Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 07:39:08 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/28/t1338205161eyrew0xgtc9h25b.htm/, Retrieved Thu, 02 May 2024 07:35:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167792, Retrieved Thu, 02 May 2024 07:35:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [Nieuwe personenwa...] [2012-05-28 11:02:37] [65d089efb1547052afcdc66fb34b47a2]
-    D  [(Partial) Autocorrelation Function] [aantal werklozen ...] [2012-05-28 11:13:00] [65d089efb1547052afcdc66fb34b47a2]
- RMP       [Exponential Smoothing] [aantal werklozen ...] [2012-05-28 11:39:08] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
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
551
556
548
540
531
521
519
572
581
563
548
539
541




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167792&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167792&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167792&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.70702730712811
beta0.214052040509199
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.70702730712811 \tabularnewline
beta & 0.214052040509199 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167792&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]0.70702730712811[/C][/ROW]
[ROW][C]beta[/C][C]0.214052040509199[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167792&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167792&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
alpha0.70702730712811
beta0.214052040509199
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13593592.1327457264960.867254273504045
14590589.6649020951950.335097904804911
15580580.163189976863-0.163189976862554
16574575.159477444201-1.15947744420134
17573575.150886410478-2.15088641047782
18573575.782492310564-2.78249231056361
19620614.3380980976955.66190190230463
20626625.9293303637920.0706696362075263
21620624.828103925079-4.82810392507872
22588604.532622479778-16.5326224797777
23566572.043002502477-6.04300250247718
24557564.930278437654-7.93027843765424
25561549.82877384057611.1712261594238
26549550.804892655077-1.80489265507674
27532535.634976730147-3.63497673014683
28526523.3501214134592.64987858654069
29511521.786294009957-10.7862940099566
30499510.862400202496-11.8624002024964
31555538.83309357948116.1669064205192
32565551.16426011516713.8357398848331
33542555.394009442529-13.3940094425293
34527521.3506270599235.64937294007689
35510506.7120256107723.28797438922817
36514506.1503625193757.84963748062455
37517510.6967769814376.3032230185629
38508506.5875778329891.41242216701062
39493495.801278821318-2.80127882131831
40490488.7183861898221.28161381017793
41469484.81487700596-15.8148770059602
42478471.8234894647416.1765105352585
43528525.2931485104882.70685148951202
44534529.9208089647614.07919103523886
45518520.294364967721-2.29436496772064
46506502.3772787425143.62272125748643
47502488.00659255740813.9934074425921
48516500.36321139336915.6367886066308
49528515.15361525909112.8463847409091
50533520.41930341780412.5806965821955
51536524.16655822891711.8334417710831
52537538.713594848931-1.71359484893128
53524537.316895722232-13.3168957222322
54536542.545880592666-6.54588059266575
55587594.089886960978-7.08988696097776
56597598.796339792836-1.79633979283631
57581588.862546578889-7.86254657888912
58564573.613545820318-9.61354582031834
59558555.7909973553032.20900264469674
60575561.38193879785613.6180612021437
61580574.7067724272175.29322757278305
62575574.1904705135860.80952948641368
