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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 03:58:20 -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/2012/Dec/21/t13560808076sscbj99i7nl6sk.htm/, Retrieved Fri, 19 Apr 2024 22:58:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203315, Retrieved Fri, 19 Apr 2024 22:58:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact64
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 08:58:20] [db26a86bf4adac007852ad52c5e0cac3] [Current]
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Dataseries X:
3,65
3,66
3,69
3,7
3,7
3,71
3,71
3,71
3,72
3,72
3,73
3,74
3,78
3,78
3,79
3,79
3,8
3,81
3,83
3,84
3,88
3,91
3,96
3,96
3,97
3,98
3,99
3,99
4
4
4,02
4,02
4,02
4,03
4,03
4,03
4,04
4,04
4,05
4,05
4,05
4,05
4,06
4,06
4,06
4,06
4,07
4,07
4,08
4,08
4,08
4,09
4,09
4,09
4,09
4,1
4,1
4,11
4,11
4,12
4,12
4,12
4,12
4,12
4,15
4,15
4,15
4,15
4,16
4,16
4,16
4,2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203315&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]3 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=203315&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203315&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.998970511234536
beta0.102472082251909
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.998970511234536 \tabularnewline
beta & 0.102472082251909 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203315&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]0.998970511234536[/C][/ROW]
[ROW][C]beta[/C][C]0.102472082251909[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203315&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203315&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
alpha0.998970511234536
beta0.102472082251909
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.693.670.0199999999999996
43.73.70202674199258-0.00202674199258013
53.73.71184194761267-0.0118419476126652
63.713.71063983247953-0.000639832479527147
73.713.72056280255977-0.0105628025597748
83.713.71949174008406-0.00949174008406439
93.723.718519000386950.00148099961305448
103.723.7286593089525-0.00865930895250289
113.733.727783324370930.00221667562907113
123.743.737999041188710.00200095881128659
133.783.748204094593780.0317959054062165
143.783.79142825939234-0.0114282593923436
153.793.79030288625912-0.000302886259118562
163.793.80026042737945-0.0102604273794493
173.83.799220353609860.000779646390139277
183.813.809288797719060.000711202280942569
193.833.819361671532660.0106383284673424
203.843.8404404610592-0.000440461059196817
213.883.85040677805260.0295932219474011
223.913.893405215883710.016594784116287
233.963.925117349064560.0348826509354438
243.963.97866933988154-0.0186693398815376
253.973.9768133544232-0.00681335442320163
263.983.98610368897154-0.00610368897154423
273.993.9954781445623-0.00547814456229601
283.994.00491672160178-0.0149167216017805
2944.0033994646104-0.00339946461040075
3044.01303961612919-0.013039616129185
314.024.011714719539750.0082852804602469
324.024.0325409016929-0.0125409016928959
334.024.03127857269176-0.0112785726917579
344.034.03012272412982-0.000122724129818508
354.034.04009867645857-0.010098676458572
364.034.03907517953306-0.00907517953305526
374.044.03814513068660.00185486931339618
384.044.04832375496764-0.00832375496764026
394.054.047482159348320.00251784065168259
404.054.05772874080506-0.00772874080506103
414.054.05694812471676-0.00694812471675554
424.054.05623606525827-0.00623606525826848
434.064.055596967475560.0044030325244373
444.064.06603673806204-0.00603673806203631
454.064.06542952540813-0.00542952540812713
464.064.06487309829689-0.00487309829689142
474.074.064373683013870.00562631698613281
484.074.07493882085889-0.00493882085888586
494.084.074444127307590.00555587269241276
504.084.08500205887156-0.0050020588715558
514.084.08450088444186-0.0045008844418577
524.094.084039628303340.00596037169665742
534.094.09463900147382-0.00463900147382468
544.094.09417503465499-0.00417503465499269
554.094.09374717295231-0.00374717295230553
