Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 28 Dec 2010 09:47:16 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/28/t129352971909e74hoq751cuj9.htm/, Retrieved Sun, 05 May 2024 05:18:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116253, Retrieved Sun, 05 May 2024 05:18:46 +0000
QR Codes:

Original text written by user:Data Paper Statistiek
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2010-12-28 09:47:16] [25b2a837ac14189684edc0746bbb952e] [Current]
-    D    [Exponential Smoothing] [] [2010-12-29 09:53:55] [dc73d270d5d96f29ff77294e1b86f79b]
Feedback Forum

Post a new message
Dataseries X:
464
460
467
460
448
443
436
431
484
510
513
503
471
471
476
475
470
461
455
456
517
525
523
519
509
512
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
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116253&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116253&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.536611617913518
beta0.166578889966966
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.536611617913518 \tabularnewline
beta & 0.166578889966966 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116253&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]0.536611617913518[/C][/ROW]
[ROW][C]beta[/C][C]0.166578889966966[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116253&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
alpha0.536611617913518
beta0.166578889966966
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13471463.0715811965817.92841880341877
14471467.7515528842053.24844711579470
15476474.6272367948171.37276320518305
16475475.035782381664-0.0357823816636937
17470471.64362085405-1.64362085404969
18461463.200087599295-2.20008759929476
19455455.052952691543-0.052952691543112
20456451.5949286431164.40507135688415
21517508.8395600156628.16043998433759
22525541.662145934044-16.6621459340436
23523536.133578501047-13.1335785010471
24519518.1994948302210.800505169779285
25509489.61309519428419.3869048057157
26512498.59908509824213.4009149017578
27519511.2869475455597.71305245444125
28517516.2452256872110.754774312789436
29510514.403062155734-4.40306215573378
30509505.845088770723.15491122927972
31501503.669307708342-2.66930770834210
32507502.7420844205534.25791557944746
33569563.5037612085285.49623879147248
34580585.011876546371-5.01187654637124
35578590.029141065672-12.0291410656716
36565581.902392373837-16.9023923738370
37547553.604492859586-6.604492859586
38555544.72139417986010.2786058201395
39562551.6710379807210.3289620192795
40561553.615427757317.38457224268984
41555552.3402042333032.65979576669702
42544551.105250362051-7.10525036205081
43537539.838465791353-2.83846579135343
44543541.1289381652331.87106183476715
45594600.06874267317-6.06874267317039
46611608.3529601087552.64703989124450
47613612.7643299012270.235670098773085
48611608.5931029135762.40689708642446
49594596.787031036753-2.78703103675298
50595599.475406005942-4.47540600594198
51591598.911923547078-7.91192354707778
52589588.4538402750720.54615972492843
53584579.4585595365324.54144046346835
54573573.015426832889-0.0154268328886928
55567566.4711663592320.528833640767857
56569570.992771866034-1.99277186603410
57621623.076464890373-2.07646489037290
58629636.795119478016-7.79511947801586
59628632.805641128437-4.80564112843717
60612624.804612392861-12.8046123928613
61595598.938635959318-3.93863595931759
62597596.6333072541310.366692745869045
63593593.915169523852-0.915169523852
64590588.5958908797091.40410912029097
65580579.4539405644580.546059435542247
66574565.9396789629678.06032103703274
67573561.88747724808211.1125227519179
68573569.7723018210453.22769817895528