63563567.250945237047-4.25094523704695
64552561.877429576789-9.87742957678859
65537545.494166460954-8.49416646095415
66545551.03149046965-6.03149046964995
67601597.7724691397433.22753086025682
68604607.87859092129-3.87859092129077
69586590.93433519012-4.93433519011978
70564573.924801089144-9.92480108914367
71549555.980901146756-6.98090114675642
72551553.661097003356-2.66109700335608
73556545.81769886859410.1823011314062
74548540.9649464259557.03505357404504
75540531.4070726204658.5929273795349
76531529.8725360812841.12746391871588
77521519.7471958194811.25280418051898
78519532.444408124361-13.4444081243612
79572575.082033387783-3.08203338778344
80581576.1154692265394.88453077346071
81563563.854139924973-0.85413992497331
82548547.6813087526210.318691247379206
83539538.8065402604220.193459739577634
84541544.874782533915-3.87478253391453

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 593 & 592.132745726496 & 0.867254273504045 \tabularnewline
14 & 590 & 589.664902095195 & 0.335097904804911 \tabularnewline
15 & 580 & 580.163189976863 & -0.163189976862554 \tabularnewline
16 & 574 & 575.159477444201 & -1.15947744420134 \tabularnewline
17 & 573 & 575.150886410478 & -2.15088641047782 \tabularnewline
18 & 573 & 575.782492310564 & -2.78249231056361 \tabularnewline
19 & 620 & 614.338098097695 & 5.66190190230463 \tabularnewline
20 & 626 & 625.929330363792 & 0.0706696362075263 \tabularnewline
21 & 620 & 624.828103925079 & -4.82810392507872 \tabularnewline
22 & 588 & 604.532622479778 & -16.5326224797777 \tabularnewline
23 & 566 & 572.043002502477 & -6.04300250247718 \tabularnewline
24 & 557 & 564.930278437654 & -7.93027843765424 \tabularnewline
25 & 561 & 549.828773840576 & 11.1712261594238 \tabularnewline
26 & 549 & 550.804892655077 & -1.80489265507674 \tabularnewline
27 & 532 & 535.634976730147 & -3.63497673014683 \tabularnewline
28 & 526 & 523.350121413459 & 2.64987858654069 \tabularnewline
29 & 511 & 521.786294009957 & -10.7862940099566 \tabularnewline
30 & 499 & 510.862400202496 & -11.8624002024964 \tabularnewline
31 & 555 & 538.833093579481 & 16.1669064205192 \tabularnewline
32 & 565 & 551.164260115167 & 13.8357398848331 \tabularnewline
33 & 542 & 555.394009442529 & -13.3940094425293 \tabularnewline
34 & 527 & 521.350627059923 & 5.64937294007689 \tabularnewline
35 & 510 & 506.712025610772 & 3.28797438922817 \tabularnewline
36 & 514 & 506.150362519375 & 7.84963748062455 \tabularnewline
37 & 517 & 510.696776981437 & 6.3032230185629 \tabularnewline
38 & 508 & 506.587577832989 & 1.41242216701062 \tabularnewline
39 & 493 & 495.801278821318 & -2.80127882131831 \tabularnewline
40 & 490 & 488.718386189822 & 1.28161381017793 \tabularnewline
41 & 469 & 484.81487700596 & -15.8148770059602 \tabularnewline
42 & 478 & 471.823489464741 & 6.1765105352585 \tabularnewline
43 & 528 & 525.293148510488 & 2.70685148951202 \tabularnewline
44 & 534 & 529.920808964761 & 4.07919103523886 \tabularnewline
45 & 518 & 520.294364967721 & -2.29436496772064 \tabularnewline
46 & 506 & 502.377278742514 & 3.62272125748643 \tabularnewline
47 & 502 & 488.006592557408 & 13.9934074425921 \tabularnewline
48 & 516 & 500.363211393369 & 15.6367886066308 \tabularnewline
49 & 528 & 515.153615259091 & 12.8463847409091 \tabularnewline
50 & 533 & 520.419303417804 & 12.5806965821955 \tabularnewline
51 & 536 & 524.166558228917 & 11.8334417710831 \tabularnewline
52 & 537 & 538.713594848931 & -1.71359484893128 \tabularnewline
53 & 524 & 537.316895722232 & -13.3168957222322 \tabularnewline
54 & 536 & 542.545880592666 & -6.54588059266575 \tabularnewline
