Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 06 Aug 2010 12:28:25 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/06/t1281097662vq6ufq92kkz09od.htm/, Retrieved Mon, 06 May 2024 19:49:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78471, Retrieved Mon, 06 May 2024 19:49:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact161
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-08-06 12:28:25] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
94
93
92
90
88
87
88
90
91
91
92
94
88
90
82
83
88
83
85
81
79
71
70
85
88
84
81
93
99
96
90
95
93
86
77
89
90
84
76
96
104
101
95
101
95
90
88
99
81
79
70
95
100
105
107
106
99
86
81
95
82
78
68
96
98
107
102
98
93
69
65
90
87
80
67
85
85
92
87
85
79
58
47
67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78471&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78471&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.889089461093732
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.889089461093732 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78471&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]0.889089461093732[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78471&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
alpha0.889089461093732
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
392920
49091-1
58889.1109105389063-1.11091053890627
68787.1232116865467-0.123211686546739
78886.01366547455441.98633452544556
89086.77969456733473.2203054326653
99188.64283418902032.35716581097969
109189.73856546961281.26143453038719
119289.86009361643982.13990638356022
129490.76266182979043.23733817020963
138892.6409450789202-4.64094507892023
149087.51472971973742.48527028026257
158288.7243573338883-6.72435733388835
168381.74580209569991.25419790430013
178881.8608962345396.13910376546104
188386.3191086929712-3.31910869297121
198582.3681241338262.63187586617408
208183.7080972293482-2.70809722934823
217980.3003565231176-1.30035652311759
227178.1442232427492-7.14422324274925
237070.79236964992-0.792369649920005
248569.087882144885615.9121178551144
258882.23517843354925.76482156645078
268486.3606205333665-2.36062053336647
278183.2618176955089-2.26181769550888
289380.250859419516612.7491405804834
299990.58598594762688.41401405237318
309697.0667971670864-1.06679716708638
319095.1183190487052-5.11831904870523
329589.56767552398615.43232447601389
339393.3974979648516-0.397497964851595
348692.0440867134958-6.04408671349583
357785.67035291459-8.67035291459004
368976.961633514264712.0383664857353
379086.6648182855163.33518171448405
388488.6300931986962-4.63009319869624
397683.5135261318536-7.51352613185364
409675.833329232370220.1666707676298
4110492.763303677216911.2366963227831
42101101.753731955314-0.753731955314052
4395100.083596817355-5.08359681735476
4410194.5638244625956.43617553740499
459599.286160302651-4.28616030265107
469094.4753803490057-4.47538034900568
478889.4963668463187-1.49636684631874
489987.165962853326711.8340371466733
498196.6874805626257-15.6874805626257
507981.7399069232824-2.73990692328240
517078.3038845534143-8.30388455341426
529569.920988310834625.0790116891654
5310091.21847329831818.78152670168193
5410598.02603614109676.97396385890332
55107103.2265139100963.7734860899038
