Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 20:26:46 +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/2014/Nov/28/t141720642862ej8motdqare1t.htm/, Retrieved Sun, 19 May 2024 16:29:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261021, Retrieved Sun, 19 May 2024 16:29:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 20:26:46] [c260288012d574817ee98c3ddd4d9474] [Current]
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Dataseries X:
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
539
541
562
559
546
536
528
530
582
599
584
571
563
565
578
572
565
561
551
553
611
622
613
599
591
596




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=261021&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=261021&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261021&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
alpha1
beta0.0557587924246431
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0557587924246431 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261021&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0557587924246431[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261021&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261021&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
alpha1
beta0.0557587924246431
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3532537-5
4526519.7212060378776.27879396212325
5511514.071304007088-3.07130400708786
6499498.9000518044840.0999481955162764
7555486.90562479517168.0943752048292
8565546.70248492750318.2975150724974
9542557.722732272317-15.7227322723168
10527533.846051707196-6.84605170719635
11510518.464324131126-8.46432413112643
12514500.99236363888413.0076363611159
13517505.71765373467911.2823462653212
14508509.34674373815-1.34674373814977
15493500.271650933605-7.27165093360509
16490484.8661924586145.13380754138626
17469482.152447367662-13.152447367662
18478460.41908278501217.5809172149876
19528470.39937349863857.6006265013622
20534523.61111487525710.3888851247434
21518530.190386564451-12.1903865644507
22506513.510665330427-7.51066533042729
23502501.0918797012970.908120298702954
24516497.14251539252918.857484607471
25528512.19398596240815.8060140375921
26533525.0753102181917.92468978180898
27536530.5171813507655.48281864923547
28537533.8228966977293.17710330227078
29524535.000048141272-11.0000481412723
30536521.38669874030214.613301259698
31587534.2015187718852.7984812281197
32597588.1454983270158.85450167298461
33581598.639214647823-17.639214647823
34564581.655673339741-17.6556733397413
35558563.671214314873-5.6712143148734
36575557.35499425309517.6450057469053
37580575.3388584658684.66114153413196
38575580.598758089132-5.59875808913159
39563575.286578099004-12.2865780990038
40552562.601493341172-10.6014933411724
41537551.010366874571-14.0103668745706
42545535.2291657362189.77083426378158
43601543.77397565574857.2260243442519
44604602.9648296684471.0351703315531
45586606.022549516088-20.0225495160881
46564586.906116333808-22.9061163338084
47549563.628898947897-14.6288989478969
48551547.813209208063.18679079193998
49556549.9909008143296.0090991856714
50548555.325960928482-7.32596092848155
51540546.917474193759-6.91747419375929
52531538.531764186087-7.53176418608655
53521529.111802110243-8.11180211024327
