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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 13 Dec 2012 11:03:07 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/13/t13554147588i12doxmtnmck6d.htm/, Retrieved Mon, 29 Apr 2024 00:35:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=199302, Retrieved Mon, 29 Apr 2024 00:35:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:59:32] [74be16979710d4c4e7c6647856088456]
- RMPD  [Exponential Smoothing] [] [2010-12-08 19:04:28] [bcc4ad4a6c0f95d5b548de29638ac6c2]
- R PD      [Exponential Smoothing] [exponential smoot...] [2012-12-13 16:03:07] [397a0972e70513d74eb96ad1976c3720] [Current]
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Dataseries X:
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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199302&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199302&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.948539541872876
beta0.106971000311536
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.948539541872876 \tabularnewline
beta & 0.106971000311536 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199302&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]0.948539541872876[/C][/ROW]
[ROW][C]beta[/C][C]0.106971000311536[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199302&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
alpha0.948539541872876
beta0.106971000311536
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13562542.60375360456519.3962463954354
14561562.678933206395-1.67893320639473
15555557.137124532184-2.13712453218363
16544545.296186541333-1.29618654133264
17537537.632301941893-0.632301941892933
18543543.773941164935-0.773941164935422
19594610.624553799895-16.6245537998951
20611605.2204962327225.77950376727813
21613607.9324975430035.06750245699664
22611599.19282229549811.8071777045018
23594592.6598632433431.34013675665688
24595604.422702468874-9.42270246887358
25591605.459975445823-14.4599754458228
26589589.750678483175-0.750678483175307
27584582.4060250105451.59397498945452
28573571.6103940580161.38960594198386
29567564.4689853740532.53101462594702
30569572.567019939157-3.56701993915703
31621637.298145630072-16.2981456300724
32629632.134000993396-3.13400099339594
33628623.6641505255474.3358494744532
34612611.6498599887230.35014001127729
35595590.1440617830464.85593821695431
36597601.488049543399-4.48804954339937
37593604.226360276144-11.2263602761443
38590589.8906975471380.109302452862153
39580581.207594724467-1.2075947244673
40574565.3661137196218.63388628037865
41573563.4339095829019.5660904170993
42573576.913257121291-3.91325712129094
43620639.963572355659-19.9635723556589
44626630.448972435654-4.44897243565447
45620619.4735270422590.526472957741362
46588601.870139678719-13.8701396787188
47566564.668413912851.33158608714996
48557568.276074636279-11.2760746362794
49561559.4501707984031.54982920159671
50549554.888995403089-5.88899540308944
51532537.417050194715-5.4170501947151
52526515.2759823231610.7240176768399
53511512.60155946387-1.60155946386953
54499509.754974120899-10.7549741208985
55555551.0703317993793.92966820062145
56565560.1051941468244.89480585317574
57542555.981011405067-13.9810114050669
58527521.9516652540445.0483347459558
59510503.5156946266776.48430537332337
60514509.3323201098614.66767989013937
61517515.8075278316191.19247216838119
62508510.715216383636-2.71521638363578
63493497.137331636749-4.13733163674885
64490478.28185124600511.7181487539953
65469477.108866318261-8.10886631826145
66478467.30340490505810.6965950949416
67528529.452570270776-1.45257027077594
68534534.633319338108-0.633319338108436
69518525.705125960583-7.70512596058279
