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of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 03 Dec 2013 12:19:00 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/03/t138609123134jr0xmilck8q9p.htm/, Retrieved Sat, 20 Apr 2024 07:07:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=230368, Retrieved Sat, 20 Apr 2024 07:07:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact56
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [triple exp] [2013-12-03 17:19:00] [b86744663ec671173a5f381479557f00] [Current]
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Dataseries X:
4
5
7
5
6
5
3
7
7
11
13
13
9
7
6
3
5
1
5
2
9
4
4
10
8
6
7
0
7
4
5
11
2
4
5
12
10
6
6
8
3
10
2
5
4
3
8
5
7
1
7
4
8
7
10
2
6
6
11
8
8
6
11
15
9
5
10
4
9
3
7
7
9
15
11
10
6
5
6
6
14
11
1
9
13
10
11
7
6
4
6
8
6
7
12
20
10
14
11
13
7
9
8
7
9
10
12
13
11
11
14
10
9
12
8
13
14
15
14
14
15
14
21
10
8
12
13
6
12
12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 5 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230368&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230368&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230368&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 time5 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0841194846606648
beta0.0680967631501524
gamma0.300614650868198

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0841194846606648 \tabularnewline
beta & 0.0680967631501524 \tabularnewline
gamma & 0.300614650868198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230368&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]0.0841194846606648[/C][/ROW]
[ROW][C]beta[/C][C]0.0680967631501524[/C][/ROW]
[ROW][C]gamma[/C][C]0.300614650868198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230368&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230368&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
alpha0.0841194846606648
beta0.0680967631501524
gamma0.300614650868198







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1399.71981837606838-0.719818376068377
1477.6177025901437-0.617702590143703
1566.52063836761192-0.520638367611924
1633.51209011644914-0.512090116449142
1755.95966088540428-0.959660885404284
1812.1974183737589-1.1974183737589
1952.074983362075942.92501663792406
2025.85774739511894-3.85774739511894
2195.297850615198583.70214938480142
2249.56176201451054-5.56176201451054
23411.0145387163797-7.01453871637967
241010.3882607901164-0.38826079011643
2585.993972380694682.00602761930532
2664.080548752440881.91945124755912
2773.169446656783163.83055334321684
2800.50001039526213-0.50001039526213
2972.79617655756274.2038234424373
304-0.5967919729653364.59679197296534
3150.9367732766766384.06322672332336
32112.987900354356468.01209964564354
3325.61602324157187-3.61602324157187
3446.77989721284628-2.77989721284628
3558.14879876245385-3.14879876245385
36129.776347377052742.22365262294726
37106.380194590585233.61980540941477
3864.707138768231711.29286123176829
3964.394371641641921.60562835835808
4080.4575745144516747.54242548554833
4134.88354861401334-1.88354861401334
42101.210027731351868.78997226864814
4323.09675518109314-1.09675518109314
4455.9188402417452-0.918840241745198
4544.66078217864928-0.660782178649276
4636.38700854317207-3.38700854317207
4787.683344793976240.316655206023759
48511.1815113027812-6.1815113027812
4977.51449638011792-0.514496380117916
5014.88108927364355-3.88108927364355
5174.217662452893742.78233754710626
5242.019608231892151.98039176810785
5383.355817585483594.64418241451641
5473.180844999841713.81915500015829
55101.909601056289598.09039894371041
5625.58837124622382-3.58837124622382
5764.196393863492591.80360613650741
5865.413025843163620.586974156836379
59118.11984104237622.8801589576238
60810.1156818117182-2.11568181171817
6188.44541030481837-0.445410304818367
6264.985741306157991.01425869384201
63116.691613359483084.30838664051692
