Free Statistics

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 14:30:21 +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/t1305728791bu0z0h4f62x8b0w.htm/, Retrieved Tue, 14 May 2024 16:11:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121860, Retrieved Tue, 14 May 2024 16:11:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Ann-Sophie Coeman...] [2011-05-18 14:30:21] [fc42f3d005062709f652b08fadb3432c] [Current]
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Dataseries X:
600
425
398
582
458
455
621
635
589
220
351
379
683
524
536
598
581
632
645
722
689
645
354
486
423
479
684
601
608
463
602
485
563
645
486
435
479
579
563
202
389
467
466
706
546
689
531
528
579
684
651
637
548
496
582
467
693
615
708
648
899
852
745
689
582
674
684
542
489
472
398
486
549
766
654
628
689
648
578
536
548
496
475
687
642
584
596
609
678
694
485
489
537
706
489
598




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121860&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121860&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121860&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'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.102723846750587
beta0.0340175164889182
gamma0.50686474160226

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.102723846750587 \tabularnewline
beta & 0.0340175164889182 \tabularnewline
gamma & 0.50686474160226 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121860&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]0.102723846750587[/C][/ROW]
[ROW][C]beta[/C][C]0.0340175164889182[/C][/ROW]
[ROW][C]gamma[/C][C]0.50686474160226[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121860&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121860&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
alpha0.102723846750587
beta0.0340175164889182
gamma0.50686474160226







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13683610.1381758938172.8618241061897
14524479.46673680843544.5332631915651
15536497.97460667445838.0253933255424
16598549.054661229648.9453387704002
17581532.19639103052748.8036089694732
18632591.16115225931840.8388477406818
19645729.658622663509-84.6586226635087
20722739.362973822626-17.3629738226256
21689682.88563466146.11436533859955
22645256.602963515161388.397036484839
23354476.997965622894-122.997965622894
24486498.767626701021-12.7676267010207
25423947.082145169763-524.082145169763
26479683.494731547057-204.494731547057
27684674.2252481113749.77475188862627
28601740.071117509099-139.071117509099
29608695.09744888087-87.0974488808699
30463744.564947816607-281.564947816607
31602801.14831659405-199.14831659405
32485832.454778639389-347.454778639389
33563744.339694678477-181.339694678477
34645430.305762185496214.694237814504
35486398.26420308092787.7357969190726
36435488.602564406121-53.6025644061212
37479678.172154738252-199.172154738252
38579586.773157239927-7.77315723992717
39563694.869138127748-131.869138127748
40202673.648360753349-471.648360753349
41389614.01379803094-225.013798030941
42467554.751022690543-87.751022690543
43466653.405619433389-187.405619433389
44706609.08783253887696.9121674611237
45546636.021533068656-90.0215330686558
46689507.229770687397181.770229312603
47531416.008185786757114.991814213243
48528441.7761864360586.22381356395
49579572.2454942477366.75450575226432
50684587.3858174784896.61418252152
51651648.2041108316812.79588916831869
52637460.891552133065176.108447866935
