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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 06:44:06 +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/2011/May/19/t13057873493bb371fsdtvrjf1.htm/, Retrieved Sat, 11 May 2024 11:25:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121942, Retrieved Sat, 11 May 2024 11:25:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact124
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Oefening 10; Eige...] [2011-05-19 06:44:06] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
190,2
180,7
193,6
192,8
195,5
197,2
196,9
178,9
172,4
156,4
143,7
153,6
168,8
185,8
199,9
205,4
197,5
199,6
200,5
193,7
179,6
169,1
169,8
195,5
194,8
204,5
203,8
204,8
204,9
240
248,3
258,4
254,9
288,3
333,6
346,3
357,5
490,7
468,2
471,2
517,1
609,2
682
614
554,2
406,8
348,6
298,8
313,7
282,1
232,9
239,3
241,9
265,7
276
271,5
254,6
269,9
293,5
306,1
365,4
347,9
352,1
377,9
377,4
372,2
362,5
341,9
354,8
369,2
406,7
454,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121942&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121942&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121942&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121942&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121942&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121942&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
alpha1
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13168.8166.5279113247862.27208867521364
14185.8185.7334353146850.0665646853146598
15199.9199.6834353146850.216564685314694
16205.4205.2709353146850.12906468531466
17197.5196.5834353146850.916564685314682
18199.6197.4667686480192.13323135198135
19200.5206.187601981352-5.68760198135203
20193.7183.8792686480199.82073135198132
21179.6187.425101981352-7.82510198135199
22169.1163.5126019813525.58739801864803
23169.8156.49176864801913.3082313519814
24195.5180.21676864801915.2832313519813
25194.8211.150101981352-16.350101981352
26204.5211.733435314685-7.23343531468535
27203.8218.383435314685-14.5834353146853
28204.8209.170935314685-4.37093531468534
29204.9195.9834353146858.91656468531468
30240204.86676864801935.1332313519814
31248.3246.5876019813521.71239801864797
32258.4231.67926864801926.7207313519813
33254.9252.1251019813522.77489801864806
34288.3238.81260198135249.4873980186481
35333.6275.69176864801957.9082313519814
36346.3344.0167686480192.28323135198133
37357.5361.950101981352-4.45010198135196
38490.7374.433435314685116.266564685315
39468.2504.583435314685-36.3834353146853
40471.2473.570935314685-2.37093531468537
41517.1462.38343531468554.7165646853147
42609.2517.06676864801992.1332313519814
43682615.78760198135266.212398018648
44614665.379268648019-51.3792686480188
45554.2607.725101981352-53.5251019813519
46406.8538.112601981352-131.312601981352
47348.6394.191768648019-45.5917686480186
48298.8359.016768648019-60.2167686480187
49313.7314.450101981352-0.750101981351975
50282.1330.633435314685-48.5334353146853
51232.9295.983435314685-63.0834353146853
52239.3238.2709353146851.02906468531467
53241.9230.48343531468511.4165646853147
54265.7241.86676864801923.8332313519813