69620623.937596823766-3.93759682376572
70626633.160244599522-7.16024459952166
71620630.106143626558-10.1061436265580
72588614.289777716373-26.2897777163729
73566582.826085556346-16.8260855563458
74557571.978445650377-14.9784456503767
75561555.438459166515.56154083349043
76549550.254857467324-1.25485746732409
77532534.636256526055-2.63625652605481
78526517.9596793327878.0403206672131
79511510.3726428041430.627357195856575
80499503.101562688043-4.10156268804326
81555543.48272056712811.5172794328715
82565554.35592389348910.6440761065107
83542555.932855417494-13.9328554174937
84527526.6637832705710.336216729428997
85510512.353382708619-2.35338270861905
86514509.9019351899934.09806481000726
87517514.5956282985042.40437170149607
88508505.7560109646642.24398903533626
89493492.884360690520.115639309479718
90490484.3874247913585.61257520864183
91469473.601079162435-4.60107916243538
92478462.40420094075215.5957990592484
93528523.4246611522044.57533884779582
94534532.3794580802911.62054191970924
95518519.130346449903-1.13034644990262
96506505.8925190879180.107480912082281
97502492.7417482997469.2582517002544
98516503.0774084618112.9225915381903
99528516.07705962675911.9229403732409
100533517.47719697697915.5228030230213
101536517.13812848883718.8618715111627
102537529.3168146249777.68318537502341
103524523.1627415530290.837258446970736
104536532.9833080907583.01669190924167
105587589.76266759015-2.76266759015039
106597600.370403048525-3.37040304852474
107581589.682047832455-8.68204783245471
108564578.804137022419-14.8041370224188
109558566.397709905406-8.39770990540592
110575571.8844846235543.11551537644561
111580581.209177648417-1.20917764841727
112575578.107606064073-3.10760606407325
113563568.530194661399-5.53019466139949
114552559.471044825142-7.47104482514192
115537537.68940729755-0.689407297549792
116545543.2409000858931.75909991410708
117601592.0951478979258.90485210207453
118604605.152945466706-1.15294546670555
119586589.862116780835-3.86211678083487
120564575.833544283051-11.8335442830514
121549565.35518379774-16.3551837977404

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 471 & 463.071581196581 & 7.92841880341877 \tabularnewline
14 & 471 & 467.751552884205 & 3.24844711579470 \tabularnewline
15 & 476 & 474.627236794817 & 1.37276320518305 \tabularnewline
16 & 475 & 475.035782381664 & -0.0357823816636937 \tabularnewline
17 & 470 & 471.64362085405 & -1.64362085404969 \tabularnewline
18 & 461 & 463.200087599295 & -2.20008759929476 \tabularnewline
19 & 455 & 455.052952691543 & -0.052952691543112 \tabularnewline
20 & 456 & 451.594928643116 & 4.40507135688415 \tabularnewline
21 & 517 & 508.839560015662 & 8.16043998433759 \tabularnewline
22 & 525 & 541.662145934044 & -16.6621459340436 \tabularnewline
23 & 523 & 536.133578501047 & -13.1335785010471 \tabularnewline
24 & 519 & 518.199494830221 & 0.800505169779285 \tabularnewline
25 & 509 & 489.613095194284 & 19.3869048057157 \tabularnewline
26 & 512 & 498.599085098242 & 13.4009149017578 \tabularnewline
27 & 519 & 511.286947545559 & 7.71305245444125 \tabularnewline
28 & 517 & 516.245225687211 & 0.754774312789436 \tabularnewline
29 & 510 & 514.403062155734 & -4.40306215573378 \tabularnewline
30 & 509 & 505.84508877072 & 3.15491122927972 \tabularnewline
31 & 501 & 503.669307708342 & -2.66930770834210 \tabularnewline
32 & 507 & 502.742084420553 & 4.25791557944746 \tabularnewline
33 & 569 & 563.503761208528 & 5.49623879147248 \tabularnewline
34 & 580 & 585.011876546371 & -5.01187654637124 \tabularnewline
35 & 578 & 590.029141065672 & -12.0291410656716 \tabularnewline
36 & 565 & 581.902392373837 & -16.9023923738370 \tabularnewline
37 & 547 & 553.604492859586 & -6.604492859586 \tabularnewline