70506500.9327438988915.06725610110948
71502484.96757082773717.0324291722632
72516503.34264975586212.6573502441378

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 562 & 542.603753604565 & 19.3962463954354 \tabularnewline
14 & 561 & 562.678933206395 & -1.67893320639473 \tabularnewline
15 & 555 & 557.137124532184 & -2.13712453218363 \tabularnewline
16 & 544 & 545.296186541333 & -1.29618654133264 \tabularnewline
17 & 537 & 537.632301941893 & -0.632301941892933 \tabularnewline
18 & 543 & 543.773941164935 & -0.773941164935422 \tabularnewline
19 & 594 & 610.624553799895 & -16.6245537998951 \tabularnewline
20 & 611 & 605.220496232722 & 5.77950376727813 \tabularnewline
21 & 613 & 607.932497543003 & 5.06750245699664 \tabularnewline
22 & 611 & 599.192822295498 & 11.8071777045018 \tabularnewline
23 & 594 & 592.659863243343 & 1.34013675665688 \tabularnewline
24 & 595 & 604.422702468874 & -9.42270246887358 \tabularnewline
25 & 591 & 605.459975445823 & -14.4599754458228 \tabularnewline
26 & 589 & 589.750678483175 & -0.750678483175307 \tabularnewline
27 & 584 & 582.406025010545 & 1.59397498945452 \tabularnewline
28 & 573 & 571.610394058016 & 1.38960594198386 \tabularnewline
29 & 567 & 564.468985374053 & 2.53101462594702 \tabularnewline
30 & 569 & 572.567019939157 & -3.56701993915703 \tabularnewline
31 & 621 & 637.298145630072 & -16.2981456300724 \tabularnewline
32 & 629 & 632.134000993396 & -3.13400099339594 \tabularnewline
33 & 628 & 623.664150525547 & 4.3358494744532 \tabularnewline
34 & 612 & 611.649859988723 & 0.35014001127729 \tabularnewline
35 & 595 & 590.144061783046 & 4.85593821695431 \tabularnewline
36 & 597 & 601.488049543399 & -4.48804954339937 \tabularnewline
37 & 593 & 604.226360276144 & -11.2263602761443 \tabularnewline
38 & 590 & 589.890697547138 & 0.109302452862153 \tabularnewline
39 & 580 & 581.207594724467 & -1.2075947244673 \tabularnewline
40 & 574 & 565.366113719621 & 8.63388628037865 \tabularnewline
41 & 573 & 563.433909582901 & 9.5660904170993 \tabularnewline
42 & 573 & 576.913257121291 & -3.91325712129094 \tabularnewline
43 & 620 & 639.963572355659 & -19.9635723556589 \tabularnewline
44 & 626 & 630.448972435654 & -4.44897243565447 \tabularnewline
45 & 620 & 619.473527042259 & 0.526472957741362 \tabularnewline
46 & 588 & 601.870139678719 & -13.8701396787188 \tabularnewline
47 & 566 & 564.66841391285 & 1.33158608714996 \tabularnewline
48 & 557 & 568.276074636279 & -11.2760746362794 \tabularnewline
49 & 561 & 559.450170798403 & 1.54982920159671 \tabularnewline
50 & 549 & 554.888995403089 & -5.88899540308944 \tabularnewline
51 & 532 & 537.417050194715 & -5.4170501947151 \tabularnewline
52 & 526 & 515.27598232316 & 10.7240176768399 \tabularnewline
53 & 511 & 512.60155946387 & -1.60155946386953 \tabularnewline
54 & 499 & 509.754974120899 & -10.7549741208985 \tabularnewline
55 & 555 & 551.070331799379 & 3.92966820062145 \tabularnewline
56 & 565 & 560.105194146824 & 4.89480585317574 \tabularnewline
57 & 542 & 555.981011405067 & -13.9810114050669 \tabularnewline
58 & 527 & 521.951665254044 & 5.0483347459558 \tabularnewline
59 & 510 & 503.515694626677 & 6.48430537332337 \tabularnewline
60 & 514 & 509.332320109861 & 4.66767989013937 \tabularnewline
61 & 517 & 515.807527831619 & 1.19247216838119 \tabularnewline
62 & 508 & 510.715216383636 & -2.71521638363578 \tabularnewline
63 & 493 & 497.137331636749 & -4.13733163674885 \tabularnewline
64 & 490 & 478.281851246005 & 11.7181487539953 \tabularnewline
65 & 469 & 477.108866318261 & -8.10886631826145 \tabularnewline
66 & 478 & 467.303404905058 & 10.6965950949416 \tabularnewline
67 & 528 & 529.452570270776 & -1.45257027077594 \tabularnewline
