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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 06:10:57 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t1243944875e8vj37zsmfgv8mx.htm/, Retrieved Fri, 10 May 2024 10:25:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41206, Retrieved Fri, 10 May 2024 10:25:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Van der linden Ke...] [2009-06-02 12:10:57] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
155
176
180
181
208
183
185
205
180
196
183
147
128
158
186
165
191
168
171
169
157
175
156
129
89
138
146
151
156
129
146
141
137
155
147
128
92
136
159
131
134
148
146
144
161
140
141
139
94
136
164
141
159
162
154
166
156
147
161
135
98
150
173
144
167
161
156
175
163
159
167
148
119
150
161
136
166
155
140
141




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41206&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41206&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.3969420535359
beta0.0141114199930199
gamma0.748470071977163

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.3969420535359 \tabularnewline
beta & 0.0141114199930199 \tabularnewline
gamma & 0.748470071977163 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41206&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]0.3969420535359[/C][/ROW]
[ROW][C]beta[/C][C]0.0141114199930199[/C][/ROW]
[ROW][C]gamma[/C][C]0.748470071977163[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41206&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
alpha0.3969420535359
beta0.0141114199930199
gamma0.748470071977163







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13128132.711239909822-4.71123990982153
14158162.035845855414-4.03584585541398
15186189.872729176268-3.87272917626845
16165167.325171462959-2.32517146295910
17191193.090291447698-2.09029144769787
18168169.380749569493-1.38074956949299
19171166.7743965012054.22560349879512
20169186.777689862744-17.7776898627438
21157156.5347478063370.465252193663417
22175169.1844398233875.81556017661254
23156159.642212085019-3.64221208501897
24129126.6315514869382.36844851306249
2589108.830295004100-19.8302950041004
26138125.10636426553712.8936357344631
27146153.961101046977-7.96110104697655
28151133.90227523616417.0977247638365
29156163.126103617622-7.12610361762194
30129141.027605450006-12.0276054500063
31146136.1407474449419.85925255505938
32141146.248096189310-5.24809618931027
33137131.2717687777505.72823122224952
34155145.8580815419089.14191845809154
35147135.37510130635511.6248986936453
36128114.08779133324213.9122086667578
379292.2353524910681-0.235352491068141
38136131.1686450940794.83135490592053
39159147.24188586463811.7581141353619
40131146.173778234449-15.1737782344485
41134151.040510383096-17.0405103830955
42148124.34587548461023.6541245153904
43146143.9717650715422.02823492845809
44144144.413956293347-0.413956293347411
45161136.46701363023224.5329863697678
46140161.582316185765-21.5823161857653
47141140.1601934704170.839806529582859
48139116.27766308360222.7223369163978
499491.8489413263682.15105867363202
50136134.5464007161891.45359928381100
51164152.48669036029111.5133096397090
52141139.1206400302291.87935996977117
53159150.4617142557348.53828574426637
54162151.94961172076110.0503882792389
55154156.979452763920-2.97945276392025
56166154.71729941120211.2827005887980
57156162.851672916130-6.85167291613024
