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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 computationSun, 21 Aug 2011 08:57:53 -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/2011/Aug/21/t1313931506u52y9lg7gbl894m.htm/, Retrieved Wed, 15 May 2024 17:03:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124236, Retrieved Wed, 15 May 2024 17:03:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsBlij Arnaud
Estimated Impact189
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2- Stap 27] [2011-08-21 12:57:53] [084e0343a0486ff05530df6c705c8bb4] [Current]
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Dataseries X:
600
700
720
630
660
740
700
670
720
630
700
770
570
640
720
630
700
700
670
760
870
670
810
810
610
600
730
630
750
770
660
790
890
680
800
860
670
610
690
680
740
760
670
750
890
730
750
940
740
640
640
750
770
780
640
730
970
780
720
1050
790
610
530
750
730
870
670
750
1090
830
740
1010
780
640
590
770
650
880
700
790
1140
860
630
1060
840
720
570
790
570
800
790
780
1120
850
600
1050
810
750
550
740
500
750
820
810
1090
820
630
1080




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124236&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124236&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124236&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0136210064431747
beta0.365691863903782
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0136210064431747 \tabularnewline
beta & 0.365691863903782 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124236&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]0.0136210064431747[/C][/ROW]
[ROW][C]beta[/C][C]0.365691863903782[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124236&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124236&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
alpha0.0136210064431747
beta0.365691863903782
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13570574.922542735043-4.92254273504261
14640644.680914839205-4.68091483920489
15720716.9192620946183.08073790538162
16630621.3620096419858.63799035801492
17700687.59014584553812.4098541544623
18700683.93147324591416.0685267540862
19670712.069340913775-42.0693409137751
20760687.53909441960972.4609055803911
21870743.679799532504126.320200467496
22670658.68333489136511.316665108635
23810730.51010902882479.4898909711765
24810805.3280841808184.67191581918155
25610607.2114083680732.78859163192737
26600678.760132776549-78.7601327765489
27730758.723364619258-28.7233646192582
28630669.134033095665-39.1340330956649
29750739.11356440132510.8864355986746
30770739.71700174349530.2829982565054
31660711.447339640101-51.4473396401011
32790800.457698184927-10.4576981849272
33890908.879733967047-18.8797339670471
34680708.030262920971-28.0302629209706
35800845.931573874018-45.9315738740177
36860843.9834113176916.0165886823096
37670642.96120670413127.0387932958689
38610633.320703778174-23.3207037781735
39690762.588851530456-72.5888515304561
40680661.10922331480818.8907766851919
41740780.483337449509-40.4833374495086
42760798.528638161839-38.5286381618387
43670687.371056265862-17.3710562658615
44750816.113078835265-66.1130788352651
45890914.028678076143-24.0286780761431
46730702.6165012643927.3834987356104
47750822.424464918535-72.4244649185348
48940879.89718382798760.1028161720128
49740689.2445216883250.7554783116801
