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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 18:25:41 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461605166hr1qtsjbo3usulg.htm/, Retrieved Sun, 05 May 2024 21:57:22 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294757, Retrieved Sun, 05 May 2024 21:57:22 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact47
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave10/oef2] [2016-04-25 17:25:41] [efea2b8bc7c91838390b884e612c3e3f] [Current]
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Dataseries X:
92,94
92,97
93,37
92,6
92,84
92,55
92,93
92,44
93,36
93,24
92,65
92,06
92,88
91,69
91,66
90,26
91,11
92,33
91,82
92,24
93,35
93,53
93,34
92,59
92,42
92,64
94,44
93,59
93,39
93,33
93,72
95,43
97,06
97,7
97,59
96,97
97,75
99,27
100,63
99,8
99,5
99,72
99,77
100,18
101,11
100,67
101,13
100,46
101,6
102,3
103,26
104,56
104,61
104,62
105,03
104,93
104,73
104,33
104,6
104,41
104,63
105,55
106,12
106,62
106,72
106,52
106,79
106,95
106,92
106,74
108,13
107,86




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294757&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294757&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999957558403617
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999957558403617 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294757&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]0.999957558403617[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294757&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
alpha0.999957558403617
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
292.9792.940.0300000000000011
393.3792.96999872675210.400001273247895
492.693.3699830233074-0.769983023307418
592.8492.60003267930870.239967320691321
692.5592.8399898154038-0.289989815403842
792.9392.55001230763070.379987692369312
892.4492.9299838727157-0.489983872715726
993.3692.44002079569770.919979204302251
1093.2493.3599609546139-0.11996095461393
1192.6593.2400050913344-0.590005091334419
1292.0692.650025040758-0.590025040757951
1392.8892.06002504160460.819974958395349
1491.6992.8799651989538-1.18996519895377
1591.6691.6900505040227-0.0300505040226824
1690.2691.6600012753914-1.40000127539135
1791.1190.26005941828910.849940581710925
1892.3391.10996392716491.22003607283511
1991.8292.3299482197214-0.509948219721423
2092.2491.82002164301650.419978356983478
2193.3592.23998217544811.11001782455192
2293.5393.34995288907150.180047110928498
2393.3493.5299923585132-0.18999235851318
2492.5993.340008063579-0.750008063579003
2592.4292.5900318315395-0.170031831539518
2692.6492.42000721642240.219992783577638
2794.4492.63999066315511.80000933684492
2893.5994.4399236047302-0.849923604730236
2993.3993.5900360721146-0.200036072114585
3093.3393.3900084898502-0.0600084898502331
3193.7293.33000254685610.389997453143891
3295.4393.71998344788551.71001655211451
3397.0695.42992742416771.6300725758323
3497.797.05993081711770.640069182882343
3597.5997.6999728344421-0.10997283444209
3696.9797.5900046674227-0.620004667422663
3797.7596.97002631398790.779973686012141
3899.2797.74996689667161.52003310332836
