Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 06 Jan 2017 13:52:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Jan/06/t1483710861jejax470hphoohf.htm/, Retrieved Tue, 14 May 2024 15:19:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Tue, 14 May 2024 15:19:43 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
480
548
634
489
399
658
497
495
445
525
565
427
477
511
538
444
559
433
459
492
526
523
636
519
671
599
579
593
684
599
721
516
556
700
579
552
734
760
714
698
800
712
782
610
596
748
581
641
598
609
526
716
552
464
631
465
539
537
488
520
477
480
645
455
379
477
424
316
381
376
389
472




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.334136447964717
beta0
gamma0.463024210865687

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.334136447964717 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.463024210865687 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.334136447964717[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.463024210865687[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.334136447964717
beta0
gamma0.463024210865687







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13477501.872596153846-24.8725961538464
14511528.016737740822-17.0167377408217
15538544.827474620306-6.82747462030557
16444444.00114901959-0.00114901958994551
17559554.8724142744154.12758572558539
18433422.20657362491410.7934263750859
19459481.10136662607-22.1013666260698
20492472.12981033728519.8701896627152
21526433.05748078238592.9425192176145
22523548.734613202801-25.7346132028008
23636574.09072347495461.9092765250465
24519458.2318517465860.7681482534196
25671530.573193828017140.426806171983
26599614.37193769564-15.3719376956398
27579634.873723568764-55.8737235687638
28593519.76388946020373.236110539797
29684656.37932659680627.6206734031945
30599533.61853445032765.3814655496728
31721600.611356223012120.388643776988
32516652.191196093721-136.191196093721
33556583.502068469141-27.5020684691408
34700622.34481525081777.6551847491833
35579709.268795895477-130.268795895477
36552528.84440333518523.155596664815
37734613.177657188001120.822342811999
38760642.391377239614117.608622760386
39714694.83967132576319.1603286742371
40698644.60742396653253.3925760334677
41800760.52867440486339.4713255951372
42712653.36968262588558.6303173741151
43782735.06601486845246.9339851315477
44610682.995602928313-72.9956029283132
45596668.932474059044-72.9324740590445
46748725.01639867693622.9836013230637
47581729.567371519449-148.567371519449
48641590.33117746495250.6688225350481
49598713.969329752655-115.969329752655
50609663.071496357481-54.0714963574812
51526627.802518600678-101.802518600678
52716547.706351674937168.293648325063
53552697.728164387797-145.728164387797
54464534.594199735566-70.5941997355656
55631569.50580358592461.4941964140755
56465485.324884210156-20.3248842101565
57539488.88042552650850.1195744734918
58537615.652500467166-78.6525004671663
59488533.352104595331-45.3521045953308
60520490.03059261825229.9694073817479
61477555.375949525936-78.3759495259362
62480536.123214219122-56.1232142191219
63645485.452686135566159.547313864434
64455575.956628567562-120.956628567562
65379532.513019130815-153.513019130815
66477389.94247446485687.0575255351445
67424518.255564148921-94.2555641489207
68316356.807254881641-40.8072548816413
69381375.2376872937935.76231270620696
70376447.486544138118-71.4865441381182
71389377.84743200461511.1525679953845
72472376.62863721152595.3713627884752

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 477 & 501.872596153846 & -24.8725961538464 \tabularnewline
