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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Apr 2015 14:41:04 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/02/t1427982133849xv039ncodiex.htm/, Retrieved Thu, 09 May 2024 09:03:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278556, Retrieved Thu, 09 May 2024 09:03:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact126
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2015-04-02 13:41:04] [642cc750ae8ad788b94759782886fa51] [Current]
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Dataseries X:
473
475
552
530
525
548
487
483
550
528
560
546
521
507
596
520
590
568
503
515
529
573
590
529
524
516
598
532
582
573
535
538
554
590
607
529
563
562
593
588
576
558
543
494
585
586
553
541
506
500
570
541
544
545
552
460
526
569
549
525
473
498
582
573
528
571
518
483
551
562
580
515
492
509
601
579
561
537
513
499
563
561
546
558
507
517
544
529
557
532
512
488
518
567
537
484
487
484
534
514
523
489
495
468
513
544
520
509






Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=278556&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=278556&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278556&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.18814763010543
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.18814763010543 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278556&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]0.18814763010543[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278556&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278556&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
alpha0.18814763010543
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24754732
3552473.37629526021178.6237047397892
4530488.16915897711141.8308410228888
5525496.03953258088528.9604674191153
6548501.48837589253746.5116241074633
7487510.239427740711-23.2394277407105
8483505.866984486289-22.8669844862894
9550501.56461554753648.4353844524636
10528510.67761834551317.3223816544872
11560513.93678340158646.0632165984136
12546522.60346843961123.396531560389
13521527.005470405385-6.00547040538504
14507525.875555380944-18.8755553809435
15596522.32416436909573.6758356309048
16520536.186098239087-16.1860982390872
17590533.14072221474956.8592777852507
18568543.8386605795524.1613394204495
19503548.384559331681-45.384559331681
20515539.845562050046-24.8455620500459
21529535.170928431692-6.17092843169235
22573534.00988287171938.9901171282808
23590541.34578100693848.6542189930616
24529550.499957005114-21.4999570051135
25524546.454791047233-22.4547910472328
26516542.229975327183-26.2299753271833
27598537.2948676316560.7051323683502
28532548.716394421991-16.7163944219913
29582545.57124442758636.428755572414
30573552.42522845622620.5747715437744
31535556.296322962147-21.2963229621473
32538552.289470266859-14.2894702668594
33554549.6009403006884.39905969931215
34590550.42861295780639.5713870421943
35607557.87387564977949.1261243502207
36529567.116839522538-38.1168395225379
37563559.9452464992633.05475350073664
38562560.5199911309831.48000886901673
39593560.79845129222432.2015487077762
40588566.85709636731621.1429036326836
41576570.8350835793535.1649164206467
42558571.806850363591-13.8068503635906
43543569.209124188461-26.2091241884607
44494564.277939585263-70.2779395852629
45585551.05531180360333.9446881963969
46586557.44192444242328.558075557577
47553562.815058678953-9.81505867895282
48541560.968378649162-19.9683786491621
49506557.211375529274-51.2113755292744
50500547.576076589002-47.5760765890021
51570538.62475052906731.3752494709331