64154.532756542207510.4672434577925
6597.496528523115151.50347147688485
6656.99245700153578-1.99245700153578
67106.537290470219853.46270952978015
6846.71374924283833-2.71374924283833
6996.987361557096312.01263844290369
7037.99526230407373-4.99526230407373
71710.9405588791711-3.94055887917112
72711.0247634506755-4.02476345067552
7399.680445697255-0.680445697254996
74156.628219436573838.37178056342617
75119.927438328969141.07256167103086
76109.241023308242290.758976691757709
7768.91349754432559-2.91349754432559
7857.04337345222289-2.04337345222289
7968.05361182270462-2.05361182270462
8066.00162782587766-0.00162782587765609
81147.756354597089326.24364540291068
82117.166606376997153.83339362300285
83111.1714321602257-10.1714321602257
84910.6991017752916-1.69910177529156
851310.47530749560482.5246925043952
861010.2074876046989-0.207487604698931
871110.74867436069780.251325639302234
8879.87545894799324-2.87545894799324
8968.17887563887136-2.17887563887136
9046.5621254097142-2.5621254097142
9167.47494528625126-1.47494528625126
9285.988957535438782.01104246456122
9369.59636348685671-3.59636348685671
9477.4227863963117-0.422786396311701
95127.096811138879724.90318886112028
962010.19469840770889.80530159229116
971012.1369600485836-2.13696004858359
981410.73344434023333.26655565976666
991111.7217730077917-0.721773007791704
100139.928821796760143.07117820323986
10178.98132801021227-1.98132801021227
10297.333881148960121.66611885103988
10388.98413421948083-0.984134219480833
10478.58445695483906-1.58445695483906
105910.410181358519-1.41018135851904
106109.371440430246980.628559569753024
1071210.68347543809981.31652456190018
1081314.8919797358977-1.89197973589765
1091112.5578795881579-1.5578795881579
1101112.6897630427986-1.68976304279856
1111412.13363555487761.86636444512243
1121011.5880867222319-1.58808672223195
11398.816263905580260.183736094419737
114128.326281977498183.67371802250182
11589.39832670404699-1.39832670404699
116138.778750002377624.22124999762238
1171411.15431424343862.84568575656139
1181511.07275799258173.92724200741834
1191412.90845029889711.09154970110294
1201416.2701113484316-2.27011134843162
1211514.04949346070090.950506539299052
1221414.4237423450953-0.423742345095253
1232115.02813461137545.97186538862456
1241013.9752762437439-3.97527624374387
125811.5752425297502-3.57524252975016
1261211.7931788554930.20682114450698
1271311.22049431854521.7795056814548
128612.4770361561907-6.47703615619067
1291213.5742325025081-1.57423250250808
1301213.3936348300439-1.39363483004386

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9 & 9.71981837606838 & -0.719818376068377 \tabularnewline
14 & 7 & 7.6177025901437 & -0.617702590143703 \tabularnewline
15 & 6 & 6.52063836761192 & -0.520638367611924 \tabularnewline
16 & 3 & 3.51209011644914 & -0.512090116449142 \tabularnewline
17 & 5 & 5.95966088540428 & -0.959660885404284 \tabularnewline
18 & 1 & 2.1974183737589 & -1.1974183737589 \tabularnewline
19 & 5 & 2.07498336207594 & 2.92501663792406 \tabularnewline
20 & 2 & 5.85774739511894 & -3.85774739511894 \tabularnewline
21 & 9 & 5.29785061519858 & 3.70214938480142 \tabularnewline
22 & 4 & 9.56176201451054 & -5.56176201451054 \tabularnewline
23 & 4 & 11.0145387163797 & -7.01453871637967 \tabularnewline
24 & 10 & 10.3882607901164 & -0.38826079011643 \tabularnewline
25 & 8 & 5.99397238069468 & 2.00602761930532 \tabularnewline
26 & 6 & 4.08054875244088 & 1.91945124755912 \tabularnewline
27 & 7 & 3.16944665678316 & 3.83055334321684 \tabularnewline
28 & 0 & 0.50001039526213 & -0.50001039526213 \tabularnewline
29 & 7 & 2.7961765575627 & 4.2038234424373 \tabularnewline
30 & 4 & -0.596791972965336 & 4.59679197296534 \tabularnewline
31 & 5 & 0.936773276676638 & 4.06322672332336 \tabularnewline
32 & 11 & 2.98790035435646 & 8.01209964564354 \tabularnewline
33 & 2 & 5.61602324157187 & -3.61602324157187 \tabularnewline