14 & 511 & 528.016737740822 & -17.0167377408217 \tabularnewline
15 & 538 & 544.827474620306 & -6.82747462030557 \tabularnewline
16 & 444 & 444.00114901959 & -0.00114901958994551 \tabularnewline
17 & 559 & 554.872414274415 & 4.12758572558539 \tabularnewline
18 & 433 & 422.206573624914 & 10.7934263750859 \tabularnewline
19 & 459 & 481.10136662607 & -22.1013666260698 \tabularnewline
20 & 492 & 472.129810337285 & 19.8701896627152 \tabularnewline
21 & 526 & 433.057480782385 & 92.9425192176145 \tabularnewline
22 & 523 & 548.734613202801 & -25.7346132028008 \tabularnewline
23 & 636 & 574.090723474954 & 61.9092765250465 \tabularnewline
24 & 519 & 458.23185174658 & 60.7681482534196 \tabularnewline
25 & 671 & 530.573193828017 & 140.426806171983 \tabularnewline
26 & 599 & 614.37193769564 & -15.3719376956398 \tabularnewline
27 & 579 & 634.873723568764 & -55.8737235687638 \tabularnewline
28 & 593 & 519.763889460203 & 73.236110539797 \tabularnewline
29 & 684 & 656.379326596806 & 27.6206734031945 \tabularnewline
30 & 599 & 533.618534450327 & 65.3814655496728 \tabularnewline
31 & 721 & 600.611356223012 & 120.388643776988 \tabularnewline
32 & 516 & 652.191196093721 & -136.191196093721 \tabularnewline
33 & 556 & 583.502068469141 & -27.5020684691408 \tabularnewline
34 & 700 & 622.344815250817 & 77.6551847491833 \tabularnewline
35 & 579 & 709.268795895477 & -130.268795895477 \tabularnewline
36 & 552 & 528.844403335185 & 23.155596664815 \tabularnewline
37 & 734 & 613.177657188001 & 120.822342811999 \tabularnewline
38 & 760 & 642.391377239614 & 117.608622760386 \tabularnewline
39 & 714 & 694.839671325763 & 19.1603286742371 \tabularnewline
40 & 698 & 644.607423966532 & 53.3925760334677 \tabularnewline
41 & 800 & 760.528674404863 & 39.4713255951372 \tabularnewline
42 & 712 & 653.369682625885 & 58.6303173741151 \tabularnewline
43 & 782 & 735.066014868452 & 46.9339851315477 \tabularnewline
44 & 610 & 682.995602928313 & -72.9956029283132 \tabularnewline
45 & 596 & 668.932474059044 & -72.9324740590445 \tabularnewline
46 & 748 & 725.016398676936 & 22.9836013230637 \tabularnewline
47 & 581 & 729.567371519449 & -148.567371519449 \tabularnewline
48 & 641 & 590.331177464952 & 50.6688225350481 \tabularnewline
49 & 598 & 713.969329752655 & -115.969329752655 \tabularnewline
50 & 609 & 663.071496357481 & -54.0714963574812 \tabularnewline
51 & 526 & 627.802518600678 & -101.802518600678 \tabularnewline
52 & 716 & 547.706351674937 & 168.293648325063 \tabularnewline
53 & 552 & 697.728164387797 & -145.728164387797 \tabularnewline
54 & 464 & 534.594199735566 & -70.5941997355656 \tabularnewline
55 & 631 & 569.505803585924 & 61.4941964140755 \tabularnewline
56 & 465 & 485.324884210156 & -20.3248842101565 \tabularnewline
57 & 539 & 488.880425526508 & 50.1195744734918 \tabularnewline
58 & 537 & 615.652500467166 & -78.6525004671663 \tabularnewline
59 & 488 & 533.352104595331 & -45.3521045953308 \tabularnewline
60 & 520 & 490.030592618252 & 29.9694073817479 \tabularnewline
61 & 477 & 555.375949525936 & -78.3759495259362 \tabularnewline
62 & 480 & 536.123214219122 & -56.1232142191219 \tabularnewline
63 & 645 & 485.452686135566 & 159.547313864434 \tabularnewline
64 & 455 & 575.956628567562 & -120.956628567562 \tabularnewline
65 & 379 & 532.513019130815 & -153.513019130815 \tabularnewline
66 & 477 & 389.942474464856 & 87.0575255351445 \tabularnewline
67 & 424 & 518.255564148921 & -94.2555641489207 \tabularnewline
68 & 316 & 356.807254881641 & -40.8072548816413 \tabularnewline
69 & 381 & 375.237687293793 & 5.76231270620696 \tabularnewline
