[/C][/ROW]
[ROW][C]41[/C][C]620[/C][C]615.32355318812[/C][C]4.67644681188051[/C][/ROW]
[ROW][C]42[/C][C]626[/C][C]658.955127329477[/C][C]-32.9551273294775[/C][/ROW]
[ROW][C]43[/C][C]620[/C][C]626.880318524231[/C][C]-6.88031852423103[/C][/ROW]
[ROW][C]44[/C][C]573[/C][C]566.206458202869[/C][C]6.79354179713096[/C][/ROW]
[ROW][C]45[/C][C]573[/C][C]570.992389696145[/C][C]2.0076103038549[/C][/ROW]
[ROW][C]46[/C][C]574[/C][C]586.461483491403[/C][C]-12.4614834914028[/C][/ROW]
[ROW][C]47[/C][C]580[/C][C]571.248324422297[/C][C]8.7516755777026[/C][/ROW]
[ROW][C]48[/C][C]590[/C][C]581.966968799496[/C][C]8.0330312005043[/C][/ROW]
[ROW][C]49[/C][C]593[/C][C]583.588958021232[/C][C]9.41104197876837[/C][/ROW]
[ROW][C]50[/C][C]597[/C][C]588.759268924386[/C][C]8.24073107561446[/C][/ROW]
[ROW][C]51[/C][C]595[/C][C]602.668128288203[/C][C]-7.66812828820298[/C][/ROW]
[ROW][C]52[/C][C]612[/C][C]612.783174609366[/C][C]-0.783174609365915[/C][/ROW]
[ROW][C]53[/C][C]628[/C][C]634.76138608244[/C][C]-6.76138608243957[/C][/ROW]
[ROW][C]54[/C][C]629[/C][C]648.972535709871[/C][C]-19.9725357098707[/C][/ROW]
[ROW][C]55[/C][C]621[/C][C]626.481679579038[/C][C]-5.48167957903843[/C][/ROW]
[ROW][C]56[/C][C]569[/C][C]564.646871190517[/C][C]4.35312880948345[/C][/ROW]
[ROW][C]57[/C][C]567[/C][C]560.445069744188[/C][C]6.55493025581222[/C][/ROW]
[ROW][C]58[/C][C]573[/C][C]573.091463343326[/C][C]-0.0914633433263816[/C][/ROW]
[ROW][C]59[/C][C]584[/C][C]575.309684723872[/C][C]8.69031527612822[/C][/ROW]
[ROW][C]60[/C][C]589[/C][C]589.270115136402[/C][C]-0.270115136401614[/C][/ROW]
[ROW][C]61[/C][C]591[/C][C]583.110089541434[/C][C]7.88991045856551[/C][/ROW]
[ROW][C]62[/C][C]595[/C][C]584.730691311106[/C][C]10.2693086888941[/C][/ROW]
[ROW][C]63[/C][C]594[/C][C]596.339202920928[/C][C]-2.33920292092773[/C][/ROW]
[ROW][C]64[/C][C]611[/C][C]614.130133911347[/C][C]-3.13013391134746[/C][/ROW]
[ROW][C]65[/C][C]613[/C][C]633.807436630685[/C][C]-20.8074366306846[/C][/ROW]
[ROW][C]66[/C][C]611[/C][C]626.402002233322[/C][C]-15.402002233322[/C][/ROW]
[ROW][C]67[/C][C]594[/C][C]605.333710089779[/C][C]-11.3337100897794[/C][/ROW]
[ROW][C]68[/C][C]543[/C][C]534.773495842194[/C][C]8.22650415780572[/C][/ROW]
[ROW][C]69[/C][C]537[/C][C]528.643846670708[/C][C]8.3561533292924[/C][/ROW]
[ROW][C]70[/C][C]544[/C][C]536.407767125581[/C][C]7.59223287441876[/C][/ROW]
[ROW][C]71[/C][C]555[/C][C]545.893027476715[/C][C]9.10697252328453[/C][/ROW]
[ROW][C]72[/C][C]561[/C][C]558.320150856424[/C][C]2.67984914357612[/C][/ROW]
[ROW][C]73[/C][C]562[/C][C]558.029040514368[/C][C]3.97095948563231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76921&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76921&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
13528557.922684722142-29.9226847221424
14516504.98523942639211.0147605736081
15502489.66392793047412.3360720695259
16506499.8283506643136.17164933568688
17518515.9721879778012.02781202219933
18534532.9705978173961.02940218260392
19528531.104441925337-3.10444192533748
20478482.285441358656-4.28544135865587
21469465.4325945940733.56740540592727
22490479.25900522863510.7409947713649
23493492.8464428830260.153557116974355
24508496.34878055420311.6512194457973
25517508.3768697354638.62313026453728
26514528.589728203554-14.5897282035536
27510511.985660040853-1.98566004085342
28527520.7833929513836.21660704861677
29542548.437020320311-6.43702032031149
30565566.40612780695-1.40612780695005
31555567.485189897755-12.4851898977553
32499508.858460230444-9.85846023044382
33511485.95294761576525.0470523842353
34526529.655536278595-3.65553627859458
35532531.2683300645690.731669935431455
36549539.6184537292429.38154627075812
37561549.3598082010411.6401917989602
38557569.553232218153-12.5532322181531
39566559.723013681916.27698631809051
40588585.85507924792.14492075210023
41620615.323553188124.67644681188051
42626658.955127329477-32.9551273294775
43620626.880318524231-6.88031852423103
44573566.2064582028696.79354179713096
45573570.9923896961452.0076103038549
46574586.461483491403-12.4614834914028
47580571.2483244222978.7516755777026
48590581.9669687994968.0330312005043
49593583.5889580212329.41104197876837
50597588.7592689243868.24073107561446
51595602.668128288203-7.66812828820298
52612612.783174609366-0.783174609365915
53628634.76138608244-6.76138608243957
54629648.972535709871-19.9725357098707
55621626.481679579038-5.48167957903843
56569564.6468711905174.35312880948345
57567560.4450697441886.55493025581222
58573573.091463343326-0.0914633433263816
59584575.3096847238728.69031527612822
60589589.270115136402-0.270115136401614
61591583.1100895414347.88991045856551
62595584.73069131110610.2693086888941
63594596.339202920928-2.33920292092773
64611614.130133911347-3.13013391134746
65613633.807436630685-20.8074366306846
66611626.402002233322-15.402002233322
67594605.333710089779-11.3337100897794
68543534.7734958421948.22650415780572
69537528.6438466707088.3561533292924
70544536.4077671255817.59223287441876
71555545.8930274767159.10697252328453
72561558.3201508564242.67984914357612
73562558.0290405143683.97095948563231