34 & 4 & 6.77989721284628 & -2.77989721284628 \tabularnewline
35 & 5 & 8.14879876245385 & -3.14879876245385 \tabularnewline
36 & 12 & 9.77634737705274 & 2.22365262294726 \tabularnewline
37 & 10 & 6.38019459058523 & 3.61980540941477 \tabularnewline
38 & 6 & 4.70713876823171 & 1.29286123176829 \tabularnewline
39 & 6 & 4.39437164164192 & 1.60562835835808 \tabularnewline
40 & 8 & 0.457574514451674 & 7.54242548554833 \tabularnewline
41 & 3 & 4.88354861401334 & -1.88354861401334 \tabularnewline
42 & 10 & 1.21002773135186 & 8.78997226864814 \tabularnewline
43 & 2 & 3.09675518109314 & -1.09675518109314 \tabularnewline
44 & 5 & 5.9188402417452 & -0.918840241745198 \tabularnewline
45 & 4 & 4.66078217864928 & -0.660782178649276 \tabularnewline
46 & 3 & 6.38700854317207 & -3.38700854317207 \tabularnewline
47 & 8 & 7.68334479397624 & 0.316655206023759 \tabularnewline
48 & 5 & 11.1815113027812 & -6.1815113027812 \tabularnewline
49 & 7 & 7.51449638011792 & -0.514496380117916 \tabularnewline
50 & 1 & 4.88108927364355 & -3.88108927364355 \tabularnewline
51 & 7 & 4.21766245289374 & 2.78233754710626 \tabularnewline
52 & 4 & 2.01960823189215 & 1.98039176810785 \tabularnewline
53 & 8 & 3.35581758548359 & 4.64418241451641 \tabularnewline
54 & 7 & 3.18084499984171 & 3.81915500015829 \tabularnewline
55 & 10 & 1.90960105628959 & 8.09039894371041 \tabularnewline
56 & 2 & 5.58837124622382 & -3.58837124622382 \tabularnewline
57 & 6 & 4.19639386349259 & 1.80360613650741 \tabularnewline
58 & 6 & 5.41302584316362 & 0.586974156836379 \tabularnewline
59 & 11 & 8.1198410423762 & 2.8801589576238 \tabularnewline
60 & 8 & 10.1156818117182 & -2.11568181171817 \tabularnewline
61 & 8 & 8.44541030481837 & -0.445410304818367 \tabularnewline
62 & 6 & 4.98574130615799 & 1.01425869384201 \tabularnewline
63 & 11 & 6.69161335948308 & 4.30838664051692 \tabularnewline
64 & 15 & 4.5327565422075 & 10.4672434577925 \tabularnewline
65 & 9 & 7.49652852311515 & 1.50347147688485 \tabularnewline
66 & 5 & 6.99245700153578 & -1.99245700153578 \tabularnewline
67 & 10 & 6.53729047021985 & 3.46270952978015 \tabularnewline
68 & 4 & 6.71374924283833 & -2.71374924283833 \tabularnewline
69 & 9 & 6.98736155709631 & 2.01263844290369 \tabularnewline
70 & 3 & 7.99526230407373 & -4.99526230407373 \tabularnewline
71 & 7 & 10.9405588791711 & -3.94055887917112 \tabularnewline
72 & 7 & 11.0247634506755 & -4.02476345067552 \tabularnewline
73 & 9 & 9.680445697255 & -0.680445697254996 \tabularnewline
74 & 15 & 6.62821943657383 & 8.37178056342617 \tabularnewline
75 & 11 & 9.92743832896914 & 1.07256167103086 \tabularnewline
76 & 10 & 9.24102330824229 & 0.758976691757709 \tabularnewline
77 & 6 & 8.91349754432559 & -2.91349754432559 \tabularnewline
78 & 5 & 7.04337345222289 & -2.04337345222289 \tabularnewline
79 & 6 & 8.05361182270462 & -2.05361182270462 \tabularnewline
80 & 6 & 6.00162782587766 & -0.00162782587765609 \tabularnewline
81 & 14 & 7.75635459708932 & 6.24364540291068 \tabularnewline
82 & 11 & 7.16660637699715 & 3.83339362300285 \tabularnewline
83 & 1 & 11.1714321602257 & -10.1714321602257 \tabularnewline
84 & 9 & 10.6991017752916 & -1.69910177529156 \tabularnewline
85 & 13 & 10.4753074956048 & 2.5246925043952 \tabularnewline
86 & 10 & 10.2074876046989 & -0.207487604698931 \tabularnewline
87 & 11 & 10.7486743606978 & 0.251325639302234 \tabularnewline
88 & 7 & 9.87545894799324 & -2.87545894799324 \tabularnewline
89 & 6 & 8.17887563887136 & -2.17887563887136 \tabularnewline
90 & 4 & 6.5621254097142 & -2.5621254097142 \tabularnewline
91 & 6 & 7.47494528625126 & -1.47494528625126 \tabularnewline
92 & 8 & 5.98895753543878 & 2.01104246456122 \tabularnewline
93 & 6 & 9.59636348685671 & -3.59636348685671 \tabularnewline
94 & 7 & 7.4227863963117 & -0.422786396311701 \tabularnewline
95 & 12 & 7.09681113887972 & 4.90318886112028 \tabularnewline
96 & 20 & 10.1946984077088 & 9.80530159229116 \tabularnewline