56106105.5814806242130.418519375786531
5799104.953581790489-5.9535817904888
588698.6603149648057-12.6603149648057
598186.4041623554697-5.40416235546968
609580.599378559182114.4006214408179
618292.4028193154137-10.4028193154137
627882.153782296417-4.15378229641706
636877.460698232995-9.46069823299493
649668.04929113945127.9507088605490
659891.89997181746436.10002818253568
6610796.323442586931510.6765574130685
67102104.815857263653-2.81585726365287
6898101.312308246595-3.31230824659487
699397.3673698926535-4.36736989265351
706992.4843873483972-23.4843873483972
716570.6046660566943-5.60466605669427
729064.621616532737625.3783834672624
738786.1852698130760.814730186923981
748085.909637835905-5.90963783590506
756779.6554411171211-12.6554411171211
768567.403621794396417.5963782056036
778582.0483762104182.95162378958199
789283.67263381484898.3273661851511
798790.076407328735-3.07640732873506
808586.3412059947252-1.3412059947252
817984.1487538796593-5.1487538796593
825878.5710510674888-20.5710510674888
834759.2815463597635-12.2815463597635
846747.362152925363719.6378470746363

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 92 & 92 & 0 \tabularnewline
4 & 90 & 91 & -1 \tabularnewline
5 & 88 & 89.1109105389063 & -1.11091053890627 \tabularnewline
6 & 87 & 87.1232116865467 & -0.123211686546739 \tabularnewline
7 & 88 & 86.0136654745544 & 1.98633452544556 \tabularnewline
8 & 90 & 86.7796945673347 & 3.2203054326653 \tabularnewline
9 & 91 & 88.6428341890203 & 2.35716581097969 \tabularnewline
10 & 91 & 89.7385654696128 & 1.26143453038719 \tabularnewline
11 & 92 & 89.8600936164398 & 2.13990638356022 \tabularnewline
12 & 94 & 90.7626618297904 & 3.23733817020963 \tabularnewline
13 & 88 & 92.6409450789202 & -4.64094507892023 \tabularnewline
14 & 90 & 87.5147297197374 & 2.48527028026257 \tabularnewline
15 & 82 & 88.7243573338883 & -6.72435733388835 \tabularnewline
16 & 83 & 81.7458020956999 & 1.25419790430013 \tabularnewline
17 & 88 & 81.860896234539 & 6.13910376546104 \tabularnewline
18 & 83 & 86.3191086929712 & -3.31910869297121 \tabularnewline
19 & 85 & 82.368124133826 & 2.63187586617408 \tabularnewline
20 & 81 & 83.7080972293482 & -2.70809722934823 \tabularnewline
21 & 79 & 80.3003565231176 & -1.30035652311759 \tabularnewline
22 & 71 & 78.1442232427492 & -7.14422324274925 \tabularnewline
23 & 70 & 70.79236964992 & -0.792369649920005 \tabularnewline
24 & 85 & 69.0878821448856 & 15.9121178551144 \tabularnewline
25 & 88 & 82.2351784335492 & 5.76482156645078 \tabularnewline
26 & 84 & 86.3606205333665 & -2.36062053336647 \tabularnewline
27 & 81 & 83.2618176955089 & -2.26181769550888 \tabularnewline
28 & 93 & 80.2508594195166 & 12.7491405804834 \tabularnewline
29 & 99 & 90.5859859476268 & 8.41401405237318 \tabularnewline
30 & 96 & 97.0667971670864 & -1.06679716708638 \tabularnewline
31 & 90 & 95.1183190487052 & -5.11831904870523 \tabularnewline
32 & 95 & 89.5676755239861 & 5.43232447601389 \tabularnewline
33 & 93 & 93.3974979648516 & -0.397497964851595 \tabularnewline
34 & 86 & 92.0440867134958 & -6.04408671349583 \tabularnewline
35 & 77 & 85.67035291459 & -8.67035291459004 \tabularnewline
36 & 89 & 76.9616335142647 & 12.0383664857353 \tabularnewline