55276272.2876019813523.71239801864795
56271.5259.37926864801912.1207313519814
57254.6265.225101981352-10.6251019813519
58269.9238.51260198135231.387398018648
59293.5257.29176864801936.2082313519815
60306.1303.9167686480192.18323135198136
61365.4321.75010198135243.649898018648
62347.9382.333435314685-34.4334353146853
63352.1361.783435314685-9.6834353146852
64377.9357.47093531468520.4290646853146
65377.4369.0834353146858.31656468531475
66372.2377.366768648019-5.1667686480186
67362.5378.787601981352-16.287601981352
68341.9345.879268648019-3.97926864801866
69354.8335.62510198135219.1748980186481
70369.2338.71260198135230.487398018648
71406.7356.59176864801950.1082313519814
72454.7417.11676864801937.5832313519813

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 168.8 & 166.527911324786 & 2.27208867521364 \tabularnewline
14 & 185.8 & 185.733435314685 & 0.0665646853146598 \tabularnewline
15 & 199.9 & 199.683435314685 & 0.216564685314694 \tabularnewline
16 & 205.4 & 205.270935314685 & 0.12906468531466 \tabularnewline
17 & 197.5 & 196.583435314685 & 0.916564685314682 \tabularnewline
18 & 199.6 & 197.466768648019 & 2.13323135198135 \tabularnewline
19 & 200.5 & 206.187601981352 & -5.68760198135203 \tabularnewline
20 & 193.7 & 183.879268648019 & 9.82073135198132 \tabularnewline
21 & 179.6 & 187.425101981352 & -7.82510198135199 \tabularnewline
22 & 169.1 & 163.512601981352 & 5.58739801864803 \tabularnewline
23 & 169.8 & 156.491768648019 & 13.3082313519814 \tabularnewline
24 & 195.5 & 180.216768648019 & 15.2832313519813 \tabularnewline
25 & 194.8 & 211.150101981352 & -16.350101981352 \tabularnewline
26 & 204.5 & 211.733435314685 & -7.23343531468535 \tabularnewline
27 & 203.8 & 218.383435314685 & -14.5834353146853 \tabularnewline
28 & 204.8 & 209.170935314685 & -4.37093531468534 \tabularnewline
29 & 204.9 & 195.983435314685 & 8.91656468531468 \tabularnewline
30 & 240 & 204.866768648019 & 35.1332313519814 \tabularnewline
31 & 248.3 & 246.587601981352 & 1.71239801864797 \tabularnewline
32 & 258.4 & 231.679268648019 & 26.7207313519813 \tabularnewline
33 & 254.9 & 252.125101981352 & 2.77489801864806 \tabularnewline
34 & 288.3 & 238.812601981352 & 49.4873980186481 \tabularnewline
35 & 333.6 & 275.691768648019 & 57.9082313519814 \tabularnewline
36 & 346.3 & 344.016768648019 & 2.28323135198133 \tabularnewline
37 & 357.5 & 361.950101981352 & -4.45010198135196 \tabularnewline
38 & 490.7 & 374.433435314685 & 116.266564685315 \tabularnewline
39 & 468.2 & 504.583435314685 & -36.3834353146853 \tabularnewline
40 & 471.2 & 473.570935314685 & -2.37093531468537 \tabularnewline
41 & 517.1 & 462.383435314685 & 54.7165646853147 \tabularnewline
42 & 609.2 & 517.066768648019 & 92.1332313519814 \tabularnewline
43 & 682 & 615.787601981352 & 66.212398018648 \tabularnewline
44 & 614 & 665.379268648019 & -51.3792686480188 \tabularnewline
45 & 554.2 & 607.725101981352 & -53.5251019813519 \tabularnewline
46 & 406.8 & 538.112601981352 & -131.312601981352 \tabularnewline
47 & 348.6 & 394.191768648019 & -45.5917686480186 \tabularnewline
48 & 298.8 & 359.016768648019 & -60.2167686480187 \tabularnewline