50640629.26862140539410.7313785946064
51640709.588250889338-69.5882508893376
52750697.58274784277552.4172521572254
53770758.21481616359411.7851838364063
54780778.5271641216391.47283587836148
55640688.610110954082-48.6101109540823
56730768.519188467019-38.5191884670195
57970908.12993029171161.8700697082892
58780748.83565875686231.1643412431375
59720770.501461934234-50.5014619342342
601050959.35894020870790.6410597912931
61790760.41835560783929.5816443921611
62610661.085780037995-51.0857800379948
63530661.440550243944-131.440550243944
64750768.730877917933-18.7308779179325
65730787.755479102214-57.7554791022143
66870796.04260211370273.9573978862981
67670657.16701942924812.8329805707523
68750747.6274657871012.3725342128987
691090986.781713006687103.218286993313
70830797.93378304260632.0662169573936
71740739.2335530306020.766446969397862
7210101068.43985558374-58.4398555837406
73780806.928813758096-26.9288137580959
74640626.6642717963613.33572820364
75590548.36357567284441.6364243271561
76770769.7752565415330.22474345846706
77650751.248842661942-101.248842661942
78880889.329550053899-9.32955005389897
79700689.08000691848410.9199930815164
80790769.23923598261220.7607640173883
8111401108.2504790529731.7495209470294
82860848.02457041258511.9754295874153
83630757.855579070196-127.855579070196
8410601025.9477200400234.052279959983
85840796.27670866276243.7232913372378
86720656.54090718968363.4590928103174
87570606.938112283468-36.9381122834678
88790786.1404882361673.85951176383321
89570667.298846371783-97.2988463717835
90800895.846967874485-95.8469678744849
91790713.708095114576.2919048854997
92780804.105509302043-24.1055093020432
9311201152.76224873436-32.7622487343644
94850871.24907867844-21.2490786784396
95600641.631874349017-41.6318743490168
9610501069.96117597717-19.9611759771728
97810848.184879467288-38.1848794672876
98750725.48354422409524.5164557759053
99550574.809798421725-24.8097984217254
100740792.968886930964-52.9688869309635
101500571.839231523523-71.8392315235233
102750800.559583648789-50.5595836487895
103820787.45066189247932.549338107521
104810776.62339540447333.3766045955268
10510901116.21163427589-26.2116342758882
106820844.864029606444-24.8640296064441
107630593.79440845966436.2055915403359
10810801043.6491558129136.3508441870913

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 570 & 574.922542735043 & -4.92254273504261 \tabularnewline
14 & 640 & 644.680914839205 & -4.68091483920489 \tabularnewline
15 & 720 & 716.919262094618 & 3.08073790538162 \tabularnewline
16 & 630 & 621.362009641985 & 8.63799035801492 \tabularnewline
17 & 700 & 687.590145845538 & 12.4098541544623 \tabularnewline
18 & 700 & 683.931473245914 & 16.0685267540862 \tabularnewline
19 & 670 & 712.069340913775 & -42.0693409137751 \tabularnewline
20 & 760 & 687.539094419609 & 72.4609055803911 \tabularnewline
21 & 870 & 743.679799532504 & 126.320200467496 \tabularnewline
22 & 670 & 658.683334891365 & 11.316665108635 \tabularnewline
23 & 810 & 730.510109028824 & 79.4898909711765 \tabularnewline
24 & 810 & 805.328084180818 & 4.67191581918155 \tabularnewline
25 & 610 & 607.211408368073 & 2.78859163192737 \tabularnewline
26 & 600 & 678.760132776549 & -78.7601327765489 \tabularnewline
27 & 730 & 758.723364619258 & -28.7233646192582 \tabularnewline
28 & 630 & 669.134033095665 & -39.1340330956649 \tabularnewline