37 & 90 & 86.664818285516 & 3.33518171448405 \tabularnewline
38 & 84 & 88.6300931986962 & -4.63009319869624 \tabularnewline
39 & 76 & 83.5135261318536 & -7.51352613185364 \tabularnewline
40 & 96 & 75.8333292323702 & 20.1666707676298 \tabularnewline
41 & 104 & 92.7633036772169 & 11.2366963227831 \tabularnewline
42 & 101 & 101.753731955314 & -0.753731955314052 \tabularnewline
43 & 95 & 100.083596817355 & -5.08359681735476 \tabularnewline
44 & 101 & 94.563824462595 & 6.43617553740499 \tabularnewline
45 & 95 & 99.286160302651 & -4.28616030265107 \tabularnewline
46 & 90 & 94.4753803490057 & -4.47538034900568 \tabularnewline
47 & 88 & 89.4963668463187 & -1.49636684631874 \tabularnewline
48 & 99 & 87.1659628533267 & 11.8340371466733 \tabularnewline
49 & 81 & 96.6874805626257 & -15.6874805626257 \tabularnewline
50 & 79 & 81.7399069232824 & -2.73990692328240 \tabularnewline
51 & 70 & 78.3038845534143 & -8.30388455341426 \tabularnewline
52 & 95 & 69.9209883108346 & 25.0790116891654 \tabularnewline
53 & 100 & 91.2184732983181 & 8.78152670168193 \tabularnewline
54 & 105 & 98.0260361410967 & 6.97396385890332 \tabularnewline
55 & 107 & 103.226513910096 & 3.7734860899038 \tabularnewline
56 & 106 & 105.581480624213 & 0.418519375786531 \tabularnewline
57 & 99 & 104.953581790489 & -5.9535817904888 \tabularnewline
58 & 86 & 98.6603149648057 & -12.6603149648057 \tabularnewline
59 & 81 & 86.4041623554697 & -5.40416235546968 \tabularnewline
60 & 95 & 80.5993785591821 & 14.4006214408179 \tabularnewline
61 & 82 & 92.4028193154137 & -10.4028193154137 \tabularnewline
62 & 78 & 82.153782296417 & -4.15378229641706 \tabularnewline
63 & 68 & 77.460698232995 & -9.46069823299493 \tabularnewline
64 & 96 & 68.049291139451 & 27.9507088605490 \tabularnewline
65 & 98 & 91.8999718174643 & 6.10002818253568 \tabularnewline
66 & 107 & 96.3234425869315 & 10.6765574130685 \tabularnewline
67 & 102 & 104.815857263653 & -2.81585726365287 \tabularnewline
68 & 98 & 101.312308246595 & -3.31230824659487 \tabularnewline
69 & 93 & 97.3673698926535 & -4.36736989265351 \tabularnewline
70 & 69 & 92.4843873483972 & -23.4843873483972 \tabularnewline
71 & 65 & 70.6046660566943 & -5.60466605669427 \tabularnewline
72 & 90 & 64.6216165327376 & 25.3783834672624 \tabularnewline
73 & 87 & 86.185269813076 & 0.814730186923981 \tabularnewline
74 & 80 & 85.909637835905 & -5.90963783590506 \tabularnewline
75 & 67 & 79.6554411171211 & -12.6554411171211 \tabularnewline
76 & 85 & 67.4036217943964 & 17.5963782056036 \tabularnewline
77 & 85 & 82.048376210418 & 2.95162378958199 \tabularnewline
78 & 92 & 83.6726338148489 & 8.3273661851511 \tabularnewline
79 & 87 & 90.076407328735 & -3.07640732873506 \tabularnewline
80 & 85 & 86.3412059947252 & -1.3412059947252 \tabularnewline
81 & 79 & 84.1487538796593 & -5.1487538796593 \tabularnewline
82 & 58 & 78.5710510674888 & -20.5710510674888 \tabularnewline
83 & 47 & 59.2815463597635 & -12.2815463597635 \tabularnewline
84 & 67 & 47.3621529253637 & 19.6378470746363 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78471&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]3[/C][C]92[/C][C]92[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]90[/C][C]91[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]88[/C][C]89.1109105389063[/C][C]-1.11091053890627[/C][/ROW]