97 & 10 & 12.1369600485836 & -2.13696004858359 \tabularnewline
98 & 14 & 10.7334443402333 & 3.26655565976666 \tabularnewline
99 & 11 & 11.7217730077917 & -0.721773007791704 \tabularnewline
100 & 13 & 9.92882179676014 & 3.07117820323986 \tabularnewline
101 & 7 & 8.98132801021227 & -1.98132801021227 \tabularnewline
102 & 9 & 7.33388114896012 & 1.66611885103988 \tabularnewline
103 & 8 & 8.98413421948083 & -0.984134219480833 \tabularnewline
104 & 7 & 8.58445695483906 & -1.58445695483906 \tabularnewline
105 & 9 & 10.410181358519 & -1.41018135851904 \tabularnewline
106 & 10 & 9.37144043024698 & 0.628559569753024 \tabularnewline
107 & 12 & 10.6834754380998 & 1.31652456190018 \tabularnewline
108 & 13 & 14.8919797358977 & -1.89197973589765 \tabularnewline
109 & 11 & 12.5578795881579 & -1.5578795881579 \tabularnewline
110 & 11 & 12.6897630427986 & -1.68976304279856 \tabularnewline
111 & 14 & 12.1336355548776 & 1.86636444512243 \tabularnewline
112 & 10 & 11.5880867222319 & -1.58808672223195 \tabularnewline
113 & 9 & 8.81626390558026 & 0.183736094419737 \tabularnewline
114 & 12 & 8.32628197749818 & 3.67371802250182 \tabularnewline
115 & 8 & 9.39832670404699 & -1.39832670404699 \tabularnewline
116 & 13 & 8.77875000237762 & 4.22124999762238 \tabularnewline
117 & 14 & 11.1543142434386 & 2.84568575656139 \tabularnewline
118 & 15 & 11.0727579925817 & 3.92724200741834 \tabularnewline
119 & 14 & 12.9084502988971 & 1.09154970110294 \tabularnewline
120 & 14 & 16.2701113484316 & -2.27011134843162 \tabularnewline
121 & 15 & 14.0494934607009 & 0.950506539299052 \tabularnewline
122 & 14 & 14.4237423450953 & -0.423742345095253 \tabularnewline
123 & 21 & 15.0281346113754 & 5.97186538862456 \tabularnewline
124 & 10 & 13.9752762437439 & -3.97527624374387 \tabularnewline
125 & 8 & 11.5752425297502 & -3.57524252975016 \tabularnewline
126 & 12 & 11.793178855493 & 0.20682114450698 \tabularnewline
127 & 13 & 11.2204943185452 & 1.7795056814548 \tabularnewline
128 & 6 & 12.4770361561907 & -6.47703615619067 \tabularnewline
129 & 12 & 13.5742325025081 & -1.57423250250808 \tabularnewline
130 & 12 & 13.3936348300439 & -1.39363483004386 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230368&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]9[/C][C]9.71981837606838[/C][C]-0.719818376068377[/C][/ROW]
[ROW][C]14[/C][C]7[/C][C]7.6177025901437[/C][C]-0.617702590143703[/C][/ROW]
[ROW][C]15[/C][C]6[/C][C]6.52063836761192[/C][C]-0.520638367611924[/C][/ROW]
[ROW][C]16[/C][C]3[/C][C]3.51209011644914[/C][C]-0.512090116449142[/C][/ROW]
[ROW][C]17[/C][C]5[/C][C]5.95966088540428[/C][C]-0.959660885404284[/C][/ROW]
[ROW][C]18[/C][C]1[/C][C]2.1974183737589[/C][C]-1.1974183737589[/C][/ROW]
[ROW][C]19[/C][C]5[/C][C]2.07498336207594[/C][C]2.92501663792406[/C][/ROW]
[ROW][C]20[/C][C]2[/C][C]5.85774739511894[/C][C]-3.85774739511894[/C][/ROW]
[ROW][C]21[/C][C]9[/C][C]5.29785061519858[/C][C]3.70214938480142[/C][/ROW]
[ROW][C]22[/C][C]4[/C][C]9.56176201451054[/C][C]-5.56176201451054[/C][/ROW]
[ROW][C]23[/C][C]4[/C][C]11.0145387163797[/C][C]-7.01453871637967[/C][/ROW]
[ROW][C]24[/C][C]10[/C][C]10.3882607901164[/C][C]-0.38826079011643[/C][/ROW]
[ROW][C]25[/C][C]8[/C][C]5.99397238069468[/C][C]2.00602761930532[/C][/ROW]
[ROW][C]26[/C][C]6[/C][C]4.08054875244088[/C][C]1.91945124755912[/C][/ROW]
[ROW][C]27[/C][C]7[/C][C]3.16944665678316[/C][C]3.83055334321684[/C][/ROW]
[ROW][C]28[/C][C]0[/C][C]0.50001039526213[/C][C]-0.50001039526213[/C][/ROW]
[ROW][C]29[/C][C]7[/C][C]2.7961765575627[/C][C]4.2038234424373[/C][/ROW]
[ROW][C]30[/C][C]4[/C][C]-0.596791972965336[/C][C]4.59679197296534[/C][/ROW]
[ROW][C]31[/C][C]5[/C][C]0.936773276676638[/C][C]4.06322672332336[/C][/ROW]
[ROW][C]32[/C][C]11[/C][C]2.98790035435646[/C][C]8.01209964564354[/C][/ROW]
[ROW][C]33[/C][C]2[/C][C]5.61602324157187[/C][C]-3.61602324157187[/C][/ROW]
[ROW][C]34[/C][C]4[/C][C]6.77989721284628[/C][C]-2.77989721284628[/C][/ROW]
