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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 Nov 2011 12:17:18 -0500
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/Nov/28/t1322500660c4weegrmy70t11v.htm/, Retrieved Tue, 30 Apr 2024 13:16:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=147892, Retrieved Tue, 30 Apr 2024 13:16:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [ws8 smoothing] [2011-11-28 17:17:18] [cb05b01fd3da20a46af540a30bcf4c06] [Current]
- R  D      [Exponential Smoothing] [ws 8 smoothing si...] [2011-11-28 20:34:45] [620e5553455d245695b6e856984b13e0]
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Dataseries X:
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118




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=147892&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=147892&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147892&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
alpha0.536698164531748
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.536698164531748 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147892&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]0.536698164531748[/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=147892&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147892&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
alpha0.536698164531748
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21738220995-3613
3936719055.9095315468-9688.9095315468
43112413855.889569651517268.1104303485
52655123123.65274255113427.34725744895
63065124963.10372483685687.89627516318
72585928015.7872157639-2156.78721576386
82510026858.2434757779-1758.24347577786
92577825914.597429528-136.597429527963
102041825841.2858398205-5423.28583982055
111868822930.6182838578-4242.61828385784
122042420653.6128381025-229.612838102505
132477620530.380049344245.61995066004
141981422808.9964841586-2994.99648415858
151273821201.5873683316-8463.58736833163
163156616659.19556239414906.804437606
173011124659.65014309085451.34985690917
183001927585.37960551442433.62039448561
193193428891.49920440183042.50079559816
202582630524.4037969858-4698.40379698576
212683528002.7791029145-1167.77910291451
222020527376.0342018018-7171.03420180176
231778923527.3533079004-5738.35330790037
242052020447.589620115672.4103798844408
252251820486.45213809262031.54786190742
261557221576.7801467367-6004.78014673669
271150918354.0256635664-6845.02566356643
282544714680.312953757610766.6870462424
292409020458.77412956363631.22587043635
302778622407.6463892275378.35361077296
312619525294.1989003316900.801099668417
322051625777.6571971318-5261.6571971318
332275922953.7354370359-194.735437035903
341902822849.2212854094-3821.22128540945
351697120798.3788352606-3827.37883526055
362003618744.23163940861291.76836059144
372248519437.52134753823047.47865246183
381873021073.0975467641-2343.09754676412
391453819815.561394097-5277.56139409697
402756116983.103880681510577.8961193185
412598522660.24131252723324.75868747276
423467024444.633197604910225.3668023951
433206629932.56879211422133.43120788581
442718631077.5774055413-3891.57740554125
452958628988.974954854597.025045145958
462135929309.3972007634-7950.39720076336
472155325042.4336158153-3489.43361581532
481957323169.6609989519-3596.66099895186
492425621239.33964237153016.66035762853
502238022858.3757193264-478.375719326388
511616722601.6323488074-6434.63234880736
522729719148.17697776588148.82302223416
532828723521.6353368934765.36466310704
543347426079.1978049077394.80219509304
552822930047.9745700887-1818.97457008873
562878529071.7342569922-286.734256992186
572559728917.8445075561-3320.84450755611
581813027135.5533556554-9005.55335565541
592019822302.2893990824-2104.28939908243