68 & 534 & 534.633319338108 & -0.633319338108436 \tabularnewline
69 & 518 & 525.705125960583 & -7.70512596058279 \tabularnewline
70 & 506 & 500.932743898891 & 5.06725610110948 \tabularnewline
71 & 502 & 484.967570827737 & 17.0324291722632 \tabularnewline
72 & 516 & 503.342649755862 & 12.6573502441378 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199302&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]562[/C][C]542.603753604565[/C][C]19.3962463954354[/C][/ROW]
[ROW][C]14[/C][C]561[/C][C]562.678933206395[/C][C]-1.67893320639473[/C][/ROW]
[ROW][C]15[/C][C]555[/C][C]557.137124532184[/C][C]-2.13712453218363[/C][/ROW]
[ROW][C]16[/C][C]544[/C][C]545.296186541333[/C][C]-1.29618654133264[/C][/ROW]
[ROW][C]17[/C][C]537[/C][C]537.632301941893[/C][C]-0.632301941892933[/C][/ROW]
[ROW][C]18[/C][C]543[/C][C]543.773941164935[/C][C]-0.773941164935422[/C][/ROW]
[ROW][C]19[/C][C]594[/C][C]610.624553799895[/C][C]-16.6245537998951[/C][/ROW]
[ROW][C]20[/C][C]611[/C][C]605.220496232722[/C][C]5.77950376727813[/C][/ROW]
[ROW][C]21[/C][C]613[/C][C]607.932497543003[/C][C]5.06750245699664[/C][/ROW]
[ROW][C]22[/C][C]611[/C][C]599.192822295498[/C][C]11.8071777045018[/C][/ROW]
[ROW][C]23[/C][C]594[/C][C]592.659863243343[/C][C]1.34013675665688[/C][/ROW]
[ROW][C]24[/C][C]595[/C][C]604.422702468874[/C][C]-9.42270246887358[/C][/ROW]
[ROW][C]25[/C][C]591[/C][C]605.459975445823[/C][C]-14.4599754458228[/C][/ROW]
[ROW][C]26[/C][C]589[/C][C]589.750678483175[/C][C]-0.750678483175307[/C][/ROW]
[ROW][C]27[/C][C]584[/C][C]582.406025010545[/C][C]1.59397498945452[/C][/ROW]
[ROW][C]28[/C][C]573[/C][C]571.610394058016[/C][C]1.38960594198386[/C][/ROW]
[ROW][C]29[/C][C]567[/C][C]564.468985374053[/C][C]2.53101462594702[/C][/ROW]
[ROW][C]30[/C][C]569[/C][C]572.567019939157[/C][C]-3.56701993915703[/C][/ROW]
[ROW][C]31[/C][C]621[/C][C]637.298145630072[/C][C]-16.2981456300724[/C][/ROW]
[ROW][C]32[/C][C]629[/C][C]632.134000993396[/C][C]-3.13400099339594[/C][/ROW]
[ROW][C]33[/C][C]628[/C][C]623.664150525547[/C][C]4.3358494744532[/C][/ROW]
[ROW][C]34[/C][C]612[/C][C]611.649859988723[/C][C]0.35014001127729[/C][/ROW]
[ROW][C]35[/C][C]595[/C][C]590.144061783046[/C][C]4.85593821695431[/C][/ROW]
[ROW][C]36[/C][C]597[/C][C]601.488049543399[/C][C]-4.48804954339937[/C][/ROW]
[ROW][C]37[/C][C]593[/C][C]604.226360276144[/C][C]-11.2263602761443[/C][/ROW]
[ROW][C]38[/C][C]590[/C][C]589.890697547138[/C][C]0.109302452862153[/C][/ROW]
[ROW][C]39[/C][C]580[/C][C]581.207594724467[/C][C]-1.2075947244673[/C][/ROW]
[ROW][C]40[/C][C]574[/C][C]565.366113719621[/C][C]8.63388628037865[/C][/ROW]
[ROW][C]41[/C][C]573[/C][C]563.433909582901[/C][C]9.5660904170993[/C][/ROW]
[ROW][C]42[/C][C]573[/C][C]576.913257121291[/C][C]-3.91325712129094[/C][/ROW]
[ROW][C]43[/C][C]620[/C][C]639.963572355659[/C][C]-19.9635723556589[/C][/ROW]
[ROW][C]44[/C][C]626[/C][C]630.448972435654[/C][C]-4.44897243565447[/C][/ROW]
[ROW][C]45[/C][C]620[/C][C]619.473527042259[/C][C]0.526472957741362[/C][/ROW]
[ROW][C]46[/C][C]588[/C][C]601.870139678719[/C][C]-13.8701396787188[/C][/ROW]
[ROW][C]47[/C][C]566[/C][C]564.66841391285[/C][C]1.33158608714996[/C][/ROW]
[ROW][C]48[/C][C]557[/C][C]568.276074636279[/C][C]-11.2760746362794[/C][/ROW]
[ROW][C]49[/C][C]561[/C][C]559.450170798403[/C][C]1.54982920159671[/C][/ROW]
[ROW][C]50[/C][C]549[/C][C]554.888995403089[/C][C]-5.88899540308944[/C][/ROW]
[ROW][C]51[/C][C]532[/C][C]537.417050194715[/C][C]-5.4170501947151[/C][/ROW]
[ROW][C]52[/C][C]526[/C][C]515.27598232316[/C][C]10.7240176768399[/C][/ROW]
[ROW][C]53[/C][C]511[/C][C]512.60155946387[/C][C]-1.60155946386953[/C][/ROW]
[ROW][C]54[/C][C]499[/C][C]509.754974120899[/C][C]-10.7549741208985[/C][/ROW]
[ROW][C]55[/C][C]555[/C][C]551.070331799379[/C][C]3.92966820062145[/C][/ROW]