49 & 313.7 & 314.450101981352 & -0.750101981351975 \tabularnewline
50 & 282.1 & 330.633435314685 & -48.5334353146853 \tabularnewline
51 & 232.9 & 295.983435314685 & -63.0834353146853 \tabularnewline
52 & 239.3 & 238.270935314685 & 1.02906468531467 \tabularnewline
53 & 241.9 & 230.483435314685 & 11.4165646853147 \tabularnewline
54 & 265.7 & 241.866768648019 & 23.8332313519813 \tabularnewline
55 & 276 & 272.287601981352 & 3.71239801864795 \tabularnewline
56 & 271.5 & 259.379268648019 & 12.1207313519814 \tabularnewline
57 & 254.6 & 265.225101981352 & -10.6251019813519 \tabularnewline
58 & 269.9 & 238.512601981352 & 31.387398018648 \tabularnewline
59 & 293.5 & 257.291768648019 & 36.2082313519815 \tabularnewline
60 & 306.1 & 303.916768648019 & 2.18323135198136 \tabularnewline
61 & 365.4 & 321.750101981352 & 43.649898018648 \tabularnewline
62 & 347.9 & 382.333435314685 & -34.4334353146853 \tabularnewline
63 & 352.1 & 361.783435314685 & -9.6834353146852 \tabularnewline
64 & 377.9 & 357.470935314685 & 20.4290646853146 \tabularnewline
65 & 377.4 & 369.083435314685 & 8.31656468531475 \tabularnewline
66 & 372.2 & 377.366768648019 & -5.1667686480186 \tabularnewline
67 & 362.5 & 378.787601981352 & -16.287601981352 \tabularnewline
68 & 341.9 & 345.879268648019 & -3.97926864801866 \tabularnewline
69 & 354.8 & 335.625101981352 & 19.1748980186481 \tabularnewline
70 & 369.2 & 338.712601981352 & 30.487398018648 \tabularnewline
71 & 406.7 & 356.591768648019 & 50.1082313519814 \tabularnewline
72 & 454.7 & 417.116768648019 & 37.5832313519813 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121942&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]168.8[/C][C]166.527911324786[/C][C]2.27208867521364[/C][/ROW]
[ROW][C]14[/C][C]185.8[/C][C]185.733435314685[/C][C]0.0665646853146598[/C][/ROW]
[ROW][C]15[/C][C]199.9[/C][C]199.683435314685[/C][C]0.216564685314694[/C][/ROW]
[ROW][C]16[/C][C]205.4[/C][C]205.270935314685[/C][C]0.12906468531466[/C][/ROW]
[ROW][C]17[/C][C]197.5[/C][C]196.583435314685[/C][C]0.916564685314682[/C][/ROW]
[ROW][C]18[/C][C]199.6[/C][C]197.466768648019[/C][C]2.13323135198135[/C][/ROW]
[ROW][C]19[/C][C]200.5[/C][C]206.187601981352[/C][C]-5.68760198135203[/C][/ROW]
[ROW][C]20[/C][C]193.7[/C][C]183.879268648019[/C][C]9.82073135198132[/C][/ROW]
[ROW][C]21[/C][C]179.6[/C][C]187.425101981352[/C][C]-7.82510198135199[/C][/ROW]
[ROW][C]22[/C][C]169.1[/C][C]163.512601981352[/C][C]5.58739801864803[/C][/ROW]
[ROW][C]23[/C][C]169.8[/C][C]156.491768648019[/C][C]13.3082313519814[/C][/ROW]
[ROW][C]24[/C][C]195.5[/C][C]180.216768648019[/C][C]15.2832313519813[/C][/ROW]
[ROW][C]25[/C][C]194.8[/C][C]211.150101981352[/C][C]-16.350101981352[/C][/ROW]
[ROW][C]26[/C][C]204.5[/C][C]211.733435314685[/C][C]-7.23343531468535[/C][/ROW]
[ROW][C]27[/C][C]203.8[/C][C]218.383435314685[/C][C]-14.5834353146853[/C][/ROW]
[ROW][C]28[/C][C]204.8[/C][C]209.170935314685[/C][C]-4.37093531468534[/C][/ROW]
[ROW][C]29[/C][C]204.9[/C][C]195.983435314685[/C][C]8.91656468531468[/C][/ROW]
[ROW][C]30[/C][C]240[/C][C]204.866768648019[/C][C]35.1332313519814[/C][/ROW]
[ROW][C]31[/C][C]248.3[/C][C]246.587601981352[/C][C]1.71239801864797[/C][/ROW]