602284921172.92114095131676.07885904872
612311822072.46958821321045.53041178681

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 17382 & 20995 & -3613 \tabularnewline
3 & 9367 & 19055.9095315468 & -9688.9095315468 \tabularnewline
4 & 31124 & 13855.8895696515 & 17268.1104303485 \tabularnewline
5 & 26551 & 23123.6527425511 & 3427.34725744895 \tabularnewline
6 & 30651 & 24963.1037248368 & 5687.89627516318 \tabularnewline
7 & 25859 & 28015.7872157639 & -2156.78721576386 \tabularnewline
8 & 25100 & 26858.2434757779 & -1758.24347577786 \tabularnewline
9 & 25778 & 25914.597429528 & -136.597429527963 \tabularnewline
10 & 20418 & 25841.2858398205 & -5423.28583982055 \tabularnewline
11 & 18688 & 22930.6182838578 & -4242.61828385784 \tabularnewline
12 & 20424 & 20653.6128381025 & -229.612838102505 \tabularnewline
13 & 24776 & 20530.38004934 & 4245.61995066004 \tabularnewline
14 & 19814 & 22808.9964841586 & -2994.99648415858 \tabularnewline
15 & 12738 & 21201.5873683316 & -8463.58736833163 \tabularnewline
16 & 31566 & 16659.195562394 & 14906.804437606 \tabularnewline
17 & 30111 & 24659.6501430908 & 5451.34985690917 \tabularnewline
18 & 30019 & 27585.3796055144 & 2433.62039448561 \tabularnewline
19 & 31934 & 28891.4992044018 & 3042.50079559816 \tabularnewline
20 & 25826 & 30524.4037969858 & -4698.40379698576 \tabularnewline
21 & 26835 & 28002.7791029145 & -1167.77910291451 \tabularnewline
22 & 20205 & 27376.0342018018 & -7171.03420180176 \tabularnewline
23 & 17789 & 23527.3533079004 & -5738.35330790037 \tabularnewline
24 & 20520 & 20447.5896201156 & 72.4103798844408 \tabularnewline
25 & 22518 & 20486.4521380926 & 2031.54786190742 \tabularnewline
26 & 15572 & 21576.7801467367 & -6004.78014673669 \tabularnewline
27 & 11509 & 18354.0256635664 & -6845.02566356643 \tabularnewline
28 & 25447 & 14680.3129537576 & 10766.6870462424 \tabularnewline
29 & 24090 & 20458.7741295636 & 3631.22587043635 \tabularnewline
30 & 27786 & 22407.646389227 & 5378.35361077296 \tabularnewline
31 & 26195 & 25294.1989003316 & 900.801099668417 \tabularnewline
32 & 20516 & 25777.6571971318 & -5261.6571971318 \tabularnewline
33 & 22759 & 22953.7354370359 & -194.735437035903 \tabularnewline
34 & 19028 & 22849.2212854094 & -3821.22128540945 \tabularnewline
35 & 16971 & 20798.3788352606 & -3827.37883526055 \tabularnewline
36 & 20036 & 18744.2316394086 & 1291.76836059144 \tabularnewline
37 & 22485 & 19437.5213475382 & 3047.47865246183 \tabularnewline
38 & 18730 & 21073.0975467641 & -2343.09754676412 \tabularnewline
39 & 14538 & 19815.561394097 & -5277.56139409697 \tabularnewline
40 & 27561 & 16983.1038806815 & 10577.8961193185 \tabularnewline
41 & 25985 & 22660.2413125272 & 3324.75868747276 \tabularnewline
42 & 34670 & 24444.6331976049 & 10225.3668023951 \tabularnewline
43 & 32066 & 29932.5687921142 & 2133.43120788581 \tabularnewline
44 & 27186 & 31077.5774055413 & -3891.57740554125 \tabularnewline
45 & 29586 & 28988.974954854 & 597.025045145958 \tabularnewline
46 & 21359 & 29309.3972007634 & -7950.39720076336 \tabularnewline
47 & 21553 & 25042.4336158153 & -3489.43361581532 \tabularnewline
48 & 19573 & 23169.6609989519 & -3596.66099895186 \tabularnewline
49 & 24256 & 21239.3396423715 & 3016.66035762853 \tabularnewline
50 & 22380 & 22858.3757193264 & -478.375719326388 \tabularnewline
51 & 16167 & 22601.6323488074 & -6434.63234880736 \tabularnewline
52 & 27297 & 19148.1769777658 & 8148.82302223416 \tabularnewline
53 & 28287 & 23521.635336893 & 4765.36466310704 \tabularnewline
54 & 33474 & 26079.197804907 & 7394.80219509304 \tabularnewline
55 & 28229 & 30047.9745700887 & -1818.97457008873 \tabularnewline
56 & 28785 & 29071.7342569922 & -286.734256992186 \tabularnewline
57 & 25597 & 28917.8445075561 & -3320.84450755611 \tabularnewline