39100.6399.26993548736851.36006451263147
4099.8100.629942276691-0.8299422766909
4199.599.8000352240751-0.300035224075131
4299.7299.50001273397390.219987266026109
4399.7799.71999066338920.0500093366107563
44100.1899.76999787752390.410002122476101
45101.11100.1799825988550.930017401144582
46100.67101.109960528577-0.439960528576833
47101.13100.6700186726270.459981327372816
48100.46101.129980477658-0.669980477658157
49101.6100.4600284350411.13997156495898
50102.3101.5999516177870.700048382213055
51103.26102.2999702888290.960029711170904
52104.56103.2599592548061.30004074519351
53104.61104.5599448241950.0500551758045731
54104.62104.6099978755780.0100021244215753
55105.03104.6199995754940.410000424506123
56104.93105.029982598927-0.0999825989274683
57104.73104.930004243421-0.200004243421105
58104.33104.730008488499-0.400008488499381
59104.6104.3300169769990.269983023001188
60104.41104.599988541489-0.189988541489498
61104.63104.4100080634170.219991936583014
62105.55104.6299906631910.920009336808974
63106.12105.5499609533350.570039046664945
64106.62106.1199758066330.500024193367139
65106.72106.6199787781750.100021221824989
66106.52106.71999575494-0.199995754939678
67106.79106.5200084881390.269991511860908
68106.95106.7899885411290.16001145887077
69106.92106.949993208858-0.0299932088582437
70106.74106.92000127296-0.180001272959672
71108.13106.7400076395411.38999236045862
72107.86108.129941006505-0.269941006505263

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 92.97 & 92.94 & 0.0300000000000011 \tabularnewline
3 & 93.37 & 92.9699987267521 & 0.400001273247895 \tabularnewline
4 & 92.6 & 93.3699830233074 & -0.769983023307418 \tabularnewline
5 & 92.84 & 92.6000326793087 & 0.239967320691321 \tabularnewline
6 & 92.55 & 92.8399898154038 & -0.289989815403842 \tabularnewline
7 & 92.93 & 92.5500123076307 & 0.379987692369312 \tabularnewline
8 & 92.44 & 92.9299838727157 & -0.489983872715726 \tabularnewline
9 & 93.36 & 92.4400207956977 & 0.919979204302251 \tabularnewline
10 & 93.24 & 93.3599609546139 & -0.11996095461393 \tabularnewline
11 & 92.65 & 93.2400050913344 & -0.590005091334419 \tabularnewline
12 & 92.06 & 92.650025040758 & -0.590025040757951 \tabularnewline
13 & 92.88 & 92.0600250416046 & 0.819974958395349 \tabularnewline
14 & 91.69 & 92.8799651989538 & -1.18996519895377 \tabularnewline
15 & 91.66 & 91.6900505040227 & -0.0300505040226824 \tabularnewline
16 & 90.26 & 91.6600012753914 & -1.40000127539135 \tabularnewline
17 & 91.11 & 90.2600594182891 & 0.849940581710925 \tabularnewline
18 & 92.33 & 91.1099639271649 & 1.22003607283511 \tabularnewline
19 & 91.82 & 92.3299482197214 & -0.509948219721423 \tabularnewline
20 & 92.24 & 91.8200216430165 & 0.419978356983478 \tabularnewline
21 & 93.35 & 92.2399821754481 & 1.11001782455192 \tabularnewline
22 & 93.53 & 93.3499528890715 & 0.180047110928498 \tabularnewline
23 & 93.34 & 93.5299923585132 & -0.18999235851318 \tabularnewline
24 & 92.59 & 93.340008063579 & -0.750008063579003 \tabularnewline
25 & 92.42 & 92.5900318315395 & -0.170031831539518 \tabularnewline
26 & 92.64 & 92.4200072164224 & 0.219992783577638 \tabularnewline