[ROW][C]6[/C][C]87[/C][C]87.1232116865467[/C][C]-0.123211686546739[/C][/ROW]
[ROW][C]7[/C][C]88[/C][C]86.0136654745544[/C][C]1.98633452544556[/C][/ROW]
[ROW][C]8[/C][C]90[/C][C]86.7796945673347[/C][C]3.2203054326653[/C][/ROW]
[ROW][C]9[/C][C]91[/C][C]88.6428341890203[/C][C]2.35716581097969[/C][/ROW]
[ROW][C]10[/C][C]91[/C][C]89.7385654696128[/C][C]1.26143453038719[/C][/ROW]
[ROW][C]11[/C][C]92[/C][C]89.8600936164398[/C][C]2.13990638356022[/C][/ROW]
[ROW][C]12[/C][C]94[/C][C]90.7626618297904[/C][C]3.23733817020963[/C][/ROW]
[ROW][C]13[/C][C]88[/C][C]92.6409450789202[/C][C]-4.64094507892023[/C][/ROW]
[ROW][C]14[/C][C]90[/C][C]87.5147297197374[/C][C]2.48527028026257[/C][/ROW]
[ROW][C]15[/C][C]82[/C][C]88.7243573338883[/C][C]-6.72435733388835[/C][/ROW]
[ROW][C]16[/C][C]83[/C][C]81.7458020956999[/C][C]1.25419790430013[/C][/ROW]
[ROW][C]17[/C][C]88[/C][C]81.860896234539[/C][C]6.13910376546104[/C][/ROW]
[ROW][C]18[/C][C]83[/C][C]86.3191086929712[/C][C]-3.31910869297121[/C][/ROW]
[ROW][C]19[/C][C]85[/C][C]82.368124133826[/C][C]2.63187586617408[/C][/ROW]
[ROW][C]20[/C][C]81[/C][C]83.7080972293482[/C][C]-2.70809722934823[/C][/ROW]
[ROW][C]21[/C][C]79[/C][C]80.3003565231176[/C][C]-1.30035652311759[/C][/ROW]
[ROW][C]22[/C][C]71[/C][C]78.1442232427492[/C][C]-7.14422324274925[/C][/ROW]
[ROW][C]23[/C][C]70[/C][C]70.79236964992[/C][C]-0.792369649920005[/C][/ROW]
[ROW][C]24[/C][C]85[/C][C]69.0878821448856[/C][C]15.9121178551144[/C][/ROW]
[ROW][C]25[/C][C]88[/C][C]82.2351784335492[/C][C]5.76482156645078[/C][/ROW]
[ROW][C]26[/C][C]84[/C][C]86.3606205333665[/C][C]-2.36062053336647[/C][/ROW]
[ROW][C]27[/C][C]81[/C][C]83.2618176955089[/C][C]-2.26181769550888[/C][/ROW]
[ROW][C]28[/C][C]93[/C][C]80.2508594195166[/C][C]12.7491405804834[/C][/ROW]
[ROW][C]29[/C][C]99[/C][C]90.5859859476268[/C][C]8.41401405237318[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]97.0667971670864[/C][C]-1.06679716708638[/C][/ROW]
[ROW][C]31[/C][C]90[/C][C]95.1183190487052[/C][C]-5.11831904870523[/C][/ROW]
[ROW][C]32[/C][C]95[/C][C]89.5676755239861[/C][C]5.43232447601389[/C][/ROW]
[ROW][C]33[/C][C]93[/C][C]93.3974979648516[/C][C]-0.397497964851595[/C][/ROW]
[ROW][C]34[/C][C]86[/C][C]92.0440867134958[/C][C]-6.04408671349583[/C][/ROW]
[ROW][C]35[/C][C]77[/C][C]85.67035291459[/C][C]-8.67035291459004[/C][/ROW]
[ROW][C]36[/C][C]89[/C][C]76.9616335142647[/C][C]12.0383664857353[/C][/ROW]
[ROW][C]37[/C][C]90[/C][C]86.664818285516[/C][C]3.33518171448405[/C][/ROW]
[ROW][C]38[/C][C]84[/C][C]88.6300931986962[/C][C]-4.63009319869624[/C][/ROW]
[ROW][C]39[/C][C]76[/C][C]83.5135261318536[/C][C]-7.51352613185364[/C][/ROW]
[ROW][C]40[/C][C]96[/C][C]75.8333292323702[/C][C]20.1666707676298[/C][/ROW]
[ROW][C]41[/C][C]104[/C][C]92.7633036772169[/C][C]11.2366963227831[/C][/ROW]
[ROW][C]42[/C][C]101[/C][C]101.753731955314[/C][C]-0.753731955314052[/C][/ROW]
[ROW][C]43[/C][C]95[/C][C]100.083596817355[/C][C]-5.08359681735476[/C][/ROW]
[ROW][C]44[/C][C]101[/C][C]94.563824462595[/C][C]6.43617553740499[/C][/ROW]
[ROW][C]45[/C][C]95[/C][C]99.286160302651[/C][C]-4.28616030265107[/C][/ROW]
[ROW][C]46[/C][C]90[/C][C]94.4753803490057[/C][C]-4.47538034900568[/C][/ROW]