58147154.32957591457-7.32957591457014
59161148.94912054519112.0508794548088
60135137.762111693425-2.76211169342454
619893.72059733803994.27940266196015
62150137.96453497706812.0354650229324
63173166.0132482737336.98675172626656
64144145.910747362506-1.91074736250616
65167159.4025010004787.59749899952249
66161161.341465694832-0.341465694831726
67156156.534217737577-0.534217737576796
68175161.83341962571113.1665803742893
69163162.6418971155920.35810288440814
70159156.7752531849242.22474681507646
71167164.5607847497592.43921525024095
72148142.2265603995645.77343960043552
73119102.28867597765316.7113240223466
74150160.756366135467-10.7563661354669
75161178.968330529485-17.9683305294851
76136145.093550740936-9.0935507409362
77166159.6936419725416.3063580274586
78155157.718226366012-2.71822636601217
79140152.069585565496-12.0695855654961
80141158.102515288249-17.1025152882493

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 128 & 132.711239909822 & -4.71123990982153 \tabularnewline
14 & 158 & 162.035845855414 & -4.03584585541398 \tabularnewline
15 & 186 & 189.872729176268 & -3.87272917626845 \tabularnewline
16 & 165 & 167.325171462959 & -2.32517146295910 \tabularnewline
17 & 191 & 193.090291447698 & -2.09029144769787 \tabularnewline
18 & 168 & 169.380749569493 & -1.38074956949299 \tabularnewline
19 & 171 & 166.774396501205 & 4.22560349879512 \tabularnewline
20 & 169 & 186.777689862744 & -17.7776898627438 \tabularnewline
21 & 157 & 156.534747806337 & 0.465252193663417 \tabularnewline
22 & 175 & 169.184439823387 & 5.81556017661254 \tabularnewline
23 & 156 & 159.642212085019 & -3.64221208501897 \tabularnewline
24 & 129 & 126.631551486938 & 2.36844851306249 \tabularnewline
25 & 89 & 108.830295004100 & -19.8302950041004 \tabularnewline
26 & 138 & 125.106364265537 & 12.8936357344631 \tabularnewline
27 & 146 & 153.961101046977 & -7.96110104697655 \tabularnewline
28 & 151 & 133.902275236164 & 17.0977247638365 \tabularnewline
29 & 156 & 163.126103617622 & -7.12610361762194 \tabularnewline
30 & 129 & 141.027605450006 & -12.0276054500063 \tabularnewline
31 & 146 & 136.140747444941 & 9.85925255505938 \tabularnewline
32 & 141 & 146.248096189310 & -5.24809618931027 \tabularnewline
33 & 137 & 131.271768777750 & 5.72823122224952 \tabularnewline
34 & 155 & 145.858081541908 & 9.14191845809154 \tabularnewline
35 & 147 & 135.375101306355 & 11.6248986936453 \tabularnewline
36 & 128 & 114.087791333242 & 13.9122086667578 \tabularnewline
37 & 92 & 92.2353524910681 & -0.235352491068141 \tabularnewline
38 & 136 & 131.168645094079 & 4.83135490592053 \tabularnewline
39 & 159 & 147.241885864638 & 11.7581141353619 \tabularnewline
40 & 131 & 146.173778234449 & -15.1737782344485 \tabularnewline
41 & 134 & 151.040510383096 & -17.0405103830955 \tabularnewline
42 & 148 & 124.345875484610 & 23.6541245153904 \tabularnewline
43 & 146 & 143.971765071542 & 2.02823492845809 \tabularnewline
44 & 144 & 144.413956293347 & -0.413956293347411 \tabularnewline
45 & 161 & 136.467013630232 & 24.5329863697678 \tabularnewline
46 & 140 & 161.582316185765 & -21.5823161857653 \tabularnewline
47 & 141 & 140.160193470417 & 0.839806529582859 \tabularnewline
48 & 139 & 116.277663083602 & 22.7223369163978 \tabularnewline
49 & 94 & 91.848941326368 & 2.15105867363202 \tabularnewline
50 & 136 & 134.546400716189 & 1.45359928381100 \tabularnewline
51 & 164 & 152.486690360291 & 11.5133096397090 \tabularnewline