52541544.52792936099-3.52792936098956
53544543.864157812540.135842187460071
54545543.8897161981791.1102838018212
55552544.0986134642367.90138653576412
56460545.585240615487-85.5852406154869
57526529.48258042168-3.48258042168004
58569528.82734116868940.1726588313106
59549536.38573172283412.6142682771656
60525538.759076404697-13.7590764046972
61473536.170338786714-63.1703387867138
62498524.284989251036-26.2849892510364
63582519.33953081610762.6604691838927
64573531.12894959435141.8710504056489
65528539.006888498199-11.0068884981989
66571536.93596851242834.0640314875719
67518543.345035308652-25.3450353086515
68483538.57642698039-55.5764269803904
69551528.11985395430222.8801460456976
70562532.42469920926629.5753007907335
71580537.98922196269842.0107780373017
72515545.893450289302-30.8934502893018
73492540.08092083159-48.0809208315897
74509531.034609523839-22.0346095238392
75601526.8888499616374.1111500383697
76579540.83268720573838.1673127942624
77561548.01377665547112.9862233445293
78537550.457103801764-13.4571038017637
79513547.925181613379-34.925181613379
80499541.35409146182-42.35409146182
81563533.3852695280129.6147304719901
82561538.95721088252622.0427891174741
83546543.1045094158922.89549058410762
84558543.64928910728514.3507108927151
85507546.349341352077-39.3493413520774
86517538.945856030474-21.9458560304745
87544534.8167952277069.18320477229429
88529536.544593442386-7.54459344238569
89557535.12509606609221.8749039339082
90532539.240807400041-7.24080740004058
91512537.878466647673-25.8784666476731
92488533.009494477151-45.009494477151
93518524.541064759032-6.54106475903154
94567523.31037892625443.6896210737464
95537531.5304775914835.46952240851681
96484532.559555270454-48.5595552704542
97487523.423190027345-36.4231900273446
98484516.57025314282-32.57025314282
99534510.44223720206423.5577627979355
100514514.874574443082-0.874574443081883
101523514.7100253342658.28997466573469
102489516.269764421257-27.2697644212574
103495511.139022871864-16.1390228718644
104468508.102503966306-40.1025039663058
105513500.55731288375212.4426871162483
106544502.89837497681741.1016250231828
107520510.6315483184119.36845168158891
108509512.394200300059-3.39420030005931

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 475 & 473 & 2 \tabularnewline
3 & 552 & 473.376295260211 & 78.6237047397892 \tabularnewline
4 & 530 & 488.169158977111 & 41.8308410228888 \tabularnewline
5 & 525 & 496.039532580885 & 28.9604674191153 \tabularnewline
6 & 548 & 501.488375892537 & 46.5116241074633 \tabularnewline
7 & 487 & 510.239427740711 & -23.2394277407105 \tabularnewline
8 & 483 & 505.866984486289 & -22.8669844862894 \tabularnewline
9 & 550 & 501.564615547536 & 48.4353844524636 \tabularnewline
10 & 528 & 510.677618345513 & 17.3223816544872 \tabularnewline
11 & 560 & 513.936783401586 & 46.0632165984136 \tabularnewline
12 & 546 & 522.603468439611 & 23.396531560389 \tabularnewline
13 & 521 & 527.005470405385 & -6.00547040538504 \tabularnewline
14 & 507 & 525.875555380944 & -18.8755553809435 \tabularnewline
15 & 596 & 522.324164369095 & 73.6758356309048 \tabularnewline
16 & 520 & 536.186098239087 & -16.1860982390872 \tabularnewline
17 & 590 & 533.140722214749 & 56.8592777852507 \tabularnewline
18 & 568 & 543.83866057955 & 24.1613394204495 \tabularnewline
19 & 503 & 548.384559331681 & -45.384559331681 \tabularnewline
20 & 515 & 539.845562050046 & -24.8455620500459 \tabularnewline
21 & 529 & 535.170928431692 & -6.17092843169235 \tabularnewline
22 & 573 & 534.009882871719 & 38.9901171282808 \tabularnewline
23 & 590 & 541.345781006938 & 48.6542189930616 \tabularnewline