38 & 555 & 544.721394179860 & 10.2786058201395 \tabularnewline
39 & 562 & 551.67103798072 & 10.3289620192795 \tabularnewline
40 & 561 & 553.61542775731 & 7.38457224268984 \tabularnewline
41 & 555 & 552.340204233303 & 2.65979576669702 \tabularnewline
42 & 544 & 551.105250362051 & -7.10525036205081 \tabularnewline
43 & 537 & 539.838465791353 & -2.83846579135343 \tabularnewline
44 & 543 & 541.128938165233 & 1.87106183476715 \tabularnewline
45 & 594 & 600.06874267317 & -6.06874267317039 \tabularnewline
46 & 611 & 608.352960108755 & 2.64703989124450 \tabularnewline
47 & 613 & 612.764329901227 & 0.235670098773085 \tabularnewline
48 & 611 & 608.593102913576 & 2.40689708642446 \tabularnewline
49 & 594 & 596.787031036753 & -2.78703103675298 \tabularnewline
50 & 595 & 599.475406005942 & -4.47540600594198 \tabularnewline
51 & 591 & 598.911923547078 & -7.91192354707778 \tabularnewline
52 & 589 & 588.453840275072 & 0.54615972492843 \tabularnewline
53 & 584 & 579.458559536532 & 4.54144046346835 \tabularnewline
54 & 573 & 573.015426832889 & -0.0154268328886928 \tabularnewline
55 & 567 & 566.471166359232 & 0.528833640767857 \tabularnewline
56 & 569 & 570.992771866034 & -1.99277186603410 \tabularnewline
57 & 621 & 623.076464890373 & -2.07646489037290 \tabularnewline
58 & 629 & 636.795119478016 & -7.79511947801586 \tabularnewline
59 & 628 & 632.805641128437 & -4.80564112843717 \tabularnewline
60 & 612 & 624.804612392861 & -12.8046123928613 \tabularnewline
61 & 595 & 598.938635959318 & -3.93863595931759 \tabularnewline
62 & 597 & 596.633307254131 & 0.366692745869045 \tabularnewline
63 & 593 & 593.915169523852 & -0.915169523852 \tabularnewline
64 & 590 & 588.595890879709 & 1.40410912029097 \tabularnewline
65 & 580 & 579.453940564458 & 0.546059435542247 \tabularnewline
66 & 574 & 565.939678962967 & 8.06032103703274 \tabularnewline
67 & 573 & 561.887477248082 & 11.1125227519179 \tabularnewline
68 & 573 & 569.772301821045 & 3.22769817895528 \tabularnewline
69 & 620 & 623.937596823766 & -3.93759682376572 \tabularnewline
70 & 626 & 633.160244599522 & -7.16024459952166 \tabularnewline
71 & 620 & 630.106143626558 & -10.1061436265580 \tabularnewline
72 & 588 & 614.289777716373 & -26.2897777163729 \tabularnewline
73 & 566 & 582.826085556346 & -16.8260855563458 \tabularnewline
74 & 557 & 571.978445650377 & -14.9784456503767 \tabularnewline
75 & 561 & 555.43845916651 & 5.56154083349043 \tabularnewline
76 & 549 & 550.254857467324 & -1.25485746732409 \tabularnewline
77 & 532 & 534.636256526055 & -2.63625652605481 \tabularnewline
78 & 526 & 517.959679332787 & 8.0403206672131 \tabularnewline
79 & 511 & 510.372642804143 & 0.627357195856575 \tabularnewline
80 & 499 & 503.101562688043 & -4.10156268804326 \tabularnewline
81 & 555 & 543.482720567128 & 11.5172794328715 \tabularnewline
82 & 565 & 554.355923893489 & 10.6440761065107 \tabularnewline
83 & 542 & 555.932855417494 & -13.9328554174937 \tabularnewline
84 & 527 & 526.663783270571 & 0.336216729428997 \tabularnewline
85 & 510 & 512.353382708619 & -2.35338270861905 \tabularnewline
86 & 514 & 509.901935189993 & 4.09806481000726 \tabularnewline
87 & 517 & 514.595628298504 & 2.40437170149607 \tabularnewline
88 & 508 & 505.756010964664 & 2.24398903533626 \tabularnewline
89 & 493 & 492.88436069052 & 0.115639309479718 \tabularnewline
90 & 490 & 484.387424791358 & 5.61257520864183 \tabularnewline
91 & 469 & 473.601079162435 & -4.60107916243538 \tabularnewline
92 & 478 & 462.404200940752 & 15.5957990592484 \tabularnewline
93 & 528 & 523.424661152204 & 4.57533884779582 \tabularnewline
94 & 534 & 532.379458080291 & 1.62054191970924 \tabularnewline