53548592.48774980799-44.48774980799
54496619.640641855753-123.640641855753
55582679.550607004092-97.5506070040924
56467797.193773178553-330.193773178553
57693684.3647197268538.63528027314658
58615686.968240860749-71.9682408607486
59708520.973475514394187.026524485606
60648540.058158972345107.941841027655
61899647.03632273249251.963677267511
62852737.085895624876114.914104375124
63745758.87680124095-13.8768012409498
64689627.39270459163561.6072954083651
65582648.307551540508-66.3075515405077
66674635.12223045612538.8777695438753
67684736.630252879207-52.6302528792074
68542749.375383720764-207.375383720764
69489818.101760276982-329.101760276982
70472743.94473633468-271.944736334681
71398666.818447517795-268.818447517795
72486599.398719650655-113.398719650655
73549738.342798272456-189.342798272456
74766715.53748954191550.4625104580851
75654672.91159799633-18.9115979963302
76628581.69290213525746.3070978647434
77689544.290750695768144.709249304232
78648594.11911610791453.8808838920863
79578647.527191025146-69.5271910251463
80536587.830021981531-51.8300219815306
81548605.900260290522-57.900260290522
82496579.890039983033-83.8900399830329
83475518.708453726366-43.7084537263661
84687542.978851488934144.021148511066
85642675.867165716623-33.8671657166227
86584784.80647889131-200.806478891309
87596682.126276186204-86.1262761862039
88609611.885449999294-2.88544999929354
89678611.65819042061366.3418095793871
90694610.91419809834483.085801901656
91485609.959056543955-124.959056543955
92489552.216077041558-63.2160770415579
93537564.49793121961-27.4979312196098
94706528.92431163553177.07568836447
95489511.597224588999-22.5972245889991
96598624.972270032514-26.9722700325143

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 683 & 610.13817589381 & 72.8618241061897 \tabularnewline
14 & 524 & 479.466736808435 & 44.5332631915651 \tabularnewline
15 & 536 & 497.974606674458 & 38.0253933255424 \tabularnewline
16 & 598 & 549.0546612296 & 48.9453387704002 \tabularnewline
17 & 581 & 532.196391030527 & 48.8036089694732 \tabularnewline
18 & 632 & 591.161152259318 & 40.8388477406818 \tabularnewline
19 & 645 & 729.658622663509 & -84.6586226635087 \tabularnewline
20 & 722 & 739.362973822626 & -17.3629738226256 \tabularnewline
21 & 689 & 682.8856346614 & 6.11436533859955 \tabularnewline
22 & 645 & 256.602963515161 & 388.397036484839 \tabularnewline
23 & 354 & 476.997965622894 & -122.997965622894 \tabularnewline
24 & 486 & 498.767626701021 & -12.7676267010207 \tabularnewline
25 & 423 & 947.082145169763 & -524.082145169763 \tabularnewline
26 & 479 & 683.494731547057 & -204.494731547057 \tabularnewline
27 & 684 & 674.225248111374 & 9.77475188862627 \tabularnewline
28 & 601 & 740.071117509099 & -139.071117509099 \tabularnewline
29 & 608 & 695.09744888087 & -87.0974488808699 \tabularnewline
30 & 463 & 744.564947816607 & -281.564947816607 \tabularnewline
31 & 602 & 801.14831659405 & -199.14831659405 \tabularnewline
32 & 485 & 832.454778639389 & -347.454778639389 \tabularnewline
33 & 563 & 744.339694678477 & -181.339694678477 \tabularnewline
34 & 645 & 430.305762185496 & 214.694237814504 \tabularnewline
35 & 486 & 398.264203080927 & 87.7357969190726 \tabularnewline
36 & 435 & 488.602564406121 & -53.6025644061212 \tabularnewline
37 & 479 & 678.172154738252 & -199.172154738252 \tabularnewline
38 & 579 & 586.773157239927 & -7.77315723992717 \tabularnewline
39 & 563 & 694.869138127748 & -131.869138127748 \tabularnewline