29 & 750 & 739.113564401325 & 10.8864355986746 \tabularnewline
30 & 770 & 739.717001743495 & 30.2829982565054 \tabularnewline
31 & 660 & 711.447339640101 & -51.4473396401011 \tabularnewline
32 & 790 & 800.457698184927 & -10.4576981849272 \tabularnewline
33 & 890 & 908.879733967047 & -18.8797339670471 \tabularnewline
34 & 680 & 708.030262920971 & -28.0302629209706 \tabularnewline
35 & 800 & 845.931573874018 & -45.9315738740177 \tabularnewline
36 & 860 & 843.98341131769 & 16.0165886823096 \tabularnewline
37 & 670 & 642.961206704131 & 27.0387932958689 \tabularnewline
38 & 610 & 633.320703778174 & -23.3207037781735 \tabularnewline
39 & 690 & 762.588851530456 & -72.5888515304561 \tabularnewline
40 & 680 & 661.109223314808 & 18.8907766851919 \tabularnewline
41 & 740 & 780.483337449509 & -40.4833374495086 \tabularnewline
42 & 760 & 798.528638161839 & -38.5286381618387 \tabularnewline
43 & 670 & 687.371056265862 & -17.3710562658615 \tabularnewline
44 & 750 & 816.113078835265 & -66.1130788352651 \tabularnewline
45 & 890 & 914.028678076143 & -24.0286780761431 \tabularnewline
46 & 730 & 702.61650126439 & 27.3834987356104 \tabularnewline
47 & 750 & 822.424464918535 & -72.4244649185348 \tabularnewline
48 & 940 & 879.897183827987 & 60.1028161720128 \tabularnewline
49 & 740 & 689.24452168832 & 50.7554783116801 \tabularnewline
50 & 640 & 629.268621405394 & 10.7313785946064 \tabularnewline
51 & 640 & 709.588250889338 & -69.5882508893376 \tabularnewline
52 & 750 & 697.582747842775 & 52.4172521572254 \tabularnewline
53 & 770 & 758.214816163594 & 11.7851838364063 \tabularnewline
54 & 780 & 778.527164121639 & 1.47283587836148 \tabularnewline
55 & 640 & 688.610110954082 & -48.6101109540823 \tabularnewline
56 & 730 & 768.519188467019 & -38.5191884670195 \tabularnewline
57 & 970 & 908.129930291711 & 61.8700697082892 \tabularnewline
58 & 780 & 748.835658756862 & 31.1643412431375 \tabularnewline
59 & 720 & 770.501461934234 & -50.5014619342342 \tabularnewline
60 & 1050 & 959.358940208707 & 90.6410597912931 \tabularnewline
61 & 790 & 760.418355607839 & 29.5816443921611 \tabularnewline
62 & 610 & 661.085780037995 & -51.0857800379948 \tabularnewline
63 & 530 & 661.440550243944 & -131.440550243944 \tabularnewline
64 & 750 & 768.730877917933 & -18.7308779179325 \tabularnewline
65 & 730 & 787.755479102214 & -57.7554791022143 \tabularnewline
66 & 870 & 796.042602113702 & 73.9573978862981 \tabularnewline
67 & 670 & 657.167019429248 & 12.8329805707523 \tabularnewline
68 & 750 & 747.627465787101 & 2.3725342128987 \tabularnewline
69 & 1090 & 986.781713006687 & 103.218286993313 \tabularnewline
70 & 830 & 797.933783042606 & 32.0662169573936 \tabularnewline
71 & 740 & 739.233553030602 & 0.766446969397862 \tabularnewline
72 & 1010 & 1068.43985558374 & -58.4398555837406 \tabularnewline
73 & 780 & 806.928813758096 & -26.9288137580959 \tabularnewline
74 & 640 & 626.66427179636 & 13.33572820364 \tabularnewline
75 & 590 & 548.363575672844 & 41.6364243271561 \tabularnewline
76 & 770 & 769.775256541533 & 0.22474345846706 \tabularnewline
77 & 650 & 751.248842661942 & -101.248842661942 \tabularnewline
78 & 880 & 889.329550053899 & -9.32955005389897 \tabularnewline
79 & 700 & 689.080006918484 & 10.9199930815164 \tabularnewline
80 & 790 & 769.239235982612 & 20.7607640173883 \tabularnewline
81 & 1140 & 1108.25047905297 & 31.7495209470294 \tabularnewline