54519518.6594978201880.340502179811551
55572516.67848381055355.3215161894474
56581572.7631447483778.23685525162341
57563582.222421850584-19.2224218505837
58548563.150602820718-15.1506028207181
59539547.305823502929-8.30582350292946
60541537.8427008143143.15729918568616
61562540.01874800423121.981251995769
62559562.244396071497-3.24439607149691
63546559.063492464403-13.063492464403
64536545.335087899739-9.33508789973939
65528534.814574671272-6.81457467127211
66530526.4346022167143.56539778328568
67582528.63340449162453.3665955083761
68599583.60906141298515.3909385870147
69584601.467241562879-17.4672415628791
70571585.493289266343-14.4932892663434
71563571.685160958591-8.68516095859104
72565563.2008868715261.79911312847366
73578565.30120324700512.6987967529946
74572579.009272819198-7.00927281919837
75565572.618444231025-7.61844423102502
76561565.193648980549-4.19364898054857
77551560.95981617754-9.95981617754035
78553550.4044688547092.59553114529081
79611552.54919253707158.4508074629288
80622613.8083389774498.19166102255053
81613625.265096104019-12.2650961040189
82599615.581209156287-16.5812091562866
83591600.656660956792-9.6566609567916
84596592.1182172029873.88178279701333

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 532 & 537 & -5 \tabularnewline
4 & 526 & 519.721206037877 & 6.27879396212325 \tabularnewline
5 & 511 & 514.071304007088 & -3.07130400708786 \tabularnewline
6 & 499 & 498.900051804484 & 0.0999481955162764 \tabularnewline
7 & 555 & 486.905624795171 & 68.0943752048292 \tabularnewline
8 & 565 & 546.702484927503 & 18.2975150724974 \tabularnewline
9 & 542 & 557.722732272317 & -15.7227322723168 \tabularnewline
10 & 527 & 533.846051707196 & -6.84605170719635 \tabularnewline
11 & 510 & 518.464324131126 & -8.46432413112643 \tabularnewline
12 & 514 & 500.992363638884 & 13.0076363611159 \tabularnewline
13 & 517 & 505.717653734679 & 11.2823462653212 \tabularnewline
14 & 508 & 509.34674373815 & -1.34674373814977 \tabularnewline
15 & 493 & 500.271650933605 & -7.27165093360509 \tabularnewline
16 & 490 & 484.866192458614 & 5.13380754138626 \tabularnewline
17 & 469 & 482.152447367662 & -13.152447367662 \tabularnewline
18 & 478 & 460.419082785012 & 17.5809172149876 \tabularnewline
19 & 528 & 470.399373498638 & 57.6006265013622 \tabularnewline
20 & 534 & 523.611114875257 & 10.3888851247434 \tabularnewline
21 & 518 & 530.190386564451 & -12.1903865644507 \tabularnewline
22 & 506 & 513.510665330427 & -7.51066533042729 \tabularnewline
23 & 502 & 501.091879701297 & 0.908120298702954 \tabularnewline
24 & 516 & 497.142515392529 & 18.857484607471 \tabularnewline
25 & 528 & 512.193985962408 & 15.8060140375921 \tabularnewline
26 & 533 & 525.075310218191 & 7.92468978180898 \tabularnewline
27 & 536 & 530.517181350765 & 5.48281864923547 \tabularnewline
28 & 537 & 533.822896697729 & 3.17710330227078 \tabularnewline
29 & 524 & 535.000048141272 & -11.0000481412723 \tabularnewline
30 & 536 & 521.386698740302 & 14.613301259698 \tabularnewline
31 & 587 & 534.20151877188 & 52.7984812281197 \tabularnewline
32 & 597 & 588.145498327015 & 8.85450167298461 \tabularnewline
33 & 581 & 598.639214647823 & -17.639214647823 \tabularnewline
34 & 564 & 581.655673339741 & -17.6556733397413 \tabularnewline
35 & 558 & 563.671214314873 & -5.6712143148734 \tabularnewline