40 & 202 & 673.648360753349 & -471.648360753349 \tabularnewline
41 & 389 & 614.01379803094 & -225.013798030941 \tabularnewline
42 & 467 & 554.751022690543 & -87.751022690543 \tabularnewline
43 & 466 & 653.405619433389 & -187.405619433389 \tabularnewline
44 & 706 & 609.087832538876 & 96.9121674611237 \tabularnewline
45 & 546 & 636.021533068656 & -90.0215330686558 \tabularnewline
46 & 689 & 507.229770687397 & 181.770229312603 \tabularnewline
47 & 531 & 416.008185786757 & 114.991814213243 \tabularnewline
48 & 528 & 441.77618643605 & 86.22381356395 \tabularnewline
49 & 579 & 572.245494247736 & 6.75450575226432 \tabularnewline
50 & 684 & 587.38581747848 & 96.61418252152 \tabularnewline
51 & 651 & 648.204110831681 & 2.79588916831869 \tabularnewline
52 & 637 & 460.891552133065 & 176.108447866935 \tabularnewline
53 & 548 & 592.48774980799 & -44.48774980799 \tabularnewline
54 & 496 & 619.640641855753 & -123.640641855753 \tabularnewline
55 & 582 & 679.550607004092 & -97.5506070040924 \tabularnewline
56 & 467 & 797.193773178553 & -330.193773178553 \tabularnewline
57 & 693 & 684.364719726853 & 8.63528027314658 \tabularnewline
58 & 615 & 686.968240860749 & -71.9682408607486 \tabularnewline
59 & 708 & 520.973475514394 & 187.026524485606 \tabularnewline
60 & 648 & 540.058158972345 & 107.941841027655 \tabularnewline
61 & 899 & 647.03632273249 & 251.963677267511 \tabularnewline
62 & 852 & 737.085895624876 & 114.914104375124 \tabularnewline
63 & 745 & 758.87680124095 & -13.8768012409498 \tabularnewline
64 & 689 & 627.392704591635 & 61.6072954083651 \tabularnewline
65 & 582 & 648.307551540508 & -66.3075515405077 \tabularnewline
66 & 674 & 635.122230456125 & 38.8777695438753 \tabularnewline
67 & 684 & 736.630252879207 & -52.6302528792074 \tabularnewline
68 & 542 & 749.375383720764 & -207.375383720764 \tabularnewline
69 & 489 & 818.101760276982 & -329.101760276982 \tabularnewline
70 & 472 & 743.94473633468 & -271.944736334681 \tabularnewline
71 & 398 & 666.818447517795 & -268.818447517795 \tabularnewline
72 & 486 & 599.398719650655 & -113.398719650655 \tabularnewline
73 & 549 & 738.342798272456 & -189.342798272456 \tabularnewline
74 & 766 & 715.537489541915 & 50.4625104580851 \tabularnewline
75 & 654 & 672.91159799633 & -18.9115979963302 \tabularnewline
76 & 628 & 581.692902135257 & 46.3070978647434 \tabularnewline
77 & 689 & 544.290750695768 & 144.709249304232 \tabularnewline
78 & 648 & 594.119116107914 & 53.8808838920863 \tabularnewline
79 & 578 & 647.527191025146 & -69.5271910251463 \tabularnewline
80 & 536 & 587.830021981531 & -51.8300219815306 \tabularnewline
81 & 548 & 605.900260290522 & -57.900260290522 \tabularnewline
82 & 496 & 579.890039983033 & -83.8900399830329 \tabularnewline
83 & 475 & 518.708453726366 & -43.7084537263661 \tabularnewline
84 & 687 & 542.978851488934 & 144.021148511066 \tabularnewline
85 & 642 & 675.867165716623 & -33.8671657166227 \tabularnewline
86 & 584 & 784.80647889131 & -200.806478891309 \tabularnewline
87 & 596 & 682.126276186204 & -86.1262761862039 \tabularnewline
88 & 609 & 611.885449999294 & -2.88544999929354 \tabularnewline
89 & 678 & 611.658190420613 & 66.3418095793871 \tabularnewline
90 & 694 & 610.914198098344 & 83.085801901656 \tabularnewline
91 & 485 & 609.959056543955 & -124.959056543955 \tabularnewline
92 & 489 & 552.216077041558 & -63.2160770415579 \tabularnewline
93 & 537 & 564.49793121961 & -27.4979312196098 \tabularnewline