24 & 529 & 550.499957005114 & -21.4999570051135 \tabularnewline
25 & 524 & 546.454791047233 & -22.4547910472328 \tabularnewline
26 & 516 & 542.229975327183 & -26.2299753271833 \tabularnewline
27 & 598 & 537.29486763165 & 60.7051323683502 \tabularnewline
28 & 532 & 548.716394421991 & -16.7163944219913 \tabularnewline
29 & 582 & 545.571244427586 & 36.428755572414 \tabularnewline
30 & 573 & 552.425228456226 & 20.5747715437744 \tabularnewline
31 & 535 & 556.296322962147 & -21.2963229621473 \tabularnewline
32 & 538 & 552.289470266859 & -14.2894702668594 \tabularnewline
33 & 554 & 549.600940300688 & 4.39905969931215 \tabularnewline
34 & 590 & 550.428612957806 & 39.5713870421943 \tabularnewline
35 & 607 & 557.873875649779 & 49.1261243502207 \tabularnewline
36 & 529 & 567.116839522538 & -38.1168395225379 \tabularnewline
37 & 563 & 559.945246499263 & 3.05475350073664 \tabularnewline
38 & 562 & 560.519991130983 & 1.48000886901673 \tabularnewline
39 & 593 & 560.798451292224 & 32.2015487077762 \tabularnewline
40 & 588 & 566.857096367316 & 21.1429036326836 \tabularnewline
41 & 576 & 570.835083579353 & 5.1649164206467 \tabularnewline
42 & 558 & 571.806850363591 & -13.8068503635906 \tabularnewline
43 & 543 & 569.209124188461 & -26.2091241884607 \tabularnewline
44 & 494 & 564.277939585263 & -70.2779395852629 \tabularnewline
45 & 585 & 551.055311803603 & 33.9446881963969 \tabularnewline
46 & 586 & 557.441924442423 & 28.558075557577 \tabularnewline
47 & 553 & 562.815058678953 & -9.81505867895282 \tabularnewline
48 & 541 & 560.968378649162 & -19.9683786491621 \tabularnewline
49 & 506 & 557.211375529274 & -51.2113755292744 \tabularnewline
50 & 500 & 547.576076589002 & -47.5760765890021 \tabularnewline
51 & 570 & 538.624750529067 & 31.3752494709331 \tabularnewline
52 & 541 & 544.52792936099 & -3.52792936098956 \tabularnewline
53 & 544 & 543.86415781254 & 0.135842187460071 \tabularnewline
54 & 545 & 543.889716198179 & 1.1102838018212 \tabularnewline
55 & 552 & 544.098613464236 & 7.90138653576412 \tabularnewline
56 & 460 & 545.585240615487 & -85.5852406154869 \tabularnewline
57 & 526 & 529.48258042168 & -3.48258042168004 \tabularnewline
58 & 569 & 528.827341168689 & 40.1726588313106 \tabularnewline
59 & 549 & 536.385731722834 & 12.6142682771656 \tabularnewline
60 & 525 & 538.759076404697 & -13.7590764046972 \tabularnewline
61 & 473 & 536.170338786714 & -63.1703387867138 \tabularnewline
62 & 498 & 524.284989251036 & -26.2849892510364 \tabularnewline
63 & 582 & 519.339530816107 & 62.6604691838927 \tabularnewline
64 & 573 & 531.128949594351 & 41.8710504056489 \tabularnewline
65 & 528 & 539.006888498199 & -11.0068884981989 \tabularnewline
66 & 571 & 536.935968512428 & 34.0640314875719 \tabularnewline
67 & 518 & 543.345035308652 & -25.3450353086515 \tabularnewline
68 & 483 & 538.57642698039 & -55.5764269803904 \tabularnewline
69 & 551 & 528.119853954302 & 22.8801460456976 \tabularnewline
70 & 562 & 532.424699209266 & 29.5753007907335 \tabularnewline
71 & 580 & 537.989221962698 & 42.0107780373017 \tabularnewline
72 & 515 & 545.893450289302 & -30.8934502893018 \tabularnewline
73 & 492 & 540.08092083159 & -48.0809208315897 \tabularnewline
74 & 509 & 531.034609523839 & -22.0346095238392 \tabularnewline
75 & 601 & 526.88884996163 & 74.1111500383697 \tabularnewline
76 & 579 & 540.832687205738 & 38.1673127942624 \tabularnewline
77 & 561 & 548.013776655471 & 12.9862233445293 \tabularnewline
78 & 537 & 550.457103801764 & -13.4571038017637 \tabularnewline
79 & 513 & 547.925181613379 & -34.925181613379 \tabularnewline