27 & 94.44 & 92.6399906631551 & 1.80000933684492 \tabularnewline
28 & 93.59 & 94.4399236047302 & -0.849923604730236 \tabularnewline
29 & 93.39 & 93.5900360721146 & -0.200036072114585 \tabularnewline
30 & 93.33 & 93.3900084898502 & -0.0600084898502331 \tabularnewline
31 & 93.72 & 93.3300025468561 & 0.389997453143891 \tabularnewline
32 & 95.43 & 93.7199834478855 & 1.71001655211451 \tabularnewline
33 & 97.06 & 95.4299274241677 & 1.6300725758323 \tabularnewline
34 & 97.7 & 97.0599308171177 & 0.640069182882343 \tabularnewline
35 & 97.59 & 97.6999728344421 & -0.10997283444209 \tabularnewline
36 & 96.97 & 97.5900046674227 & -0.620004667422663 \tabularnewline
37 & 97.75 & 96.9700263139879 & 0.779973686012141 \tabularnewline
38 & 99.27 & 97.7499668966716 & 1.52003310332836 \tabularnewline
39 & 100.63 & 99.2699354873685 & 1.36006451263147 \tabularnewline
40 & 99.8 & 100.629942276691 & -0.8299422766909 \tabularnewline
41 & 99.5 & 99.8000352240751 & -0.300035224075131 \tabularnewline
42 & 99.72 & 99.5000127339739 & 0.219987266026109 \tabularnewline
43 & 99.77 & 99.7199906633892 & 0.0500093366107563 \tabularnewline
44 & 100.18 & 99.7699978775239 & 0.410002122476101 \tabularnewline
45 & 101.11 & 100.179982598855 & 0.930017401144582 \tabularnewline
46 & 100.67 & 101.109960528577 & -0.439960528576833 \tabularnewline
47 & 101.13 & 100.670018672627 & 0.459981327372816 \tabularnewline
48 & 100.46 & 101.129980477658 & -0.669980477658157 \tabularnewline
49 & 101.6 & 100.460028435041 & 1.13997156495898 \tabularnewline
50 & 102.3 & 101.599951617787 & 0.700048382213055 \tabularnewline
51 & 103.26 & 102.299970288829 & 0.960029711170904 \tabularnewline
52 & 104.56 & 103.259959254806 & 1.30004074519351 \tabularnewline
53 & 104.61 & 104.559944824195 & 0.0500551758045731 \tabularnewline
54 & 104.62 & 104.609997875578 & 0.0100021244215753 \tabularnewline
55 & 105.03 & 104.619999575494 & 0.410000424506123 \tabularnewline
56 & 104.93 & 105.029982598927 & -0.0999825989274683 \tabularnewline
57 & 104.73 & 104.930004243421 & -0.200004243421105 \tabularnewline
58 & 104.33 & 104.730008488499 & -0.400008488499381 \tabularnewline
59 & 104.6 & 104.330016976999 & 0.269983023001188 \tabularnewline
60 & 104.41 & 104.599988541489 & -0.189988541489498 \tabularnewline
61 & 104.63 & 104.410008063417 & 0.219991936583014 \tabularnewline
62 & 105.55 & 104.629990663191 & 0.920009336808974 \tabularnewline
63 & 106.12 & 105.549960953335 & 0.570039046664945 \tabularnewline
64 & 106.62 & 106.119975806633 & 0.500024193367139 \tabularnewline
65 & 106.72 & 106.619978778175 & 0.100021221824989 \tabularnewline
66 & 106.52 & 106.71999575494 & -0.199995754939678 \tabularnewline
67 & 106.79 & 106.520008488139 & 0.269991511860908 \tabularnewline
68 & 106.95 & 106.789988541129 & 0.16001145887077 \tabularnewline
69 & 106.92 & 106.949993208858 & -0.0299932088582437 \tabularnewline
70 & 106.74 & 106.92000127296 & -0.180001272959672 \tabularnewline
71 & 108.13 & 106.740007639541 & 1.38999236045862 \tabularnewline