82 & 860 & 848.024570412585 & 11.9754295874153 \tabularnewline
83 & 630 & 757.855579070196 & -127.855579070196 \tabularnewline
84 & 1060 & 1025.94772004002 & 34.052279959983 \tabularnewline
85 & 840 & 796.276708662762 & 43.7232913372378 \tabularnewline
86 & 720 & 656.540907189683 & 63.4590928103174 \tabularnewline
87 & 570 & 606.938112283468 & -36.9381122834678 \tabularnewline
88 & 790 & 786.140488236167 & 3.85951176383321 \tabularnewline
89 & 570 & 667.298846371783 & -97.2988463717835 \tabularnewline
90 & 800 & 895.846967874485 & -95.8469678744849 \tabularnewline
91 & 790 & 713.7080951145 & 76.2919048854997 \tabularnewline
92 & 780 & 804.105509302043 & -24.1055093020432 \tabularnewline
93 & 1120 & 1152.76224873436 & -32.7622487343644 \tabularnewline
94 & 850 & 871.24907867844 & -21.2490786784396 \tabularnewline
95 & 600 & 641.631874349017 & -41.6318743490168 \tabularnewline
96 & 1050 & 1069.96117597717 & -19.9611759771728 \tabularnewline
97 & 810 & 848.184879467288 & -38.1848794672876 \tabularnewline
98 & 750 & 725.483544224095 & 24.5164557759053 \tabularnewline
99 & 550 & 574.809798421725 & -24.8097984217254 \tabularnewline
100 & 740 & 792.968886930964 & -52.9688869309635 \tabularnewline
101 & 500 & 571.839231523523 & -71.8392315235233 \tabularnewline
102 & 750 & 800.559583648789 & -50.5595836487895 \tabularnewline
103 & 820 & 787.450661892479 & 32.549338107521 \tabularnewline
104 & 810 & 776.623395404473 & 33.3766045955268 \tabularnewline
105 & 1090 & 1116.21163427589 & -26.2116342758882 \tabularnewline
106 & 820 & 844.864029606444 & -24.8640296064441 \tabularnewline
107 & 630 & 593.794408459664 & 36.2055915403359 \tabularnewline
108 & 1080 & 1043.64915581291 & 36.3508441870913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124236&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]570[/C][C]574.922542735043[/C][C]-4.92254273504261[/C][/ROW]
[ROW][C]14[/C][C]640[/C][C]644.680914839205[/C][C]-4.68091483920489[/C][/ROW]
[ROW][C]15[/C][C]720[/C][C]716.919262094618[/C][C]3.08073790538162[/C][/ROW]
[ROW][C]16[/C][C]630[/C][C]621.362009641985[/C][C]8.63799035801492[/C][/ROW]
[ROW][C]17[/C][C]700[/C][C]687.590145845538[/C][C]12.4098541544623[/C][/ROW]
[ROW][C]18[/C][C]700[/C][C]683.931473245914[/C][C]16.0685267540862[/C][/ROW]
[ROW][C]19[/C][C]670[/C][C]712.069340913775[/C][C]-42.0693409137751[/C][/ROW]
[ROW][C]20[/C][C]760[/C][C]687.539094419609[/C][C]72.4609055803911[/C][/ROW]
[ROW][C]21[/C][C]870[/C][C]743.679799532504[/C][C]126.320200467496[/C][/ROW]
[ROW][C]22[/C][C]670[/C][C]658.683334891365[/C][C]11.316665108635[/C][/ROW]
[ROW][C]23[/C][C]810[/C][C]730.510109028824[/C][C]79.4898909711765[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]805.328084180818[/C][C]4.67191581918155[/C][/ROW]
[ROW][C]25[/C][C]610[/C][C]607.211408368073[/C][C]2.78859163192737[/C][/ROW]
[ROW][C]26[/C][C]600[/C][C]678.760132776549[/C][C]-78.7601327765489[/C][/ROW]
[ROW][C]27[/C][C]730[/C][C]758.723364619258[/C][C]-28.7233646192582[/C][/ROW]
[ROW][C]28[/C][C]630[/C][C]669.134033095665[/C][C]-39.1340330956649[/C][/ROW]
[ROW][C]29[/C][C]750[/C][C]739.113564401325[/C][C]10.8864355986746[/C][/ROW]
[ROW][C]30[/C][C]770[/C][C]739.717001743495[/C][C]30.2829982565054[/C][/ROW]
[ROW][C]31[/C][C]660[/C][C]711.447339640101[/C][C]-51.4473396401011[/C][/ROW]
[ROW][C]32[/C][C]790[/C][C]800.457698184927[/C][C]-10.4576981849272[/C][/ROW]
