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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 Apr 2016 13:52:44 +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/26/t1461675188s9ern6xqcwcinpl.htm/, Retrieved Fri, 03 May 2024 17:46:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294874, Retrieved Fri, 03 May 2024 17:46:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 12:52:44] [4661a511bc27dc3517a7b8e15be46886] [Current]
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Dataseries X:
17887
17118
15945
15085
14027
15158
23783
25166
21839
18522
16850
16679
17806
17542
16380
15434
14478
15506
22357
27204
24182
20760
18731
18377
18775
18943
17974
17192
1604
17101
25972
28139
26131
22600
20320
19662
20440
19694
18260
16832
15539
16676
25216
26994
24865
21793
19505
18696
19221
18742
17633
16379
15007
15762
24146
25720
23731
20542
18807
18459




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294874&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294874&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294874&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294874&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]0.999933893038648[/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=294874&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294874&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21711817887-769
31594517118.0508362533-1173.05083625328
41508515945.0775468263-860.077546826296
51402715085.0568571131-1058.05685711315
61515814027.06994492381130.93005507624
72378315157.92523765068625.07476234944
82516623782.4298225161383.57017748397
92183925165.9085363797-3326.90853637975
101852221839.219931814-3317.21993181403
111685018522.2192913298-1672.21929132983
121667916850.1105453361-171.110545336061
131780616679.01131159821126.98868840179
141754217805.9254982023-263.92549820233
151638017542.0174473127-1162.01744731271
161543416380.0768174425-946.076817442479
171447815434.0625422636-956.062542263608
181550614478.06320238951027.93679761047
192235715505.93204622186851.06795377815
202720422356.54709671564847.45290328444
212418227203.6795496183-3021.67954961827
222076024182.1997540532-3422.19975405321
231873120760.2262312269-2029.22623122688
241837718731.13414598-354.134145980042
251877518377.0234107323397.976589267695
261894318774.973690977168.026309023004
271797418942.9888922913-968.988892291283
281719217974.0640569113-782.064056911251
29160417192.0516998784-15588.0516998784
30171011605.0304787312815495.9695212687
312597217099.97560854188872.02439145825
322813925971.41349742642167.58650257356
332613128138.8567074428-2007.85670744285
342260026131.1327333058-3531.13273330576
352032022600.2334324551-2280.23343245513
361966220320.1507393034-658.150739303393
372044019662.0435083455777.956491654513
381969420439.9485716603-745.948571660272
391826019694.0493123934-1434.0493123934
401683218260.0948006425-1428.09480064247
411553916832.0944070078-1293.09440700779
421667615539.0854825421136.91451745801
432521616675.92484203598540.07515796407
442699425215.43544158161778.56455841841
452486526993.8824245015-2128.88242450147
462179324865.1407339482-3072.14073394816
471950521793.2030898888-2288.20308988877
481869619505.1512661532-809.151266153229
491922118696.0534905315524.946509468522
501874219220.9652973814-478.965297381386
511763318742.0316629404-1109.0316629404
521637917633.0733147133-1254.07331471328
531500716379.0829029761-1372.08290297615
541576215007.0907042314754.909295768563
552414615761.95009524048384.04990475964
562572024145.4457559371574.55424406303
572373125719.8959110034-1988.89591100344
582054223731.1314798651-3189.13147986512
591880720542.2108237915-1735.21082379149