58 & 18130 & 27135.5533556554 & -9005.55335565541 \tabularnewline
59 & 20198 & 22302.2893990824 & -2104.28939908243 \tabularnewline
60 & 22849 & 21172.9211409513 & 1676.07885904872 \tabularnewline
61 & 23118 & 22072.4695882132 & 1045.53041178681 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147892&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]17382[/C][C]20995[/C][C]-3613[/C][/ROW]
[ROW][C]3[/C][C]9367[/C][C]19055.9095315468[/C][C]-9688.9095315468[/C][/ROW]
[ROW][C]4[/C][C]31124[/C][C]13855.8895696515[/C][C]17268.1104303485[/C][/ROW]
[ROW][C]5[/C][C]26551[/C][C]23123.6527425511[/C][C]3427.34725744895[/C][/ROW]
[ROW][C]6[/C][C]30651[/C][C]24963.1037248368[/C][C]5687.89627516318[/C][/ROW]
[ROW][C]7[/C][C]25859[/C][C]28015.7872157639[/C][C]-2156.78721576386[/C][/ROW]
[ROW][C]8[/C][C]25100[/C][C]26858.2434757779[/C][C]-1758.24347577786[/C][/ROW]
[ROW][C]9[/C][C]25778[/C][C]25914.597429528[/C][C]-136.597429527963[/C][/ROW]
[ROW][C]10[/C][C]20418[/C][C]25841.2858398205[/C][C]-5423.28583982055[/C][/ROW]
[ROW][C]11[/C][C]18688[/C][C]22930.6182838578[/C][C]-4242.61828385784[/C][/ROW]
[ROW][C]12[/C][C]20424[/C][C]20653.6128381025[/C][C]-229.612838102505[/C][/ROW]
[ROW][C]13[/C][C]24776[/C][C]20530.38004934[/C][C]4245.61995066004[/C][/ROW]
[ROW][C]14[/C][C]19814[/C][C]22808.9964841586[/C][C]-2994.99648415858[/C][/ROW]
[ROW][C]15[/C][C]12738[/C][C]21201.5873683316[/C][C]-8463.58736833163[/C][/ROW]
[ROW][C]16[/C][C]31566[/C][C]16659.195562394[/C][C]14906.804437606[/C][/ROW]
[ROW][C]17[/C][C]30111[/C][C]24659.6501430908[/C][C]5451.34985690917[/C][/ROW]
[ROW][C]18[/C][C]30019[/C][C]27585.3796055144[/C][C]2433.62039448561[/C][/ROW]
[ROW][C]19[/C][C]31934[/C][C]28891.4992044018[/C][C]3042.50079559816[/C][/ROW]
[ROW][C]20[/C][C]25826[/C][C]30524.4037969858[/C][C]-4698.40379698576[/C][/ROW]
[ROW][C]21[/C][C]26835[/C][C]28002.7791029145[/C][C]-1167.77910291451[/C][/ROW]
[ROW][C]22[/C][C]20205[/C][C]27376.0342018018[/C][C]-7171.03420180176[/C][/ROW]
[ROW][C]23[/C][C]17789[/C][C]23527.3533079004[/C][C]-5738.35330790037[/C][/ROW]
[ROW][C]24[/C][C]20520[/C][C]20447.5896201156[/C][C]72.4103798844408[/C][/ROW]
[ROW][C]25[/C][C]22518[/C][C]20486.4521380926[/C][C]2031.54786190742[/C][/ROW]
[ROW][C]26[/C][C]15572[/C][C]21576.7801467367[/C][C]-6004.78014673669[/C][/ROW]
[ROW][C]27[/C][C]11509[/C][C]18354.0256635664[/C][C]-6845.02566356643[/C][/ROW]
[ROW][C]28[/C][C]25447[/C][C]14680.3129537576[/C][C]10766.6870462424[/C][/ROW]
[ROW][C]29[/C][C]24090[/C][C]20458.7741295636[/C][C]3631.22587043635[/C][/ROW]
[ROW][C]30[/C][C]27786[/C][C]22407.646389227[/C][C]5378.35361077296[/C][/ROW]
[ROW][C]31[/C][C]26195[/C][C]25294.1989003316[/C][C]900.801099668417[/C][/ROW]
[ROW][C]32[/C][C]20516[/C][C]25777.6571971318[/C][C]-5261.6571971318[/C][/ROW]
[ROW][C]33[/C][C]22759[/C][C]22953.7354370359[/C][C]-194.735437035903[/C][/ROW]
[ROW][C]34[/C][C]19028[/C][C]22849.2212854094[/C][C]-3821.22128540945[/C][/ROW]
[ROW][C]35[/C][C]16971[/C][C]20798.3788352606[/C][C]-3827.37883526055[/C][/ROW]
[ROW][C]36[/C][C]20036[/C][C]18744.2316394086[/C][C]1291.76836059144[/C][/ROW]
[ROW][C]37[/C][C]22485[/C][C]19437.5213475382[/C][C]3047.47865246183[/C][/ROW]
[ROW][C]38[/C][C]18730[/C][C]21073.0975467641[/C][C]-2343.09754676412[/C][/ROW]
[ROW][C]39[/C][C]14538[/C][C]19815.561394097[/C][C]-5277.56139409697[/C][/ROW]
[ROW][C]40[/C][C]27561[/C][C]16983.1038806815[/C][C]10577.8961193185[/C][/ROW]
[ROW][C]41[/C][C]25985[/C][C]22660.2413125272[/C][C]3324.75868747276[/C][/ROW]
[ROW][C]42[/C][C]34670[/C][C]24444.6331976049[/C][C]10225.3668023951[/C][/ROW]
[ROW][C]43[/C][C]32066[/C][C]29932.5687921142[/C][C]2133.43120788581[/C][/ROW]
[ROW][C]44[/C][C]27186[/C][C]31077.5774055413[/C][C]-3891.57740554125[/C][/ROW]