70 & 376 & 447.486544138118 & -71.4865441381182 \tabularnewline
71 & 389 & 377.847432004615 & 11.1525679953845 \tabularnewline
72 & 472 & 376.628637211525 & 95.3713627884752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]477[/C][C]501.872596153846[/C][C]-24.8725961538464[/C][/ROW]
[ROW][C]14[/C][C]511[/C][C]528.016737740822[/C][C]-17.0167377408217[/C][/ROW]
[ROW][C]15[/C][C]538[/C][C]544.827474620306[/C][C]-6.82747462030557[/C][/ROW]
[ROW][C]16[/C][C]444[/C][C]444.00114901959[/C][C]-0.00114901958994551[/C][/ROW]
[ROW][C]17[/C][C]559[/C][C]554.872414274415[/C][C]4.12758572558539[/C][/ROW]
[ROW][C]18[/C][C]433[/C][C]422.206573624914[/C][C]10.7934263750859[/C][/ROW]
[ROW][C]19[/C][C]459[/C][C]481.10136662607[/C][C]-22.1013666260698[/C][/ROW]
[ROW][C]20[/C][C]492[/C][C]472.129810337285[/C][C]19.8701896627152[/C][/ROW]
[ROW][C]21[/C][C]526[/C][C]433.057480782385[/C][C]92.9425192176145[/C][/ROW]
[ROW][C]22[/C][C]523[/C][C]548.734613202801[/C][C]-25.7346132028008[/C][/ROW]
[ROW][C]23[/C][C]636[/C][C]574.090723474954[/C][C]61.9092765250465[/C][/ROW]
[ROW][C]24[/C][C]519[/C][C]458.23185174658[/C][C]60.7681482534196[/C][/ROW]
[ROW][C]25[/C][C]671[/C][C]530.573193828017[/C][C]140.426806171983[/C][/ROW]
[ROW][C]26[/C][C]599[/C][C]614.37193769564[/C][C]-15.3719376956398[/C][/ROW]
[ROW][C]27[/C][C]579[/C][C]634.873723568764[/C][C]-55.8737235687638[/C][/ROW]
[ROW][C]28[/C][C]593[/C][C]519.763889460203[/C][C]73.236110539797[/C][/ROW]
[ROW][C]29[/C][C]684[/C][C]656.379326596806[/C][C]27.6206734031945[/C][/ROW]
[ROW][C]30[/C][C]599[/C][C]533.618534450327[/C][C]65.3814655496728[/C][/ROW]
[ROW][C]31[/C][C]721[/C][C]600.611356223012[/C][C]120.388643776988[/C][/ROW]
[ROW][C]32[/C][C]516[/C][C]652.191196093721[/C][C]-136.191196093721[/C][/ROW]
[ROW][C]33[/C][C]556[/C][C]583.502068469141[/C][C]-27.5020684691408[/C][/ROW]
[ROW][C]34[/C][C]700[/C][C]622.344815250817[/C][C]77.6551847491833[/C][/ROW]
[ROW][C]35[/C][C]579[/C][C]709.268795895477[/C][C]-130.268795895477[/C][/ROW]
[ROW][C]36[/C][C]552[/C][C]528.844403335185[/C][C]23.155596664815[/C][/ROW]
[ROW][C]37[/C][C]734[/C][C]613.177657188001[/C][C]120.822342811999[/C][/ROW]
[ROW][C]38[/C][C]760[/C][C]642.391377239614[/C][C]117.608622760386[/C][/ROW]
[ROW][C]39[/C][C]714[/C][C]694.839671325763[/C][C]19.1603286742371[/C][/ROW]
[ROW][C]40[/C][C]698[/C][C]644.607423966532[/C][C]53.3925760334677[/C][/ROW]
[ROW][C]41[/C][C]800[/C][C]760.528674404863[/C][C]39.4713255951372[/C][/ROW]
[ROW][C]42[/C][C]712[/C][C]653.369682625885[/C][C]58.6303173741151[/C][/ROW]
[ROW][C]43[/C][C]782[/C][C]735.066014868452[/C][C]46.9339851315477[/C][/ROW]
[ROW][C]44[/C][C]610[/C][C]682.995602928313[/C][C]-72.9956029283132[/C][/ROW]
[ROW][C]45[/C][C]596[/C][C]668.932474059044[/C][C]-72.9324740590445[/C][/ROW]
[ROW][C]46[/C][C]748[/C][C]725.016398676936[/C][C]22.9836013230637[/C][/ROW]
[ROW][C]47[/C][C]581[/C][C]729.567371519449[/C][C]-148.567371519449[/C][/ROW]
[ROW][C]48[/C][C]641[/C][C]590.331177464952[/C][C]50.6688225350481[/C][/ROW]
[ROW][C]49[/C][C]598[/C][C]713.969329752655[/C][C]-115.969329752655[/C][/ROW]
[ROW][C]50[/C][C]609[/C][C]663.071496357481[/C][C]-54.0714963574812[/C][/ROW]
[ROW][C]51[/C][C]526[/C][C]627.802518600678[/C][C]-101.802518600678[/C][/ROW]
[ROW][C]52[/C][C]716[/C][C]547.706351674937[/C][C]168.293648325063[/C][/ROW]
[ROW][C]53[/C][C]552[/C][C]697.728164387797[/C][C]-145.728164387797[/C][/ROW]
[ROW][C]54[/C][C]464[/C][C]534.594199735566[/C][C]-70.5941997355656[/C][/ROW]
[ROW][C]55[/C][C]631[/C][C]569.505803585924[/C][C]61.4941964140755[/C][/ROW]