55 & 587 & 594.089886960978 & -7.08988696097776 \tabularnewline
56 & 597 & 598.796339792836 & -1.79633979283631 \tabularnewline
57 & 581 & 588.862546578889 & -7.86254657888912 \tabularnewline
58 & 564 & 573.613545820318 & -9.61354582031834 \tabularnewline
59 & 558 & 555.790997355303 & 2.20900264469674 \tabularnewline
60 & 575 & 561.381938797856 & 13.6180612021437 \tabularnewline
61 & 580 & 574.706772427217 & 5.29322757278305 \tabularnewline
62 & 575 & 574.190470513586 & 0.80952948641368 \tabularnewline
63 & 563 & 567.250945237047 & -4.25094523704695 \tabularnewline
64 & 552 & 561.877429576789 & -9.87742957678859 \tabularnewline
65 & 537 & 545.494166460954 & -8.49416646095415 \tabularnewline
66 & 545 & 551.03149046965 & -6.03149046964995 \tabularnewline
67 & 601 & 597.772469139743 & 3.22753086025682 \tabularnewline
68 & 604 & 607.87859092129 & -3.87859092129077 \tabularnewline
69 & 586 & 590.93433519012 & -4.93433519011978 \tabularnewline
70 & 564 & 573.924801089144 & -9.92480108914367 \tabularnewline
71 & 549 & 555.980901146756 & -6.98090114675642 \tabularnewline
72 & 551 & 553.661097003356 & -2.66109700335608 \tabularnewline
73 & 556 & 545.817698868594 & 10.1823011314062 \tabularnewline
74 & 548 & 540.964946425955 & 7.03505357404504 \tabularnewline
75 & 540 & 531.407072620465 & 8.5929273795349 \tabularnewline
76 & 531 & 529.872536081284 & 1.12746391871588 \tabularnewline
77 & 521 & 519.747195819481 & 1.25280418051898 \tabularnewline
78 & 519 & 532.444408124361 & -13.4444081243612 \tabularnewline
79 & 572 & 575.082033387783 & -3.08203338778344 \tabularnewline
80 & 581 & 576.115469226539 & 4.88453077346071 \tabularnewline
81 & 563 & 563.854139924973 & -0.85413992497331 \tabularnewline
82 & 548 & 547.681308752621 & 0.318691247379206 \tabularnewline
83 & 539 & 538.806540260422 & 0.193459739577634 \tabularnewline
84 & 541 & 544.874782533915 & -3.87478253391453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167792&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]593[/C][C]592.132745726496[/C][C]0.867254273504045[/C][/ROW]
[ROW][C]14[/C][C]590[/C][C]589.664902095195[/C][C]0.335097904804911[/C][/ROW]
[ROW][C]15[/C][C]580[/C][C]580.163189976863[/C][C]-0.163189976862554[/C][/ROW]
[ROW][C]16[/C][C]574[/C][C]575.159477444201[/C][C]-1.15947744420134[/C][/ROW]
[ROW][C]17[/C][C]573[/C][C]575.150886410478[/C][C]-2.15088641047782[/C][/ROW]
[ROW][C]18[/C][C]573[/C][C]575.782492310564[/C][C]-2.78249231056361[/C][/ROW]
[ROW][C]19[/C][C]620[/C][C]614.338098097695[/C][C]5.66190190230463[/C][/ROW]
[ROW][C]20[/C][C]626[/C][C]625.929330363792[/C][C]0.0706696362075263[/C][/ROW]
[ROW][C]21[/C][C]620[/C][C]624.828103925079[/C][C]-4.82810392507872[/C][/ROW]
[ROW][C]22[/C][C]588[/C][C]604.532622479778[/C][C]-16.5326224797777[/C][/ROW]
[ROW][C]23[/C][C]566[/C][C]572.043002502477[/C][C]-6.04300250247718[/C][/ROW]
[ROW][C]24[/C][C]557[/C][C]564.930278437654[/C][C]-7.93027843765424[/C][/ROW]
[ROW][C]25[/C][C]561[/C][C]549.828773840576[/C][C]11.1712261594238[/C][/ROW]
[ROW][C]26[/C][C]549[/C][C]550.804892655077[/C][C]-1.80489265507674[/C][/ROW]
[ROW][C]27[/C][C]532[/C][C]535.634976730147[/C][C]-3.63497673014683[/C][/ROW]
[ROW][C]28[/C][C]526[/C][C]523.350121413459[/C][C]2.64987858654069[/C][/ROW]
[ROW][C]29[/C][C]511[/C][C]521.786294009957[/C][C]-10.7862940099566[/C][/ROW]
[ROW][C]30[/C][C]499[/C][C]510.862400202496[/C][C]-11.8624002024964[/C][/ROW]
[ROW][C]31[/C][C]555[/C][C]538.833093579481[/C][C]16.1669064205192[/C][/ROW]
[ROW][C]32[/C][C]565[/C][C]551.164260115167[/C][C]13.8357398848331[/C][/ROW]