36 & 575 & 557.354994253095 & 17.6450057469053 \tabularnewline
37 & 580 & 575.338858465868 & 4.66114153413196 \tabularnewline
38 & 575 & 580.598758089132 & -5.59875808913159 \tabularnewline
39 & 563 & 575.286578099004 & -12.2865780990038 \tabularnewline
40 & 552 & 562.601493341172 & -10.6014933411724 \tabularnewline
41 & 537 & 551.010366874571 & -14.0103668745706 \tabularnewline
42 & 545 & 535.229165736218 & 9.77083426378158 \tabularnewline
43 & 601 & 543.773975655748 & 57.2260243442519 \tabularnewline
44 & 604 & 602.964829668447 & 1.0351703315531 \tabularnewline
45 & 586 & 606.022549516088 & -20.0225495160881 \tabularnewline
46 & 564 & 586.906116333808 & -22.9061163338084 \tabularnewline
47 & 549 & 563.628898947897 & -14.6288989478969 \tabularnewline
48 & 551 & 547.81320920806 & 3.18679079193998 \tabularnewline
49 & 556 & 549.990900814329 & 6.0090991856714 \tabularnewline
50 & 548 & 555.325960928482 & -7.32596092848155 \tabularnewline
51 & 540 & 546.917474193759 & -6.91747419375929 \tabularnewline
52 & 531 & 538.531764186087 & -7.53176418608655 \tabularnewline
53 & 521 & 529.111802110243 & -8.11180211024327 \tabularnewline
54 & 519 & 518.659497820188 & 0.340502179811551 \tabularnewline
55 & 572 & 516.678483810553 & 55.3215161894474 \tabularnewline
56 & 581 & 572.763144748377 & 8.23685525162341 \tabularnewline
57 & 563 & 582.222421850584 & -19.2224218505837 \tabularnewline
58 & 548 & 563.150602820718 & -15.1506028207181 \tabularnewline
59 & 539 & 547.305823502929 & -8.30582350292946 \tabularnewline
60 & 541 & 537.842700814314 & 3.15729918568616 \tabularnewline
61 & 562 & 540.018748004231 & 21.981251995769 \tabularnewline
62 & 559 & 562.244396071497 & -3.24439607149691 \tabularnewline
63 & 546 & 559.063492464403 & -13.063492464403 \tabularnewline
64 & 536 & 545.335087899739 & -9.33508789973939 \tabularnewline
65 & 528 & 534.814574671272 & -6.81457467127211 \tabularnewline
66 & 530 & 526.434602216714 & 3.56539778328568 \tabularnewline
67 & 582 & 528.633404491624 & 53.3665955083761 \tabularnewline
68 & 599 & 583.609061412985 & 15.3909385870147 \tabularnewline
69 & 584 & 601.467241562879 & -17.4672415628791 \tabularnewline
70 & 571 & 585.493289266343 & -14.4932892663434 \tabularnewline
71 & 563 & 571.685160958591 & -8.68516095859104 \tabularnewline
72 & 565 & 563.200886871526 & 1.79911312847366 \tabularnewline
73 & 578 & 565.301203247005 & 12.6987967529946 \tabularnewline
74 & 572 & 579.009272819198 & -7.00927281919837 \tabularnewline
75 & 565 & 572.618444231025 & -7.61844423102502 \tabularnewline
76 & 561 & 565.193648980549 & -4.19364898054857 \tabularnewline
77 & 551 & 560.95981617754 & -9.95981617754035 \tabularnewline
78 & 553 & 550.404468854709 & 2.59553114529081 \tabularnewline
79 & 611 & 552.549192537071 & 58.4508074629288 \tabularnewline
80 & 622 & 613.808338977449 & 8.19166102255053 \tabularnewline
81 & 613 & 625.265096104019 & -12.2650961040189 \tabularnewline
82 & 599 & 615.581209156287 & -16.5812091562866 \tabularnewline
83 & 591 & 600.656660956792 & -9.6566609567916 \tabularnewline
84 & 596 & 592.118217202987 & 3.88178279701333 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261021&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]3[/C][C]532[/C][C]537[/C][C]-5[/C][/ROW]