80 & 499 & 541.35409146182 & -42.35409146182 \tabularnewline
81 & 563 & 533.38526952801 & 29.6147304719901 \tabularnewline
82 & 561 & 538.957210882526 & 22.0427891174741 \tabularnewline
83 & 546 & 543.104509415892 & 2.89549058410762 \tabularnewline
84 & 558 & 543.649289107285 & 14.3507108927151 \tabularnewline
85 & 507 & 546.349341352077 & -39.3493413520774 \tabularnewline
86 & 517 & 538.945856030474 & -21.9458560304745 \tabularnewline
87 & 544 & 534.816795227706 & 9.18320477229429 \tabularnewline
88 & 529 & 536.544593442386 & -7.54459344238569 \tabularnewline
89 & 557 & 535.125096066092 & 21.8749039339082 \tabularnewline
90 & 532 & 539.240807400041 & -7.24080740004058 \tabularnewline
91 & 512 & 537.878466647673 & -25.8784666476731 \tabularnewline
92 & 488 & 533.009494477151 & -45.009494477151 \tabularnewline
93 & 518 & 524.541064759032 & -6.54106475903154 \tabularnewline
94 & 567 & 523.310378926254 & 43.6896210737464 \tabularnewline
95 & 537 & 531.530477591483 & 5.46952240851681 \tabularnewline
96 & 484 & 532.559555270454 & -48.5595552704542 \tabularnewline
97 & 487 & 523.423190027345 & -36.4231900273446 \tabularnewline
98 & 484 & 516.57025314282 & -32.57025314282 \tabularnewline
99 & 534 & 510.442237202064 & 23.5577627979355 \tabularnewline
100 & 514 & 514.874574443082 & -0.874574443081883 \tabularnewline
101 & 523 & 514.710025334265 & 8.28997466573469 \tabularnewline
102 & 489 & 516.269764421257 & -27.2697644212574 \tabularnewline
103 & 495 & 511.139022871864 & -16.1390228718644 \tabularnewline
104 & 468 & 508.102503966306 & -40.1025039663058 \tabularnewline
105 & 513 & 500.557312883752 & 12.4426871162483 \tabularnewline
106 & 544 & 502.898374976817 & 41.1016250231828 \tabularnewline
107 & 520 & 510.631548318411 & 9.36845168158891 \tabularnewline
108 & 509 & 512.394200300059 & -3.39420030005931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278556&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]2[/C][C]475[/C][C]473[/C][C]2[/C][/ROW]
[ROW][C]3[/C][C]552[/C][C]473.376295260211[/C][C]78.6237047397892[/C][/ROW]
[ROW][C]4[/C][C]530[/C][C]488.169158977111[/C][C]41.8308410228888[/C][/ROW]
[ROW][C]5[/C][C]525[/C][C]496.039532580885[/C][C]28.9604674191153[/C][/ROW]
[ROW][C]6[/C][C]548[/C][C]501.488375892537[/C][C]46.5116241074633[/C][/ROW]
[ROW][C]7[/C][C]487[/C][C]510.239427740711[/C][C]-23.2394277407105[/C][/ROW]
[ROW][C]8[/C][C]483[/C][C]505.866984486289[/C][C]-22.8669844862894[/C][/ROW]
[ROW][C]9[/C][C]550[/C][C]501.564615547536[/C][C]48.4353844524636[/C][/ROW]
[ROW][C]10[/C][C]528[/C][C]510.677618345513[/C][C]17.3223816544872[/C][/ROW]
[ROW][C]11[/C][C]560[/C][C]513.936783401586[/C][C]46.0632165984136[/C][/ROW]
[ROW][C]12[/C][C]546[/C][C]522.603468439611[/C][C]23.396531560389[/C][/ROW]
[ROW][C]13[/C][C]521[/C][C]527.005470405385[/C][C]-6.00547040538504[/C][/ROW]
[ROW][C]14[/C][C]507[/C][C]525.875555380944[/C][C]-18.8755553809435[/C][/ROW]
[ROW][C]15[/C][C]596[/C][C]522.324164369095[/C][C]73.6758356309048[/C][/ROW]
[ROW][C]16[/C][C]520[/C][C]536.186098239087[/C][C]-16.1860982390872[/C][/ROW]
[ROW][C]17[/C][C]590[/C][C]533.140722214749[/C][C]56.8592777852507[/C][/ROW]
[ROW][C]18[/C][C]568[/C][C]543.83866057955[/C][C]24.1613394204495[/C][/ROW]
[ROW][C]19[/C][C]503[/C][C]548.384559331681[/C][C]-45.384559331681[/C][/ROW]
[ROW][C]20[/C][C]515[/C][C]539.845562050046[/C][C]-24.8455620500459[/C][/ROW]
[ROW][C]21[/C][C]529[/C][C]535.170928431692[/C][C]-6.17092843169235[/C][/ROW]
[ROW][C]22[/C][C]573[/C][C]534.009882871719[/C][C]38.9901171282808[/C][/ROW]
[ROW][C]23[/C][C]590[/C][C]541.345781006938[/C][C]48.6542189930616[/C][/ROW]