[ROW][C]35[/C][C]5[/C][C]8.14879876245385[/C][C]-3.14879876245385[/C][/ROW]
[ROW][C]36[/C][C]12[/C][C]9.77634737705274[/C][C]2.22365262294726[/C][/ROW]
[ROW][C]37[/C][C]10[/C][C]6.38019459058523[/C][C]3.61980540941477[/C][/ROW]
[ROW][C]38[/C][C]6[/C][C]4.70713876823171[/C][C]1.29286123176829[/C][/ROW]
[ROW][C]39[/C][C]6[/C][C]4.39437164164192[/C][C]1.60562835835808[/C][/ROW]
[ROW][C]40[/C][C]8[/C][C]0.457574514451674[/C][C]7.54242548554833[/C][/ROW]
[ROW][C]41[/C][C]3[/C][C]4.88354861401334[/C][C]-1.88354861401334[/C][/ROW]
[ROW][C]42[/C][C]10[/C][C]1.21002773135186[/C][C]8.78997226864814[/C][/ROW]
[ROW][C]43[/C][C]2[/C][C]3.09675518109314[/C][C]-1.09675518109314[/C][/ROW]
[ROW][C]44[/C][C]5[/C][C]5.9188402417452[/C][C]-0.918840241745198[/C][/ROW]
[ROW][C]45[/C][C]4[/C][C]4.66078217864928[/C][C]-0.660782178649276[/C][/ROW]
[ROW][C]46[/C][C]3[/C][C]6.38700854317207[/C][C]-3.38700854317207[/C][/ROW]
[ROW][C]47[/C][C]8[/C][C]7.68334479397624[/C][C]0.316655206023759[/C][/ROW]
[ROW][C]48[/C][C]5[/C][C]11.1815113027812[/C][C]-6.1815113027812[/C][/ROW]
[ROW][C]49[/C][C]7[/C][C]7.51449638011792[/C][C]-0.514496380117916[/C][/ROW]
[ROW][C]50[/C][C]1[/C][C]4.88108927364355[/C][C]-3.88108927364355[/C][/ROW]
[ROW][C]51[/C][C]7[/C][C]4.21766245289374[/C][C]2.78233754710626[/C][/ROW]
[ROW][C]52[/C][C]4[/C][C]2.01960823189215[/C][C]1.98039176810785[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]3.35581758548359[/C][C]4.64418241451641[/C][/ROW]
[ROW][C]54[/C][C]7[/C][C]3.18084499984171[/C][C]3.81915500015829[/C][/ROW]
[ROW][C]55[/C][C]10[/C][C]1.90960105628959[/C][C]8.09039894371041[/C][/ROW]
[ROW][C]56[/C][C]2[/C][C]5.58837124622382[/C][C]-3.58837124622382[/C][/ROW]
[ROW][C]57[/C][C]6[/C][C]4.19639386349259[/C][C]1.80360613650741[/C][/ROW]
[ROW][C]58[/C][C]6[/C][C]5.41302584316362[/C][C]0.586974156836379[/C][/ROW]
[ROW][C]59[/C][C]11[/C][C]8.1198410423762[/C][C]2.8801589576238[/C][/ROW]
[ROW][C]60[/C][C]8[/C][C]10.1156818117182[/C][C]-2.11568181171817[/C][/ROW]
[ROW][C]61[/C][C]8[/C][C]8.44541030481837[/C][C]-0.445410304818367[/C][/ROW]
[ROW][C]62[/C][C]6[/C][C]4.98574130615799[/C][C]1.01425869384201[/C][/ROW]
[ROW][C]63[/C][C]11[/C][C]6.69161335948308[/C][C]4.30838664051692[/C][/ROW]
[ROW][C]64[/C][C]15[/C][C]4.5327565422075[/C][C]10.4672434577925[/C][/ROW]
[ROW][C]65[/C][C]9[/C][C]7.49652852311515[/C][C]1.50347147688485[/C][/ROW]
[ROW][C]66[/C][C]5[/C][C]6.99245700153578[/C][C]-1.99245700153578[/C][/ROW]
[ROW][C]67[/C][C]10[/C][C]6.53729047021985[/C][C]3.46270952978015[/C][/ROW]
[ROW][C]68[/C][C]4[/C][C]6.71374924283833[/C][C]-2.71374924283833[/C][/ROW]
[ROW][C]69[/C][C]9[/C][C]6.98736155709631[/C][C]2.01263844290369[/C][/ROW]
[ROW][C]70[/C][C]3[/C][C]7.99526230407373[/C][C]-4.99526230407373[/C][/ROW]
[ROW][C]71[/C][C]7[/C][C]10.9405588791711[/C][C]-3.94055887917112[/C][/ROW]
[ROW][C]72[/C][C]7[/C][C]11.0247634506755[/C][C]-4.02476345067552[/C][/ROW]
[ROW][C]73[/C][C]9[/C][C]9.680445697255[/C][C]-0.680445697254996[/C][/ROW]
[ROW][C]74[/C][C]15[/C][C]6.62821943657383[/C][C]8.37178056342617[/C][/ROW]
[ROW][C]75[/C][C]11[/C][C]9.92743832896914[/C][C]1.07256167103086[/C][/ROW]
[ROW][C]76[/C][C]10[/C][C]9.24102330824229[/C][C]0.758976691757709[/C][/ROW]
[ROW][C]77[/C][C]6[/C][C]8.91349754432559[/C][C]-2.91349754432559[/C][/ROW]
[ROW][C]78[/C][C]5[/C][C]7.04337345222289[/C][C]-2.04337345222289[/C][/ROW]
[ROW][C]79[/C][C]6[/C][C]8.05361182270462[/C][C]-2.05361182270462[/C][/ROW]
[ROW][C]80[/C][C]6[/C][C]6.00162782587766[/C][C]-0.00162782587765609[/C][/ROW]
[ROW][C]81[/C][C]14[/C][C]7.75635459708932[/C][C]6.24364540291068[/C][/ROW]
[ROW][C]82[/C][C]11[/C][C]7.16660637699715[/C][C]3.83339362300285[/C][/ROW]
[ROW][C]83[/C][C]1[/C][C]11.1714321602257[/C][C]-10.1714321602257[/C][/ROW]
[ROW][C]84[/C][C]9[/C][C]10.6991017752916[/C][C]-1.69910177529156[/C][/ROW]
[ROW][C]85[/C][C]13[/C][C]10.4753074956048[/C][C]2.5246925043952[/C][/ROW]