94 & 706 & 528.92431163553 & 177.07568836447 \tabularnewline
95 & 489 & 511.597224588999 & -22.5972245889991 \tabularnewline
96 & 598 & 624.972270032514 & -26.9722700325143 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121860&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]683[/C][C]610.13817589381[/C][C]72.8618241061897[/C][/ROW]
[ROW][C]14[/C][C]524[/C][C]479.466736808435[/C][C]44.5332631915651[/C][/ROW]
[ROW][C]15[/C][C]536[/C][C]497.974606674458[/C][C]38.0253933255424[/C][/ROW]
[ROW][C]16[/C][C]598[/C][C]549.0546612296[/C][C]48.9453387704002[/C][/ROW]
[ROW][C]17[/C][C]581[/C][C]532.196391030527[/C][C]48.8036089694732[/C][/ROW]
[ROW][C]18[/C][C]632[/C][C]591.161152259318[/C][C]40.8388477406818[/C][/ROW]
[ROW][C]19[/C][C]645[/C][C]729.658622663509[/C][C]-84.6586226635087[/C][/ROW]
[ROW][C]20[/C][C]722[/C][C]739.362973822626[/C][C]-17.3629738226256[/C][/ROW]
[ROW][C]21[/C][C]689[/C][C]682.8856346614[/C][C]6.11436533859955[/C][/ROW]
[ROW][C]22[/C][C]645[/C][C]256.602963515161[/C][C]388.397036484839[/C][/ROW]
[ROW][C]23[/C][C]354[/C][C]476.997965622894[/C][C]-122.997965622894[/C][/ROW]
[ROW][C]24[/C][C]486[/C][C]498.767626701021[/C][C]-12.7676267010207[/C][/ROW]
[ROW][C]25[/C][C]423[/C][C]947.082145169763[/C][C]-524.082145169763[/C][/ROW]
[ROW][C]26[/C][C]479[/C][C]683.494731547057[/C][C]-204.494731547057[/C][/ROW]
[ROW][C]27[/C][C]684[/C][C]674.225248111374[/C][C]9.77475188862627[/C][/ROW]
[ROW][C]28[/C][C]601[/C][C]740.071117509099[/C][C]-139.071117509099[/C][/ROW]
[ROW][C]29[/C][C]608[/C][C]695.09744888087[/C][C]-87.0974488808699[/C][/ROW]
[ROW][C]30[/C][C]463[/C][C]744.564947816607[/C][C]-281.564947816607[/C][/ROW]
[ROW][C]31[/C][C]602[/C][C]801.14831659405[/C][C]-199.14831659405[/C][/ROW]
[ROW][C]32[/C][C]485[/C][C]832.454778639389[/C][C]-347.454778639389[/C][/ROW]
[ROW][C]33[/C][C]563[/C][C]744.339694678477[/C][C]-181.339694678477[/C][/ROW]
[ROW][C]34[/C][C]645[/C][C]430.305762185496[/C][C]214.694237814504[/C][/ROW]
[ROW][C]35[/C][C]486[/C][C]398.264203080927[/C][C]87.7357969190726[/C][/ROW]
[ROW][C]36[/C][C]435[/C][C]488.602564406121[/C][C]-53.6025644061212[/C][/ROW]
[ROW][C]37[/C][C]479[/C][C]678.172154738252[/C][C]-199.172154738252[/C][/ROW]
[ROW][C]38[/C][C]579[/C][C]586.773157239927[/C][C]-7.77315723992717[/C][/ROW]
[ROW][C]39[/C][C]563[/C][C]694.869138127748[/C][C]-131.869138127748[/C][/ROW]
[ROW][C]40[/C][C]202[/C][C]673.648360753349[/C][C]-471.648360753349[/C][/ROW]
[ROW][C]41[/C][C]389[/C][C]614.01379803094[/C][C]-225.013798030941[/C][/ROW]
[ROW][C]42[/C][C]467[/C][C]554.751022690543[/C][C]-87.751022690543[/C][/ROW]
[ROW][C]43[/C][C]466[/C][C]653.405619433389[/C][C]-187.405619433389[/C][/ROW]
[ROW][C]44[/C][C]706[/C][C]609.087832538876[/C][C]96.9121674611237[/C][/ROW]
[ROW][C]45[/C][C]546[/C][C]636.021533068656[/C][C]-90.0215330686558[/C][/ROW]
[ROW][C]46[/C][C]689[/C][C]507.229770687397[/C][C]181.770229312603[/C][/ROW]
[ROW][C]47[/C][C]531[/C][C]416.008185786757[/C][C]114.991814213243[/C][/ROW]
[ROW][C]48[/C][C]528[/C][C]441.77618643605[/C][C]86.22381356395[/C][/ROW]
[ROW][C]49[/C][C]579[/C][C]572.245494247736[/C][C]6.75450575226432[/C][/ROW]
[ROW][C]50[/C][C]684[/C][C]587.38581747848[/C][C]96.61418252152[/C][/ROW]
[ROW][C]51[/C][C]651[/C][C]648.204110831681[/C][C]2.79588916831869[/C][/ROW]
[ROW][C]52[/C][C]637[/C][C]460.891552133065[/C][C]176.108447866935[/C][/ROW]
[ROW][C]53[/C][C]548[/C][C]592.48774980799[/C][C]-44.48774980799[/C][/ROW]