[ROW][C]24[/C][C]529[/C][C]550.499957005114[/C][C]-21.4999570051135[/C][/ROW]
[ROW][C]25[/C][C]524[/C][C]546.454791047233[/C][C]-22.4547910472328[/C][/ROW]
[ROW][C]26[/C][C]516[/C][C]542.229975327183[/C][C]-26.2299753271833[/C][/ROW]
[ROW][C]27[/C][C]598[/C][C]537.29486763165[/C][C]60.7051323683502[/C][/ROW]
[ROW][C]28[/C][C]532[/C][C]548.716394421991[/C][C]-16.7163944219913[/C][/ROW]
[ROW][C]29[/C][C]582[/C][C]545.571244427586[/C][C]36.428755572414[/C][/ROW]
[ROW][C]30[/C][C]573[/C][C]552.425228456226[/C][C]20.5747715437744[/C][/ROW]
[ROW][C]31[/C][C]535[/C][C]556.296322962147[/C][C]-21.2963229621473[/C][/ROW]
[ROW][C]32[/C][C]538[/C][C]552.289470266859[/C][C]-14.2894702668594[/C][/ROW]
[ROW][C]33[/C][C]554[/C][C]549.600940300688[/C][C]4.39905969931215[/C][/ROW]
[ROW][C]34[/C][C]590[/C][C]550.428612957806[/C][C]39.5713870421943[/C][/ROW]
[ROW][C]35[/C][C]607[/C][C]557.873875649779[/C][C]49.1261243502207[/C][/ROW]
[ROW][C]36[/C][C]529[/C][C]567.116839522538[/C][C]-38.1168395225379[/C][/ROW]
[ROW][C]37[/C][C]563[/C][C]559.945246499263[/C][C]3.05475350073664[/C][/ROW]
[ROW][C]38[/C][C]562[/C][C]560.519991130983[/C][C]1.48000886901673[/C][/ROW]
[ROW][C]39[/C][C]593[/C][C]560.798451292224[/C][C]32.2015487077762[/C][/ROW]
[ROW][C]40[/C][C]588[/C][C]566.857096367316[/C][C]21.1429036326836[/C][/ROW]
[ROW][C]41[/C][C]576[/C][C]570.835083579353[/C][C]5.1649164206467[/C][/ROW]
[ROW][C]42[/C][C]558[/C][C]571.806850363591[/C][C]-13.8068503635906[/C][/ROW]
[ROW][C]43[/C][C]543[/C][C]569.209124188461[/C][C]-26.2091241884607[/C][/ROW]
[ROW][C]44[/C][C]494[/C][C]564.277939585263[/C][C]-70.2779395852629[/C][/ROW]
[ROW][C]45[/C][C]585[/C][C]551.055311803603[/C][C]33.9446881963969[/C][/ROW]
[ROW][C]46[/C][C]586[/C][C]557.441924442423[/C][C]28.558075557577[/C][/ROW]
[ROW][C]47[/C][C]553[/C][C]562.815058678953[/C][C]-9.81505867895282[/C][/ROW]
[ROW][C]48[/C][C]541[/C][C]560.968378649162[/C][C]-19.9683786491621[/C][/ROW]
[ROW][C]49[/C][C]506[/C][C]557.211375529274[/C][C]-51.2113755292744[/C][/ROW]
[ROW][C]50[/C][C]500[/C][C]547.576076589002[/C][C]-47.5760765890021[/C][/ROW]
[ROW][C]51[/C][C]570[/C][C]538.624750529067[/C][C]31.3752494709331[/C][/ROW]
[ROW][C]52[/C][C]541[/C][C]544.52792936099[/C][C]-3.52792936098956[/C][/ROW]
[ROW][C]53[/C][C]544[/C][C]543.86415781254[/C][C]0.135842187460071[/C][/ROW]
[ROW][C]54[/C][C]545[/C][C]543.889716198179[/C][C]1.1102838018212[/C][/ROW]
[ROW][C]55[/C][C]552[/C][C]544.098613464236[/C][C]7.90138653576412[/C][/ROW]
[ROW][C]56[/C][C]460[/C][C]545.585240615487[/C][C]-85.5852406154869[/C][/ROW]
[ROW][C]57[/C][C]526[/C][C]529.48258042168[/C][C]-3.48258042168004[/C][/ROW]
[ROW][C]58[/C][C]569[/C][C]528.827341168689[/C][C]40.1726588313106[/C][/ROW]
[ROW][C]59[/C][C]549[/C][C]536.385731722834[/C][C]12.6142682771656[/C][/ROW]
[ROW][C]60[/C][C]525[/C][C]538.759076404697[/C][C]-13.7590764046972[/C][/ROW]
[ROW][C]61[/C][C]473[/C][C]536.170338786714[/C][C]-63.1703387867138[/C][/ROW]
[ROW][C]62[/C][C]498[/C][C]524.284989251036[/C][C]-26.2849892510364[/C][/ROW]
[ROW][C]63[/C][C]582[/C][C]519.339530816107[/C][C]62.6604691838927[/C][/ROW]
[ROW][C]64[/C][C]573[/C][C]531.128949594351[/C][C]41.8710504056489[/C][/ROW]
[ROW][C]65[/C][C]528[/C][C]539.006888498199[/C][C]-11.0068884981989[/C][/ROW]
[ROW][C]66[/C][C]571[/C][C]536.935968512428[/C][C]34.0640314875719[/C][/ROW]
[ROW][C]67[/C][C]518[/C][C]543.345035308652[/C][C]-25.3450353086515[/C][/ROW]
[ROW][C]68[/C][C]483[/C][C]538.57642698039[/C][C]-55.5764269803904[/C][/ROW]
[ROW][C]69[/C][C]551[/C][C]528.119853954302[/C][C]22.8801460456976[/C][/ROW]
[ROW][C]70[/C][C]562[/C][C]532.424699209266[/C][C]29.5753007907335[/C][/ROW]