564.14.093363147162240.0066368528377625
574.14.10403184890702-0.00403184890702413
584.114.103630105598080.00636989440192259
594.114.11427146147856-0.00427146147855773
604.124.113845161695870.00615483830413144
614.124.12446447773669-0.00446447773668979
624.124.12401839684838-0.0040183968483829
634.124.12360658803694-0.00360658803693514
644.124.12323696997131-0.00323696997130618
654.154.122905231880960.0270947681190385
664.154.15564760467305-0.00564760467304559
674.154.15510318655501-0.00510318655500885
684.154.1545802302851-0.00458023028509658
694.164.154110829359150.00588917064085415
704.164.16470290553549-0.00470290553548836
714.164.16423238956371-0.00423238956370486
724.24.163798649892410.0362013501075946

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.69 & 3.67 & 0.0199999999999996 \tabularnewline
4 & 3.7 & 3.70202674199258 & -0.00202674199258013 \tabularnewline
5 & 3.7 & 3.71184194761267 & -0.0118419476126652 \tabularnewline
6 & 3.71 & 3.71063983247953 & -0.000639832479527147 \tabularnewline
7 & 3.71 & 3.72056280255977 & -0.0105628025597748 \tabularnewline
8 & 3.71 & 3.71949174008406 & -0.00949174008406439 \tabularnewline
9 & 3.72 & 3.71851900038695 & 0.00148099961305448 \tabularnewline
10 & 3.72 & 3.7286593089525 & -0.00865930895250289 \tabularnewline
11 & 3.73 & 3.72778332437093 & 0.00221667562907113 \tabularnewline
12 & 3.74 & 3.73799904118871 & 0.00200095881128659 \tabularnewline
13 & 3.78 & 3.74820409459378 & 0.0317959054062165 \tabularnewline
14 & 3.78 & 3.79142825939234 & -0.0114282593923436 \tabularnewline
15 & 3.79 & 3.79030288625912 & -0.000302886259118562 \tabularnewline
16 & 3.79 & 3.80026042737945 & -0.0102604273794493 \tabularnewline
17 & 3.8 & 3.79922035360986 & 0.000779646390139277 \tabularnewline
18 & 3.81 & 3.80928879771906 & 0.000711202280942569 \tabularnewline
19 & 3.83 & 3.81936167153266 & 0.0106383284673424 \tabularnewline
20 & 3.84 & 3.8404404610592 & -0.000440461059196817 \tabularnewline
21 & 3.88 & 3.8504067780526 & 0.0295932219474011 \tabularnewline
22 & 3.91 & 3.89340521588371 & 0.016594784116287 \tabularnewline
23 & 3.96 & 3.92511734906456 & 0.0348826509354438 \tabularnewline
24 & 3.96 & 3.97866933988154 & -0.0186693398815376 \tabularnewline
25 & 3.97 & 3.9768133544232 & -0.00681335442320163 \tabularnewline
26 & 3.98 & 3.98610368897154 & -0.00610368897154423 \tabularnewline
27 & 3.99 & 3.9954781445623 & -0.00547814456229601 \tabularnewline
28 & 3.99 & 4.00491672160178 & -0.0149167216017805 \tabularnewline
29 & 4 & 4.0033994646104 & -0.00339946461040075 \tabularnewline
30 & 4 & 4.01303961612919 & -0.013039616129185 \tabularnewline
31 & 4.02 & 4.01171471953975 & 0.0082852804602469 \tabularnewline
32 & 4.02 & 4.0325409016929 & -0.0125409016928959 \tabularnewline
33 & 4.02 & 4.03127857269176 & -0.0112785726917579 \tabularnewline
34 & 4.03 & 4.03012272412982 & -0.000122724129818508 \tabularnewline
35 & 4.03 & 4.04009867645857 & -0.010098676458572 \tabularnewline
36 & 4.03 & 4.03907517953306 & -0.00907517953305526 \tabularnewline
37 & 4.04 & 4.0381451306866 & 0.00185486931339618 \tabularnewline
38 & 4.04 & 4.04832375496764 & -0.00832375496764026 \tabularnewline
39 & 4.05 & 4.04748215934832 & 0.00251784065168259 \tabularnewline
40 & 4.05 & 4.05772874080506 & -0.00772874080506103 \tabularnewline
41 & 4.05 & 4.05694812471676 & -0.00694812471675554 \tabularnewline
42 & 4.05 & 4.05623606525827 & -0.00623606525826848 \tabularnewline
43 & 4.06 & 4.05559696747556 & 0.0044030325244373 \tabularnewline
44 & 4.06 & 4.06603673806204 & -0.00603673806203631 \tabularnewline
45 & 4.06 & 4.06542952540813 & -0.00542952540812713 \tabularnewline
46 & 4.06 & 4.06487309829689 & -0.00487309829689142 \tabularnewline
47 & 4.07 & 4.06437368301387 & 0.00562631698613281 \tabularnewline
48 & 4.07 & 4.07493882085889 & -0.00493882085888586 \tabularnewline
49 & 4.08 & 4.07444412730759 & 0.00555587269241276 \tabularnewline
50 & 4.08 & 4.08500205887156 & -0.0050020588715558 \tabularnewline
51 & 4.08 & 4.08450088444186 & -0.0045008844418577 \tabularnewline