72 & 107.86 & 108.129941006505 & -0.269941006505263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294757&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]92.97[/C][C]92.94[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]3[/C][C]93.37[/C][C]92.9699987267521[/C][C]0.400001273247895[/C][/ROW]
[ROW][C]4[/C][C]92.6[/C][C]93.3699830233074[/C][C]-0.769983023307418[/C][/ROW]
[ROW][C]5[/C][C]92.84[/C][C]92.6000326793087[/C][C]0.239967320691321[/C][/ROW]
[ROW][C]6[/C][C]92.55[/C][C]92.8399898154038[/C][C]-0.289989815403842[/C][/ROW]
[ROW][C]7[/C][C]92.93[/C][C]92.5500123076307[/C][C]0.379987692369312[/C][/ROW]
[ROW][C]8[/C][C]92.44[/C][C]92.9299838727157[/C][C]-0.489983872715726[/C][/ROW]
[ROW][C]9[/C][C]93.36[/C][C]92.4400207956977[/C][C]0.919979204302251[/C][/ROW]
[ROW][C]10[/C][C]93.24[/C][C]93.3599609546139[/C][C]-0.11996095461393[/C][/ROW]
[ROW][C]11[/C][C]92.65[/C][C]93.2400050913344[/C][C]-0.590005091334419[/C][/ROW]
[ROW][C]12[/C][C]92.06[/C][C]92.650025040758[/C][C]-0.590025040757951[/C][/ROW]
[ROW][C]13[/C][C]92.88[/C][C]92.0600250416046[/C][C]0.819974958395349[/C][/ROW]
[ROW][C]14[/C][C]91.69[/C][C]92.8799651989538[/C][C]-1.18996519895377[/C][/ROW]
[ROW][C]15[/C][C]91.66[/C][C]91.6900505040227[/C][C]-0.0300505040226824[/C][/ROW]
[ROW][C]16[/C][C]90.26[/C][C]91.6600012753914[/C][C]-1.40000127539135[/C][/ROW]
[ROW][C]17[/C][C]91.11[/C][C]90.2600594182891[/C][C]0.849940581710925[/C][/ROW]
[ROW][C]18[/C][C]92.33[/C][C]91.1099639271649[/C][C]1.22003607283511[/C][/ROW]
[ROW][C]19[/C][C]91.82[/C][C]92.3299482197214[/C][C]-0.509948219721423[/C][/ROW]
[ROW][C]20[/C][C]92.24[/C][C]91.8200216430165[/C][C]0.419978356983478[/C][/ROW]
[ROW][C]21[/C][C]93.35[/C][C]92.2399821754481[/C][C]1.11001782455192[/C][/ROW]
[ROW][C]22[/C][C]93.53[/C][C]93.3499528890715[/C][C]0.180047110928498[/C][/ROW]
[ROW][C]23[/C][C]93.34[/C][C]93.5299923585132[/C][C]-0.18999235851318[/C][/ROW]
[ROW][C]24[/C][C]92.59[/C][C]93.340008063579[/C][C]-0.750008063579003[/C][/ROW]
[ROW][C]25[/C][C]92.42[/C][C]92.5900318315395[/C][C]-0.170031831539518[/C][/ROW]
[ROW][C]26[/C][C]92.64[/C][C]92.4200072164224[/C][C]0.219992783577638[/C][/ROW]
[ROW][C]27[/C][C]94.44[/C][C]92.6399906631551[/C][C]1.80000933684492[/C][/ROW]
[ROW][C]28[/C][C]93.59[/C][C]94.4399236047302[/C][C]-0.849923604730236[/C][/ROW]
[ROW][C]29[/C][C]93.39[/C][C]93.5900360721146[/C][C]-0.200036072114585[/C][/ROW]
[ROW][C]30[/C][C]93.33[/C][C]93.3900084898502[/C][C]-0.0600084898502331[/C][/ROW]
[ROW][C]31[/C][C]93.72[/C][C]93.3300025468561[/C][C]0.389997453143891[/C][/ROW]
[ROW][C]32[/C][C]95.43[/C][C]93.7199834478855[/C][C]1.71001655211451[/C][/ROW]
[ROW][C]33[/C][C]97.06[/C][C]95.4299274241677[/C][C]1.6300725758323[/C][/ROW]
[ROW][C]34[/C][C]97.7[/C][C]97.0599308171177[/C][C]0.640069182882343[/C][/ROW]
[ROW][C]35[/C][C]97.59[/C][C]97.6999728344421[/C][C]-0.10997283444209[/C][/ROW]
[ROW][C]36[/C][C]96.97[/C][C]97.5900046674227[/C][C]-0.620004667422663[/C][/ROW]
[ROW][C]37[/C][C]97.75[/C][C]96.9700263139879[/C][C]0.779973686012141[/C][/ROW]
[ROW][C]38[/C][C]99.27[/C][C]97.7499668966716[/C][C]1.52003310332836[/C][/ROW]
[ROW][C]39[/C][C]100.63[/C][C]99.2699354873685[/C][C]1.36006451263147[/C][/ROW]
[ROW][C]40[/C][C]99.8[/C][C]100.629942276691[/C][C]-0.8299422766909[/C][/ROW]