[ROW][C]56[/C][C]565[/C][C]560.105194146824[/C][C]4.89480585317574[/C][/ROW]
[ROW][C]57[/C][C]542[/C][C]555.981011405067[/C][C]-13.9810114050669[/C][/ROW]
[ROW][C]58[/C][C]527[/C][C]521.951665254044[/C][C]5.0483347459558[/C][/ROW]
[ROW][C]59[/C][C]510[/C][C]503.515694626677[/C][C]6.48430537332337[/C][/ROW]
[ROW][C]60[/C][C]514[/C][C]509.332320109861[/C][C]4.66767989013937[/C][/ROW]
[ROW][C]61[/C][C]517[/C][C]515.807527831619[/C][C]1.19247216838119[/C][/ROW]
[ROW][C]62[/C][C]508[/C][C]510.715216383636[/C][C]-2.71521638363578[/C][/ROW]
[ROW][C]63[/C][C]493[/C][C]497.137331636749[/C][C]-4.13733163674885[/C][/ROW]
[ROW][C]64[/C][C]490[/C][C]478.281851246005[/C][C]11.7181487539953[/C][/ROW]
[ROW][C]65[/C][C]469[/C][C]477.108866318261[/C][C]-8.10886631826145[/C][/ROW]
[ROW][C]66[/C][C]478[/C][C]467.303404905058[/C][C]10.6965950949416[/C][/ROW]
[ROW][C]67[/C][C]528[/C][C]529.452570270776[/C][C]-1.45257027077594[/C][/ROW]
[ROW][C]68[/C][C]534[/C][C]534.633319338108[/C][C]-0.633319338108436[/C][/ROW]
[ROW][C]69[/C][C]518[/C][C]525.705125960583[/C][C]-7.70512596058279[/C][/ROW]
[ROW][C]70[/C][C]506[/C][C]500.932743898891[/C][C]5.06725610110948[/C][/ROW]
[ROW][C]71[/C][C]502[/C][C]484.967570827737[/C][C]17.0324291722632[/C][/ROW]
[ROW][C]72[/C][C]516[/C][C]503.342649755862[/C][C]12.6573502441378[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199302&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
13562542.60375360456519.3962463954354
14561562.678933206395-1.67893320639473
15555557.137124532184-2.13712453218363
16544545.296186541333-1.29618654133264
17537537.632301941893-0.632301941892933
18543543.773941164935-0.773941164935422
19594610.624553799895-16.6245537998951
20611605.2204962327225.77950376727813
21613607.9324975430035.06750245699664
22611599.19282229549811.8071777045018
23594592.6598632433431.34013675665688
24595604.422702468874-9.42270246887358
25591605.459975445823-14.4599754458228
26589589.750678483175-0.750678483175307
27584582.4060250105451.59397498945452
28573571.6103940580161.38960594198386
29567564.4689853740532.53101462594702
30569572.567019939157-3.56701993915703
31621637.298145630072-16.2981456300724
32629632.134000993396-3.13400099339594
33628623.6641505255474.3358494744532
34612611.6498599887230.35014001127729
35595590.1440617830464.85593821695431
36597601.488049543399-4.48804954339937
37593604.226360276144-11.2263602761443
38590589.8906975471380.109302452862153
39580581.207594724467-1.2075947244673
40574565.3661137196218.63388628037865
41573563.4339095829019.5660904170993
42573576.913257121291-3.91325712129094
43620639.963572355659-19.9635723556589
44626630.448972435654-4.44897243565447
45620619.4735270422590.526472957741362
46588601.870139678719-13.8701396787188
47566564.668413912851.33158608714996
48557568.276074636279-11.2760746362794
49561559.4501707984031.54982920159671
50549554.888995403089-5.88899540308944
51532537.417050194715-5.4170501947151
52526515.2759823231610.7240176768399
53511512.60155946387-1.60155946386953
54499509.754974120899-10.7549741208985
55555551.0703317993793.92966820062145
56565560.1051941468244.89480585317574
57542555.981011405067-13.9810114050669
58527521.9516652540445.0483347459558
59510503.5156946266776.48430537332337
60514509.3323201098614.66767989013937
61517515.8075278316191.19247216838119
62508510.715216383636-2.71521638363578
63493497.137331636749-4.13733163674885
64490478.28185124600511.7181487539953
65469477.108866318261-8.10886631826145
66478467.30340490505810.6965950949416
67528529.452570270776-1.45257027077594
68534534.633319338108-0.633319338108436
69518525.705125960583-7.70512596058279
70506500.9327438988915.06725610110948