[ROW][C]33[/C][C]890[/C][C]908.879733967047[/C][C]-18.8797339670471[/C][/ROW]
[ROW][C]34[/C][C]680[/C][C]708.030262920971[/C][C]-28.0302629209706[/C][/ROW]
[ROW][C]35[/C][C]800[/C][C]845.931573874018[/C][C]-45.9315738740177[/C][/ROW]
[ROW][C]36[/C][C]860[/C][C]843.98341131769[/C][C]16.0165886823096[/C][/ROW]
[ROW][C]37[/C][C]670[/C][C]642.961206704131[/C][C]27.0387932958689[/C][/ROW]
[ROW][C]38[/C][C]610[/C][C]633.320703778174[/C][C]-23.3207037781735[/C][/ROW]
[ROW][C]39[/C][C]690[/C][C]762.588851530456[/C][C]-72.5888515304561[/C][/ROW]
[ROW][C]40[/C][C]680[/C][C]661.109223314808[/C][C]18.8907766851919[/C][/ROW]
[ROW][C]41[/C][C]740[/C][C]780.483337449509[/C][C]-40.4833374495086[/C][/ROW]
[ROW][C]42[/C][C]760[/C][C]798.528638161839[/C][C]-38.5286381618387[/C][/ROW]
[ROW][C]43[/C][C]670[/C][C]687.371056265862[/C][C]-17.3710562658615[/C][/ROW]
[ROW][C]44[/C][C]750[/C][C]816.113078835265[/C][C]-66.1130788352651[/C][/ROW]
[ROW][C]45[/C][C]890[/C][C]914.028678076143[/C][C]-24.0286780761431[/C][/ROW]
[ROW][C]46[/C][C]730[/C][C]702.61650126439[/C][C]27.3834987356104[/C][/ROW]
[ROW][C]47[/C][C]750[/C][C]822.424464918535[/C][C]-72.4244649185348[/C][/ROW]
[ROW][C]48[/C][C]940[/C][C]879.897183827987[/C][C]60.1028161720128[/C][/ROW]
[ROW][C]49[/C][C]740[/C][C]689.24452168832[/C][C]50.7554783116801[/C][/ROW]
[ROW][C]50[/C][C]640[/C][C]629.268621405394[/C][C]10.7313785946064[/C][/ROW]
[ROW][C]51[/C][C]640[/C][C]709.588250889338[/C][C]-69.5882508893376[/C][/ROW]
[ROW][C]52[/C][C]750[/C][C]697.582747842775[/C][C]52.4172521572254[/C][/ROW]
[ROW][C]53[/C][C]770[/C][C]758.214816163594[/C][C]11.7851838364063[/C][/ROW]
[ROW][C]54[/C][C]780[/C][C]778.527164121639[/C][C]1.47283587836148[/C][/ROW]
[ROW][C]55[/C][C]640[/C][C]688.610110954082[/C][C]-48.6101109540823[/C][/ROW]
[ROW][C]56[/C][C]730[/C][C]768.519188467019[/C][C]-38.5191884670195[/C][/ROW]
[ROW][C]57[/C][C]970[/C][C]908.129930291711[/C][C]61.8700697082892[/C][/ROW]
[ROW][C]58[/C][C]780[/C][C]748.835658756862[/C][C]31.1643412431375[/C][/ROW]
[ROW][C]59[/C][C]720[/C][C]770.501461934234[/C][C]-50.5014619342342[/C][/ROW]
[ROW][C]60[/C][C]1050[/C][C]959.358940208707[/C][C]90.6410597912931[/C][/ROW]
[ROW][C]61[/C][C]790[/C][C]760.418355607839[/C][C]29.5816443921611[/C][/ROW]
[ROW][C]62[/C][C]610[/C][C]661.085780037995[/C][C]-51.0857800379948[/C][/ROW]
[ROW][C]63[/C][C]530[/C][C]661.440550243944[/C][C]-131.440550243944[/C][/ROW]
[ROW][C]64[/C][C]750[/C][C]768.730877917933[/C][C]-18.7308779179325[/C][/ROW]
[ROW][C]65[/C][C]730[/C][C]787.755479102214[/C][C]-57.7554791022143[/C][/ROW]
[ROW][C]66[/C][C]870[/C][C]796.042602113702[/C][C]73.9573978862981[/C][/ROW]
[ROW][C]67[/C][C]670[/C][C]657.167019429248[/C][C]12.8329805707523[/C][/ROW]
[ROW][C]68[/C][C]750[/C][C]747.627465787101[/C][C]2.3725342128987[/C][/ROW]
[ROW][C]69[/C][C]1090[/C][C]986.781713006687[/C][C]103.218286993313[/C][/ROW]
[ROW][C]70[/C][C]830[/C][C]797.933783042606[/C][C]32.0662169573936[/C][/ROW]
[ROW][C]71[/C][C]740[/C][C]739.233553030602[/C][C]0.766446969397862[/C][/ROW]
[ROW][C]72[/C][C]1010[/C][C]1068.43985558374[/C][C]-58.4398555837406[/C][/ROW]
[ROW][C]73[/C][C]780[/C][C]806.928813758096[/C][C]-26.9288137580959[/C][/ROW]
[ROW][C]74[/C][C]640[/C][C]626.66427179636[/C][C]13.33572820364[/C][/ROW]
[ROW][C]75[/C][C]590[/C][C]548.363575672844[/C][C]41.6364243271561[/C][/ROW]