[ROW][C]41[/C][C]99.5[/C][C]99.8000352240751[/C][C]-0.300035224075131[/C][/ROW]
[ROW][C]42[/C][C]99.72[/C][C]99.5000127339739[/C][C]0.219987266026109[/C][/ROW]
[ROW][C]43[/C][C]99.77[/C][C]99.7199906633892[/C][C]0.0500093366107563[/C][/ROW]
[ROW][C]44[/C][C]100.18[/C][C]99.7699978775239[/C][C]0.410002122476101[/C][/ROW]
[ROW][C]45[/C][C]101.11[/C][C]100.179982598855[/C][C]0.930017401144582[/C][/ROW]
[ROW][C]46[/C][C]100.67[/C][C]101.109960528577[/C][C]-0.439960528576833[/C][/ROW]
[ROW][C]47[/C][C]101.13[/C][C]100.670018672627[/C][C]0.459981327372816[/C][/ROW]
[ROW][C]48[/C][C]100.46[/C][C]101.129980477658[/C][C]-0.669980477658157[/C][/ROW]
[ROW][C]49[/C][C]101.6[/C][C]100.460028435041[/C][C]1.13997156495898[/C][/ROW]
[ROW][C]50[/C][C]102.3[/C][C]101.599951617787[/C][C]0.700048382213055[/C][/ROW]
[ROW][C]51[/C][C]103.26[/C][C]102.299970288829[/C][C]0.960029711170904[/C][/ROW]
[ROW][C]52[/C][C]104.56[/C][C]103.259959254806[/C][C]1.30004074519351[/C][/ROW]
[ROW][C]53[/C][C]104.61[/C][C]104.559944824195[/C][C]0.0500551758045731[/C][/ROW]
[ROW][C]54[/C][C]104.62[/C][C]104.609997875578[/C][C]0.0100021244215753[/C][/ROW]
[ROW][C]55[/C][C]105.03[/C][C]104.619999575494[/C][C]0.410000424506123[/C][/ROW]
[ROW][C]56[/C][C]104.93[/C][C]105.029982598927[/C][C]-0.0999825989274683[/C][/ROW]
[ROW][C]57[/C][C]104.73[/C][C]104.930004243421[/C][C]-0.200004243421105[/C][/ROW]
[ROW][C]58[/C][C]104.33[/C][C]104.730008488499[/C][C]-0.400008488499381[/C][/ROW]
[ROW][C]59[/C][C]104.6[/C][C]104.330016976999[/C][C]0.269983023001188[/C][/ROW]
[ROW][C]60[/C][C]104.41[/C][C]104.599988541489[/C][C]-0.189988541489498[/C][/ROW]
[ROW][C]61[/C][C]104.63[/C][C]104.410008063417[/C][C]0.219991936583014[/C][/ROW]
[ROW][C]62[/C][C]105.55[/C][C]104.629990663191[/C][C]0.920009336808974[/C][/ROW]
[ROW][C]63[/C][C]106.12[/C][C]105.549960953335[/C][C]0.570039046664945[/C][/ROW]
[ROW][C]64[/C][C]106.62[/C][C]106.119975806633[/C][C]0.500024193367139[/C][/ROW]
[ROW][C]65[/C][C]106.72[/C][C]106.619978778175[/C][C]0.100021221824989[/C][/ROW]
[ROW][C]66[/C][C]106.52[/C][C]106.71999575494[/C][C]-0.199995754939678[/C][/ROW]
[ROW][C]67[/C][C]106.79[/C][C]106.520008488139[/C][C]0.269991511860908[/C][/ROW]
[ROW][C]68[/C][C]106.95[/C][C]106.789988541129[/C][C]0.16001145887077[/C][/ROW]
[ROW][C]69[/C][C]106.92[/C][C]106.949993208858[/C][C]-0.0299932088582437[/C][/ROW]
[ROW][C]70[/C][C]106.74[/C][C]106.92000127296[/C][C]-0.180001272959672[/C][/ROW]
[ROW][C]71[/C][C]108.13[/C][C]106.740007639541[/C][C]1.38999236045862[/C][/ROW]
[ROW][C]72[/C][C]107.86[/C][C]108.129941006505[/C][C]-0.269941006505263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294757&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294757&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
292.9792.940.0300000000000011
393.3792.96999872675210.400001273247895
492.693.3699830233074-0.769983023307418
592.8492.60003267930870.239967320691321
692.5592.8399898154038-0.289989815403842
792.9392.55001230763070.379987692369312
892.4492.9299838727157-0.489983872715726
993.3692.44002079569770.919979204302251