[ROW][C]71[/C][C]580[/C][C]537.989221962698[/C][C]42.0107780373017[/C][/ROW]
[ROW][C]72[/C][C]515[/C][C]545.893450289302[/C][C]-30.8934502893018[/C][/ROW]
[ROW][C]73[/C][C]492[/C][C]540.08092083159[/C][C]-48.0809208315897[/C][/ROW]
[ROW][C]74[/C][C]509[/C][C]531.034609523839[/C][C]-22.0346095238392[/C][/ROW]
[ROW][C]75[/C][C]601[/C][C]526.88884996163[/C][C]74.1111500383697[/C][/ROW]
[ROW][C]76[/C][C]579[/C][C]540.832687205738[/C][C]38.1673127942624[/C][/ROW]
[ROW][C]77[/C][C]561[/C][C]548.013776655471[/C][C]12.9862233445293[/C][/ROW]
[ROW][C]78[/C][C]537[/C][C]550.457103801764[/C][C]-13.4571038017637[/C][/ROW]
[ROW][C]79[/C][C]513[/C][C]547.925181613379[/C][C]-34.925181613379[/C][/ROW]
[ROW][C]80[/C][C]499[/C][C]541.35409146182[/C][C]-42.35409146182[/C][/ROW]
[ROW][C]81[/C][C]563[/C][C]533.38526952801[/C][C]29.6147304719901[/C][/ROW]
[ROW][C]82[/C][C]561[/C][C]538.957210882526[/C][C]22.0427891174741[/C][/ROW]
[ROW][C]83[/C][C]546[/C][C]543.104509415892[/C][C]2.89549058410762[/C][/ROW]
[ROW][C]84[/C][C]558[/C][C]543.649289107285[/C][C]14.3507108927151[/C][/ROW]
[ROW][C]85[/C][C]507[/C][C]546.349341352077[/C][C]-39.3493413520774[/C][/ROW]
[ROW][C]86[/C][C]517[/C][C]538.945856030474[/C][C]-21.9458560304745[/C][/ROW]
[ROW][C]87[/C][C]544[/C][C]534.816795227706[/C][C]9.18320477229429[/C][/ROW]
[ROW][C]88[/C][C]529[/C][C]536.544593442386[/C][C]-7.54459344238569[/C][/ROW]
[ROW][C]89[/C][C]557[/C][C]535.125096066092[/C][C]21.8749039339082[/C][/ROW]
[ROW][C]90[/C][C]532[/C][C]539.240807400041[/C][C]-7.24080740004058[/C][/ROW]
[ROW][C]91[/C][C]512[/C][C]537.878466647673[/C][C]-25.8784666476731[/C][/ROW]
[ROW][C]92[/C][C]488[/C][C]533.009494477151[/C][C]-45.009494477151[/C][/ROW]
[ROW][C]93[/C][C]518[/C][C]524.541064759032[/C][C]-6.54106475903154[/C][/ROW]
[ROW][C]94[/C][C]567[/C][C]523.310378926254[/C][C]43.6896210737464[/C][/ROW]
[ROW][C]95[/C][C]537[/C][C]531.530477591483[/C][C]5.46952240851681[/C][/ROW]
[ROW][C]96[/C][C]484[/C][C]532.559555270454[/C][C]-48.5595552704542[/C][/ROW]
[ROW][C]97[/C][C]487[/C][C]523.423190027345[/C][C]-36.4231900273446[/C][/ROW]
[ROW][C]98[/C][C]484[/C][C]516.57025314282[/C][C]-32.57025314282[/C][/ROW]
[ROW][C]99[/C][C]534[/C][C]510.442237202064[/C][C]23.5577627979355[/C][/ROW]
[ROW][C]100[/C][C]514[/C][C]514.874574443082[/C][C]-0.874574443081883[/C][/ROW]
[ROW][C]101[/C][C]523[/C][C]514.710025334265[/C][C]8.28997466573469[/C][/ROW]
[ROW][C]102[/C][C]489[/C][C]516.269764421257[/C][C]-27.2697644212574[/C][/ROW]
[ROW][C]103[/C][C]495[/C][C]511.139022871864[/C][C]-16.1390228718644[/C][/ROW]
[ROW][C]104[/C][C]468[/C][C]508.102503966306[/C][C]-40.1025039663058[/C][/ROW]
[ROW][C]105[/C][C]513[/C][C]500.557312883752[/C][C]12.4426871162483[/C][/ROW]
[ROW][C]106[/C][C]544[/C][C]502.898374976817[/C][C]41.1016250231828[/C][/ROW]
[ROW][C]107[/C][C]520[/C][C]510.631548318411[/C][C]9.36845168158891[/C][/ROW]
[ROW][C]108[/C][C]509[/C][C]512.394200300059[/C][C]-3.39420030005931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278556&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278556&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
24754732
3552473.37629526021178.6237047397892
4530488.16915897711141.8308410228888
5525496.03953258088528.9604674191153
6548501.48837589253746.5116241074633
7487510.239427740711-23.2394277407105
8483505.866984486289-22.8669844862894
9550501.56461554753648.4353844524636
10528510.67761834551317.3223816544872
11560513.93678340158646.0632165984136
12546522.60346843961123.396531560389
13521527.005470405385-6.00547040538504
14507525.875555380944-18.8755553809435