71502484.96757082773717.0324291722632
72516503.34264975586212.6573502441378







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73520.776912236434504.51284332318537.040981149688
74517.728502638549494.229076358091541.227928919007
75510.119883747012480.414482196152539.825285297871
76499.574685313812464.231949365214534.91742126241
77488.743325503902448.047011282721529.439639725084
78491.203303334769444.222961474621538.183645194917
79546.786284149115488.220833488875605.351734809355
80556.628819766394490.564551381027622.69308815176
81550.61750682108478.75694701731622.478066624849
82536.581318803463460.030384302401613.132253304524
83518.34068619776437.888717695586598.792654699933
84521.696250914116429.175056936472614.217444891759

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 520.776912236434 & 504.51284332318 & 537.040981149688 \tabularnewline
74 & 517.728502638549 & 494.229076358091 & 541.227928919007 \tabularnewline
75 & 510.119883747012 & 480.414482196152 & 539.825285297871 \tabularnewline
76 & 499.574685313812 & 464.231949365214 & 534.91742126241 \tabularnewline
77 & 488.743325503902 & 448.047011282721 & 529.439639725084 \tabularnewline
78 & 491.203303334769 & 444.222961474621 & 538.183645194917 \tabularnewline
79 & 546.786284149115 & 488.220833488875 & 605.351734809355 \tabularnewline
80 & 556.628819766394 & 490.564551381027 & 622.69308815176 \tabularnewline
81 & 550.61750682108 & 478.75694701731 & 622.478066624849 \tabularnewline
82 & 536.581318803463 & 460.030384302401 & 613.132253304524 \tabularnewline
83 & 518.34068619776 & 437.888717695586 & 598.792654699933 \tabularnewline
84 & 521.696250914116 & 429.175056936472 & 614.217444891759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=199302&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]520.776912236434[/C][C]504.51284332318[/C][C]537.040981149688[/C][/ROW]
[ROW][C]74[/C][C]517.728502638549[/C][C]494.229076358091[/C][C]541.227928919007[/C][/ROW]
[ROW][C]75[/C][C]510.119883747012[/C][C]480.414482196152[/C][C]539.825285297871[/C][/ROW]
[ROW][C]76[/C][C]499.574685313812[/C][C]464.231949365214[/C][C]534.91742126241[/C][/ROW]
[ROW][C]77[/C][C]488.743325503902[/C][C]448.047011282721[/C][C]529.439639725084[/C][/ROW]
[ROW][C]78[/C][C]491.203303334769[/C][C]444.222961474621[/C][C]538.183645194917[/C][/ROW]
[ROW][C]79[/C][C]546.786284149115[/C][C]488.220833488875[/C][C]605.351734809355[/C][/ROW]
[ROW][C]80[/C][C]556.628819766394[/C][C]490.564551381027[/C][C]622.69308815176[/C][/ROW]
[ROW][C]81[/C][C]550.61750682108[/C][C]478.75694701731[/C][C]622.478066624849[/C][/ROW]
[ROW][C]82[/C][C]536.581318803463[/C][C]460.030384302401[/C][C]613.132253304524[/C][/ROW]
[ROW][C]83[/C][C]518.34068619776[/C][C]437.888717695586[/C][C]598.792654699933[/C][/ROW]
[ROW][C]84[/C][C]521.696250914116[/C][C]429.175056936472[/C][C]614.217444891759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=199302&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=199302&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
73520.776912236434504.51284332318537.040981149688
74517.728502638549494.229076358091541.227928919007
75510.119883747012480.414482196152539.825285297871
76499.574685313812464.231949365214534.91742126241
77488.743325503902448.047011282721529.439639725084
78491.203303334769444.222961474621538.183645194917
79546.786284149115488.220833488875605.351734809355
80556.628819766394490.564551381027622.69308815176
81550.61750682108478.75694701731622.478066624849
82536.581318803463460.030384302401613.132253304524
83518.34068619776437.888717695586598.792654699933
84521.696250914116429.175056936472614.217444891759



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')