601845918807.1147095149-348.114709514866

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 17118 & 17887 & -769 \tabularnewline
3 & 15945 & 17118.0508362533 & -1173.05083625328 \tabularnewline
4 & 15085 & 15945.0775468263 & -860.077546826296 \tabularnewline
5 & 14027 & 15085.0568571131 & -1058.05685711315 \tabularnewline
6 & 15158 & 14027.0699449238 & 1130.93005507624 \tabularnewline
7 & 23783 & 15157.9252376506 & 8625.07476234944 \tabularnewline
8 & 25166 & 23782.429822516 & 1383.57017748397 \tabularnewline
9 & 21839 & 25165.9085363797 & -3326.90853637975 \tabularnewline
10 & 18522 & 21839.219931814 & -3317.21993181403 \tabularnewline
11 & 16850 & 18522.2192913298 & -1672.21929132983 \tabularnewline
12 & 16679 & 16850.1105453361 & -171.110545336061 \tabularnewline
13 & 17806 & 16679.0113115982 & 1126.98868840179 \tabularnewline
14 & 17542 & 17805.9254982023 & -263.92549820233 \tabularnewline
15 & 16380 & 17542.0174473127 & -1162.01744731271 \tabularnewline
16 & 15434 & 16380.0768174425 & -946.076817442479 \tabularnewline
17 & 14478 & 15434.0625422636 & -956.062542263608 \tabularnewline
18 & 15506 & 14478.0632023895 & 1027.93679761047 \tabularnewline
19 & 22357 & 15505.9320462218 & 6851.06795377815 \tabularnewline
20 & 27204 & 22356.5470967156 & 4847.45290328444 \tabularnewline
21 & 24182 & 27203.6795496183 & -3021.67954961827 \tabularnewline
22 & 20760 & 24182.1997540532 & -3422.19975405321 \tabularnewline
23 & 18731 & 20760.2262312269 & -2029.22623122688 \tabularnewline
24 & 18377 & 18731.13414598 & -354.134145980042 \tabularnewline
25 & 18775 & 18377.0234107323 & 397.976589267695 \tabularnewline
26 & 18943 & 18774.973690977 & 168.026309023004 \tabularnewline
27 & 17974 & 18942.9888922913 & -968.988892291283 \tabularnewline
28 & 17192 & 17974.0640569113 & -782.064056911251 \tabularnewline
29 & 1604 & 17192.0516998784 & -15588.0516998784 \tabularnewline
30 & 17101 & 1605.03047873128 & 15495.9695212687 \tabularnewline
31 & 25972 & 17099.9756085418 & 8872.02439145825 \tabularnewline
32 & 28139 & 25971.4134974264 & 2167.58650257356 \tabularnewline
33 & 26131 & 28138.8567074428 & -2007.85670744285 \tabularnewline
34 & 22600 & 26131.1327333058 & -3531.13273330576 \tabularnewline
35 & 20320 & 22600.2334324551 & -2280.23343245513 \tabularnewline
36 & 19662 & 20320.1507393034 & -658.150739303393 \tabularnewline
37 & 20440 & 19662.0435083455 & 777.956491654513 \tabularnewline
38 & 19694 & 20439.9485716603 & -745.948571660272 \tabularnewline
39 & 18260 & 19694.0493123934 & -1434.0493123934 \tabularnewline
40 & 16832 & 18260.0948006425 & -1428.09480064247 \tabularnewline
41 & 15539 & 16832.0944070078 & -1293.09440700779 \tabularnewline
42 & 16676 & 15539.085482542 & 1136.91451745801 \tabularnewline
43 & 25216 & 16675.9248420359 & 8540.07515796407 \tabularnewline
44 & 26994 & 25215.4354415816 & 1778.56455841841 \tabularnewline
45 & 24865 & 26993.8824245015 & -2128.88242450147 \tabularnewline
46 & 21793 & 24865.1407339482 & -3072.14073394816 \tabularnewline
47 & 19505 & 21793.2030898888 & -2288.20308988877 \tabularnewline
48 & 18696 & 19505.1512661532 & -809.151266153229 \tabularnewline
49 & 19221 & 18696.0534905315 & 524.946509468522 \tabularnewline
50 & 18742 & 19220.9652973814 & -478.965297381386 \tabularnewline
51 & 17633 & 18742.0316629404 & -1109.0316629404 \tabularnewline
52 & 16379 & 17633.0733147133 & -1254.07331471328 \tabularnewline
53 & 15007 & 16379.0829029761 & -1372.08290297615 \tabularnewline
54 & 15762 & 15007.0907042314 & 754.909295768563 \tabularnewline
55 & 24146 & 15761.9500952404 & 8384.04990475964 \tabularnewline
56 & 25720 & 24145.445755937 & 1574.55424406303 \tabularnewline
57 & 23731 & 25719.8959110034 & -1988.89591100344 \tabularnewline