[ROW][C]76[/C][C]770[/C][C]769.775256541533[/C][C]0.22474345846706[/C][/ROW]
[ROW][C]77[/C][C]650[/C][C]751.248842661942[/C][C]-101.248842661942[/C][/ROW]
[ROW][C]78[/C][C]880[/C][C]889.329550053899[/C][C]-9.32955005389897[/C][/ROW]
[ROW][C]79[/C][C]700[/C][C]689.080006918484[/C][C]10.9199930815164[/C][/ROW]
[ROW][C]80[/C][C]790[/C][C]769.239235982612[/C][C]20.7607640173883[/C][/ROW]
[ROW][C]81[/C][C]1140[/C][C]1108.25047905297[/C][C]31.7495209470294[/C][/ROW]
[ROW][C]82[/C][C]860[/C][C]848.024570412585[/C][C]11.9754295874153[/C][/ROW]
[ROW][C]83[/C][C]630[/C][C]757.855579070196[/C][C]-127.855579070196[/C][/ROW]
[ROW][C]84[/C][C]1060[/C][C]1025.94772004002[/C][C]34.052279959983[/C][/ROW]
[ROW][C]85[/C][C]840[/C][C]796.276708662762[/C][C]43.7232913372378[/C][/ROW]
[ROW][C]86[/C][C]720[/C][C]656.540907189683[/C][C]63.4590928103174[/C][/ROW]
[ROW][C]87[/C][C]570[/C][C]606.938112283468[/C][C]-36.9381122834678[/C][/ROW]
[ROW][C]88[/C][C]790[/C][C]786.140488236167[/C][C]3.85951176383321[/C][/ROW]
[ROW][C]89[/C][C]570[/C][C]667.298846371783[/C][C]-97.2988463717835[/C][/ROW]
[ROW][C]90[/C][C]800[/C][C]895.846967874485[/C][C]-95.8469678744849[/C][/ROW]
[ROW][C]91[/C][C]790[/C][C]713.7080951145[/C][C]76.2919048854997[/C][/ROW]
[ROW][C]92[/C][C]780[/C][C]804.105509302043[/C][C]-24.1055093020432[/C][/ROW]
[ROW][C]93[/C][C]1120[/C][C]1152.76224873436[/C][C]-32.7622487343644[/C][/ROW]
[ROW][C]94[/C][C]850[/C][C]871.24907867844[/C][C]-21.2490786784396[/C][/ROW]
[ROW][C]95[/C][C]600[/C][C]641.631874349017[/C][C]-41.6318743490168[/C][/ROW]
[ROW][C]96[/C][C]1050[/C][C]1069.96117597717[/C][C]-19.9611759771728[/C][/ROW]
[ROW][C]97[/C][C]810[/C][C]848.184879467288[/C][C]-38.1848794672876[/C][/ROW]
[ROW][C]98[/C][C]750[/C][C]725.483544224095[/C][C]24.5164557759053[/C][/ROW]
[ROW][C]99[/C][C]550[/C][C]574.809798421725[/C][C]-24.8097984217254[/C][/ROW]
[ROW][C]100[/C][C]740[/C][C]792.968886930964[/C][C]-52.9688869309635[/C][/ROW]
[ROW][C]101[/C][C]500[/C][C]571.839231523523[/C][C]-71.8392315235233[/C][/ROW]
[ROW][C]102[/C][C]750[/C][C]800.559583648789[/C][C]-50.5595836487895[/C][/ROW]
[ROW][C]103[/C][C]820[/C][C]787.450661892479[/C][C]32.549338107521[/C][/ROW]
[ROW][C]104[/C][C]810[/C][C]776.623395404473[/C][C]33.3766045955268[/C][/ROW]
[ROW][C]105[/C][C]1090[/C][C]1116.21163427589[/C][C]-26.2116342758882[/C][/ROW]
[ROW][C]106[/C][C]820[/C][C]844.864029606444[/C][C]-24.8640296064441[/C][/ROW]
[ROW][C]107[/C][C]630[/C][C]593.794408459664[/C][C]36.2055915403359[/C][/ROW]
[ROW][C]108[/C][C]1080[/C][C]1043.64915581291[/C][C]36.3508441870913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124236&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124236&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
13570574.922542735043-4.92254273504261
14640644.680914839205-4.68091483920489
15720716.9192620946183.08073790538162
16630621.3620096419858.63799035801492
17700687.59014584553812.4098541544623
18700683.93147324591416.0685267540862
19670712.069340913775-42.0693409137751
20760687.53909441960972.4609055803911
21870743.679799532504126.320200467496
22670658.68333489136511.316665108635
23810730.51010902882479.4898909711765
24810805.3280841808184.67191581918155
25610607.2114083680732.78859163192737
26600678.760132776549-78.7601327765489
27730758.723364619258-28.7233646192582
28630669.134033095665-39.1340330956649
29750739.11356440132510.8864355986746