[ROW][C]33[/C][C]542[/C][C]555.394009442529[/C][C]-13.3940094425293[/C][/ROW]
[ROW][C]34[/C][C]527[/C][C]521.350627059923[/C][C]5.64937294007689[/C][/ROW]
[ROW][C]35[/C][C]510[/C][C]506.712025610772[/C][C]3.28797438922817[/C][/ROW]
[ROW][C]36[/C][C]514[/C][C]506.150362519375[/C][C]7.84963748062455[/C][/ROW]
[ROW][C]37[/C][C]517[/C][C]510.696776981437[/C][C]6.3032230185629[/C][/ROW]
[ROW][C]38[/C][C]508[/C][C]506.587577832989[/C][C]1.41242216701062[/C][/ROW]
[ROW][C]39[/C][C]493[/C][C]495.801278821318[/C][C]-2.80127882131831[/C][/ROW]
[ROW][C]40[/C][C]490[/C][C]488.718386189822[/C][C]1.28161381017793[/C][/ROW]
[ROW][C]41[/C][C]469[/C][C]484.81487700596[/C][C]-15.8148770059602[/C][/ROW]
[ROW][C]42[/C][C]478[/C][C]471.823489464741[/C][C]6.1765105352585[/C][/ROW]
[ROW][C]43[/C][C]528[/C][C]525.293148510488[/C][C]2.70685148951202[/C][/ROW]
[ROW][C]44[/C][C]534[/C][C]529.920808964761[/C][C]4.07919103523886[/C][/ROW]
[ROW][C]45[/C][C]518[/C][C]520.294364967721[/C][C]-2.29436496772064[/C][/ROW]
[ROW][C]46[/C][C]506[/C][C]502.377278742514[/C][C]3.62272125748643[/C][/ROW]
[ROW][C]47[/C][C]502[/C][C]488.006592557408[/C][C]13.9934074425921[/C][/ROW]
[ROW][C]48[/C][C]516[/C][C]500.363211393369[/C][C]15.6367886066308[/C][/ROW]
[ROW][C]49[/C][C]528[/C][C]515.153615259091[/C][C]12.8463847409091[/C][/ROW]
[ROW][C]50[/C][C]533[/C][C]520.419303417804[/C][C]12.5806965821955[/C][/ROW]
[ROW][C]51[/C][C]536[/C][C]524.166558228917[/C][C]11.8334417710831[/C][/ROW]
[ROW][C]52[/C][C]537[/C][C]538.713594848931[/C][C]-1.71359484893128[/C][/ROW]
[ROW][C]53[/C][C]524[/C][C]537.316895722232[/C][C]-13.3168957222322[/C][/ROW]
[ROW][C]54[/C][C]536[/C][C]542.545880592666[/C][C]-6.54588059266575[/C][/ROW]
[ROW][C]55[/C][C]587[/C][C]594.089886960978[/C][C]-7.08988696097776[/C][/ROW]
[ROW][C]56[/C][C]597[/C][C]598.796339792836[/C][C]-1.79633979283631[/C][/ROW]
[ROW][C]57[/C][C]581[/C][C]588.862546578889[/C][C]-7.86254657888912[/C][/ROW]
[ROW][C]58[/C][C]564[/C][C]573.613545820318[/C][C]-9.61354582031834[/C][/ROW]
[ROW][C]59[/C][C]558[/C][C]555.790997355303[/C][C]2.20900264469674[/C][/ROW]
[ROW][C]60[/C][C]575[/C][C]561.381938797856[/C][C]13.6180612021437[/C][/ROW]
[ROW][C]61[/C][C]580[/C][C]574.706772427217[/C][C]5.29322757278305[/C][/ROW]
[ROW][C]62[/C][C]575[/C][C]574.190470513586[/C][C]0.80952948641368[/C][/ROW]
[ROW][C]63[/C][C]563[/C][C]567.250945237047[/C][C]-4.25094523704695[/C][/ROW]
[ROW][C]64[/C][C]552[/C][C]561.877429576789[/C][C]-9.87742957678859[/C][/ROW]
[ROW][C]65[/C][C]537[/C][C]545.494166460954[/C][C]-8.49416646095415[/C][/ROW]
[ROW][C]66[/C][C]545[/C][C]551.03149046965[/C][C]-6.03149046964995[/C][/ROW]
[ROW][C]67[/C][C]601[/C][C]597.772469139743[/C][C]3.22753086025682[/C][/ROW]
[ROW][C]68[/C][C]604[/C][C]607.87859092129[/C][C]-3.87859092129077[/C][/ROW]
[ROW][C]69[/C][C]586[/C][C]590.93433519012[/C][C]-4.93433519011978[/C][/ROW]
[ROW][C]70[/C][C]564[/C][C]573.924801089144[/C][C]-9.92480108914367[/C][/ROW]
[ROW][C]71[/C][C]549[/C][C]555.980901146756[/C][C]-6.98090114675642[/C][/ROW]
[ROW][C]72[/C][C]551[/C][C]553.661097003356[/C][C]-2.66109700335608[/C][/ROW]
[ROW][C]73[/C][C]556[/C][C]545.817698868594[/C][C]10.1823011314062[/C][/ROW]
[ROW][C]74[/C][C]548[/C][C]540.964946425955[/C][C]7.03505357404504[/C][/ROW]
[ROW][C]75[/C][C]540[/C][C]531.407072620465[/C][C]8.5929273795349[/C][/ROW]
[ROW][C]76[/C][C]531[/C][C]529.872536081284[/C][C]1.12746391871588[/C][/ROW]
[ROW][C]77[/C][C]521[/C][C]519.747195819481[/C][C]1.25280418051898[/C][/ROW]