[ROW][C]32[/C][C]258.4[/C][C]231.679268648019[/C][C]26.7207313519813[/C][/ROW]
[ROW][C]33[/C][C]254.9[/C][C]252.125101981352[/C][C]2.77489801864806[/C][/ROW]
[ROW][C]34[/C][C]288.3[/C][C]238.812601981352[/C][C]49.4873980186481[/C][/ROW]
[ROW][C]35[/C][C]333.6[/C][C]275.691768648019[/C][C]57.9082313519814[/C][/ROW]
[ROW][C]36[/C][C]346.3[/C][C]344.016768648019[/C][C]2.28323135198133[/C][/ROW]
[ROW][C]37[/C][C]357.5[/C][C]361.950101981352[/C][C]-4.45010198135196[/C][/ROW]
[ROW][C]38[/C][C]490.7[/C][C]374.433435314685[/C][C]116.266564685315[/C][/ROW]
[ROW][C]39[/C][C]468.2[/C][C]504.583435314685[/C][C]-36.3834353146853[/C][/ROW]
[ROW][C]40[/C][C]471.2[/C][C]473.570935314685[/C][C]-2.37093531468537[/C][/ROW]
[ROW][C]41[/C][C]517.1[/C][C]462.383435314685[/C][C]54.7165646853147[/C][/ROW]
[ROW][C]42[/C][C]609.2[/C][C]517.066768648019[/C][C]92.1332313519814[/C][/ROW]
[ROW][C]43[/C][C]682[/C][C]615.787601981352[/C][C]66.212398018648[/C][/ROW]
[ROW][C]44[/C][C]614[/C][C]665.379268648019[/C][C]-51.3792686480188[/C][/ROW]
[ROW][C]45[/C][C]554.2[/C][C]607.725101981352[/C][C]-53.5251019813519[/C][/ROW]
[ROW][C]46[/C][C]406.8[/C][C]538.112601981352[/C][C]-131.312601981352[/C][/ROW]
[ROW][C]47[/C][C]348.6[/C][C]394.191768648019[/C][C]-45.5917686480186[/C][/ROW]
[ROW][C]48[/C][C]298.8[/C][C]359.016768648019[/C][C]-60.2167686480187[/C][/ROW]
[ROW][C]49[/C][C]313.7[/C][C]314.450101981352[/C][C]-0.750101981351975[/C][/ROW]
[ROW][C]50[/C][C]282.1[/C][C]330.633435314685[/C][C]-48.5334353146853[/C][/ROW]
[ROW][C]51[/C][C]232.9[/C][C]295.983435314685[/C][C]-63.0834353146853[/C][/ROW]
[ROW][C]52[/C][C]239.3[/C][C]238.270935314685[/C][C]1.02906468531467[/C][/ROW]
[ROW][C]53[/C][C]241.9[/C][C]230.483435314685[/C][C]11.4165646853147[/C][/ROW]
[ROW][C]54[/C][C]265.7[/C][C]241.866768648019[/C][C]23.8332313519813[/C][/ROW]
[ROW][C]55[/C][C]276[/C][C]272.287601981352[/C][C]3.71239801864795[/C][/ROW]
[ROW][C]56[/C][C]271.5[/C][C]259.379268648019[/C][C]12.1207313519814[/C][/ROW]
[ROW][C]57[/C][C]254.6[/C][C]265.225101981352[/C][C]-10.6251019813519[/C][/ROW]
[ROW][C]58[/C][C]269.9[/C][C]238.512601981352[/C][C]31.387398018648[/C][/ROW]
[ROW][C]59[/C][C]293.5[/C][C]257.291768648019[/C][C]36.2082313519815[/C][/ROW]
[ROW][C]60[/C][C]306.1[/C][C]303.916768648019[/C][C]2.18323135198136[/C][/ROW]
[ROW][C]61[/C][C]365.4[/C][C]321.750101981352[/C][C]43.649898018648[/C][/ROW]
[ROW][C]62[/C][C]347.9[/C][C]382.333435314685[/C][C]-34.4334353146853[/C][/ROW]
[ROW][C]63[/C][C]352.1[/C][C]361.783435314685[/C][C]-9.6834353146852[/C][/ROW]
[ROW][C]64[/C][C]377.9[/C][C]357.470935314685[/C][C]20.4290646853146[/C][/ROW]
[ROW][C]65[/C][C]377.4[/C][C]369.083435314685[/C][C]8.31656468531475[/C][/ROW]
[ROW][C]66[/C][C]372.2[/C][C]377.366768648019[/C][C]-5.1667686480186[/C][/ROW]
[ROW][C]67[/C][C]362.5[/C][C]378.787601981352[/C][C]-16.287601981352[/C][/ROW]
[ROW][C]68[/C][C]341.9[/C][C]345.879268648019[/C][C]-3.97926864801866[/C][/ROW]
[ROW][C]69[/C][C]354.8[/C][C]335.625101981352[/C][C]19.1748980186481[/C][/ROW]
[ROW][C]70[/C][C]369.2[/C][C]338.712601981352[/C][C]30.487398018648[/C][/ROW]
[ROW][C]71[/C][C]406.7[/C][C]356.591768648019[/C][C]50.1082313519814[/C][/ROW]