30770739.71700174349530.2829982565054
31660711.447339640101-51.4473396401011
32790800.457698184927-10.4576981849272
33890908.879733967047-18.8797339670471
34680708.030262920971-28.0302629209706
35800845.931573874018-45.9315738740177
36860843.9834113176916.0165886823096
37670642.96120670413127.0387932958689
38610633.320703778174-23.3207037781735
39690762.588851530456-72.5888515304561
40680661.10922331480818.8907766851919
41740780.483337449509-40.4833374495086
42760798.528638161839-38.5286381618387
43670687.371056265862-17.3710562658615
44750816.113078835265-66.1130788352651
45890914.028678076143-24.0286780761431
46730702.6165012643927.3834987356104
47750822.424464918535-72.4244649185348
48940879.89718382798760.1028161720128
49740689.2445216883250.7554783116801
50640629.26862140539410.7313785946064
51640709.588250889338-69.5882508893376
52750697.58274784277552.4172521572254
53770758.21481616359411.7851838364063
54780778.5271641216391.47283587836148
55640688.610110954082-48.6101109540823
56730768.519188467019-38.5191884670195
57970908.12993029171161.8700697082892
58780748.83565875686231.1643412431375
59720770.501461934234-50.5014619342342
601050959.35894020870790.6410597912931
61790760.41835560783929.5816443921611
62610661.085780037995-51.0857800379948
63530661.440550243944-131.440550243944
64750768.730877917933-18.7308779179325
65730787.755479102214-57.7554791022143
66870796.04260211370273.9573978862981
67670657.16701942924812.8329805707523
68750747.6274657871012.3725342128987
691090986.781713006687103.218286993313
70830797.93378304260632.0662169573936
71740739.2335530306020.766446969397862
7210101068.43985558374-58.4398555837406
73780806.928813758096-26.9288137580959
74640626.6642717963613.33572820364
75590548.36357567284441.6364243271561
76770769.7752565415330.22474345846706
77650751.248842661942-101.248842661942
78880889.329550053899-9.32955005389897
79700689.08000691848410.9199930815164
80790769.23923598261220.7607640173883
8111401108.2504790529731.7495209470294
82860848.02457041258511.9754295874153
83630757.855579070196-127.855579070196
8410601025.9477200400234.052279959983
85840796.27670866276243.7232913372378
86720656.54090718968363.4590928103174
87570606.938112283468-36.9381122834678
88790786.1404882361673.85951176383321
89570667.298846371783-97.2988463717835
90800895.846967874485-95.8469678744849
91790713.708095114576.2919048854997
92780804.105509302043-24.1055093020432
9311201152.76224873436-32.7622487343644
94850871.24907867844-21.2490786784396
95600641.631874349017-41.6318743490168
9610501069.96117597717-19.9611759771728
97810848.184879467288-38.1848794672876
98750725.48354422409524.5164557759053
99550574.809798421725-24.8097984217254
100740792.968886930964-52.9688869309635
101500571.839231523523-71.8392315235233
102750800.559583648789-50.5595836487895
103820787.45066189247932.549338107521
104810776.62339540447333.3766045955268
10510901116.21163427589-26.2116342758882
106820844.864029606444-24.8640296064441
107630593.79440845966436.2055915403359
10810801043.6491558129136.3508441870913







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109804.034602146083707.566025276352900.503179015814
110743.261060473429646.775794148835839.746326798023
111543.037273324054446.525189056908639.549357591199
112733.320621170144636.769207428788829.872034911499
113494.124844959904397.519215352069590.73047456774