52 & 141 & 139.120640030229 & 1.87935996977117 \tabularnewline
53 & 159 & 150.461714255734 & 8.53828574426637 \tabularnewline
54 & 162 & 151.949611720761 & 10.0503882792389 \tabularnewline
55 & 154 & 156.979452763920 & -2.97945276392025 \tabularnewline
56 & 166 & 154.717299411202 & 11.2827005887980 \tabularnewline
57 & 156 & 162.851672916130 & -6.85167291613024 \tabularnewline
58 & 147 & 154.32957591457 & -7.32957591457014 \tabularnewline
59 & 161 & 148.949120545191 & 12.0508794548088 \tabularnewline
60 & 135 & 137.762111693425 & -2.76211169342454 \tabularnewline
61 & 98 & 93.7205973380399 & 4.27940266196015 \tabularnewline
62 & 150 & 137.964534977068 & 12.0354650229324 \tabularnewline
63 & 173 & 166.013248273733 & 6.98675172626656 \tabularnewline
64 & 144 & 145.910747362506 & -1.91074736250616 \tabularnewline
65 & 167 & 159.402501000478 & 7.59749899952249 \tabularnewline
66 & 161 & 161.341465694832 & -0.341465694831726 \tabularnewline
67 & 156 & 156.534217737577 & -0.534217737576796 \tabularnewline
68 & 175 & 161.833419625711 & 13.1665803742893 \tabularnewline
69 & 163 & 162.641897115592 & 0.35810288440814 \tabularnewline
70 & 159 & 156.775253184924 & 2.22474681507646 \tabularnewline
71 & 167 & 164.560784749759 & 2.43921525024095 \tabularnewline
72 & 148 & 142.226560399564 & 5.77343960043552 \tabularnewline
73 & 119 & 102.288675977653 & 16.7113240223466 \tabularnewline
74 & 150 & 160.756366135467 & -10.7563661354669 \tabularnewline
75 & 161 & 178.968330529485 & -17.9683305294851 \tabularnewline
76 & 136 & 145.093550740936 & -9.0935507409362 \tabularnewline
77 & 166 & 159.693641972541 & 6.3063580274586 \tabularnewline
78 & 155 & 157.718226366012 & -2.71822636601217 \tabularnewline
79 & 140 & 152.069585565496 & -12.0695855654961 \tabularnewline
80 & 141 & 158.102515288249 & -17.1025152882493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41206&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]128[/C][C]132.711239909822[/C][C]-4.71123990982153[/C][/ROW]
[ROW][C]14[/C][C]158[/C][C]162.035845855414[/C][C]-4.03584585541398[/C][/ROW]
[ROW][C]15[/C][C]186[/C][C]189.872729176268[/C][C]-3.87272917626845[/C][/ROW]
[ROW][C]16[/C][C]165[/C][C]167.325171462959[/C][C]-2.32517146295910[/C][/ROW]
[ROW][C]17[/C][C]191[/C][C]193.090291447698[/C][C]-2.09029144769787[/C][/ROW]
[ROW][C]18[/C][C]168[/C][C]169.380749569493[/C][C]-1.38074956949299[/C][/ROW]
[ROW][C]19[/C][C]171[/C][C]166.774396501205[/C][C]4.22560349879512[/C][/ROW]
[ROW][C]20[/C][C]169[/C][C]186.777689862744[/C][C]-17.7776898627438[/C][/ROW]
[ROW][C]21[/C][C]157[/C][C]156.534747806337[/C][C]0.465252193663417[/C][/ROW]
[ROW][C]22[/C][C]175[/C][C]169.184439823387[/C][C]5.81556017661254[/C][/ROW]
[ROW][C]23[/C][C]156[/C][C]159.642212085019[/C][C]-3.64221208501897[/C][/ROW]
[ROW][C]24[/C][C]129[/C][C]126.631551486938[/C][C]2.36844851306249[/C][/ROW]
[ROW][C]25[/C][C]89[/C][C]108.830295004100[/C][C]-19.8302950041004[/C][/ROW]
[ROW][C]26[/C][C]138[/C][C]125.106364265537[/C][C]12.8936357344631[/C][/ROW]
[ROW][C]27[/C][C]146[/C][C]153.961101046977[/C][C]-7.96110104697655[/C][/ROW]
[ROW][C]28[/C][C]151[/C][C]133.902275236164[/C][C]17.0977247638365[/C][/ROW]
[ROW][C]29[/C][C]156[/C][C]163.126103617622[/C][C]-7.12610361762194[/C][/ROW]
[ROW][C]30[/C][C]129[/C][C]141.027605450006[/C][C]-12.0276054500063[/C][/ROW]
[ROW][C]31[/C][C]146[/C][C]136.140747444941[/C][C]9.85925255505938[/C][/ROW]