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74556.846094315295535.968093672714577.724094957877
75552.109219829979516.917706840608587.300732819349
76565.915888503798511.615199170959620.216577836638
77580.581005338465503.573374408028657.588636268902
78598.884428951282495.397014171471702.371843731094
79608.429558402593477.065378531278739.793738273908
80572.074063850002422.261660783816721.886466916188
81576.959654924434397.978196574608755.94111327426
82591.640772587362378.176151978137805.105393196587
83604.903714443352354.81661333167854.990815555034
84612.822622438737326.074549841523899.57069503595
85612.463691973161292.119083229454932.808300716867

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 556.846094315295 & 535.968093672714 & 577.724094957877 \tabularnewline
75 & 552.109219829979 & 516.917706840608 & 587.300732819349 \tabularnewline
76 & 565.915888503798 & 511.615199170959 & 620.216577836638 \tabularnewline
77 & 580.581005338465 & 503.573374408028 & 657.588636268902 \tabularnewline
78 & 598.884428951282 & 495.397014171471 & 702.371843731094 \tabularnewline
79 & 608.429558402593 & 477.065378531278 & 739.793738273908 \tabularnewline
80 & 572.074063850002 & 422.261660783816 & 721.886466916188 \tabularnewline
81 & 576.959654924434 & 397.978196574608 & 755.94111327426 \tabularnewline
82 & 591.640772587362 & 378.176151978137 & 805.105393196587 \tabularnewline
83 & 604.903714443352 & 354.81661333167 & 854.990815555034 \tabularnewline
84 & 612.822622438737 & 326.074549841523 & 899.57069503595 \tabularnewline
85 & 612.463691973161 & 292.119083229454 & 932.808300716867 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76921&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]74[/C][C]556.846094315295[/C][C]535.968093672714[/C][C]577.724094957877[/C][/ROW]
[ROW][C]75[/C][C]552.109219829979[/C][C]516.917706840608[/C][C]587.300732819349[/C][/ROW]
[ROW][C]76[/C][C]565.915888503798[/C][C]511.615199170959[/C][C]620.216577836638[/C][/ROW]
[ROW][C]77[/C][C]580.581005338465[/C][C]503.573374408028[/C][C]657.588636268902[/C][/ROW]
[ROW][C]78[/C][C]598.884428951282[/C][C]495.397014171471[/C][C]702.371843731094[/C][/ROW]
[ROW][C]79[/C][C]608.429558402593[/C][C]477.065378531278[/C][C]739.793738273908[/C][/ROW]
[ROW][C]80[/C][C]572.074063850002[/C][C]422.261660783816[/C][C]721.886466916188[/C][/ROW]
[ROW][C]81[/C][C]576.959654924434[/C][C]397.978196574608[/C][C]755.94111327426[/C][/ROW]
[ROW][C]82[/C][C]591.640772587362[/C][C]378.176151978137[/C][C]805.105393196587[/C][/ROW]
[ROW][C]83[/C][C]604.903714443352[/C][C]354.81661333167[/C][C]854.990815555034[/C][/ROW]
[ROW][C]84[/C][C]612.822622438737[/C][C]326.074549841523[/C][C]899.57069503595[/C][/ROW]
[ROW][C]85[/C][C]612.463691973161[/C][C]292.119083229454[/C][C]932.808300716867[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76921&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76921&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
74556.846094315295535.968093672714577.724094957877
75552.109219829979516.917706840608587.300732819349
76565.915888503798511.615199170959620.216577836638
77580.581005338465503.573374408028657.588636268902
78598.884428951282495.397014171471702.371843731094
79608.429558402593477.065378531278739.793738273908
80572.074063850002422.261660783816721.886466916188
81576.959654924434397.978196574608755.94111327426
82591.640772587362378.176151978137805.105393196587
83604.903714443352354.81661333167854.990815555034
84612.822622438737326.074549841523899.57069503595
85612.463691973161292.119083229454932.808300716867



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')