95 & 518 & 519.130346449903 & -1.13034644990262 \tabularnewline
96 & 506 & 505.892519087918 & 0.107480912082281 \tabularnewline
97 & 502 & 492.741748299746 & 9.2582517002544 \tabularnewline
98 & 516 & 503.07740846181 & 12.9225915381903 \tabularnewline
99 & 528 & 516.077059626759 & 11.9229403732409 \tabularnewline
100 & 533 & 517.477196976979 & 15.5228030230213 \tabularnewline
101 & 536 & 517.138128488837 & 18.8618715111627 \tabularnewline
102 & 537 & 529.316814624977 & 7.68318537502341 \tabularnewline
103 & 524 & 523.162741553029 & 0.837258446970736 \tabularnewline
104 & 536 & 532.983308090758 & 3.01669190924167 \tabularnewline
105 & 587 & 589.76266759015 & -2.76266759015039 \tabularnewline
106 & 597 & 600.370403048525 & -3.37040304852474 \tabularnewline
107 & 581 & 589.682047832455 & -8.68204783245471 \tabularnewline
108 & 564 & 578.804137022419 & -14.8041370224188 \tabularnewline
109 & 558 & 566.397709905406 & -8.39770990540592 \tabularnewline
110 & 575 & 571.884484623554 & 3.11551537644561 \tabularnewline
111 & 580 & 581.209177648417 & -1.20917764841727 \tabularnewline
112 & 575 & 578.107606064073 & -3.10760606407325 \tabularnewline
113 & 563 & 568.530194661399 & -5.53019466139949 \tabularnewline
114 & 552 & 559.471044825142 & -7.47104482514192 \tabularnewline
115 & 537 & 537.68940729755 & -0.689407297549792 \tabularnewline
116 & 545 & 543.240900085893 & 1.75909991410708 \tabularnewline
117 & 601 & 592.095147897925 & 8.90485210207453 \tabularnewline
118 & 604 & 605.152945466706 & -1.15294546670555 \tabularnewline
119 & 586 & 589.862116780835 & -3.86211678083487 \tabularnewline
120 & 564 & 575.833544283051 & -11.8335442830514 \tabularnewline
121 & 549 & 565.35518379774 & -16.3551837977404 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116253&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]471[/C][C]463.071581196581[/C][C]7.92841880341877[/C][/ROW]
[ROW][C]14[/C][C]471[/C][C]467.751552884205[/C][C]3.24844711579470[/C][/ROW]
[ROW][C]15[/C][C]476[/C][C]474.627236794817[/C][C]1.37276320518305[/C][/ROW]
[ROW][C]16[/C][C]475[/C][C]475.035782381664[/C][C]-0.0357823816636937[/C][/ROW]
[ROW][C]17[/C][C]470[/C][C]471.64362085405[/C][C]-1.64362085404969[/C][/ROW]
[ROW][C]18[/C][C]461[/C][C]463.200087599295[/C][C]-2.20008759929476[/C][/ROW]
[ROW][C]19[/C][C]455[/C][C]455.052952691543[/C][C]-0.052952691543112[/C][/ROW]
[ROW][C]20[/C][C]456[/C][C]451.594928643116[/C][C]4.40507135688415[/C][/ROW]
[ROW][C]21[/C][C]517[/C][C]508.839560015662[/C][C]8.16043998433759[/C][/ROW]
[ROW][C]22[/C][C]525[/C][C]541.662145934044[/C][C]-16.6621459340436[/C][/ROW]
[ROW][C]23[/C][C]523[/C][C]536.133578501047[/C][C]-13.1335785010471[/C][/ROW]
[ROW][C]24[/C][C]519[/C][C]518.199494830221[/C][C]0.800505169779285[/C][/ROW]
[ROW][C]25[/C][C]509[/C][C]489.613095194284[/C][C]19.3869048057157[/C][/ROW]
[ROW][C]26[/C][C]512[/C][C]498.599085098242[/C][C]13.4009149017578[/C][/ROW]
[ROW][C]27[/C][C]519[/C][C]511.286947545559[/C][C]7.71305245444125[/C][/ROW]
[ROW][C]28[/C][C]517[/C][C]516.245225687211[/C][C]0.754774312789436[/C][/ROW]
[ROW][C]29[/C][C]510[/C][C]514.403062155734[/C][C]-4.40306215573378[/C][/ROW]
[ROW][C]30[/C][C]509[/C][C]505.84508877072[/C][C]3.15491122927972[/C][/ROW]
[ROW][C]31[/C][C]501[/C][C]503.669307708342[/C][C]-2.66930770834210[/C][/ROW]
[ROW][C]32[/C][C]507[/C][C]502.742084420553[/C][C]4.25791557944746[/C][/ROW]
[ROW][C]33[/C][C]569[/C][C]563.503761208528[/C][C]5.49623879147248[/C][/ROW]
[ROW][C]34[/C][C]580[/C][C]585.011876546371[/C][C]-5.01187654637124[/C][/ROW]
[ROW][C]35[/C][C]578[/C][C]590.029141065672[/C][C]-12.0291410656716[/C][/ROW]
[ROW][C]36[/C][C]565[/C][C]581.902392373837[/C][C]-16.9023923738370[/C][/ROW]