58 & 20542 & 23731.1314798651 & -3189.13147986512 \tabularnewline
59 & 18807 & 20542.2108237915 & -1735.21082379149 \tabularnewline
60 & 18459 & 18807.1147095149 & -348.114709514866 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294874&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]17118[/C][C]17887[/C][C]-769[/C][/ROW]
[ROW][C]3[/C][C]15945[/C][C]17118.0508362533[/C][C]-1173.05083625328[/C][/ROW]
[ROW][C]4[/C][C]15085[/C][C]15945.0775468263[/C][C]-860.077546826296[/C][/ROW]
[ROW][C]5[/C][C]14027[/C][C]15085.0568571131[/C][C]-1058.05685711315[/C][/ROW]
[ROW][C]6[/C][C]15158[/C][C]14027.0699449238[/C][C]1130.93005507624[/C][/ROW]
[ROW][C]7[/C][C]23783[/C][C]15157.9252376506[/C][C]8625.07476234944[/C][/ROW]
[ROW][C]8[/C][C]25166[/C][C]23782.429822516[/C][C]1383.57017748397[/C][/ROW]
[ROW][C]9[/C][C]21839[/C][C]25165.9085363797[/C][C]-3326.90853637975[/C][/ROW]
[ROW][C]10[/C][C]18522[/C][C]21839.219931814[/C][C]-3317.21993181403[/C][/ROW]
[ROW][C]11[/C][C]16850[/C][C]18522.2192913298[/C][C]-1672.21929132983[/C][/ROW]
[ROW][C]12[/C][C]16679[/C][C]16850.1105453361[/C][C]-171.110545336061[/C][/ROW]
[ROW][C]13[/C][C]17806[/C][C]16679.0113115982[/C][C]1126.98868840179[/C][/ROW]
[ROW][C]14[/C][C]17542[/C][C]17805.9254982023[/C][C]-263.92549820233[/C][/ROW]
[ROW][C]15[/C][C]16380[/C][C]17542.0174473127[/C][C]-1162.01744731271[/C][/ROW]
[ROW][C]16[/C][C]15434[/C][C]16380.0768174425[/C][C]-946.076817442479[/C][/ROW]
[ROW][C]17[/C][C]14478[/C][C]15434.0625422636[/C][C]-956.062542263608[/C][/ROW]
[ROW][C]18[/C][C]15506[/C][C]14478.0632023895[/C][C]1027.93679761047[/C][/ROW]
[ROW][C]19[/C][C]22357[/C][C]15505.9320462218[/C][C]6851.06795377815[/C][/ROW]
[ROW][C]20[/C][C]27204[/C][C]22356.5470967156[/C][C]4847.45290328444[/C][/ROW]
[ROW][C]21[/C][C]24182[/C][C]27203.6795496183[/C][C]-3021.67954961827[/C][/ROW]
[ROW][C]22[/C][C]20760[/C][C]24182.1997540532[/C][C]-3422.19975405321[/C][/ROW]
[ROW][C]23[/C][C]18731[/C][C]20760.2262312269[/C][C]-2029.22623122688[/C][/ROW]
[ROW][C]24[/C][C]18377[/C][C]18731.13414598[/C][C]-354.134145980042[/C][/ROW]
[ROW][C]25[/C][C]18775[/C][C]18377.0234107323[/C][C]397.976589267695[/C][/ROW]
[ROW][C]26[/C][C]18943[/C][C]18774.973690977[/C][C]168.026309023004[/C][/ROW]
[ROW][C]27[/C][C]17974[/C][C]18942.9888922913[/C][C]-968.988892291283[/C][/ROW]
[ROW][C]28[/C][C]17192[/C][C]17974.0640569113[/C][C]-782.064056911251[/C][/ROW]
[ROW][C]29[/C][C]1604[/C][C]17192.0516998784[/C][C]-15588.0516998784[/C][/ROW]
[ROW][C]30[/C][C]17101[/C][C]1605.03047873128[/C][C]15495.9695212687[/C][/ROW]
[ROW][C]31[/C][C]25972[/C][C]17099.9756085418[/C][C]8872.02439145825[/C][/ROW]
[ROW][C]32[/C][C]28139[/C][C]25971.4134974264[/C][C]2167.58650257356[/C][/ROW]
[ROW][C]33[/C][C]26131[/C][C]28138.8567074428[/C][C]-2007.85670744285[/C][/ROW]
[ROW][C]34[/C][C]22600[/C][C]26131.1327333058[/C][C]-3531.13273330576[/C][/ROW]
[ROW][C]35[/C][C]20320[/C][C]22600.2334324551[/C][C]-2280.23343245513[/C][/ROW]
[ROW][C]36[/C][C]19662[/C][C]20320.1507393034[/C][C]-658.150739303393[/C][/ROW]
[ROW][C]37[/C][C]20440[/C][C]19662.0435083455[/C][C]777.956491654513[/C][/ROW]
[ROW][C]38[/C][C]19694[/C][C]20439.9485716603[/C][C]-745.948571660272[/C][/ROW]
[ROW][C]39[/C][C]18260[/C][C]19694.0493123934[/C][C]-1434.0493123934[/C][/ROW]
[ROW][C]40[/C][C]16832[/C][C]18260.0948006425[/C][C]-1428.09480064247[/C][/ROW]
[ROW][C]41[/C][C]15539[/C][C]16832.0944070078[/C][C]-1293.09440700779[/C][/ROW]
[ROW][C]42[/C][C]16676[/C][C]15539.085482542[/C][C]1136.91451745801[/C][/ROW]
[ROW][C]43[/C][C]25216[/C][C]16675.9248420359[/C][C]8540.07515796407[/C][/ROW]
[ROW][C]44[/C][C]26994[/C][C]25215.4354415816[/C][C]1778.56455841841[/C][/ROW]