[ROW][C]47[/C][C]88[/C][C]89.4963668463187[/C][C]-1.49636684631874[/C][/ROW]
[ROW][C]48[/C][C]99[/C][C]87.1659628533267[/C][C]11.8340371466733[/C][/ROW]
[ROW][C]49[/C][C]81[/C][C]96.6874805626257[/C][C]-15.6874805626257[/C][/ROW]
[ROW][C]50[/C][C]79[/C][C]81.7399069232824[/C][C]-2.73990692328240[/C][/ROW]
[ROW][C]51[/C][C]70[/C][C]78.3038845534143[/C][C]-8.30388455341426[/C][/ROW]
[ROW][C]52[/C][C]95[/C][C]69.9209883108346[/C][C]25.0790116891654[/C][/ROW]
[ROW][C]53[/C][C]100[/C][C]91.2184732983181[/C][C]8.78152670168193[/C][/ROW]
[ROW][C]54[/C][C]105[/C][C]98.0260361410967[/C][C]6.97396385890332[/C][/ROW]
[ROW][C]55[/C][C]107[/C][C]103.226513910096[/C][C]3.7734860899038[/C][/ROW]
[ROW][C]56[/C][C]106[/C][C]105.581480624213[/C][C]0.418519375786531[/C][/ROW]
[ROW][C]57[/C][C]99[/C][C]104.953581790489[/C][C]-5.9535817904888[/C][/ROW]
[ROW][C]58[/C][C]86[/C][C]98.6603149648057[/C][C]-12.6603149648057[/C][/ROW]
[ROW][C]59[/C][C]81[/C][C]86.4041623554697[/C][C]-5.40416235546968[/C][/ROW]
[ROW][C]60[/C][C]95[/C][C]80.5993785591821[/C][C]14.4006214408179[/C][/ROW]
[ROW][C]61[/C][C]82[/C][C]92.4028193154137[/C][C]-10.4028193154137[/C][/ROW]
[ROW][C]62[/C][C]78[/C][C]82.153782296417[/C][C]-4.15378229641706[/C][/ROW]
[ROW][C]63[/C][C]68[/C][C]77.460698232995[/C][C]-9.46069823299493[/C][/ROW]
[ROW][C]64[/C][C]96[/C][C]68.049291139451[/C][C]27.9507088605490[/C][/ROW]
[ROW][C]65[/C][C]98[/C][C]91.8999718174643[/C][C]6.10002818253568[/C][/ROW]
[ROW][C]66[/C][C]107[/C][C]96.3234425869315[/C][C]10.6765574130685[/C][/ROW]
[ROW][C]67[/C][C]102[/C][C]104.815857263653[/C][C]-2.81585726365287[/C][/ROW]
[ROW][C]68[/C][C]98[/C][C]101.312308246595[/C][C]-3.31230824659487[/C][/ROW]
[ROW][C]69[/C][C]93[/C][C]97.3673698926535[/C][C]-4.36736989265351[/C][/ROW]
[ROW][C]70[/C][C]69[/C][C]92.4843873483972[/C][C]-23.4843873483972[/C][/ROW]
[ROW][C]71[/C][C]65[/C][C]70.6046660566943[/C][C]-5.60466605669427[/C][/ROW]
[ROW][C]72[/C][C]90[/C][C]64.6216165327376[/C][C]25.3783834672624[/C][/ROW]
[ROW][C]73[/C][C]87[/C][C]86.185269813076[/C][C]0.814730186923981[/C][/ROW]
[ROW][C]74[/C][C]80[/C][C]85.909637835905[/C][C]-5.90963783590506[/C][/ROW]
[ROW][C]75[/C][C]67[/C][C]79.6554411171211[/C][C]-12.6554411171211[/C][/ROW]
[ROW][C]76[/C][C]85[/C][C]67.4036217943964[/C][C]17.5963782056036[/C][/ROW]
[ROW][C]77[/C][C]85[/C][C]82.048376210418[/C][C]2.95162378958199[/C][/ROW]
[ROW][C]78[/C][C]92[/C][C]83.6726338148489[/C][C]8.3273661851511[/C][/ROW]
[ROW][C]79[/C][C]87[/C][C]90.076407328735[/C][C]-3.07640732873506[/C][/ROW]
[ROW][C]80[/C][C]85[/C][C]86.3412059947252[/C][C]-1.3412059947252[/C][/ROW]
[ROW][C]81[/C][C]79[/C][C]84.1487538796593[/C][C]-5.1487538796593[/C][/ROW]
[ROW][C]82[/C][C]58[/C][C]78.5710510674888[/C][C]-20.5710510674888[/C][/ROW]
[ROW][C]83[/C][C]47[/C][C]59.2815463597635[/C][C]-12.2815463597635[/C][/ROW]
[ROW][C]84[/C][C]67[/C][C]47.3621529253637[/C][C]19.6378470746363[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78471&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78471&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
392920
49091-1
58889.1109105389063-1.11091053890627
68787.1232116865467-0.123211686546739
78886.01366547455441.98633452544556
89086.77969456733473.2203054326653
99188.64283418902032.35716581097969