[ROW][C]37[/C][C]547[/C][C]553.604492859586[/C][C]-6.604492859586[/C][/ROW]
[ROW][C]38[/C][C]555[/C][C]544.721394179860[/C][C]10.2786058201395[/C][/ROW]
[ROW][C]39[/C][C]562[/C][C]551.67103798072[/C][C]10.3289620192795[/C][/ROW]
[ROW][C]40[/C][C]561[/C][C]553.61542775731[/C][C]7.38457224268984[/C][/ROW]
[ROW][C]41[/C][C]555[/C][C]552.340204233303[/C][C]2.65979576669702[/C][/ROW]
[ROW][C]42[/C][C]544[/C][C]551.105250362051[/C][C]-7.10525036205081[/C][/ROW]
[ROW][C]43[/C][C]537[/C][C]539.838465791353[/C][C]-2.83846579135343[/C][/ROW]
[ROW][C]44[/C][C]543[/C][C]541.128938165233[/C][C]1.87106183476715[/C][/ROW]
[ROW][C]45[/C][C]594[/C][C]600.06874267317[/C][C]-6.06874267317039[/C][/ROW]
[ROW][C]46[/C][C]611[/C][C]608.352960108755[/C][C]2.64703989124450[/C][/ROW]
[ROW][C]47[/C][C]613[/C][C]612.764329901227[/C][C]0.235670098773085[/C][/ROW]
[ROW][C]48[/C][C]611[/C][C]608.593102913576[/C][C]2.40689708642446[/C][/ROW]
[ROW][C]49[/C][C]594[/C][C]596.787031036753[/C][C]-2.78703103675298[/C][/ROW]
[ROW][C]50[/C][C]595[/C][C]599.475406005942[/C][C]-4.47540600594198[/C][/ROW]
[ROW][C]51[/C][C]591[/C][C]598.911923547078[/C][C]-7.91192354707778[/C][/ROW]
[ROW][C]52[/C][C]589[/C][C]588.453840275072[/C][C]0.54615972492843[/C][/ROW]
[ROW][C]53[/C][C]584[/C][C]579.458559536532[/C][C]4.54144046346835[/C][/ROW]
[ROW][C]54[/C][C]573[/C][C]573.015426832889[/C][C]-0.0154268328886928[/C][/ROW]
[ROW][C]55[/C][C]567[/C][C]566.471166359232[/C][C]0.528833640767857[/C][/ROW]
[ROW][C]56[/C][C]569[/C][C]570.992771866034[/C][C]-1.99277186603410[/C][/ROW]
[ROW][C]57[/C][C]621[/C][C]623.076464890373[/C][C]-2.07646489037290[/C][/ROW]
[ROW][C]58[/C][C]629[/C][C]636.795119478016[/C][C]-7.79511947801586[/C][/ROW]
[ROW][C]59[/C][C]628[/C][C]632.805641128437[/C][C]-4.80564112843717[/C][/ROW]
[ROW][C]60[/C][C]612[/C][C]624.804612392861[/C][C]-12.8046123928613[/C][/ROW]
[ROW][C]61[/C][C]595[/C][C]598.938635959318[/C][C]-3.93863595931759[/C][/ROW]
[ROW][C]62[/C][C]597[/C][C]596.633307254131[/C][C]0.366692745869045[/C][/ROW]
[ROW][C]63[/C][C]593[/C][C]593.915169523852[/C][C]-0.915169523852[/C][/ROW]
[ROW][C]64[/C][C]590[/C][C]588.595890879709[/C][C]1.40410912029097[/C][/ROW]
[ROW][C]65[/C][C]580[/C][C]579.453940564458[/C][C]0.546059435542247[/C][/ROW]
[ROW][C]66[/C][C]574[/C][C]565.939678962967[/C][C]8.06032103703274[/C][/ROW]
[ROW][C]67[/C][C]573[/C][C]561.887477248082[/C][C]11.1125227519179[/C][/ROW]
[ROW][C]68[/C][C]573[/C][C]569.772301821045[/C][C]3.22769817895528[/C][/ROW]
[ROW][C]69[/C][C]620[/C][C]623.937596823766[/C][C]-3.93759682376572[/C][/ROW]
[ROW][C]70[/C][C]626[/C][C]633.160244599522[/C][C]-7.16024459952166[/C][/ROW]
[ROW][C]71[/C][C]620[/C][C]630.106143626558[/C][C]-10.1061436265580[/C][/ROW]
[ROW][C]72[/C][C]588[/C][C]614.289777716373[/C][C]-26.2897777163729[/C][/ROW]
[ROW][C]73[/C][C]566[/C][C]582.826085556346[/C][C]-16.8260855563458[/C][/ROW]
[ROW][C]74[/C][C]557[/C][C]571.978445650377[/C][C]-14.9784456503767[/C][/ROW]
[ROW][C]75[/C][C]561[/C][C]555.43845916651[/C][C]5.56154083349043[/C][/ROW]
[ROW][C]76[/C][C]549[/C][C]550.254857467324[/C][C]-1.25485746732409[/C][/ROW]
[ROW][C]77[/C][C]532[/C][C]534.636256526055[/C][C]-2.63625652605481[/C][/ROW]
[ROW][C]78[/C][C]526[/C][C]517.959679332787[/C][C]8.0403206672131[/C][/ROW]
[ROW][C]79[/C][C]511[/C][C]510.372642804143[/C][C]0.627357195856575[/C][/ROW]
[ROW][C]80[/C][C]499[/C][C]503.101562688043[/C][C]-4.10156268804326[/C][/ROW]
[ROW][C]81[/C][C]555[/C][C]543.482720567128[/C][C]11.5172794328715[/C][/ROW]
[ROW][C]82[/C][C]565[/C][C]554.355923893489[/C][C]10.6440761065107[/C][/ROW]
[ROW][C]83[/C][C]542[/C][C]555.932855417494[/C][C]-13.9328554174937[/C][/ROW]