[ROW][C]86[/C][C]10[/C][C]10.2074876046989[/C][C]-0.207487604698931[/C][/ROW]
[ROW][C]87[/C][C]11[/C][C]10.7486743606978[/C][C]0.251325639302234[/C][/ROW]
[ROW][C]88[/C][C]7[/C][C]9.87545894799324[/C][C]-2.87545894799324[/C][/ROW]
[ROW][C]89[/C][C]6[/C][C]8.17887563887136[/C][C]-2.17887563887136[/C][/ROW]
[ROW][C]90[/C][C]4[/C][C]6.5621254097142[/C][C]-2.5621254097142[/C][/ROW]
[ROW][C]91[/C][C]6[/C][C]7.47494528625126[/C][C]-1.47494528625126[/C][/ROW]
[ROW][C]92[/C][C]8[/C][C]5.98895753543878[/C][C]2.01104246456122[/C][/ROW]
[ROW][C]93[/C][C]6[/C][C]9.59636348685671[/C][C]-3.59636348685671[/C][/ROW]
[ROW][C]94[/C][C]7[/C][C]7.4227863963117[/C][C]-0.422786396311701[/C][/ROW]
[ROW][C]95[/C][C]12[/C][C]7.09681113887972[/C][C]4.90318886112028[/C][/ROW]
[ROW][C]96[/C][C]20[/C][C]10.1946984077088[/C][C]9.80530159229116[/C][/ROW]
[ROW][C]97[/C][C]10[/C][C]12.1369600485836[/C][C]-2.13696004858359[/C][/ROW]
[ROW][C]98[/C][C]14[/C][C]10.7334443402333[/C][C]3.26655565976666[/C][/ROW]
[ROW][C]99[/C][C]11[/C][C]11.7217730077917[/C][C]-0.721773007791704[/C][/ROW]
[ROW][C]100[/C][C]13[/C][C]9.92882179676014[/C][C]3.07117820323986[/C][/ROW]
[ROW][C]101[/C][C]7[/C][C]8.98132801021227[/C][C]-1.98132801021227[/C][/ROW]
[ROW][C]102[/C][C]9[/C][C]7.33388114896012[/C][C]1.66611885103988[/C][/ROW]
[ROW][C]103[/C][C]8[/C][C]8.98413421948083[/C][C]-0.984134219480833[/C][/ROW]
[ROW][C]104[/C][C]7[/C][C]8.58445695483906[/C][C]-1.58445695483906[/C][/ROW]
[ROW][C]105[/C][C]9[/C][C]10.410181358519[/C][C]-1.41018135851904[/C][/ROW]
[ROW][C]106[/C][C]10[/C][C]9.37144043024698[/C][C]0.628559569753024[/C][/ROW]
[ROW][C]107[/C][C]12[/C][C]10.6834754380998[/C][C]1.31652456190018[/C][/ROW]
[ROW][C]108[/C][C]13[/C][C]14.8919797358977[/C][C]-1.89197973589765[/C][/ROW]
[ROW][C]109[/C][C]11[/C][C]12.5578795881579[/C][C]-1.5578795881579[/C][/ROW]
[ROW][C]110[/C][C]11[/C][C]12.6897630427986[/C][C]-1.68976304279856[/C][/ROW]
[ROW][C]111[/C][C]14[/C][C]12.1336355548776[/C][C]1.86636444512243[/C][/ROW]
[ROW][C]112[/C][C]10[/C][C]11.5880867222319[/C][C]-1.58808672223195[/C][/ROW]
[ROW][C]113[/C][C]9[/C][C]8.81626390558026[/C][C]0.183736094419737[/C][/ROW]
[ROW][C]114[/C][C]12[/C][C]8.32628197749818[/C][C]3.67371802250182[/C][/ROW]
[ROW][C]115[/C][C]8[/C][C]9.39832670404699[/C][C]-1.39832670404699[/C][/ROW]
[ROW][C]116[/C][C]13[/C][C]8.77875000237762[/C][C]4.22124999762238[/C][/ROW]
[ROW][C]117[/C][C]14[/C][C]11.1543142434386[/C][C]2.84568575656139[/C][/ROW]
[ROW][C]118[/C][C]15[/C][C]11.0727579925817[/C][C]3.92724200741834[/C][/ROW]
[ROW][C]119[/C][C]14[/C][C]12.9084502988971[/C][C]1.09154970110294[/C][/ROW]
[ROW][C]120[/C][C]14[/C][C]16.2701113484316[/C][C]-2.27011134843162[/C][/ROW]
[ROW][C]121[/C][C]15[/C][C]14.0494934607009[/C][C]0.950506539299052[/C][/ROW]
[ROW][C]122[/C][C]14[/C][C]14.4237423450953[/C][C]-0.423742345095253[/C][/ROW]
[ROW][C]123[/C][C]21[/C][C]15.0281346113754[/C][C]5.97186538862456[/C][/ROW]
[ROW][C]124[/C][C]10[/C][C]13.9752762437439[/C][C]-3.97527624374387[/C][/ROW]
[ROW][C]125[/C][C]8[/C][C]11.5752425297502[/C][C]-3.57524252975016[/C][/ROW]
[ROW][C]126[/C][C]12[/C][C]11.793178855493[/C][C]0.20682114450698[/C][/ROW]
[ROW][C]127[/C][C]13[/C][C]11.2204943185452[/C][C]1.7795056814548[/C][/ROW]
[ROW][C]128[/C][C]6[/C][C]12.4770361561907[/C][C]-6.47703615619067[/C][/ROW]
[ROW][C]129[/C][C]12[/C][C]13.5742325025081[/C][C]-1.57423250250808[/C][/ROW]
[ROW][C]130[/C][C]12[/C][C]13.3936348300439[/C][C]-1.39363483004386[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230368&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230368&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
1399.71981837606838-0.719818376068377
1477.6177025901437-0.617702590143703
1566.52063836761192-0.520638367611924
1633.51209011644914-0.512090116449142
1755.95966088540428-0.959660885404284
1812.1974183737589-1.1974183737589
1952.074983362075942.92501663792406