109189.73856546961281.26143453038719
119289.86009361643982.13990638356022
129490.76266182979043.23733817020963
138892.6409450789202-4.64094507892023
149087.51472971973742.48527028026257
158288.7243573338883-6.72435733388835
168381.74580209569991.25419790430013
178881.8608962345396.13910376546104
188386.3191086929712-3.31910869297121
198582.3681241338262.63187586617408
208183.7080972293482-2.70809722934823
217980.3003565231176-1.30035652311759
227178.1442232427492-7.14422324274925
237070.79236964992-0.792369649920005
248569.087882144885615.9121178551144
258882.23517843354925.76482156645078
268486.3606205333665-2.36062053336647
278183.2618176955089-2.26181769550888
289380.250859419516612.7491405804834
299990.58598594762688.41401405237318
309697.0667971670864-1.06679716708638
319095.1183190487052-5.11831904870523
329589.56767552398615.43232447601389
339393.3974979648516-0.397497964851595
348692.0440867134958-6.04408671349583
357785.67035291459-8.67035291459004
368976.961633514264712.0383664857353
379086.6648182855163.33518171448405
388488.6300931986962-4.63009319869624
397683.5135261318536-7.51352613185364
409675.833329232370220.1666707676298
4110492.763303677216911.2366963227831
42101101.753731955314-0.753731955314052
4395100.083596817355-5.08359681735476
4410194.5638244625956.43617553740499
459599.286160302651-4.28616030265107
469094.4753803490057-4.47538034900568
478889.4963668463187-1.49636684631874
489987.165962853326711.8340371466733
498196.6874805626257-15.6874805626257
507981.7399069232824-2.73990692328240
517078.3038845534143-8.30388455341426
529569.920988310834625.0790116891654
5310091.21847329831818.78152670168193
5410598.02603614109676.97396385890332
55107103.2265139100963.7734860899038
56106105.5814806242130.418519375786531
5799104.953581790489-5.9535817904888
588698.6603149648057-12.6603149648057
598186.4041623554697-5.40416235546968
609580.599378559182114.4006214408179
618292.4028193154137-10.4028193154137
627882.153782296417-4.15378229641706
636877.460698232995-9.46069823299493
649668.04929113945127.9507088605490
659891.89997181746436.10002818253568
6610796.323442586931510.6765574130685
67102104.815857263653-2.81585726365287
6898101.312308246595-3.31230824659487
699397.3673698926535-4.36736989265351
706992.4843873483972-23.4843873483972
716570.6046660566943-5.60466605669427
729064.621616532737625.3783834672624
738786.1852698130760.814730186923981
748085.909637835905-5.90963783590506
756779.6554411171211-12.6554411171211
768567.403621794396417.5963782056036
778582.0483762104182.95162378958199
789283.67263381484898.3273661851511
798790.076407328735-3.07640732873506
808586.3412059947252-1.3412059947252
817984.1487538796593-5.1487538796593
825878.5710510674888-20.5710510674888
834759.2815463597635-12.2815463597635
846747.362152925363719.6378470746363







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8563.821955797993245.067190089018482.576721506968
8662.821955797993237.726424836795987.9174867591906
8761.821955797993231.691736554677291.9521750413092
8860.821955797993226.385426514742795.2584850812437
8959.821955797993221.560761534065198.0831500619213
9058.821955797993217.085120461232100.558791134754
9157.821955797993212.8774582331767102.766453362810