[ROW][C]84[/C][C]527[/C][C]526.663783270571[/C][C]0.336216729428997[/C][/ROW]
[ROW][C]85[/C][C]510[/C][C]512.353382708619[/C][C]-2.35338270861905[/C][/ROW]
[ROW][C]86[/C][C]514[/C][C]509.901935189993[/C][C]4.09806481000726[/C][/ROW]
[ROW][C]87[/C][C]517[/C][C]514.595628298504[/C][C]2.40437170149607[/C][/ROW]
[ROW][C]88[/C][C]508[/C][C]505.756010964664[/C][C]2.24398903533626[/C][/ROW]
[ROW][C]89[/C][C]493[/C][C]492.88436069052[/C][C]0.115639309479718[/C][/ROW]
[ROW][C]90[/C][C]490[/C][C]484.387424791358[/C][C]5.61257520864183[/C][/ROW]
[ROW][C]91[/C][C]469[/C][C]473.601079162435[/C][C]-4.60107916243538[/C][/ROW]
[ROW][C]92[/C][C]478[/C][C]462.404200940752[/C][C]15.5957990592484[/C][/ROW]
[ROW][C]93[/C][C]528[/C][C]523.424661152204[/C][C]4.57533884779582[/C][/ROW]
[ROW][C]94[/C][C]534[/C][C]532.379458080291[/C][C]1.62054191970924[/C][/ROW]
[ROW][C]95[/C][C]518[/C][C]519.130346449903[/C][C]-1.13034644990262[/C][/ROW]
[ROW][C]96[/C][C]506[/C][C]505.892519087918[/C][C]0.107480912082281[/C][/ROW]
[ROW][C]97[/C][C]502[/C][C]492.741748299746[/C][C]9.2582517002544[/C][/ROW]
[ROW][C]98[/C][C]516[/C][C]503.07740846181[/C][C]12.9225915381903[/C][/ROW]
[ROW][C]99[/C][C]528[/C][C]516.077059626759[/C][C]11.9229403732409[/C][/ROW]
[ROW][C]100[/C][C]533[/C][C]517.477196976979[/C][C]15.5228030230213[/C][/ROW]
[ROW][C]101[/C][C]536[/C][C]517.138128488837[/C][C]18.8618715111627[/C][/ROW]
[ROW][C]102[/C][C]537[/C][C]529.316814624977[/C][C]7.68318537502341[/C][/ROW]
[ROW][C]103[/C][C]524[/C][C]523.162741553029[/C][C]0.837258446970736[/C][/ROW]
[ROW][C]104[/C][C]536[/C][C]532.983308090758[/C][C]3.01669190924167[/C][/ROW]
[ROW][C]105[/C][C]587[/C][C]589.76266759015[/C][C]-2.76266759015039[/C][/ROW]
[ROW][C]106[/C][C]597[/C][C]600.370403048525[/C][C]-3.37040304852474[/C][/ROW]
[ROW][C]107[/C][C]581[/C][C]589.682047832455[/C][C]-8.68204783245471[/C][/ROW]
[ROW][C]108[/C][C]564[/C][C]578.804137022419[/C][C]-14.8041370224188[/C][/ROW]
[ROW][C]109[/C][C]558[/C][C]566.397709905406[/C][C]-8.39770990540592[/C][/ROW]
[ROW][C]110[/C][C]575[/C][C]571.884484623554[/C][C]3.11551537644561[/C][/ROW]
[ROW][C]111[/C][C]580[/C][C]581.209177648417[/C][C]-1.20917764841727[/C][/ROW]
[ROW][C]112[/C][C]575[/C][C]578.107606064073[/C][C]-3.10760606407325[/C][/ROW]
[ROW][C]113[/C][C]563[/C][C]568.530194661399[/C][C]-5.53019466139949[/C][/ROW]
[ROW][C]114[/C][C]552[/C][C]559.471044825142[/C][C]-7.47104482514192[/C][/ROW]
[ROW][C]115[/C][C]537[/C][C]537.68940729755[/C][C]-0.689407297549792[/C][/ROW]
[ROW][C]116[/C][C]545[/C][C]543.240900085893[/C][C]1.75909991410708[/C][/ROW]
[ROW][C]117[/C][C]601[/C][C]592.095147897925[/C][C]8.90485210207453[/C][/ROW]
[ROW][C]118[/C][C]604[/C][C]605.152945466706[/C][C]-1.15294546670555[/C][/ROW]
[ROW][C]119[/C][C]586[/C][C]589.862116780835[/C][C]-3.86211678083487[/C][/ROW]
[ROW][C]120[/C][C]564[/C][C]575.833544283051[/C][C]-11.8335442830514[/C][/ROW]
[ROW][C]121[/C][C]549[/C][C]565.35518379774[/C][C]-16.3551837977404[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116253&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116253&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
13471463.0715811965817.92841880341877
14471467.7515528842053.24844711579470
15476474.6272367948171.37276320518305
16475475.035782381664-0.0357823816636937
17470471.64362085405-1.64362085404969
18461463.200087599295-2.20008759929476
19455455.052952691543-0.052952691543112
20456451.5949286431164.40507135688415
21517508.8395600156628.16043998433759
22525541.662145934044-16.6621459340436
23523536.133578501047-13.1335785010471
24519518.1994948302210.800505169779285
25509489.61309519428419.3869048057157
26512498.59908509824213.4009149017578
27519511.2869475455597.71305245444125