[ROW][C]78[/C][C]519[/C][C]532.444408124361[/C][C]-13.4444081243612[/C][/ROW]
[ROW][C]79[/C][C]572[/C][C]575.082033387783[/C][C]-3.08203338778344[/C][/ROW]
[ROW][C]80[/C][C]581[/C][C]576.115469226539[/C][C]4.88453077346071[/C][/ROW]
[ROW][C]81[/C][C]563[/C][C]563.854139924973[/C][C]-0.85413992497331[/C][/ROW]
[ROW][C]82[/C][C]548[/C][C]547.681308752621[/C][C]0.318691247379206[/C][/ROW]
[ROW][C]83[/C][C]539[/C][C]538.806540260422[/C][C]0.193459739577634[/C][/ROW]
[ROW][C]84[/C][C]541[/C][C]544.874782533915[/C][C]-3.87478253391453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167792&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167792&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
13593592.1327457264960.867254273504045
14590589.6649020951950.335097904804911
15580580.163189976863-0.163189976862554
16574575.159477444201-1.15947744420134
17573575.150886410478-2.15088641047782
18573575.782492310564-2.78249231056361
19620614.3380980976955.66190190230463
20626625.9293303637920.0706696362075263
21620624.828103925079-4.82810392507872
22588604.532622479778-16.5326224797777
23566572.043002502477-6.04300250247718
24557564.930278437654-7.93027843765424
25561549.82877384057611.1712261594238
26549550.804892655077-1.80489265507674
27532535.634976730147-3.63497673014683
28526523.3501214134592.64987858654069
29511521.786294009957-10.7862940099566
30499510.862400202496-11.8624002024964
31555538.83309357948116.1669064205192
32565551.16426011516713.8357398848331
33542555.394009442529-13.3940094425293
34527521.3506270599235.64937294007689
35510506.7120256107723.28797438922817
36514506.1503625193757.84963748062455
37517510.6967769814376.3032230185629
38508506.5875778329891.41242216701062
39493495.801278821318-2.80127882131831
40490488.7183861898221.28161381017793
41469484.81487700596-15.8148770059602
42478471.8234894647416.1765105352585
43528525.2931485104882.70685148951202
44534529.9208089647614.07919103523886
45518520.294364967721-2.29436496772064
46506502.3772787425143.62272125748643
47502488.00659255740813.9934074425921
48516500.36321139336915.6367886066308
49528515.15361525909112.8463847409091
50533520.41930341780412.5806965821955
51536524.16655822891711.8334417710831
52537538.713594848931-1.71359484893128
53524537.316895722232-13.3168957222322
54536542.545880592666-6.54588059266575
55587594.089886960978-7.08988696097776
56597598.796339792836-1.79633979283631
57581588.862546578889-7.86254657888912
58564573.613545820318-9.61354582031834
59558555.7909973553032.20900264469674
60575561.38193879785613.6180612021437
61580574.7067724272175.29322757278305
62575574.1904705135860.80952948641368
63563567.250945237047-4.25094523704695
64552561.877429576789-9.87742957678859
65537545.494166460954-8.49416646095415
66545551.03149046965-6.03149046964995
67601597.7724691397433.22753086025682
68604607.87859092129-3.87859092129077
69586590.93433519012-4.93433519011978
70564573.924801089144-9.92480108914367
71549555.980901146756-6.98090114675642
72551553.661097003356-2.66109700335608
73556545.81769886859410.1823011314062
74548540.9649464259557.03505357404504
75540531.4070726204658.5929273795349
76531529.8725360812841.12746391871588
77521519.7471958194811.25280418051898
78519532.444408124361-13.4444081243612
79572575.082033387783-3.08203338778344
80581576.1154692265394.88453077346071
81563563.854139924973-0.85413992497331
82548547.6813087526210.318691247379206
83539538.8065402604220.193459739577634
84541544.874782533915-3.87478253391453







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85541.802353288173526.362112601255557.24259397509