[ROW][C]54[/C][C]496[/C][C]619.640641855753[/C][C]-123.640641855753[/C][/ROW]
[ROW][C]55[/C][C]582[/C][C]679.550607004092[/C][C]-97.5506070040924[/C][/ROW]
[ROW][C]56[/C][C]467[/C][C]797.193773178553[/C][C]-330.193773178553[/C][/ROW]
[ROW][C]57[/C][C]693[/C][C]684.364719726853[/C][C]8.63528027314658[/C][/ROW]
[ROW][C]58[/C][C]615[/C][C]686.968240860749[/C][C]-71.9682408607486[/C][/ROW]
[ROW][C]59[/C][C]708[/C][C]520.973475514394[/C][C]187.026524485606[/C][/ROW]
[ROW][C]60[/C][C]648[/C][C]540.058158972345[/C][C]107.941841027655[/C][/ROW]
[ROW][C]61[/C][C]899[/C][C]647.03632273249[/C][C]251.963677267511[/C][/ROW]
[ROW][C]62[/C][C]852[/C][C]737.085895624876[/C][C]114.914104375124[/C][/ROW]
[ROW][C]63[/C][C]745[/C][C]758.87680124095[/C][C]-13.8768012409498[/C][/ROW]
[ROW][C]64[/C][C]689[/C][C]627.392704591635[/C][C]61.6072954083651[/C][/ROW]
[ROW][C]65[/C][C]582[/C][C]648.307551540508[/C][C]-66.3075515405077[/C][/ROW]
[ROW][C]66[/C][C]674[/C][C]635.122230456125[/C][C]38.8777695438753[/C][/ROW]
[ROW][C]67[/C][C]684[/C][C]736.630252879207[/C][C]-52.6302528792074[/C][/ROW]
[ROW][C]68[/C][C]542[/C][C]749.375383720764[/C][C]-207.375383720764[/C][/ROW]
[ROW][C]69[/C][C]489[/C][C]818.101760276982[/C][C]-329.101760276982[/C][/ROW]
[ROW][C]70[/C][C]472[/C][C]743.94473633468[/C][C]-271.944736334681[/C][/ROW]
[ROW][C]71[/C][C]398[/C][C]666.818447517795[/C][C]-268.818447517795[/C][/ROW]
[ROW][C]72[/C][C]486[/C][C]599.398719650655[/C][C]-113.398719650655[/C][/ROW]
[ROW][C]73[/C][C]549[/C][C]738.342798272456[/C][C]-189.342798272456[/C][/ROW]
[ROW][C]74[/C][C]766[/C][C]715.537489541915[/C][C]50.4625104580851[/C][/ROW]
[ROW][C]75[/C][C]654[/C][C]672.91159799633[/C][C]-18.9115979963302[/C][/ROW]
[ROW][C]76[/C][C]628[/C][C]581.692902135257[/C][C]46.3070978647434[/C][/ROW]
[ROW][C]77[/C][C]689[/C][C]544.290750695768[/C][C]144.709249304232[/C][/ROW]
[ROW][C]78[/C][C]648[/C][C]594.119116107914[/C][C]53.8808838920863[/C][/ROW]
[ROW][C]79[/C][C]578[/C][C]647.527191025146[/C][C]-69.5271910251463[/C][/ROW]
[ROW][C]80[/C][C]536[/C][C]587.830021981531[/C][C]-51.8300219815306[/C][/ROW]
[ROW][C]81[/C][C]548[/C][C]605.900260290522[/C][C]-57.900260290522[/C][/ROW]
[ROW][C]82[/C][C]496[/C][C]579.890039983033[/C][C]-83.8900399830329[/C][/ROW]
[ROW][C]83[/C][C]475[/C][C]518.708453726366[/C][C]-43.7084537263661[/C][/ROW]
[ROW][C]84[/C][C]687[/C][C]542.978851488934[/C][C]144.021148511066[/C][/ROW]
[ROW][C]85[/C][C]642[/C][C]675.867165716623[/C][C]-33.8671657166227[/C][/ROW]
[ROW][C]86[/C][C]584[/C][C]784.80647889131[/C][C]-200.806478891309[/C][/ROW]
[ROW][C]87[/C][C]596[/C][C]682.126276186204[/C][C]-86.1262761862039[/C][/ROW]
[ROW][C]88[/C][C]609[/C][C]611.885449999294[/C][C]-2.88544999929354[/C][/ROW]
[ROW][C]89[/C][C]678[/C][C]611.658190420613[/C][C]66.3418095793871[/C][/ROW]
[ROW][C]90[/C][C]694[/C][C]610.914198098344[/C][C]83.085801901656[/C][/ROW]
[ROW][C]91[/C][C]485[/C][C]609.959056543955[/C][C]-124.959056543955[/C][/ROW]
[ROW][C]92[/C][C]489[/C][C]552.216077041558[/C][C]-63.2160770415579[/C][/ROW]
[ROW][C]93[/C][C]537[/C][C]564.49793121961[/C][C]-27.4979312196098[/C][/ROW]
[ROW][C]94[/C][C]706[/C][C]528.92431163553[/C][C]177.07568836447[/C][/ROW]
[ROW][C]95[/C][C]489[/C][C]511.597224588999[/C][C]-22.5972245889991[/C][/ROW]
[ROW][C]96[/C][C]598[/C][C]624.972270032514[/C][C]-26.9722700325143[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121860&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121860&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