[ROW][C]72[/C][C]454.7[/C][C]417.116768648019[/C][C]37.5832313519813[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121942&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121942&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
13168.8166.5279113247862.27208867521364
14185.8185.7334353146850.0665646853146598
15199.9199.6834353146850.216564685314694
16205.4205.2709353146850.12906468531466
17197.5196.5834353146850.916564685314682
18199.6197.4667686480192.13323135198135
19200.5206.187601981352-5.68760198135203
20193.7183.8792686480199.82073135198132
21179.6187.425101981352-7.82510198135199
22169.1163.5126019813525.58739801864803
23169.8156.49176864801913.3082313519814
24195.5180.21676864801915.2832313519813
25194.8211.150101981352-16.350101981352
26204.5211.733435314685-7.23343531468535
27203.8218.383435314685-14.5834353146853
28204.8209.170935314685-4.37093531468534
29204.9195.9834353146858.91656468531468
30240204.86676864801935.1332313519814
31248.3246.5876019813521.71239801864797
32258.4231.67926864801926.7207313519813
33254.9252.1251019813522.77489801864806
34288.3238.81260198135249.4873980186481
35333.6275.69176864801957.9082313519814
36346.3344.0167686480192.28323135198133
37357.5361.950101981352-4.45010198135196
38490.7374.433435314685116.266564685315
39468.2504.583435314685-36.3834353146853
40471.2473.570935314685-2.37093531468537
41517.1462.38343531468554.7165646853147
42609.2517.06676864801992.1332313519814
43682615.78760198135266.212398018648
44614665.379268648019-51.3792686480188
45554.2607.725101981352-53.5251019813519
46406.8538.112601981352-131.312601981352
47348.6394.191768648019-45.5917686480186
48298.8359.016768648019-60.2167686480187
49313.7314.450101981352-0.750101981351975
50282.1330.633435314685-48.5334353146853
51232.9295.983435314685-63.0834353146853
52239.3238.2709353146851.02906468531467
53241.9230.48343531468511.4165646853147
54265.7241.86676864801923.8332313519813
55276272.2876019813523.71239801864795
56271.5259.37926864801912.1207313519814
57254.6265.225101981352-10.6251019813519
58269.9238.51260198135231.387398018648
59293.5257.29176864801936.2082313519815
60306.1303.9167686480192.18323135198136
61365.4321.75010198135243.649898018648
62347.9382.333435314685-34.4334353146853
63352.1361.783435314685-9.6834353146852
64377.9357.47093531468520.4290646853146
65377.4369.0834353146858.31656468531475
66372.2377.366768648019-5.1667686480186
67362.5378.787601981352-16.287601981352
68341.9345.879268648019-3.97926864801866
69354.8335.62510198135219.1748980186481
70369.2338.71260198135230.487398018648
71406.7356.59176864801950.1082313519814
72454.7417.11676864801937.5832313519813







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73470.350101981352395.567542889567545.132661073137
74487.283537296037381.525027999468593.042046592607
75501.166972610723371.639780743729630.694164477716
76506.537907925408356.972789741838656.103026108978
77497.721343240093330.502457579467664.94022890072
78497.688111888112314.509000453708680.867223322516
79504.275713869464306.419660107608702.131767631319
80487.654982517482276.137963924343699.172001110622