86529.153695121077508.805381990287549.502008251867
87514.338888137682488.704801009725539.972975265639
88502.501908571381471.221252753504533.782564389259
89489.405678908764452.135133797526526.676224020002
90494.511179500654450.923688113306538.098670888003
91549.324883487293499.108076389089599.541690585496
92554.97244596653497.827112551994612.117779381065
93536.938177333632472.576897651789601.299457015476
94521.203951116235449.349904898239593.057997334231
95511.510036057931431.89597507006591.124097045802
96515.663201058625428.030563082734603.295839034516

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 541.802353288173 & 526.362112601255 & 557.24259397509 \tabularnewline
86 & 529.153695121077 & 508.805381990287 & 549.502008251867 \tabularnewline
87 & 514.338888137682 & 488.704801009725 & 539.972975265639 \tabularnewline
88 & 502.501908571381 & 471.221252753504 & 533.782564389259 \tabularnewline
89 & 489.405678908764 & 452.135133797526 & 526.676224020002 \tabularnewline
90 & 494.511179500654 & 450.923688113306 & 538.098670888003 \tabularnewline
91 & 549.324883487293 & 499.108076389089 & 599.541690585496 \tabularnewline
92 & 554.97244596653 & 497.827112551994 & 612.117779381065 \tabularnewline
93 & 536.938177333632 & 472.576897651789 & 601.299457015476 \tabularnewline
94 & 521.203951116235 & 449.349904898239 & 593.057997334231 \tabularnewline
95 & 511.510036057931 & 431.89597507006 & 591.124097045802 \tabularnewline
96 & 515.663201058625 & 428.030563082734 & 603.295839034516 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167792&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]541.802353288173[/C][C]526.362112601255[/C][C]557.24259397509[/C][/ROW]
[ROW][C]86[/C][C]529.153695121077[/C][C]508.805381990287[/C][C]549.502008251867[/C][/ROW]
[ROW][C]87[/C][C]514.338888137682[/C][C]488.704801009725[/C][C]539.972975265639[/C][/ROW]
[ROW][C]88[/C][C]502.501908571381[/C][C]471.221252753504[/C][C]533.782564389259[/C][/ROW]
[ROW][C]89[/C][C]489.405678908764[/C][C]452.135133797526[/C][C]526.676224020002[/C][/ROW]
[ROW][C]90[/C][C]494.511179500654[/C][C]450.923688113306[/C][C]538.098670888003[/C][/ROW]
[ROW][C]91[/C][C]549.324883487293[/C][C]499.108076389089[/C][C]599.541690585496[/C][/ROW]
[ROW][C]92[/C][C]554.97244596653[/C][C]497.827112551994[/C][C]612.117779381065[/C][/ROW]
[ROW][C]93[/C][C]536.938177333632[/C][C]472.576897651789[/C][C]601.299457015476[/C][/ROW]
[ROW][C]94[/C][C]521.203951116235[/C][C]449.349904898239[/C][C]593.057997334231[/C][/ROW]
[ROW][C]95[/C][C]511.510036057931[/C][C]431.89597507006[/C][C]591.124097045802[/C][/ROW]
[ROW][C]96[/C][C]515.663201058625[/C][C]428.030563082734[/C][C]603.295839034516[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167792&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167792&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
85541.802353288173526.362112601255557.24259397509
86529.153695121077508.805381990287549.502008251867
87514.338888137682488.704801009725539.972975265639
88502.501908571381471.221252753504533.782564389259
89489.405678908764452.135133797526526.676224020002
90494.511179500654450.923688113306538.098670888003
91549.324883487293499.108076389089599.541690585496
92554.97244596653497.827112551994612.117779381065
93536.938177333632472.576897651789601.299457015476
94521.203951116235449.349904898239593.057997334231
95511.510036057931431.89597507006591.124097045802
96515.663201058625428.030563082734603.295839034516



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')