[ROW][C]4[/C][C]526[/C][C]519.721206037877[/C][C]6.27879396212325[/C][/ROW]
[ROW][C]5[/C][C]511[/C][C]514.071304007088[/C][C]-3.07130400708786[/C][/ROW]
[ROW][C]6[/C][C]499[/C][C]498.900051804484[/C][C]0.0999481955162764[/C][/ROW]
[ROW][C]7[/C][C]555[/C][C]486.905624795171[/C][C]68.0943752048292[/C][/ROW]
[ROW][C]8[/C][C]565[/C][C]546.702484927503[/C][C]18.2975150724974[/C][/ROW]
[ROW][C]9[/C][C]542[/C][C]557.722732272317[/C][C]-15.7227322723168[/C][/ROW]
[ROW][C]10[/C][C]527[/C][C]533.846051707196[/C][C]-6.84605170719635[/C][/ROW]
[ROW][C]11[/C][C]510[/C][C]518.464324131126[/C][C]-8.46432413112643[/C][/ROW]
[ROW][C]12[/C][C]514[/C][C]500.992363638884[/C][C]13.0076363611159[/C][/ROW]
[ROW][C]13[/C][C]517[/C][C]505.717653734679[/C][C]11.2823462653212[/C][/ROW]
[ROW][C]14[/C][C]508[/C][C]509.34674373815[/C][C]-1.34674373814977[/C][/ROW]
[ROW][C]15[/C][C]493[/C][C]500.271650933605[/C][C]-7.27165093360509[/C][/ROW]
[ROW][C]16[/C][C]490[/C][C]484.866192458614[/C][C]5.13380754138626[/C][/ROW]
[ROW][C]17[/C][C]469[/C][C]482.152447367662[/C][C]-13.152447367662[/C][/ROW]
[ROW][C]18[/C][C]478[/C][C]460.419082785012[/C][C]17.5809172149876[/C][/ROW]
[ROW][C]19[/C][C]528[/C][C]470.399373498638[/C][C]57.6006265013622[/C][/ROW]
[ROW][C]20[/C][C]534[/C][C]523.611114875257[/C][C]10.3888851247434[/C][/ROW]
[ROW][C]21[/C][C]518[/C][C]530.190386564451[/C][C]-12.1903865644507[/C][/ROW]
[ROW][C]22[/C][C]506[/C][C]513.510665330427[/C][C]-7.51066533042729[/C][/ROW]
[ROW][C]23[/C][C]502[/C][C]501.091879701297[/C][C]0.908120298702954[/C][/ROW]
[ROW][C]24[/C][C]516[/C][C]497.142515392529[/C][C]18.857484607471[/C][/ROW]
[ROW][C]25[/C][C]528[/C][C]512.193985962408[/C][C]15.8060140375921[/C][/ROW]
[ROW][C]26[/C][C]533[/C][C]525.075310218191[/C][C]7.92468978180898[/C][/ROW]
[ROW][C]27[/C][C]536[/C][C]530.517181350765[/C][C]5.48281864923547[/C][/ROW]
[ROW][C]28[/C][C]537[/C][C]533.822896697729[/C][C]3.17710330227078[/C][/ROW]
[ROW][C]29[/C][C]524[/C][C]535.000048141272[/C][C]-11.0000481412723[/C][/ROW]
[ROW][C]30[/C][C]536[/C][C]521.386698740302[/C][C]14.613301259698[/C][/ROW]
[ROW][C]31[/C][C]587[/C][C]534.20151877188[/C][C]52.7984812281197[/C][/ROW]
[ROW][C]32[/C][C]597[/C][C]588.145498327015[/C][C]8.85450167298461[/C][/ROW]
[ROW][C]33[/C][C]581[/C][C]598.639214647823[/C][C]-17.639214647823[/C][/ROW]
[ROW][C]34[/C][C]564[/C][C]581.655673339741[/C][C]-17.6556733397413[/C][/ROW]
[ROW][C]35[/C][C]558[/C][C]563.671214314873[/C][C]-5.6712143148734[/C][/ROW]
[ROW][C]36[/C][C]575[/C][C]557.354994253095[/C][C]17.6450057469053[/C][/ROW]
[ROW][C]37[/C][C]580[/C][C]575.338858465868[/C][C]4.66114153413196[/C][/ROW]
[ROW][C]38[/C][C]575[/C][C]580.598758089132[/C][C]-5.59875808913159[/C][/ROW]
[ROW][C]39[/C][C]563[/C][C]575.286578099004[/C][C]-12.2865780990038[/C][/ROW]
[ROW][C]40[/C][C]552[/C][C]562.601493341172[/C][C]-10.6014933411724[/C][/ROW]
[ROW][C]41[/C][C]537[/C][C]551.010366874571[/C][C]-14.0103668745706[/C][/ROW]
[ROW][C]42[/C][C]545[/C][C]535.229165736218[/C][C]9.77083426378158[/C][/ROW]
[ROW][C]43[/C][C]601[/C][C]543.773975655748[/C][C]57.2260243442519[/C][/ROW]
[ROW][C]44[/C][C]604[/C][C]602.964829668447[/C][C]1.0351703315531[/C][/ROW]
[ROW][C]45[/C][C]586[/C][C]606.022549516088[/C][C]-20.0225495160881[/C][/ROW]
[ROW][C]46[/C][C]564[/C][C]586.906116333808[/C][C]-22.9061163338084[/C][/ROW]