2025.85774739511894-3.85774739511894
2195.297850615198583.70214938480142
2249.56176201451054-5.56176201451054
23411.0145387163797-7.01453871637967
241010.3882607901164-0.38826079011643
2585.993972380694682.00602761930532
2664.080548752440881.91945124755912
2773.169446656783163.83055334321684
2800.50001039526213-0.50001039526213
2972.79617655756274.2038234424373
304-0.5967919729653364.59679197296534
3150.9367732766766384.06322672332336
32112.987900354356468.01209964564354
3325.61602324157187-3.61602324157187
3446.77989721284628-2.77989721284628
3558.14879876245385-3.14879876245385
36129.776347377052742.22365262294726
37106.380194590585233.61980540941477
3864.707138768231711.29286123176829
3964.394371641641921.60562835835808
4080.4575745144516747.54242548554833
4134.88354861401334-1.88354861401334
42101.210027731351868.78997226864814
4323.09675518109314-1.09675518109314
4455.9188402417452-0.918840241745198
4544.66078217864928-0.660782178649276
4636.38700854317207-3.38700854317207
4787.683344793976240.316655206023759
48511.1815113027812-6.1815113027812
4977.51449638011792-0.514496380117916
5014.88108927364355-3.88108927364355
5174.217662452893742.78233754710626
5242.019608231892151.98039176810785
5383.355817585483594.64418241451641
5473.180844999841713.81915500015829
55101.909601056289598.09039894371041
5625.58837124622382-3.58837124622382
5764.196393863492591.80360613650741
5865.413025843163620.586974156836379
59118.11984104237622.8801589576238
60810.1156818117182-2.11568181171817
6188.44541030481837-0.445410304818367
6264.985741306157991.01425869384201
63116.691613359483084.30838664051692
64154.532756542207510.4672434577925
6597.496528523115151.50347147688485
6656.99245700153578-1.99245700153578
67106.537290470219853.46270952978015
6846.71374924283833-2.71374924283833
6996.987361557096312.01263844290369
7037.99526230407373-4.99526230407373
71710.9405588791711-3.94055887917112
72711.0247634506755-4.02476345067552
7399.680445697255-0.680445697254996
74156.628219436573838.37178056342617
75119.927438328969141.07256167103086
76109.241023308242290.758976691757709
7768.91349754432559-2.91349754432559
7857.04337345222289-2.04337345222289
7968.05361182270462-2.05361182270462
8066.00162782587766-0.00162782587765609
81147.756354597089326.24364540291068
82117.166606376997153.83339362300285
83111.1714321602257-10.1714321602257
84910.6991017752916-1.69910177529156
851310.47530749560482.5246925043952
861010.2074876046989-0.207487604698931
871110.74867436069780.251325639302234
8879.87545894799324-2.87545894799324
8968.17887563887136-2.17887563887136
9046.5621254097142-2.5621254097142
9167.47494528625126-1.47494528625126
9285.988957535438782.01104246456122
9369.59636348685671-3.59636348685671
9477.4227863963117-0.422786396311701
95127.096811138879724.90318886112028
962010.19469840770889.80530159229116
971012.1369600485836-2.13696004858359
981410.73344434023333.26655565976666
991111.7217730077917-0.721773007791704
100139.928821796760143.07117820323986
10178.98132801021227-1.98132801021227
10297.333881148960121.66611885103988
10388.98413421948083-0.984134219480833
10478.58445695483906-1.58445695483906
105910.410181358519-1.41018135851904
106109.371440430246980.628559569753024
1071210.68347543809981.31652456190018
1081314.8919797358977-1.89197973589765
1091112.5578795881579-1.5578795881579
1101112.6897630427986-1.68976304279856
1111412.13363555487761.86636444512243
1121011.5880867222319-1.58808672223195
11398.816263905580260.183736094419737
114128.326281977498183.67371802250182
11589.39832670404699-1.39832670404699
116138.778750002377624.22124999762238
1171411.15431424343862.84568575656139
1181511.07275799258173.92724200741834
1191412.90845029889711.09154970110294
1201416.2701113484316-2.27011134843162
1211514.04949346070090.950506539299052
1221414.4237423450953-0.423742345095253
1232115.02813461137545.97186538862456
1241013.9752762437439-3.97527624374387