1093.2493.3599609546139-0.11996095461393
1192.6593.2400050913344-0.590005091334419
1292.0692.650025040758-0.590025040757951
1392.8892.06002504160460.819974958395349
1491.6992.8799651989538-1.18996519895377
1591.6691.6900505040227-0.0300505040226824
1690.2691.6600012753914-1.40000127539135
1791.1190.26005941828910.849940581710925
1892.3391.10996392716491.22003607283511
1991.8292.3299482197214-0.509948219721423
2092.2491.82002164301650.419978356983478
2193.3592.23998217544811.11001782455192
2293.5393.34995288907150.180047110928498
2393.3493.5299923585132-0.18999235851318
2492.5993.340008063579-0.750008063579003
2592.4292.5900318315395-0.170031831539518
2692.6492.42000721642240.219992783577638
2794.4492.63999066315511.80000933684492
2893.5994.4399236047302-0.849923604730236
2993.3993.5900360721146-0.200036072114585
3093.3393.3900084898502-0.0600084898502331
3193.7293.33000254685610.389997453143891
3295.4393.71998344788551.71001655211451
3397.0695.42992742416771.6300725758323
3497.797.05993081711770.640069182882343
3597.5997.6999728344421-0.10997283444209
3696.9797.5900046674227-0.620004667422663
3797.7596.97002631398790.779973686012141
3899.2797.74996689667161.52003310332836
39100.6399.26993548736851.36006451263147
4099.8100.629942276691-0.8299422766909
4199.599.8000352240751-0.300035224075131
4299.7299.50001273397390.219987266026109
4399.7799.71999066338920.0500093366107563
44100.1899.76999787752390.410002122476101
45101.11100.1799825988550.930017401144582
46100.67101.109960528577-0.439960528576833
47101.13100.6700186726270.459981327372816
48100.46101.129980477658-0.669980477658157
49101.6100.4600284350411.13997156495898
50102.3101.5999516177870.700048382213055
51103.26102.2999702888290.960029711170904
52104.56103.2599592548061.30004074519351
53104.61104.5599448241950.0500551758045731
54104.62104.6099978755780.0100021244215753
55105.03104.6199995754940.410000424506123
56104.93105.029982598927-0.0999825989274683
57104.73104.930004243421-0.200004243421105
58104.33104.730008488499-0.400008488499381
59104.6104.3300169769990.269983023001188
60104.41104.599988541489-0.189988541489498
61104.63104.4100080634170.219991936583014
62105.55104.6299906631910.920009336808974
63106.12105.5499609533350.570039046664945
64106.62106.1199758066330.500024193367139
65106.72106.6199787781750.100021221824989
66106.52106.71999575494-0.199995754939678
67106.79106.5200084881390.269991511860908
68106.95106.7899885411290.16001145887077
69106.92106.949993208858-0.0299932088582437
70106.74106.92000127296-0.180001272959672
71108.13106.7400076395411.38999236045862
72107.86108.129941006505-0.269941006505263







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73107.860011456727106.475751486644109.244271426811
74107.860011456727105.902413775411109.817609138043
75107.860011456727105.46247069607110.257552217384
76107.860011456727105.091579641398110.628443272057
77107.860011456727104.764817160201110.955205753253
78107.860011456727104.469400781588111.250622131866
79107.860011456727104.197737058558111.522285854896
80107.860011456727103.944878408592111.775144504863
81107.860011456727103.707388213316112.012634700139