81481.380084498834257.032407223479705.72776177419
82465.292686480186228.809470494013701.77590246636
83452.684455128205204.658765758173700.710144498237
84463.101223776224204.046840042237722.155607510211

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 470.350101981352 & 395.567542889567 & 545.132661073137 \tabularnewline
74 & 487.283537296037 & 381.525027999468 & 593.042046592607 \tabularnewline
75 & 501.166972610723 & 371.639780743729 & 630.694164477716 \tabularnewline
76 & 506.537907925408 & 356.972789741838 & 656.103026108978 \tabularnewline
77 & 497.721343240093 & 330.502457579467 & 664.94022890072 \tabularnewline
78 & 497.688111888112 & 314.509000453708 & 680.867223322516 \tabularnewline
79 & 504.275713869464 & 306.419660107608 & 702.131767631319 \tabularnewline
80 & 487.654982517482 & 276.137963924343 & 699.172001110622 \tabularnewline
81 & 481.380084498834 & 257.032407223479 & 705.72776177419 \tabularnewline
82 & 465.292686480186 & 228.809470494013 & 701.77590246636 \tabularnewline
83 & 452.684455128205 & 204.658765758173 & 700.710144498237 \tabularnewline
84 & 463.101223776224 & 204.046840042237 & 722.155607510211 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121942&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]470.350101981352[/C][C]395.567542889567[/C][C]545.132661073137[/C][/ROW]
[ROW][C]74[/C][C]487.283537296037[/C][C]381.525027999468[/C][C]593.042046592607[/C][/ROW]
[ROW][C]75[/C][C]501.166972610723[/C][C]371.639780743729[/C][C]630.694164477716[/C][/ROW]
[ROW][C]76[/C][C]506.537907925408[/C][C]356.972789741838[/C][C]656.103026108978[/C][/ROW]
[ROW][C]77[/C][C]497.721343240093[/C][C]330.502457579467[/C][C]664.94022890072[/C][/ROW]
[ROW][C]78[/C][C]497.688111888112[/C][C]314.509000453708[/C][C]680.867223322516[/C][/ROW]
[ROW][C]79[/C][C]504.275713869464[/C][C]306.419660107608[/C][C]702.131767631319[/C][/ROW]
[ROW][C]80[/C][C]487.654982517482[/C][C]276.137963924343[/C][C]699.172001110622[/C][/ROW]
[ROW][C]81[/C][C]481.380084498834[/C][C]257.032407223479[/C][C]705.72776177419[/C][/ROW]
[ROW][C]82[/C][C]465.292686480186[/C][C]228.809470494013[/C][C]701.77590246636[/C][/ROW]
[ROW][C]83[/C][C]452.684455128205[/C][C]204.658765758173[/C][C]700.710144498237[/C][/ROW]
[ROW][C]84[/C][C]463.101223776224[/C][C]204.046840042237[/C][C]722.155607510211[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121942&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121942&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
73470.350101981352395.567542889567545.132661073137
74487.283537296037381.525027999468593.042046592607
75501.166972610723371.639780743729630.694164477716
76506.537907925408356.972789741838656.103026108978
77497.721343240093330.502457579467664.94022890072
78497.688111888112314.509000453708680.867223322516
79504.275713869464306.419660107608702.131767631319
80487.654982517482276.137963924343699.172001110622
81481.380084498834257.032407223479705.72776177419
82465.292686480186228.809470494013701.77590246636
83452.684455128205204.658765758173700.710144498237
84463.101223776224204.046840042237722.155607510211



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')