13683610.1381758938172.8618241061897
14524479.46673680843544.5332631915651
15536497.97460667445838.0253933255424
16598549.054661229648.9453387704002
17581532.19639103052748.8036089694732
18632591.16115225931840.8388477406818
19645729.658622663509-84.6586226635087
20722739.362973822626-17.3629738226256
21689682.88563466146.11436533859955
22645256.602963515161388.397036484839
23354476.997965622894-122.997965622894
24486498.767626701021-12.7676267010207
25423947.082145169763-524.082145169763
26479683.494731547057-204.494731547057
27684674.2252481113749.77475188862627
28601740.071117509099-139.071117509099
29608695.09744888087-87.0974488808699
30463744.564947816607-281.564947816607
31602801.14831659405-199.14831659405
32485832.454778639389-347.454778639389
33563744.339694678477-181.339694678477
34645430.305762185496214.694237814504
35486398.26420308092787.7357969190726
36435488.602564406121-53.6025644061212
37479678.172154738252-199.172154738252
38579586.773157239927-7.77315723992717
39563694.869138127748-131.869138127748
40202673.648360753349-471.648360753349
41389614.01379803094-225.013798030941
42467554.751022690543-87.751022690543
43466653.405619433389-187.405619433389
44706609.08783253887696.9121674611237
45546636.021533068656-90.0215330686558
46689507.229770687397181.770229312603
47531416.008185786757114.991814213243
48528441.7761864360586.22381356395
49579572.2454942477366.75450575226432
50684587.3858174784896.61418252152
51651648.2041108316812.79588916831869
52637460.891552133065176.108447866935
53548592.48774980799-44.48774980799
54496619.640641855753-123.640641855753
55582679.550607004092-97.5506070040924
56467797.193773178553-330.193773178553
57693684.3647197268538.63528027314658
58615686.968240860749-71.9682408607486
59708520.973475514394187.026524485606
60648540.058158972345107.941841027655
61899647.03632273249251.963677267511
62852737.085895624876114.914104375124
63745758.87680124095-13.8768012409498
64689627.39270459163561.6072954083651
65582648.307551540508-66.3075515405077
66674635.12223045612538.8777695438753
67684736.630252879207-52.6302528792074
68542749.375383720764-207.375383720764
69489818.101760276982-329.101760276982
70472743.94473633468-271.944736334681
71398666.818447517795-268.818447517795
72486599.398719650655-113.398719650655
73549738.342798272456-189.342798272456
74766715.53748954191550.4625104580851
75654672.91159799633-18.9115979963302
76628581.69290213525746.3070978647434
77689544.290750695768144.709249304232
78648594.11911610791453.8808838920863
79578647.527191025146-69.5271910251463
80536587.830021981531-51.8300219815306
81548605.900260290522-57.900260290522
82496579.890039983033-83.8900399830329
83475518.708453726366-43.7084537263661
84687542.978851488934144.021148511066
85642675.867165716623-33.8671657166227
86584784.80647889131-200.806478891309
87596682.126276186204-86.1262761862039
88609611.885449999294-2.88544999929354
89678611.65819042061366.3418095793871
90694610.91419809834483.085801901656
91485609.959056543955-124.959056543955
92489552.216077041558-63.2160770415579
93537564.49793121961-27.4979312196098
94706528.92431163553177.07568836447
95489511.597224588999-22.5972245889991
96598624.972270032514-26.9722700325143







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97658.508422317156488.452028936849828.564815697464
98691.951977283666518.538513659586865.365440907746
99660.589070868376484.559585203199836.618556533552