[ROW][C]47[/C][C]549[/C][C]563.628898947897[/C][C]-14.6288989478969[/C][/ROW]
[ROW][C]48[/C][C]551[/C][C]547.81320920806[/C][C]3.18679079193998[/C][/ROW]
[ROW][C]49[/C][C]556[/C][C]549.990900814329[/C][C]6.0090991856714[/C][/ROW]
[ROW][C]50[/C][C]548[/C][C]555.325960928482[/C][C]-7.32596092848155[/C][/ROW]
[ROW][C]51[/C][C]540[/C][C]546.917474193759[/C][C]-6.91747419375929[/C][/ROW]
[ROW][C]52[/C][C]531[/C][C]538.531764186087[/C][C]-7.53176418608655[/C][/ROW]
[ROW][C]53[/C][C]521[/C][C]529.111802110243[/C][C]-8.11180211024327[/C][/ROW]
[ROW][C]54[/C][C]519[/C][C]518.659497820188[/C][C]0.340502179811551[/C][/ROW]
[ROW][C]55[/C][C]572[/C][C]516.678483810553[/C][C]55.3215161894474[/C][/ROW]
[ROW][C]56[/C][C]581[/C][C]572.763144748377[/C][C]8.23685525162341[/C][/ROW]
[ROW][C]57[/C][C]563[/C][C]582.222421850584[/C][C]-19.2224218505837[/C][/ROW]
[ROW][C]58[/C][C]548[/C][C]563.150602820718[/C][C]-15.1506028207181[/C][/ROW]
[ROW][C]59[/C][C]539[/C][C]547.305823502929[/C][C]-8.30582350292946[/C][/ROW]
[ROW][C]60[/C][C]541[/C][C]537.842700814314[/C][C]3.15729918568616[/C][/ROW]
[ROW][C]61[/C][C]562[/C][C]540.018748004231[/C][C]21.981251995769[/C][/ROW]
[ROW][C]62[/C][C]559[/C][C]562.244396071497[/C][C]-3.24439607149691[/C][/ROW]
[ROW][C]63[/C][C]546[/C][C]559.063492464403[/C][C]-13.063492464403[/C][/ROW]
[ROW][C]64[/C][C]536[/C][C]545.335087899739[/C][C]-9.33508789973939[/C][/ROW]
[ROW][C]65[/C][C]528[/C][C]534.814574671272[/C][C]-6.81457467127211[/C][/ROW]
[ROW][C]66[/C][C]530[/C][C]526.434602216714[/C][C]3.56539778328568[/C][/ROW]
[ROW][C]67[/C][C]582[/C][C]528.633404491624[/C][C]53.3665955083761[/C][/ROW]
[ROW][C]68[/C][C]599[/C][C]583.609061412985[/C][C]15.3909385870147[/C][/ROW]
[ROW][C]69[/C][C]584[/C][C]601.467241562879[/C][C]-17.4672415628791[/C][/ROW]
[ROW][C]70[/C][C]571[/C][C]585.493289266343[/C][C]-14.4932892663434[/C][/ROW]
[ROW][C]71[/C][C]563[/C][C]571.685160958591[/C][C]-8.68516095859104[/C][/ROW]
[ROW][C]72[/C][C]565[/C][C]563.200886871526[/C][C]1.79911312847366[/C][/ROW]
[ROW][C]73[/C][C]578[/C][C]565.301203247005[/C][C]12.6987967529946[/C][/ROW]
[ROW][C]74[/C][C]572[/C][C]579.009272819198[/C][C]-7.00927281919837[/C][/ROW]
[ROW][C]75[/C][C]565[/C][C]572.618444231025[/C][C]-7.61844423102502[/C][/ROW]
[ROW][C]76[/C][C]561[/C][C]565.193648980549[/C][C]-4.19364898054857[/C][/ROW]
[ROW][C]77[/C][C]551[/C][C]560.95981617754[/C][C]-9.95981617754035[/C][/ROW]
[ROW][C]78[/C][C]553[/C][C]550.404468854709[/C][C]2.59553114529081[/C][/ROW]
[ROW][C]79[/C][C]611[/C][C]552.549192537071[/C][C]58.4508074629288[/C][/ROW]
[ROW][C]80[/C][C]622[/C][C]613.808338977449[/C][C]8.19166102255053[/C][/ROW]
[ROW][C]81[/C][C]613[/C][C]625.265096104019[/C][C]-12.2650961040189[/C][/ROW]
[ROW][C]82[/C][C]599[/C][C]615.581209156287[/C][C]-16.5812091562866[/C][/ROW]
[ROW][C]83[/C][C]591[/C][C]600.656660956792[/C][C]-9.6566609567916[/C][/ROW]
[ROW][C]84[/C][C]596[/C][C]592.118217202987[/C][C]3.88178279701333[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261021&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261021&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
3532537-5
4526519.7212060378776.27879396212325
5511514.071304007088-3.07130400708786
6499498.9000518044840.0999481955162764
7555486.90562479517168.0943752048292