125811.5752425297502-3.57524252975016
1261211.7931788554930.20682114450698
1271311.22049431854521.7795056814548
128612.4770361561907-6.47703615619067
1291213.5742325025081-1.57423250250808
1301213.3936348300439-1.39363483004386







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
13113.94549346234826.901467016245320.989519908451
13216.22802352203199.1556223578681423.3004246861957
13315.03633941818127.93196680101822.1407120353445
13414.89806926698267.7579487500751122.0381897838901
13517.247223014520310.067407792878124.4270382361624
13612.86732066510535.6437036072147720.0909377229959
13710.84862062689773.5769449194008618.1202963343945
13812.36588443951885.041754767165519.6900141118721
13912.16489546230034.7837896346446219.5460012899559
14010.94439356116533.5016744886431418.3871126336875
14113.91930884010716.410236755594221.42838092462
14213.91287511906646.3326199369835521.4931303011493

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
131 & 13.9454934623482 & 6.9014670162453 & 20.989519908451 \tabularnewline
132 & 16.2280235220319 & 9.15562235786814 & 23.3004246861957 \tabularnewline
133 & 15.0363394181812 & 7.931966801018 & 22.1407120353445 \tabularnewline
134 & 14.8980692669826 & 7.75794875007511 & 22.0381897838901 \tabularnewline
135 & 17.2472230145203 & 10.0674077928781 & 24.4270382361624 \tabularnewline
136 & 12.8673206651053 & 5.64370360721477 & 20.0909377229959 \tabularnewline
137 & 10.8486206268977 & 3.57694491940086 & 18.1202963343945 \tabularnewline
138 & 12.3658844395188 & 5.0417547671655 & 19.6900141118721 \tabularnewline
139 & 12.1648954623003 & 4.78378963464462 & 19.5460012899559 \tabularnewline
140 & 10.9443935611653 & 3.50167448864314 & 18.3871126336875 \tabularnewline
141 & 13.9193088401071 & 6.4102367555942 & 21.42838092462 \tabularnewline
142 & 13.9128751190664 & 6.33261993698355 & 21.4931303011493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=230368&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]131[/C][C]13.9454934623482[/C][C]6.9014670162453[/C][C]20.989519908451[/C][/ROW]
[ROW][C]132[/C][C]16.2280235220319[/C][C]9.15562235786814[/C][C]23.3004246861957[/C][/ROW]
[ROW][C]133[/C][C]15.0363394181812[/C][C]7.931966801018[/C][C]22.1407120353445[/C][/ROW]
[ROW][C]134[/C][C]14.8980692669826[/C][C]7.75794875007511[/C][C]22.0381897838901[/C][/ROW]
[ROW][C]135[/C][C]17.2472230145203[/C][C]10.0674077928781[/C][C]24.4270382361624[/C][/ROW]
[ROW][C]136[/C][C]12.8673206651053[/C][C]5.64370360721477[/C][C]20.0909377229959[/C][/ROW]
[ROW][C]137[/C][C]10.8486206268977[/C][C]3.57694491940086[/C][C]18.1202963343945[/C][/ROW]
[ROW][C]138[/C][C]12.3658844395188[/C][C]5.0417547671655[/C][C]19.6900141118721[/C][/ROW]
[ROW][C]139[/C][C]12.1648954623003[/C][C]4.78378963464462[/C][C]19.5460012899559[/C][/ROW]
[ROW][C]140[/C][C]10.9443935611653[/C][C]3.50167448864314[/C][C]18.3871126336875[/C][/ROW]
[ROW][C]141[/C][C]13.9193088401071[/C][C]6.4102367555942[/C][C]21.42838092462[/C][/ROW]
[ROW][C]142[/C][C]13.9128751190664[/C][C]6.33261993698355[/C][C]21.4931303011493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=230368&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=230368&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
13113.94549346234826.901467016245320.989519908451
13216.22802352203199.1556223578681423.3004246861957
13315.03633941818127.93196680101822.1407120353445
13414.89806926698267.7579487500751122.0381897838901
13517.247223014520310.067407792878124.4270382361624
13612.86732066510535.6437036072147720.0909377229959
13710.84862062689773.5769449194008618.1202963343945
13812.36588443951885.041754767165519.6900141118721
13912.16489546230034.7837896346446219.5460012899559
14010.94439356116533.5016744886431418.3871126336875
14113.91930884010716.410236755594221.42838092462
14213.91287511906646.3326199369835521.4931303011493



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')