100636.24588328311457.58099258753814.91077397869
101668.990136424608485.716385501104852.263887348111
102668.471446579923481.665443935433855.277449224413
103561.065488829984376.385502518933745.745475141036
104543.332928722381356.151514586947730.514342857815
105580.392652666636386.796854305303773.988451027968
106641.736950065045438.672154444971844.801745685119
107512.340330388093317.766873490839706.913787285348
108628.893827061907485.317236132536772.470417991277

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 658.508422317156 & 488.452028936849 & 828.564815697464 \tabularnewline
98 & 691.951977283666 & 518.538513659586 & 865.365440907746 \tabularnewline
99 & 660.589070868376 & 484.559585203199 & 836.618556533552 \tabularnewline
100 & 636.24588328311 & 457.58099258753 & 814.91077397869 \tabularnewline
101 & 668.990136424608 & 485.716385501104 & 852.263887348111 \tabularnewline
102 & 668.471446579923 & 481.665443935433 & 855.277449224413 \tabularnewline
103 & 561.065488829984 & 376.385502518933 & 745.745475141036 \tabularnewline
104 & 543.332928722381 & 356.151514586947 & 730.514342857815 \tabularnewline
105 & 580.392652666636 & 386.796854305303 & 773.988451027968 \tabularnewline
106 & 641.736950065045 & 438.672154444971 & 844.801745685119 \tabularnewline
107 & 512.340330388093 & 317.766873490839 & 706.913787285348 \tabularnewline
108 & 628.893827061907 & 485.317236132536 & 772.470417991277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121860&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]97[/C][C]658.508422317156[/C][C]488.452028936849[/C][C]828.564815697464[/C][/ROW]
[ROW][C]98[/C][C]691.951977283666[/C][C]518.538513659586[/C][C]865.365440907746[/C][/ROW]
[ROW][C]99[/C][C]660.589070868376[/C][C]484.559585203199[/C][C]836.618556533552[/C][/ROW]
[ROW][C]100[/C][C]636.24588328311[/C][C]457.58099258753[/C][C]814.91077397869[/C][/ROW]
[ROW][C]101[/C][C]668.990136424608[/C][C]485.716385501104[/C][C]852.263887348111[/C][/ROW]
[ROW][C]102[/C][C]668.471446579923[/C][C]481.665443935433[/C][C]855.277449224413[/C][/ROW]
[ROW][C]103[/C][C]561.065488829984[/C][C]376.385502518933[/C][C]745.745475141036[/C][/ROW]
[ROW][C]104[/C][C]543.332928722381[/C][C]356.151514586947[/C][C]730.514342857815[/C][/ROW]
[ROW][C]105[/C][C]580.392652666636[/C][C]386.796854305303[/C][C]773.988451027968[/C][/ROW]
[ROW][C]106[/C][C]641.736950065045[/C][C]438.672154444971[/C][C]844.801745685119[/C][/ROW]
[ROW][C]107[/C][C]512.340330388093[/C][C]317.766873490839[/C][C]706.913787285348[/C][/ROW]
[ROW][C]108[/C][C]628.893827061907[/C][C]485.317236132536[/C][C]772.470417991277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121860&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121860&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
97658.508422317156488.452028936849828.564815697464
98691.951977283666518.538513659586865.365440907746
99660.589070868376484.559585203199836.618556533552
100636.24588328311457.58099258753814.91077397869
101668.990136424608485.716385501104852.263887348111
102668.471446579923481.665443935433855.277449224413
103561.065488829984376.385502518933745.745475141036
104543.332928722381356.151514586947730.514342857815
105580.392652666636386.796854305303773.988451027968
106641.736950065045438.672154444971844.801745685119
107512.340330388093317.766873490839706.913787285348
108628.893827061907485.317236132536772.470417991277



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')