[ROW][C]56[/C][C]465[/C][C]485.324884210156[/C][C]-20.3248842101565[/C][/ROW]
[ROW][C]57[/C][C]539[/C][C]488.880425526508[/C][C]50.1195744734918[/C][/ROW]
[ROW][C]58[/C][C]537[/C][C]615.652500467166[/C][C]-78.6525004671663[/C][/ROW]
[ROW][C]59[/C][C]488[/C][C]533.352104595331[/C][C]-45.3521045953308[/C][/ROW]
[ROW][C]60[/C][C]520[/C][C]490.030592618252[/C][C]29.9694073817479[/C][/ROW]
[ROW][C]61[/C][C]477[/C][C]555.375949525936[/C][C]-78.3759495259362[/C][/ROW]
[ROW][C]62[/C][C]480[/C][C]536.123214219122[/C][C]-56.1232142191219[/C][/ROW]
[ROW][C]63[/C][C]645[/C][C]485.452686135566[/C][C]159.547313864434[/C][/ROW]
[ROW][C]64[/C][C]455[/C][C]575.956628567562[/C][C]-120.956628567562[/C][/ROW]
[ROW][C]65[/C][C]379[/C][C]532.513019130815[/C][C]-153.513019130815[/C][/ROW]
[ROW][C]66[/C][C]477[/C][C]389.942474464856[/C][C]87.0575255351445[/C][/ROW]
[ROW][C]67[/C][C]424[/C][C]518.255564148921[/C][C]-94.2555641489207[/C][/ROW]
[ROW][C]68[/C][C]316[/C][C]356.807254881641[/C][C]-40.8072548816413[/C][/ROW]
[ROW][C]69[/C][C]381[/C][C]375.237687293793[/C][C]5.76231270620696[/C][/ROW]
[ROW][C]70[/C][C]376[/C][C]447.486544138118[/C][C]-71.4865441381182[/C][/ROW]
[ROW][C]71[/C][C]389[/C][C]377.847432004615[/C][C]11.1525679953845[/C][/ROW]
[ROW][C]72[/C][C]472[/C][C]376.628637211525[/C][C]95.3713627884752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
13477501.872596153846-24.8725961538464
14511528.016737740822-17.0167377408217
15538544.827474620306-6.82747462030557
16444444.00114901959-0.00114901958994551
17559554.8724142744154.12758572558539
18433422.20657362491410.7934263750859
19459481.10136662607-22.1013666260698
20492472.12981033728519.8701896627152
21526433.05748078238592.9425192176145
22523548.734613202801-25.7346132028008
23636574.09072347495461.9092765250465
24519458.2318517465860.7681482534196
25671530.573193828017140.426806171983
26599614.37193769564-15.3719376956398
27579634.873723568764-55.8737235687638
28593519.76388946020373.236110539797
29684656.37932659680627.6206734031945
30599533.61853445032765.3814655496728
31721600.611356223012120.388643776988
32516652.191196093721-136.191196093721
33556583.502068469141-27.5020684691408
34700622.34481525081777.6551847491833
35579709.268795895477-130.268795895477
36552528.84440333518523.155596664815
37734613.177657188001120.822342811999
38760642.391377239614117.608622760386
39714694.83967132576319.1603286742371
40698644.60742396653253.3925760334677
41800760.52867440486339.4713255951372
42712653.36968262588558.6303173741151
43782735.06601486845246.9339851315477
44610682.995602928313-72.9956029283132
45596668.932474059044-72.9324740590445
46748725.01639867693622.9836013230637
47581729.567371519449-148.567371519449
48641590.33117746495250.6688225350481
49598713.969329752655-115.969329752655
50609663.071496357481-54.0714963574812
51526627.802518600678-101.802518600678
52716547.706351674937168.293648325063
53552697.728164387797-145.728164387797
54464534.594199735566-70.5941997355656
55631569.50580358592461.4941964140755
56465485.324884210156-20.3248842101565
57539488.88042552650850.1195744734918
58537615.652500467166-78.6525004671663
59488533.352104595331-45.3521045953308
60520490.03059261825229.9694073817479
61477555.375949525936-78.3759495259362
62480536.123214219122-56.1232142191219
63645485.452686135566159.547313864434
64455575.956628567562-120.956628567562
65379532.513019130815-153.513019130815
66477389.94247446485687.0575255351445
67424518.255564148921-94.2555641489207
68316356.807254881641-40.8072548816413
69381375.2376872937935.76231270620696
70376447.486544138118-71.4865441381182