28517516.2452256872110.754774312789436
29510514.403062155734-4.40306215573378
30509505.845088770723.15491122927972
31501503.669307708342-2.66930770834210
32507502.7420844205534.25791557944746
33569563.5037612085285.49623879147248
34580585.011876546371-5.01187654637124
35578590.029141065672-12.0291410656716
36565581.902392373837-16.9023923738370
37547553.604492859586-6.604492859586
38555544.72139417986010.2786058201395
39562551.6710379807210.3289620192795
40561553.615427757317.38457224268984
41555552.3402042333032.65979576669702
42544551.105250362051-7.10525036205081
43537539.838465791353-2.83846579135343
44543541.1289381652331.87106183476715
45594600.06874267317-6.06874267317039
46611608.3529601087552.64703989124450
47613612.7643299012270.235670098773085
48611608.5931029135762.40689708642446
49594596.787031036753-2.78703103675298
50595599.475406005942-4.47540600594198
51591598.911923547078-7.91192354707778
52589588.4538402750720.54615972492843
53584579.4585595365324.54144046346835
54573573.015426832889-0.0154268328886928
55567566.4711663592320.528833640767857
56569570.992771866034-1.99277186603410
57621623.076464890373-2.07646489037290
58629636.795119478016-7.79511947801586
59628632.805641128437-4.80564112843717
60612624.804612392861-12.8046123928613
61595598.938635959318-3.93863595931759
62597596.6333072541310.366692745869045
63593593.915169523852-0.915169523852
64590588.5958908797091.40410912029097
65580579.4539405644580.546059435542247
66574565.9396789629678.06032103703274
67573561.88747724808211.1125227519179
68573569.7723018210453.22769817895528
69620623.937596823766-3.93759682376572
70626633.160244599522-7.16024459952166
71620630.106143626558-10.1061436265580
72588614.289777716373-26.2897777163729
73566582.826085556346-16.8260855563458
74557571.978445650377-14.9784456503767
75561555.438459166515.56154083349043
76549550.254857467324-1.25485746732409
77532534.636256526055-2.63625652605481
78526517.9596793327878.0403206672131
79511510.3726428041430.627357195856575
80499503.101562688043-4.10156268804326
81555543.48272056712811.5172794328715
82565554.35592389348910.6440761065107
83542555.932855417494-13.9328554174937
84527526.6637832705710.336216729428997
85510512.353382708619-2.35338270861905
86514509.9019351899934.09806481000726
87517514.5956282985042.40437170149607
88508505.7560109646642.24398903533626
89493492.884360690520.115639309479718
90490484.3874247913585.61257520864183
91469473.601079162435-4.60107916243538
92478462.40420094075215.5957990592484
93528523.4246611522044.57533884779582
94534532.3794580802911.62054191970924
95518519.130346449903-1.13034644990262
96506505.8925190879180.107480912082281
97502492.7417482997469.2582517002544
98516503.0774084618112.9225915381903
99528516.07705962675911.9229403732409
100533517.47719697697915.5228030230213
101536517.13812848883718.8618715111627
102537529.3168146249777.68318537502341
103524523.1627415530290.837258446970736
104536532.9833080907583.01669190924167
105587589.76266759015-2.76266759015039
106597600.370403048525-3.37040304852474
107581589.682047832455-8.68204783245471
108564578.804137022419-14.8041370224188
109558566.397709905406-8.39770990540592
110575571.8844846235543.11551537644561
111580581.209177648417-1.20917764841727
112575578.107606064073-3.10760606407325
113563568.530194661399-5.53019466139949
114552559.471044825142-7.47104482514192
115537537.68940729755-0.689407297549792
116545543.2409000858931.75909991410708
117601592.0951478979258.90485210207453
118604605.152945466706-1.15294546670555
119586589.862116780835-3.86211678083487
120564575.833544283051-11.8335442830514
121549565.35518379774-16.3551837977404