15596522.32416436909573.6758356309048
16520536.186098239087-16.1860982390872
17590533.14072221474956.8592777852507
18568543.8386605795524.1613394204495
19503548.384559331681-45.384559331681
20515539.845562050046-24.8455620500459
21529535.170928431692-6.17092843169235
22573534.00988287171938.9901171282808
23590541.34578100693848.6542189930616
24529550.499957005114-21.4999570051135
25524546.454791047233-22.4547910472328
26516542.229975327183-26.2299753271833
27598537.2948676316560.7051323683502
28532548.716394421991-16.7163944219913
29582545.57124442758636.428755572414
30573552.42522845622620.5747715437744
31535556.296322962147-21.2963229621473
32538552.289470266859-14.2894702668594
33554549.6009403006884.39905969931215
34590550.42861295780639.5713870421943
35607557.87387564977949.1261243502207
36529567.116839522538-38.1168395225379
37563559.9452464992633.05475350073664
38562560.5199911309831.48000886901673
39593560.79845129222432.2015487077762
40588566.85709636731621.1429036326836
41576570.8350835793535.1649164206467
42558571.806850363591-13.8068503635906
43543569.209124188461-26.2091241884607
44494564.277939585263-70.2779395852629
45585551.05531180360333.9446881963969
46586557.44192444242328.558075557577
47553562.815058678953-9.81505867895282
48541560.968378649162-19.9683786491621
49506557.211375529274-51.2113755292744
50500547.576076589002-47.5760765890021
51570538.62475052906731.3752494709331
52541544.52792936099-3.52792936098956
53544543.864157812540.135842187460071
54545543.8897161981791.1102838018212
55552544.0986134642367.90138653576412
56460545.585240615487-85.5852406154869
57526529.48258042168-3.48258042168004
58569528.82734116868940.1726588313106
59549536.38573172283412.6142682771656
60525538.759076404697-13.7590764046972
61473536.170338786714-63.1703387867138
62498524.284989251036-26.2849892510364
63582519.33953081610762.6604691838927
64573531.12894959435141.8710504056489
65528539.006888498199-11.0068884981989
66571536.93596851242834.0640314875719
67518543.345035308652-25.3450353086515
68483538.57642698039-55.5764269803904
69551528.11985395430222.8801460456976
70562532.42469920926629.5753007907335
71580537.98922196269842.0107780373017
72515545.893450289302-30.8934502893018
73492540.08092083159-48.0809208315897
74509531.034609523839-22.0346095238392
75601526.8888499616374.1111500383697
76579540.83268720573838.1673127942624
77561548.01377665547112.9862233445293
78537550.457103801764-13.4571038017637
79513547.925181613379-34.925181613379
80499541.35409146182-42.35409146182
81563533.3852695280129.6147304719901
82561538.95721088252622.0427891174741
83546543.1045094158922.89549058410762
84558543.64928910728514.3507108927151
85507546.349341352077-39.3493413520774
86517538.945856030474-21.9458560304745
87544534.8167952277069.18320477229429
88529536.544593442386-7.54459344238569
89557535.12509606609221.8749039339082
90532539.240807400041-7.24080740004058
91512537.878466647673-25.8784666476731
92488533.009494477151-45.009494477151
93518524.541064759032-6.54106475903154
94567523.31037892625443.6896210737464
95537531.5304775914835.46952240851681
96484532.559555270454-48.5595552704542
97487523.423190027345-36.4231900273446
98484516.57025314282-32.57025314282
99534510.44223720206423.5577627979355
100514514.874574443082-0.874574443081883
101523514.7100253342658.28997466573469
102489516.269764421257-27.2697644212574
103495511.139022871864-16.1390228718644
104468508.102503966306-40.1025039663058
105513500.55731288375212.4426871162483
106544502.89837497681741.1016250231828
107520510.6315483184119.36845168158891