[ROW][C]32[/C][C]141[/C][C]146.248096189310[/C][C]-5.24809618931027[/C][/ROW]
[ROW][C]33[/C][C]137[/C][C]131.271768777750[/C][C]5.72823122224952[/C][/ROW]
[ROW][C]34[/C][C]155[/C][C]145.858081541908[/C][C]9.14191845809154[/C][/ROW]
[ROW][C]35[/C][C]147[/C][C]135.375101306355[/C][C]11.6248986936453[/C][/ROW]
[ROW][C]36[/C][C]128[/C][C]114.087791333242[/C][C]13.9122086667578[/C][/ROW]
[ROW][C]37[/C][C]92[/C][C]92.2353524910681[/C][C]-0.235352491068141[/C][/ROW]
[ROW][C]38[/C][C]136[/C][C]131.168645094079[/C][C]4.83135490592053[/C][/ROW]
[ROW][C]39[/C][C]159[/C][C]147.241885864638[/C][C]11.7581141353619[/C][/ROW]
[ROW][C]40[/C][C]131[/C][C]146.173778234449[/C][C]-15.1737782344485[/C][/ROW]
[ROW][C]41[/C][C]134[/C][C]151.040510383096[/C][C]-17.0405103830955[/C][/ROW]
[ROW][C]42[/C][C]148[/C][C]124.345875484610[/C][C]23.6541245153904[/C][/ROW]
[ROW][C]43[/C][C]146[/C][C]143.971765071542[/C][C]2.02823492845809[/C][/ROW]
[ROW][C]44[/C][C]144[/C][C]144.413956293347[/C][C]-0.413956293347411[/C][/ROW]
[ROW][C]45[/C][C]161[/C][C]136.467013630232[/C][C]24.5329863697678[/C][/ROW]
[ROW][C]46[/C][C]140[/C][C]161.582316185765[/C][C]-21.5823161857653[/C][/ROW]
[ROW][C]47[/C][C]141[/C][C]140.160193470417[/C][C]0.839806529582859[/C][/ROW]
[ROW][C]48[/C][C]139[/C][C]116.277663083602[/C][C]22.7223369163978[/C][/ROW]
[ROW][C]49[/C][C]94[/C][C]91.848941326368[/C][C]2.15105867363202[/C][/ROW]
[ROW][C]50[/C][C]136[/C][C]134.546400716189[/C][C]1.45359928381100[/C][/ROW]
[ROW][C]51[/C][C]164[/C][C]152.486690360291[/C][C]11.5133096397090[/C][/ROW]
[ROW][C]52[/C][C]141[/C][C]139.120640030229[/C][C]1.87935996977117[/C][/ROW]
[ROW][C]53[/C][C]159[/C][C]150.461714255734[/C][C]8.53828574426637[/C][/ROW]
[ROW][C]54[/C][C]162[/C][C]151.949611720761[/C][C]10.0503882792389[/C][/ROW]
[ROW][C]55[/C][C]154[/C][C]156.979452763920[/C][C]-2.97945276392025[/C][/ROW]
[ROW][C]56[/C][C]166[/C][C]154.717299411202[/C][C]11.2827005887980[/C][/ROW]
[ROW][C]57[/C][C]156[/C][C]162.851672916130[/C][C]-6.85167291613024[/C][/ROW]
[ROW][C]58[/C][C]147[/C][C]154.32957591457[/C][C]-7.32957591457014[/C][/ROW]
[ROW][C]59[/C][C]161[/C][C]148.949120545191[/C][C]12.0508794548088[/C][/ROW]
[ROW][C]60[/C][C]135[/C][C]137.762111693425[/C][C]-2.76211169342454[/C][/ROW]
[ROW][C]61[/C][C]98[/C][C]93.7205973380399[/C][C]4.27940266196015[/C][/ROW]
[ROW][C]62[/C][C]150[/C][C]137.964534977068[/C][C]12.0354650229324[/C][/ROW]
[ROW][C]63[/C][C]173[/C][C]166.013248273733[/C][C]6.98675172626656[/C][/ROW]
[ROW][C]64[/C][C]144[/C][C]145.910747362506[/C][C]-1.91074736250616[/C][/ROW]
[ROW][C]65[/C][C]167[/C][C]159.402501000478[/C][C]7.59749899952249[/C][/ROW]
[ROW][C]66[/C][C]161[/C][C]161.341465694832[/C][C]-0.341465694831726[/C][/ROW]
[ROW][C]67[/C][C]156[/C][C]156.534217737577[/C][C]-0.534217737576796[/C][/ROW]
[ROW][C]68[/C][C]175[/C][C]161.833419625711[/C][C]13.1665803742893[/C][/ROW]
[ROW][C]69[/C][C]163[/C][C]162.641897115592[/C][C]0.35810288440814[/C][/ROW]
[ROW][C]70[/C][C]159[/C][C]156.775253184924[/C][C]2.22474681507646[/C][/ROW]
[ROW][C]71[/C][C]167[/C][C]164.560784749759[/C][C]2.43921525024095[/C][/ROW]
[ROW][C]72[/C][C]148[/C][C]142.226560399564[/C][C]5.77343960043552[/C][/ROW]
[ROW][C]73[/C][C]119[/C][C]102.288675977653[/C][C]16.7113240223466[/C][/ROW]
[ROW][C]74[/C][C]150[/C][C]160.756366135467[/C][C]-10.7563661354669[/C][/ROW]