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
122568.561024560532552.643901893686584.478147227378
123570.58543727255551.806768810062589.364105735038
124563.736654902548541.77531873324585.697991071856
125551.465644931159526.041459224428576.88983063789
126541.730451673823512.593637842211570.867265505435
127525.023975938094491.947653227259558.10029864893
128530.065227641141492.840161304098567.290293978185
129579.114742983349537.545644208624620.683841758075
130579.76540093894533.668274292965625.862527584915
131560.972891379286510.173091837153611.772690921419
132542.803169970987487.133947307406598.472392634567
133535.117591698618474.418975784733595.816207612502

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
122 & 568.561024560532 & 552.643901893686 & 584.478147227378 \tabularnewline
123 & 570.58543727255 & 551.806768810062 & 589.364105735038 \tabularnewline
124 & 563.736654902548 & 541.77531873324 & 585.697991071856 \tabularnewline
125 & 551.465644931159 & 526.041459224428 & 576.88983063789 \tabularnewline
126 & 541.730451673823 & 512.593637842211 & 570.867265505435 \tabularnewline
127 & 525.023975938094 & 491.947653227259 & 558.10029864893 \tabularnewline
128 & 530.065227641141 & 492.840161304098 & 567.290293978185 \tabularnewline
129 & 579.114742983349 & 537.545644208624 & 620.683841758075 \tabularnewline
130 & 579.76540093894 & 533.668274292965 & 625.862527584915 \tabularnewline
131 & 560.972891379286 & 510.173091837153 & 611.772690921419 \tabularnewline
132 & 542.803169970987 & 487.133947307406 & 598.472392634567 \tabularnewline
133 & 535.117591698618 & 474.418975784733 & 595.816207612502 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116253&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]122[/C][C]568.561024560532[/C][C]552.643901893686[/C][C]584.478147227378[/C][/ROW]
[ROW][C]123[/C][C]570.58543727255[/C][C]551.806768810062[/C][C]589.364105735038[/C][/ROW]
[ROW][C]124[/C][C]563.736654902548[/C][C]541.77531873324[/C][C]585.697991071856[/C][/ROW]
[ROW][C]125[/C][C]551.465644931159[/C][C]526.041459224428[/C][C]576.88983063789[/C][/ROW]
[ROW][C]126[/C][C]541.730451673823[/C][C]512.593637842211[/C][C]570.867265505435[/C][/ROW]
[ROW][C]127[/C][C]525.023975938094[/C][C]491.947653227259[/C][C]558.10029864893[/C][/ROW]
[ROW][C]128[/C][C]530.065227641141[/C][C]492.840161304098[/C][C]567.290293978185[/C][/ROW]
[ROW][C]129[/C][C]579.114742983349[/C][C]537.545644208624[/C][C]620.683841758075[/C][/ROW]
[ROW][C]130[/C][C]579.76540093894[/C][C]533.668274292965[/C][C]625.862527584915[/C][/ROW]
[ROW][C]131[/C][C]560.972891379286[/C][C]510.173091837153[/C][C]611.772690921419[/C][/ROW]
[ROW][C]132[/C][C]542.803169970987[/C][C]487.133947307406[/C][C]598.472392634567[/C][/ROW]
[ROW][C]133[/C][C]535.117591698618[/C][C]474.418975784733[/C][C]595.816207612502[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116253&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116253&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
122568.561024560532552.643901893686584.478147227378
123570.58543727255551.806768810062589.364105735038
124563.736654902548541.77531873324585.697991071856
125551.465644931159526.041459224428576.88983063789
126541.730451673823512.593637842211570.867265505435
127525.023975938094491.947653227259558.10029864893
128530.065227641141492.840161304098567.290293978185
129579.114742983349537.545644208624620.683841758075
130579.76540093894533.668274292965625.862527584915
131560.972891379286510.173091837153611.772690921419
132542.803169970987487.133947307406598.472392634567
133535.117591698618474.418975784733595.816207612502



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')