[ROW][C]45[/C][C]24865[/C][C]26993.8824245015[/C][C]-2128.88242450147[/C][/ROW]
[ROW][C]46[/C][C]21793[/C][C]24865.1407339482[/C][C]-3072.14073394816[/C][/ROW]
[ROW][C]47[/C][C]19505[/C][C]21793.2030898888[/C][C]-2288.20308988877[/C][/ROW]
[ROW][C]48[/C][C]18696[/C][C]19505.1512661532[/C][C]-809.151266153229[/C][/ROW]
[ROW][C]49[/C][C]19221[/C][C]18696.0534905315[/C][C]524.946509468522[/C][/ROW]
[ROW][C]50[/C][C]18742[/C][C]19220.9652973814[/C][C]-478.965297381386[/C][/ROW]
[ROW][C]51[/C][C]17633[/C][C]18742.0316629404[/C][C]-1109.0316629404[/C][/ROW]
[ROW][C]52[/C][C]16379[/C][C]17633.0733147133[/C][C]-1254.07331471328[/C][/ROW]
[ROW][C]53[/C][C]15007[/C][C]16379.0829029761[/C][C]-1372.08290297615[/C][/ROW]
[ROW][C]54[/C][C]15762[/C][C]15007.0907042314[/C][C]754.909295768563[/C][/ROW]
[ROW][C]55[/C][C]24146[/C][C]15761.9500952404[/C][C]8384.04990475964[/C][/ROW]
[ROW][C]56[/C][C]25720[/C][C]24145.445755937[/C][C]1574.55424406303[/C][/ROW]
[ROW][C]57[/C][C]23731[/C][C]25719.8959110034[/C][C]-1988.89591100344[/C][/ROW]
[ROW][C]58[/C][C]20542[/C][C]23731.1314798651[/C][C]-3189.13147986512[/C][/ROW]
[ROW][C]59[/C][C]18807[/C][C]20542.2108237915[/C][C]-1735.21082379149[/C][/ROW]
[ROW][C]60[/C][C]18459[/C][C]18807.1147095149[/C][C]-348.114709514866[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294874&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294874&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
21711817887-769
31594517118.0508362533-1173.05083625328
41508515945.0775468263-860.077546826296
51402715085.0568571131-1058.05685711315
61515814027.06994492381130.93005507624
72378315157.92523765068625.07476234944
82516623782.4298225161383.57017748397
92183925165.9085363797-3326.90853637975
101852221839.219931814-3317.21993181403
111685018522.2192913298-1672.21929132983
121667916850.1105453361-171.110545336061
131780616679.01131159821126.98868840179
141754217805.9254982023-263.92549820233
151638017542.0174473127-1162.01744731271
161543416380.0768174425-946.076817442479
171447815434.0625422636-956.062542263608
181550614478.06320238951027.93679761047
192235715505.93204622186851.06795377815
202720422356.54709671564847.45290328444
212418227203.6795496183-3021.67954961827
222076024182.1997540532-3422.19975405321
231873120760.2262312269-2029.22623122688
241837718731.13414598-354.134145980042
251877518377.0234107323397.976589267695
261894318774.973690977168.026309023004
271797418942.9888922913-968.988892291283
281719217974.0640569113-782.064056911251
29160417192.0516998784-15588.0516998784
30171011605.0304787312815495.9695212687
312597217099.97560854188872.02439145825
322813925971.41349742642167.58650257356
332613128138.8567074428-2007.85670744285
342260026131.1327333058-3531.13273330576
352032022600.2334324551-2280.23343245513
361966220320.1507393034-658.150739303393
372044019662.0435083455777.956491654513
381969420439.9485716603-745.948571660272
391826019694.0493123934-1434.0493123934
401683218260.0948006425-1428.09480064247
411553916832.0944070078-1293.09440700779
421667615539.0854825421136.91451745801
432521616675.92484203598540.07515796407
442699425215.43544158161778.56455841841
452486526993.8824245015-2128.88242450147
462179324865.1407339482-3072.14073394816
471950521793.2030898888-2288.20308988877
481869619505.1512661532-809.151266153229
491922118696.0534905315524.946509468522
501874219220.9652973814-478.965297381386
511763318742.0316629404-1109.0316629404
521637917633.0733147133-1254.07331471328
531500716379.0829029761-1372.08290297615
541576215007.0907042314754.909295768563
552414615761.95009524048384.04990475964
562572024145.4457559371574.55424406303
572373125719.8959110034-1988.89591100344
582054223731.1314798651-3189.13147986512
591880720542.2108237915-1735.21082379149