[ROW][C]75[/C][C]161[/C][C]178.968330529485[/C][C]-17.9683305294851[/C][/ROW]
[ROW][C]76[/C][C]136[/C][C]145.093550740936[/C][C]-9.0935507409362[/C][/ROW]
[ROW][C]77[/C][C]166[/C][C]159.693641972541[/C][C]6.3063580274586[/C][/ROW]
[ROW][C]78[/C][C]155[/C][C]157.718226366012[/C][C]-2.71822636601217[/C][/ROW]
[ROW][C]79[/C][C]140[/C][C]152.069585565496[/C][C]-12.0695855654961[/C][/ROW]
[ROW][C]80[/C][C]141[/C][C]158.102515288249[/C][C]-17.1025152882493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41206&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
13128132.711239909822-4.71123990982153
14158162.035845855414-4.03584585541398
15186189.872729176268-3.87272917626845
16165167.325171462959-2.32517146295910
17191193.090291447698-2.09029144769787
18168169.380749569493-1.38074956949299
19171166.7743965012054.22560349879512
20169186.777689862744-17.7776898627438
21157156.5347478063370.465252193663417
22175169.1844398233875.81556017661254
23156159.642212085019-3.64221208501897
24129126.6315514869382.36844851306249
2589108.830295004100-19.8302950041004
26138125.10636426553712.8936357344631
27146153.961101046977-7.96110104697655
28151133.90227523616417.0977247638365
29156163.126103617622-7.12610361762194
30129141.027605450006-12.0276054500063
31146136.1407474449419.85925255505938
32141146.248096189310-5.24809618931027
33137131.2717687777505.72823122224952
34155145.8580815419089.14191845809154
35147135.37510130635511.6248986936453
36128114.08779133324213.9122086667578
379292.2353524910681-0.235352491068141
38136131.1686450940794.83135490592053
39159147.24188586463811.7581141353619
40131146.173778234449-15.1737782344485
41134151.040510383096-17.0405103830955
42148124.34587548461023.6541245153904
43146143.9717650715422.02823492845809
44144144.413956293347-0.413956293347411
45161136.46701363023224.5329863697678
46140161.582316185765-21.5823161857653
47141140.1601934704170.839806529582859
48139116.27766308360222.7223369163978
499491.8489413263682.15105867363202
50136134.5464007161891.45359928381100
51164152.48669036029111.5133096397090
52141139.1206400302291.87935996977117
53159150.4617142557348.53828574426637
54162151.94961172076110.0503882792389
55154156.979452763920-2.97945276392025
56166154.71729941120211.2827005887980
57156162.851672916130-6.85167291613024
58147154.32957591457-7.32957591457014
59161148.94912054519112.0508794548088
60135137.762111693425-2.76211169342454
619893.72059733803994.27940266196015
62150137.96453497706812.0354650229324
63173166.0132482737336.98675172626656
64144145.910747362506-1.91074736250616
65167159.4025010004787.59749899952249
66161161.341465694832-0.341465694831726
67156156.534217737577-0.534217737576796
68175161.83341962571113.1665803742893
69163162.6418971155920.35810288440814
70159156.7752531849242.22474681507646
71167164.5607847497592.43921525024095
72148142.2265603995645.77343960043552
73119102.28867597765316.7113240223466
74150160.756366135467-10.7563661354669
75161178.968330529485-17.9683305294851
76136145.093550740936-9.0935507409362
77166159.6936419725416.3063580274586
78155157.718226366012-2.71822636601217
79140152.069585565496-12.0695855654961
80141158.102515288249-17.1025152882493







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
81142.136324689947124.722436441939159.550212937954
82137.371135600819118.188185783879156.554085417759
83143.141605675039121.884313834243164.398897515835
84124.117359846772102.392175413404145.842544280141