82107.860011456727103.482764283122112.237258630333
83107.860011456727103.269117661838112.450905251617
84107.860011456727103.064980815212112.655042098243

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 107.860011456727 & 106.475751486644 & 109.244271426811 \tabularnewline
74 & 107.860011456727 & 105.902413775411 & 109.817609138043 \tabularnewline
75 & 107.860011456727 & 105.46247069607 & 110.257552217384 \tabularnewline
76 & 107.860011456727 & 105.091579641398 & 110.628443272057 \tabularnewline
77 & 107.860011456727 & 104.764817160201 & 110.955205753253 \tabularnewline
78 & 107.860011456727 & 104.469400781588 & 111.250622131866 \tabularnewline
79 & 107.860011456727 & 104.197737058558 & 111.522285854896 \tabularnewline
80 & 107.860011456727 & 103.944878408592 & 111.775144504863 \tabularnewline
81 & 107.860011456727 & 103.707388213316 & 112.012634700139 \tabularnewline
82 & 107.860011456727 & 103.482764283122 & 112.237258630333 \tabularnewline
83 & 107.860011456727 & 103.269117661838 & 112.450905251617 \tabularnewline
84 & 107.860011456727 & 103.064980815212 & 112.655042098243 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294757&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]73[/C][C]107.860011456727[/C][C]106.475751486644[/C][C]109.244271426811[/C][/ROW]
[ROW][C]74[/C][C]107.860011456727[/C][C]105.902413775411[/C][C]109.817609138043[/C][/ROW]
[ROW][C]75[/C][C]107.860011456727[/C][C]105.46247069607[/C][C]110.257552217384[/C][/ROW]
[ROW][C]76[/C][C]107.860011456727[/C][C]105.091579641398[/C][C]110.628443272057[/C][/ROW]
[ROW][C]77[/C][C]107.860011456727[/C][C]104.764817160201[/C][C]110.955205753253[/C][/ROW]
[ROW][C]78[/C][C]107.860011456727[/C][C]104.469400781588[/C][C]111.250622131866[/C][/ROW]
[ROW][C]79[/C][C]107.860011456727[/C][C]104.197737058558[/C][C]111.522285854896[/C][/ROW]
[ROW][C]80[/C][C]107.860011456727[/C][C]103.944878408592[/C][C]111.775144504863[/C][/ROW]
[ROW][C]81[/C][C]107.860011456727[/C][C]103.707388213316[/C][C]112.012634700139[/C][/ROW]
[ROW][C]82[/C][C]107.860011456727[/C][C]103.482764283122[/C][C]112.237258630333[/C][/ROW]
[ROW][C]83[/C][C]107.860011456727[/C][C]103.269117661838[/C][C]112.450905251617[/C][/ROW]
[ROW][C]84[/C][C]107.860011456727[/C][C]103.064980815212[/C][C]112.655042098243[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294757&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294757&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
73107.860011456727106.475751486644109.244271426811
74107.860011456727105.902413775411109.817609138043
75107.860011456727105.46247069607110.257552217384
76107.860011456727105.091579641398110.628443272057
77107.860011456727104.764817160201110.955205753253
78107.860011456727104.469400781588111.250622131866
79107.860011456727104.197737058558111.522285854896
80107.860011456727103.944878408592111.775144504863
81107.860011456727103.707388213316112.012634700139
82107.860011456727103.482764283122112.237258630333
83107.860011456727103.269117661838112.450905251617
84107.860011456727103.064980815212112.655042098243



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')