[ROW][C]45[/C][C]29586[/C][C]28988.974954854[/C][C]597.025045145958[/C][/ROW]
[ROW][C]46[/C][C]21359[/C][C]29309.3972007634[/C][C]-7950.39720076336[/C][/ROW]
[ROW][C]47[/C][C]21553[/C][C]25042.4336158153[/C][C]-3489.43361581532[/C][/ROW]
[ROW][C]48[/C][C]19573[/C][C]23169.6609989519[/C][C]-3596.66099895186[/C][/ROW]
[ROW][C]49[/C][C]24256[/C][C]21239.3396423715[/C][C]3016.66035762853[/C][/ROW]
[ROW][C]50[/C][C]22380[/C][C]22858.3757193264[/C][C]-478.375719326388[/C][/ROW]
[ROW][C]51[/C][C]16167[/C][C]22601.6323488074[/C][C]-6434.63234880736[/C][/ROW]
[ROW][C]52[/C][C]27297[/C][C]19148.1769777658[/C][C]8148.82302223416[/C][/ROW]
[ROW][C]53[/C][C]28287[/C][C]23521.635336893[/C][C]4765.36466310704[/C][/ROW]
[ROW][C]54[/C][C]33474[/C][C]26079.197804907[/C][C]7394.80219509304[/C][/ROW]
[ROW][C]55[/C][C]28229[/C][C]30047.9745700887[/C][C]-1818.97457008873[/C][/ROW]
[ROW][C]56[/C][C]28785[/C][C]29071.7342569922[/C][C]-286.734256992186[/C][/ROW]
[ROW][C]57[/C][C]25597[/C][C]28917.8445075561[/C][C]-3320.84450755611[/C][/ROW]
[ROW][C]58[/C][C]18130[/C][C]27135.5533556554[/C][C]-9005.55335565541[/C][/ROW]
[ROW][C]59[/C][C]20198[/C][C]22302.2893990824[/C][C]-2104.28939908243[/C][/ROW]
[ROW][C]60[/C][C]22849[/C][C]21172.9211409513[/C][C]1676.07885904872[/C][/ROW]
[ROW][C]61[/C][C]23118[/C][C]22072.4695882132[/C][C]1045.53041178681[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147892&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147892&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
21738220995-3613
3936719055.9095315468-9688.9095315468
43112413855.889569651517268.1104303485
52655123123.65274255113427.34725744895
63065124963.10372483685687.89627516318
72585928015.7872157639-2156.78721576386
82510026858.2434757779-1758.24347577786
92577825914.597429528-136.597429527963
102041825841.2858398205-5423.28583982055
111868822930.6182838578-4242.61828385784
122042420653.6128381025-229.612838102505
132477620530.380049344245.61995066004
141981422808.9964841586-2994.99648415858
151273821201.5873683316-8463.58736833163
163156616659.19556239414906.804437606
173011124659.65014309085451.34985690917
183001927585.37960551442433.62039448561
193193428891.49920440183042.50079559816
202582630524.4037969858-4698.40379698576
212683528002.7791029145-1167.77910291451
222020527376.0342018018-7171.03420180176
231778923527.3533079004-5738.35330790037
242052020447.589620115672.4103798844408
252251820486.45213809262031.54786190742
261557221576.7801467367-6004.78014673669
271150918354.0256635664-6845.02566356643
282544714680.312953757610766.6870462424
292409020458.77412956363631.22587043635
302778622407.6463892275378.35361077296
312619525294.1989003316900.801099668417
322051625777.6571971318-5261.6571971318
332275922953.7354370359-194.735437035903
341902822849.2212854094-3821.22128540945
351697120798.3788352606-3827.37883526055
362003618744.23163940861291.76836059144
372248519437.52134753823047.47865246183
381873021073.0975467641-2343.09754676412
391453819815.561394097-5277.56139409697
402756116983.103880681510577.8961193185
412598522660.24131252723324.75868747276
423467024444.633197604910225.3668023951
433206629932.56879211422133.43120788581
442718631077.5774055413-3891.57740554125
452958628988.974954854597.025045145958
462135929309.3972007634-7950.39720076336
472155325042.4336158153-3489.43361581532
481957323169.6609989519-3596.66099895186
492425621239.33964237153016.66035762853
502238022858.3757193264-478.375719326388
511616722601.6323488074-6434.63234880736
522729719148.17697776588148.82302223416
532828723521.6353368934765.36466310704
543347426079.1978049077394.80219509304
552822930047.9745700887-1818.97457008873
562878529071.7342569922-286.734256992186
572559728917.8445075561-3320.84450755611
581813027135.5533556554-9005.55335565541