8592.041873460655471.1085742980996112.975172623211
86122.65145047378796.6429781166018148.659922830972
87137.486923677882107.826741531098167.147105824666
88118.01250119346389.772109282876146.252893104049
89139.307014715856105.863473255490172.750556176223
90131.77035283365098.2106089764762165.330096690825
91123.88731905228390.3695367839728157.405101320592
92130.84111234286893.385530154248168.296694531489

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 142.136324689947 & 124.722436441939 & 159.550212937954 \tabularnewline
82 & 137.371135600819 & 118.188185783879 & 156.554085417759 \tabularnewline
83 & 143.141605675039 & 121.884313834243 & 164.398897515835 \tabularnewline
84 & 124.117359846772 & 102.392175413404 & 145.842544280141 \tabularnewline
85 & 92.0418734606554 & 71.1085742980996 & 112.975172623211 \tabularnewline
86 & 122.651450473787 & 96.6429781166018 & 148.659922830972 \tabularnewline
87 & 137.486923677882 & 107.826741531098 & 167.147105824666 \tabularnewline
88 & 118.012501193463 & 89.772109282876 & 146.252893104049 \tabularnewline
89 & 139.307014715856 & 105.863473255490 & 172.750556176223 \tabularnewline
90 & 131.770352833650 & 98.2106089764762 & 165.330096690825 \tabularnewline
91 & 123.887319052283 & 90.3695367839728 & 157.405101320592 \tabularnewline
92 & 130.841112342868 & 93.385530154248 & 168.296694531489 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41206&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]81[/C][C]142.136324689947[/C][C]124.722436441939[/C][C]159.550212937954[/C][/ROW]
[ROW][C]82[/C][C]137.371135600819[/C][C]118.188185783879[/C][C]156.554085417759[/C][/ROW]
[ROW][C]83[/C][C]143.141605675039[/C][C]121.884313834243[/C][C]164.398897515835[/C][/ROW]
[ROW][C]84[/C][C]124.117359846772[/C][C]102.392175413404[/C][C]145.842544280141[/C][/ROW]
[ROW][C]85[/C][C]92.0418734606554[/C][C]71.1085742980996[/C][C]112.975172623211[/C][/ROW]
[ROW][C]86[/C][C]122.651450473787[/C][C]96.6429781166018[/C][C]148.659922830972[/C][/ROW]
[ROW][C]87[/C][C]137.486923677882[/C][C]107.826741531098[/C][C]167.147105824666[/C][/ROW]
[ROW][C]88[/C][C]118.012501193463[/C][C]89.772109282876[/C][C]146.252893104049[/C][/ROW]
[ROW][C]89[/C][C]139.307014715856[/C][C]105.863473255490[/C][C]172.750556176223[/C][/ROW]
[ROW][C]90[/C][C]131.770352833650[/C][C]98.2106089764762[/C][C]165.330096690825[/C][/ROW]
[ROW][C]91[/C][C]123.887319052283[/C][C]90.3695367839728[/C][C]157.405101320592[/C][/ROW]
[ROW][C]92[/C][C]130.841112342868[/C][C]93.385530154248[/C][C]168.296694531489[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41206&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41206&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
81142.136324689947124.722436441939159.550212937954
82137.371135600819118.188185783879156.554085417759
83143.141605675039121.884313834243164.398897515835
84124.117359846772102.392175413404145.842544280141
8592.041873460655471.1085742980996112.975172623211
86122.65145047378796.6429781166018148.659922830972
87137.486923677882107.826741531098167.147105824666
88118.01250119346389.772109282876146.252893104049
89139.307014715856105.863473255490172.750556176223
90131.77035283365098.2106089764762165.330096690825
91123.88731905228390.3695367839728157.405101320592
92130.84111234286893.385530154248168.296694531489



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')