114744.997056295286648.319961098931841.674151491641
115814.98908237087718.220923955554911.757240786187
116804.807709021557707.926561676021901.688856367092
1171085.27173554526988.2533701916191182.2901008989
118815.847968878813718.665883109835913.030054647791
119625.716222509168528.341676332373723.090768685963
1201075.40215429763977.8042119080581173.00009668719

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 804.034602146083 & 707.566025276352 & 900.503179015814 \tabularnewline
110 & 743.261060473429 & 646.775794148835 & 839.746326798023 \tabularnewline
111 & 543.037273324054 & 446.525189056908 & 639.549357591199 \tabularnewline
112 & 733.320621170144 & 636.769207428788 & 829.872034911499 \tabularnewline
113 & 494.124844959904 & 397.519215352069 & 590.73047456774 \tabularnewline
114 & 744.997056295286 & 648.319961098931 & 841.674151491641 \tabularnewline
115 & 814.98908237087 & 718.220923955554 & 911.757240786187 \tabularnewline
116 & 804.807709021557 & 707.926561676021 & 901.688856367092 \tabularnewline
117 & 1085.27173554526 & 988.253370191619 & 1182.2901008989 \tabularnewline
118 & 815.847968878813 & 718.665883109835 & 913.030054647791 \tabularnewline
119 & 625.716222509168 & 528.341676332373 & 723.090768685963 \tabularnewline
120 & 1075.40215429763 & 977.804211908058 & 1173.00009668719 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124236&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]804.034602146083[/C][C]707.566025276352[/C][C]900.503179015814[/C][/ROW]
[ROW][C]110[/C][C]743.261060473429[/C][C]646.775794148835[/C][C]839.746326798023[/C][/ROW]
[ROW][C]111[/C][C]543.037273324054[/C][C]446.525189056908[/C][C]639.549357591199[/C][/ROW]
[ROW][C]112[/C][C]733.320621170144[/C][C]636.769207428788[/C][C]829.872034911499[/C][/ROW]
[ROW][C]113[/C][C]494.124844959904[/C][C]397.519215352069[/C][C]590.73047456774[/C][/ROW]
[ROW][C]114[/C][C]744.997056295286[/C][C]648.319961098931[/C][C]841.674151491641[/C][/ROW]
[ROW][C]115[/C][C]814.98908237087[/C][C]718.220923955554[/C][C]911.757240786187[/C][/ROW]
[ROW][C]116[/C][C]804.807709021557[/C][C]707.926561676021[/C][C]901.688856367092[/C][/ROW]
[ROW][C]117[/C][C]1085.27173554526[/C][C]988.253370191619[/C][C]1182.2901008989[/C][/ROW]
[ROW][C]118[/C][C]815.847968878813[/C][C]718.665883109835[/C][C]913.030054647791[/C][/ROW]
[ROW][C]119[/C][C]625.716222509168[/C][C]528.341676332373[/C][C]723.090768685963[/C][/ROW]
[ROW][C]120[/C][C]1075.40215429763[/C][C]977.804211908058[/C][C]1173.00009668719[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124236&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124236&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
109804.034602146083707.566025276352900.503179015814
110743.261060473429646.775794148835839.746326798023
111543.037273324054446.525189056908639.549357591199
112733.320621170144636.769207428788829.872034911499
113494.124844959904397.519215352069590.73047456774
114744.997056295286648.319961098931841.674151491641
115814.98908237087718.220923955554911.757240786187
116804.807709021557707.926561676021901.688856367092
1171085.27173554526988.2533701916191182.2901008989
118815.847968878813718.665883109835913.030054647791
119625.716222509168528.341676332373723.090768685963
1201075.40215429763977.8042119080581173.00009668719



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')