601845918807.1147095149-348.114709514866







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6118459.023012805710329.90397313626588.1420524753
6218459.02301280576963.0926035527229954.9534220586
6318459.02301280574379.5963345757332538.4496910356
6418459.02301280572201.5910138422634716.455011769
6518459.0230128057282.72155144709936635.3244741642
6618459.0230128057-1452.0737532555138370.1197788668
6718459.0230128057-3047.3856609064139965.4316865177
6818459.0230128057-4532.2678090247741450.3138346361
6918459.0230128057-5926.9010678448542844.9470934562
7018459.0230128057-7245.9790856287444164.02511124
7118459.0230128057-8500.5944268722145418.6404524835
7218459.0230128057-9699.3649401125546617.4109657238

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 18459.0230128057 & 10329.903973136 & 26588.1420524753 \tabularnewline
62 & 18459.0230128057 & 6963.09260355272 & 29954.9534220586 \tabularnewline
63 & 18459.0230128057 & 4379.59633457573 & 32538.4496910356 \tabularnewline
64 & 18459.0230128057 & 2201.59101384226 & 34716.455011769 \tabularnewline
65 & 18459.0230128057 & 282.721551447099 & 36635.3244741642 \tabularnewline
66 & 18459.0230128057 & -1452.07375325551 & 38370.1197788668 \tabularnewline
67 & 18459.0230128057 & -3047.38566090641 & 39965.4316865177 \tabularnewline
68 & 18459.0230128057 & -4532.26780902477 & 41450.3138346361 \tabularnewline
69 & 18459.0230128057 & -5926.90106784485 & 42844.9470934562 \tabularnewline
70 & 18459.0230128057 & -7245.97908562874 & 44164.02511124 \tabularnewline
71 & 18459.0230128057 & -8500.59442687221 & 45418.6404524835 \tabularnewline
72 & 18459.0230128057 & -9699.36494011255 & 46617.4109657238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294874&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]61[/C][C]18459.0230128057[/C][C]10329.903973136[/C][C]26588.1420524753[/C][/ROW]
[ROW][C]62[/C][C]18459.0230128057[/C][C]6963.09260355272[/C][C]29954.9534220586[/C][/ROW]
[ROW][C]63[/C][C]18459.0230128057[/C][C]4379.59633457573[/C][C]32538.4496910356[/C][/ROW]
[ROW][C]64[/C][C]18459.0230128057[/C][C]2201.59101384226[/C][C]34716.455011769[/C][/ROW]
[ROW][C]65[/C][C]18459.0230128057[/C][C]282.721551447099[/C][C]36635.3244741642[/C][/ROW]
[ROW][C]66[/C][C]18459.0230128057[/C][C]-1452.07375325551[/C][C]38370.1197788668[/C][/ROW]
[ROW][C]67[/C][C]18459.0230128057[/C][C]-3047.38566090641[/C][C]39965.4316865177[/C][/ROW]
[ROW][C]68[/C][C]18459.0230128057[/C][C]-4532.26780902477[/C][C]41450.3138346361[/C][/ROW]
[ROW][C]69[/C][C]18459.0230128057[/C][C]-5926.90106784485[/C][C]42844.9470934562[/C][/ROW]
[ROW][C]70[/C][C]18459.0230128057[/C][C]-7245.97908562874[/C][C]44164.02511124[/C][/ROW]
[ROW][C]71[/C][C]18459.0230128057[/C][C]-8500.59442687221[/C][C]45418.6404524835[/C][/ROW]
[ROW][C]72[/C][C]18459.0230128057[/C][C]-9699.36494011255[/C][C]46617.4109657238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294874&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294874&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
6118459.023012805710329.90397313626588.1420524753
6218459.02301280576963.0926035527229954.9534220586
6318459.02301280574379.5963345757332538.4496910356
6418459.02301280572201.5910138422634716.455011769
6518459.0230128057282.72155144709936635.3244741642
6618459.0230128057-1452.0737532555138370.1197788668
6718459.0230128057-3047.3856609064139965.4316865177
6818459.0230128057-4532.2678090247741450.3138346361
6918459.0230128057-5926.9010678448542844.9470934562
7018459.0230128057-7245.9790856287444164.02511124
7118459.0230128057-8500.5944268722145418.6404524835
7218459.0230128057-9699.3649401125546617.4109657238



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')