592019822302.2893990824-2104.28939908243
602284921172.92114095131676.07885904872
612311822072.46958821321045.53041178681







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6222633.603841181311339.157396324333928.0502860383
6322633.60384118139815.3031514345235451.9045309281
6422633.60384118138454.2828190102136812.9248633524
6522633.60384118137212.9210830540538054.2865993085
6622633.60384118136064.3018400762739202.9058422863
6722633.60384118134990.3025378298440276.9051445327
6822633.60384118133978.0311360118541289.1765463507
6922633.60384118133017.9288582783842249.2788240842
7022633.60384118132102.6755350402543164.5321473223
7122633.60384118131226.5178837483344040.6897986143
7222633.6038411813384.83665587541344882.3710264872
7322633.6038411813-426.14362801194145693.3513103745

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
62 & 22633.6038411813 & 11339.1573963243 & 33928.0502860383 \tabularnewline
63 & 22633.6038411813 & 9815.30315143452 & 35451.9045309281 \tabularnewline
64 & 22633.6038411813 & 8454.28281901021 & 36812.9248633524 \tabularnewline
65 & 22633.6038411813 & 7212.92108305405 & 38054.2865993085 \tabularnewline
66 & 22633.6038411813 & 6064.30184007627 & 39202.9058422863 \tabularnewline
67 & 22633.6038411813 & 4990.30253782984 & 40276.9051445327 \tabularnewline
68 & 22633.6038411813 & 3978.03113601185 & 41289.1765463507 \tabularnewline
69 & 22633.6038411813 & 3017.92885827838 & 42249.2788240842 \tabularnewline
70 & 22633.6038411813 & 2102.67553504025 & 43164.5321473223 \tabularnewline
71 & 22633.6038411813 & 1226.51788374833 & 44040.6897986143 \tabularnewline
72 & 22633.6038411813 & 384.836655875413 & 44882.3710264872 \tabularnewline
73 & 22633.6038411813 & -426.143628011941 & 45693.3513103745 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=147892&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]62[/C][C]22633.6038411813[/C][C]11339.1573963243[/C][C]33928.0502860383[/C][/ROW]
[ROW][C]63[/C][C]22633.6038411813[/C][C]9815.30315143452[/C][C]35451.9045309281[/C][/ROW]
[ROW][C]64[/C][C]22633.6038411813[/C][C]8454.28281901021[/C][C]36812.9248633524[/C][/ROW]
[ROW][C]65[/C][C]22633.6038411813[/C][C]7212.92108305405[/C][C]38054.2865993085[/C][/ROW]
[ROW][C]66[/C][C]22633.6038411813[/C][C]6064.30184007627[/C][C]39202.9058422863[/C][/ROW]
[ROW][C]67[/C][C]22633.6038411813[/C][C]4990.30253782984[/C][C]40276.9051445327[/C][/ROW]
[ROW][C]68[/C][C]22633.6038411813[/C][C]3978.03113601185[/C][C]41289.1765463507[/C][/ROW]
[ROW][C]69[/C][C]22633.6038411813[/C][C]3017.92885827838[/C][C]42249.2788240842[/C][/ROW]
[ROW][C]70[/C][C]22633.6038411813[/C][C]2102.67553504025[/C][C]43164.5321473223[/C][/ROW]
[ROW][C]71[/C][C]22633.6038411813[/C][C]1226.51788374833[/C][C]44040.6897986143[/C][/ROW]
[ROW][C]72[/C][C]22633.6038411813[/C][C]384.836655875413[/C][C]44882.3710264872[/C][/ROW]
[ROW][C]73[/C][C]22633.6038411813[/C][C]-426.143628011941[/C][C]45693.3513103745[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=147892&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=147892&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
6222633.603841181311339.157396324333928.0502860383
6322633.60384118139815.3031514345235451.9045309281
6422633.60384118138454.2828190102136812.9248633524
6522633.60384118137212.9210830540538054.2865993085
6622633.60384118136064.3018400762739202.9058422863
6722633.60384118134990.3025378298440276.9051445327
6822633.60384118133978.0311360118541289.1765463507
6922633.60384118133017.9288582783842249.2788240842
7022633.60384118132102.6755350402543164.5321473223
7122633.60384118131226.5178837483344040.6897986143
7222633.6038411813384.83665587541344882.3710264872
7322633.6038411813-426.14362801194145693.3513103745



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')