108509512.394200300059-3.39420030005931







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109511.7555895575444.874095498229578.637083616771
110511.7555895575443.700603694689579.810575420311
111511.7555895575442.547006607302580.964172507698
112511.7555895575441.41232543675582.09885367825
113511.7555895575440.295659104493583.215520010507
114511.7555895575439.196175877842584.315003237157
115511.7555895575438.113106120813585.398072994187
116511.7555895575437.045735991121586.465443123879
117511.7555895575435.99340193665587.51777717835
118511.7555895575434.955485870825588.555693244174
119511.7555895575433.931410927263589.579768187737
120511.7555895575432.920637710885590.590541404115

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 511.7555895575 & 444.874095498229 & 578.637083616771 \tabularnewline
110 & 511.7555895575 & 443.700603694689 & 579.810575420311 \tabularnewline
111 & 511.7555895575 & 442.547006607302 & 580.964172507698 \tabularnewline
112 & 511.7555895575 & 441.41232543675 & 582.09885367825 \tabularnewline
113 & 511.7555895575 & 440.295659104493 & 583.215520010507 \tabularnewline
114 & 511.7555895575 & 439.196175877842 & 584.315003237157 \tabularnewline
115 & 511.7555895575 & 438.113106120813 & 585.398072994187 \tabularnewline
116 & 511.7555895575 & 437.045735991121 & 586.465443123879 \tabularnewline
117 & 511.7555895575 & 435.99340193665 & 587.51777717835 \tabularnewline
118 & 511.7555895575 & 434.955485870825 & 588.555693244174 \tabularnewline
119 & 511.7555895575 & 433.931410927263 & 589.579768187737 \tabularnewline
120 & 511.7555895575 & 432.920637710885 & 590.590541404115 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278556&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]109[/C][C]511.7555895575[/C][C]444.874095498229[/C][C]578.637083616771[/C][/ROW]
[ROW][C]110[/C][C]511.7555895575[/C][C]443.700603694689[/C][C]579.810575420311[/C][/ROW]
[ROW][C]111[/C][C]511.7555895575[/C][C]442.547006607302[/C][C]580.964172507698[/C][/ROW]
[ROW][C]112[/C][C]511.7555895575[/C][C]441.41232543675[/C][C]582.09885367825[/C][/ROW]
[ROW][C]113[/C][C]511.7555895575[/C][C]440.295659104493[/C][C]583.215520010507[/C][/ROW]
[ROW][C]114[/C][C]511.7555895575[/C][C]439.196175877842[/C][C]584.315003237157[/C][/ROW]
[ROW][C]115[/C][C]511.7555895575[/C][C]438.113106120813[/C][C]585.398072994187[/C][/ROW]
[ROW][C]116[/C][C]511.7555895575[/C][C]437.045735991121[/C][C]586.465443123879[/C][/ROW]
[ROW][C]117[/C][C]511.7555895575[/C][C]435.99340193665[/C][C]587.51777717835[/C][/ROW]
[ROW][C]118[/C][C]511.7555895575[/C][C]434.955485870825[/C][C]588.555693244174[/C][/ROW]
[ROW][C]119[/C][C]511.7555895575[/C][C]433.931410927263[/C][C]589.579768187737[/C][/ROW]
[ROW][C]120[/C][C]511.7555895575[/C][C]432.920637710885[/C][C]590.590541404115[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278556&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278556&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
109511.7555895575444.874095498229578.637083616771
110511.7555895575443.700603694689579.810575420311
111511.7555895575442.547006607302580.964172507698
112511.7555895575441.41232543675582.09885367825
113511.7555895575440.295659104493583.215520010507
114511.7555895575439.196175877842584.315003237157
115511.7555895575438.113106120813585.398072994187
116511.7555895575437.045735991121586.465443123879
117511.7555895575435.99340193665587.51777717835
118511.7555895575434.955485870825588.555693244174
119511.7555895575433.931410927263589.579768187737
120511.7555895575432.920637710885590.590541404115



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