8565546.70248492750318.2975150724974
9542557.722732272317-15.7227322723168
10527533.846051707196-6.84605170719635
11510518.464324131126-8.46432413112643
12514500.99236363888413.0076363611159
13517505.71765373467911.2823462653212
14508509.34674373815-1.34674373814977
15493500.271650933605-7.27165093360509
16490484.8661924586145.13380754138626
17469482.152447367662-13.152447367662
18478460.41908278501217.5809172149876
19528470.39937349863857.6006265013622
20534523.61111487525710.3888851247434
21518530.190386564451-12.1903865644507
22506513.510665330427-7.51066533042729
23502501.0918797012970.908120298702954
24516497.14251539252918.857484607471
25528512.19398596240815.8060140375921
26533525.0753102181917.92468978180898
27536530.5171813507655.48281864923547
28537533.8228966977293.17710330227078
29524535.000048141272-11.0000481412723
30536521.38669874030214.613301259698
31587534.2015187718852.7984812281197
32597588.1454983270158.85450167298461
33581598.639214647823-17.639214647823
34564581.655673339741-17.6556733397413
35558563.671214314873-5.6712143148734
36575557.35499425309517.6450057469053
37580575.3388584658684.66114153413196
38575580.598758089132-5.59875808913159
39563575.286578099004-12.2865780990038
40552562.601493341172-10.6014933411724
41537551.010366874571-14.0103668745706
42545535.2291657362189.77083426378158
43601543.77397565574857.2260243442519
44604602.9648296684471.0351703315531
45586606.022549516088-20.0225495160881
46564586.906116333808-22.9061163338084
47549563.628898947897-14.6288989478969
48551547.813209208063.18679079193998
49556549.9909008143296.0090991856714
50548555.325960928482-7.32596092848155
51540546.917474193759-6.91747419375929
52531538.531764186087-7.53176418608655
53521529.111802110243-8.11180211024327
54519518.6594978201880.340502179811551
55572516.67848381055355.3215161894474
56581572.7631447483778.23685525162341
57563582.222421850584-19.2224218505837
58548563.150602820718-15.1506028207181
59539547.305823502929-8.30582350292946
60541537.8427008143143.15729918568616
61562540.01874800423121.981251995769
62559562.244396071497-3.24439607149691
63546559.063492464403-13.063492464403
64536545.335087899739-9.33508789973939
65528534.814574671272-6.81457467127211
66530526.4346022167143.56539778328568
67582528.63340449162453.3665955083761
68599583.60906141298515.3909385870147
69584601.467241562879-17.4672415628791
70571585.493289266343-14.4932892663434
71563571.685160958591-8.68516095859104
72565563.2008868715261.79911312847366
73578565.30120324700512.6987967529946
74572579.009272819198-7.00927281919837
75565572.618444231025-7.61844423102502
76561565.193648980549-4.19364898054857
77551560.95981617754-9.95981617754035
78553550.4044688547092.59553114529081
79611552.54919253707158.4508074629288
80622613.8083389774498.19166102255053
81613625.265096104019-12.2650961040189
82599615.581209156287-16.5812091562866
83591600.656660956792-9.6566609567916
84596592.1182172029873.88178279701333







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85597.334660724203558.329816098262636.339505350144
86598.669321448406541.949428753349655.389214143462
87600.003982172609528.612350817265671.395613527952
88601.338642896812516.664595140418686.012690653205
89602.673303621015505.48588523054699.86072201149