71389377.84743200461511.1525679953845
72472376.62863721152595.3713627884752







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73430.4231117356271.722509381792589.123714089408
74444.219399676664276.893928090029611.544871263299
75478.795267519177303.268216339257654.322318699097
76429.506201443298246.144051722734612.868351163863
77416.441118669944225.565216041102607.317021298786
78399.335401072321201.230523649771597.440278494872
79442.658588252594237.5793969317647.737779573489
80329.183197168563117.359197189664541.007197147461
81375.606728203087157.24615662184593.967299784335
82422.113518237822197.406438964566646.820597511078
83401.839208855687170.960011590655632.71840612072
84422.859510877442185.968953902339659.750067852544

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 430.4231117356 & 271.722509381792 & 589.123714089408 \tabularnewline
74 & 444.219399676664 & 276.893928090029 & 611.544871263299 \tabularnewline
75 & 478.795267519177 & 303.268216339257 & 654.322318699097 \tabularnewline
76 & 429.506201443298 & 246.144051722734 & 612.868351163863 \tabularnewline
77 & 416.441118669944 & 225.565216041102 & 607.317021298786 \tabularnewline
78 & 399.335401072321 & 201.230523649771 & 597.440278494872 \tabularnewline
79 & 442.658588252594 & 237.5793969317 & 647.737779573489 \tabularnewline
80 & 329.183197168563 & 117.359197189664 & 541.007197147461 \tabularnewline
81 & 375.606728203087 & 157.24615662184 & 593.967299784335 \tabularnewline
82 & 422.113518237822 & 197.406438964566 & 646.820597511078 \tabularnewline
83 & 401.839208855687 & 170.960011590655 & 632.71840612072 \tabularnewline
84 & 422.859510877442 & 185.968953902339 & 659.750067852544 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]430.4231117356[/C][C]271.722509381792[/C][C]589.123714089408[/C][/ROW]
[ROW][C]74[/C][C]444.219399676664[/C][C]276.893928090029[/C][C]611.544871263299[/C][/ROW]
[ROW][C]75[/C][C]478.795267519177[/C][C]303.268216339257[/C][C]654.322318699097[/C][/ROW]
[ROW][C]76[/C][C]429.506201443298[/C][C]246.144051722734[/C][C]612.868351163863[/C][/ROW]
[ROW][C]77[/C][C]416.441118669944[/C][C]225.565216041102[/C][C]607.317021298786[/C][/ROW]
[ROW][C]78[/C][C]399.335401072321[/C][C]201.230523649771[/C][C]597.440278494872[/C][/ROW]
[ROW][C]79[/C][C]442.658588252594[/C][C]237.5793969317[/C][C]647.737779573489[/C][/ROW]
[ROW][C]80[/C][C]329.183197168563[/C][C]117.359197189664[/C][C]541.007197147461[/C][/ROW]
[ROW][C]81[/C][C]375.606728203087[/C][C]157.24615662184[/C][C]593.967299784335[/C][/ROW]
[ROW][C]82[/C][C]422.113518237822[/C][C]197.406438964566[/C][C]646.820597511078[/C][/ROW]
[ROW][C]83[/C][C]401.839208855687[/C][C]170.960011590655[/C][C]632.71840612072[/C][/ROW]
[ROW][C]84[/C][C]422.859510877442[/C][C]185.968953902339[/C][C]659.750067852544[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
73430.4231117356271.722509381792589.123714089408
74444.219399676664276.893928090029611.544871263299
75478.795267519177303.268216339257654.322318699097
76429.506201443298246.144051722734612.868351163863
77416.441118669944225.565216041102607.317021298786
78399.335401072321201.230523649771597.440278494872
79442.658588252594237.5793969317647.737779573489
80329.183197168563117.359197189664541.007197147461
81375.606728203087157.24615662184593.967299784335
82422.113518237822197.406438964566646.820597511078
83401.839208855687170.960011590655632.71840612072
84422.859510877442185.968953902339659.750067852544



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
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')