9256.82195579799328.88395105457829104.759960541408
9355.82195579799325.06669266001364106.577218935973
9454.82195579799321.39779297225093108.246118623735
9553.8219557979932-2.14397679548101109.787888391467
9652.8219557979932-5.57521920630965111.219130802296

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 63.8219557979932 & 45.0671900890184 & 82.576721506968 \tabularnewline
86 & 62.8219557979932 & 37.7264248367959 & 87.9174867591906 \tabularnewline
87 & 61.8219557979932 & 31.6917365546772 & 91.9521750413092 \tabularnewline
88 & 60.8219557979932 & 26.3854265147427 & 95.2584850812437 \tabularnewline
89 & 59.8219557979932 & 21.5607615340651 & 98.0831500619213 \tabularnewline
90 & 58.8219557979932 & 17.085120461232 & 100.558791134754 \tabularnewline
91 & 57.8219557979932 & 12.8774582331767 & 102.766453362810 \tabularnewline
92 & 56.8219557979932 & 8.88395105457829 & 104.759960541408 \tabularnewline
93 & 55.8219557979932 & 5.06669266001364 & 106.577218935973 \tabularnewline
94 & 54.8219557979932 & 1.39779297225093 & 108.246118623735 \tabularnewline
95 & 53.8219557979932 & -2.14397679548101 & 109.787888391467 \tabularnewline
96 & 52.8219557979932 & -5.57521920630965 & 111.219130802296 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78471&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]63.8219557979932[/C][C]45.0671900890184[/C][C]82.576721506968[/C][/ROW]
[ROW][C]86[/C][C]62.8219557979932[/C][C]37.7264248367959[/C][C]87.9174867591906[/C][/ROW]
[ROW][C]87[/C][C]61.8219557979932[/C][C]31.6917365546772[/C][C]91.9521750413092[/C][/ROW]
[ROW][C]88[/C][C]60.8219557979932[/C][C]26.3854265147427[/C][C]95.2584850812437[/C][/ROW]
[ROW][C]89[/C][C]59.8219557979932[/C][C]21.5607615340651[/C][C]98.0831500619213[/C][/ROW]
[ROW][C]90[/C][C]58.8219557979932[/C][C]17.085120461232[/C][C]100.558791134754[/C][/ROW]
[ROW][C]91[/C][C]57.8219557979932[/C][C]12.8774582331767[/C][C]102.766453362810[/C][/ROW]
[ROW][C]92[/C][C]56.8219557979932[/C][C]8.88395105457829[/C][C]104.759960541408[/C][/ROW]
[ROW][C]93[/C][C]55.8219557979932[/C][C]5.06669266001364[/C][C]106.577218935973[/C][/ROW]
[ROW][C]94[/C][C]54.8219557979932[/C][C]1.39779297225093[/C][C]108.246118623735[/C][/ROW]
[ROW][C]95[/C][C]53.8219557979932[/C][C]-2.14397679548101[/C][C]109.787888391467[/C][/ROW]
[ROW][C]96[/C][C]52.8219557979932[/C][C]-5.57521920630965[/C][C]111.219130802296[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78471&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78471&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
8563.821955797993245.067190089018482.576721506968
8662.821955797993237.726424836795987.9174867591906
8761.821955797993231.691736554677291.9521750413092
8860.821955797993226.385426514742795.2584850812437
8959.821955797993221.560761534065198.0831500619213
9058.821955797993217.085120461232100.558791134754
9157.821955797993212.8774582331767102.766453362810
9256.82195579799328.88395105457829104.759960541408
9355.82195579799325.06669266001364106.577218935973
9454.82195579799321.39779297225093108.246118623735
9553.8219557979932-2.14397679548101109.787888391467
9652.8219557979932-5.57521920630965111.219130802296



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