90604.007964345217494.768205667895713.24772302254
91605.34262506942484.334583314678726.350666824163
92606.677285793623474.073672599406739.28089898784
93608.011946517826463.910936379611752.112956656042
94609.346607242029453.794188746406764.899025737653
95610.681267966232443.685640414028777.676895518437
96612.015928690435433.557207002624790.474650378246

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 597.334660724203 & 558.329816098262 & 636.339505350144 \tabularnewline
86 & 598.669321448406 & 541.949428753349 & 655.389214143462 \tabularnewline
87 & 600.003982172609 & 528.612350817265 & 671.395613527952 \tabularnewline
88 & 601.338642896812 & 516.664595140418 & 686.012690653205 \tabularnewline
89 & 602.673303621015 & 505.48588523054 & 699.86072201149 \tabularnewline
90 & 604.007964345217 & 494.768205667895 & 713.24772302254 \tabularnewline
91 & 605.34262506942 & 484.334583314678 & 726.350666824163 \tabularnewline
92 & 606.677285793623 & 474.073672599406 & 739.28089898784 \tabularnewline
93 & 608.011946517826 & 463.910936379611 & 752.112956656042 \tabularnewline
94 & 609.346607242029 & 453.794188746406 & 764.899025737653 \tabularnewline
95 & 610.681267966232 & 443.685640414028 & 777.676895518437 \tabularnewline
96 & 612.015928690435 & 433.557207002624 & 790.474650378246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261021&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]85[/C][C]597.334660724203[/C][C]558.329816098262[/C][C]636.339505350144[/C][/ROW]
[ROW][C]86[/C][C]598.669321448406[/C][C]541.949428753349[/C][C]655.389214143462[/C][/ROW]
[ROW][C]87[/C][C]600.003982172609[/C][C]528.612350817265[/C][C]671.395613527952[/C][/ROW]
[ROW][C]88[/C][C]601.338642896812[/C][C]516.664595140418[/C][C]686.012690653205[/C][/ROW]
[ROW][C]89[/C][C]602.673303621015[/C][C]505.48588523054[/C][C]699.86072201149[/C][/ROW]
[ROW][C]90[/C][C]604.007964345217[/C][C]494.768205667895[/C][C]713.24772302254[/C][/ROW]
[ROW][C]91[/C][C]605.34262506942[/C][C]484.334583314678[/C][C]726.350666824163[/C][/ROW]
[ROW][C]92[/C][C]606.677285793623[/C][C]474.073672599406[/C][C]739.28089898784[/C][/ROW]
[ROW][C]93[/C][C]608.011946517826[/C][C]463.910936379611[/C][C]752.112956656042[/C][/ROW]
[ROW][C]94[/C][C]609.346607242029[/C][C]453.794188746406[/C][C]764.899025737653[/C][/ROW]
[ROW][C]95[/C][C]610.681267966232[/C][C]443.685640414028[/C][C]777.676895518437[/C][/ROW]
[ROW][C]96[/C][C]612.015928690435[/C][C]433.557207002624[/C][C]790.474650378246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261021&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261021&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
85597.334660724203558.329816098262636.339505350144
86598.669321448406541.949428753349655.389214143462
87600.003982172609528.612350817265671.395613527952
88601.338642896812516.664595140418686.012690653205
89602.673303621015505.48588523054699.86072201149
90604.007964345217494.768205667895713.24772302254
91605.34262506942484.334583314678726.350666824163
92606.677285793623474.073672599406739.28089898784
93608.011946517826463.910936379611752.112956656042
94609.346607242029453.794188746406764.899025737653
95610.681267966232443.685640414028777.676895518437
96612.015928690435433.557207002624790.474650378246



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