52 & 4.09 & 4.08403962830334 & 0.00596037169665742 \tabularnewline
53 & 4.09 & 4.09463900147382 & -0.00463900147382468 \tabularnewline
54 & 4.09 & 4.09417503465499 & -0.00417503465499269 \tabularnewline
55 & 4.09 & 4.09374717295231 & -0.00374717295230553 \tabularnewline
56 & 4.1 & 4.09336314716224 & 0.0066368528377625 \tabularnewline
57 & 4.1 & 4.10403184890702 & -0.00403184890702413 \tabularnewline
58 & 4.11 & 4.10363010559808 & 0.00636989440192259 \tabularnewline
59 & 4.11 & 4.11427146147856 & -0.00427146147855773 \tabularnewline
60 & 4.12 & 4.11384516169587 & 0.00615483830413144 \tabularnewline
61 & 4.12 & 4.12446447773669 & -0.00446447773668979 \tabularnewline
62 & 4.12 & 4.12401839684838 & -0.0040183968483829 \tabularnewline
63 & 4.12 & 4.12360658803694 & -0.00360658803693514 \tabularnewline
64 & 4.12 & 4.12323696997131 & -0.00323696997130618 \tabularnewline
65 & 4.15 & 4.12290523188096 & 0.0270947681190385 \tabularnewline
66 & 4.15 & 4.15564760467305 & -0.00564760467304559 \tabularnewline
67 & 4.15 & 4.15510318655501 & -0.00510318655500885 \tabularnewline
68 & 4.15 & 4.1545802302851 & -0.00458023028509658 \tabularnewline
69 & 4.16 & 4.15411082935915 & 0.00588917064085415 \tabularnewline
70 & 4.16 & 4.16470290553549 & -0.00470290553548836 \tabularnewline
71 & 4.16 & 4.16423238956371 & -0.00423238956370486 \tabularnewline
72 & 4.2 & 4.16379864989241 & 0.0362013501075946 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203315&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]3[/C][C]3.69[/C][C]3.67[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]4[/C][C]3.7[/C][C]3.70202674199258[/C][C]-0.00202674199258013[/C][/ROW]
[ROW][C]5[/C][C]3.7[/C][C]3.71184194761267[/C][C]-0.0118419476126652[/C][/ROW]
[ROW][C]6[/C][C]3.71[/C][C]3.71063983247953[/C][C]-0.000639832479527147[/C][/ROW]
[ROW][C]7[/C][C]3.71[/C][C]3.72056280255977[/C][C]-0.0105628025597748[/C][/ROW]
[ROW][C]8[/C][C]3.71[/C][C]3.71949174008406[/C][C]-0.00949174008406439[/C][/ROW]
[ROW][C]9[/C][C]3.72[/C][C]3.71851900038695[/C][C]0.00148099961305448[/C][/ROW]
[ROW][C]10[/C][C]3.72[/C][C]3.7286593089525[/C][C]-0.00865930895250289[/C][/ROW]
[ROW][C]11[/C][C]3.73[/C][C]3.72778332437093[/C][C]0.00221667562907113[/C][/ROW]
[ROW][C]12[/C][C]3.74[/C][C]3.73799904118871[/C][C]0.00200095881128659[/C][/ROW]
[ROW][C]13[/C][C]3.78[/C][C]3.74820409459378[/C][C]0.0317959054062165[/C][/ROW]
[ROW][C]14[/C][C]3.78[/C][C]3.79142825939234[/C][C]-0.0114282593923436[/C][/ROW]
[ROW][C]15[/C][C]3.79[/C][C]3.79030288625912[/C][C]-0.000302886259118562[/C][/ROW]
[ROW][C]16[/C][C]3.79[/C][C]3.80026042737945[/C][C]-0.0102604273794493[/C][/ROW]
[ROW][C]17[/C][C]3.8[/C][C]3.79922035360986[/C][C]0.000779646390139277[/C][/ROW]
[ROW][C]18[/C][C]3.81[/C][C]3.80928879771906[/C][C]0.000711202280942569[/C][/ROW]
[ROW][C]19[/C][C]3.83[/C][C]3.81936167153266[/C][C]0.0106383284673424[/C][/ROW]
[ROW][C]20[/C][C]3.84[/C][C]3.8404404610592[/C][C]-0.000440461059196817[/C][/ROW]
[ROW][C]21[/C][C]3.88[/C][C]3.8504067780526[/C][C]0.0295932219474011[/C][/ROW]
[ROW][C]22[/C][C]3.91[/C][C]3.89340521588371[/C][C]0.016594784116287[/C][/ROW]
[ROW][C]23[/C][C]3.96[/C][C]3.92511734906456[/C][C]0.0348826509354438[/C][/ROW]
[ROW][C]24[/C][C]3.96[/C][C]3.97866933988154[/C][C]-0.0186693398815376[/C][/ROW]
[ROW][C]25[/C][C]3.97[/C][C]3.9768133544232[/C][C]-0.00681335442320163[/C][/ROW]
[ROW][C]26[/C][C]3.98[/C][C]3.98610368897154[/C][C]-0.00610368897154423[/C][/ROW]
[ROW][C]27[/C][C]3.99[/C][C]3.9954781445623[/C][C]-0.00547814456229601[/C][/ROW]
[ROW][C]28[/C][C]3.99[/C][C]4.00491672160178[/C][C]-0.0149167216017805[/C][/ROW]
[ROW][C]29[/C][C]4[/C][C]4.0033994646104[/C][C]-0.00339946461040075[/C][/ROW]
[ROW][C]30[/C][C]4[/C][C]4.01303961612919[/C][C]-0.013039616129185[/C][/ROW]
[ROW][C]31[/C][C]4.02[/C][C]4.01171471953975[/C][C]0.0082852804602469[/C][/ROW]
[ROW][C]32[/C][C]4.02[/C][C]4.0325409016929[/C][C]-0.0125409016928959[/C][/ROW]
[ROW][C]33[/C][C]4.02[/C][C]4.03127857269176[/C][C]-0.0112785726917579[/C][/ROW]
[ROW][C]34[/C][C]4.03[/C][C]4.03012272412982[/C][C]-0.000122724129818508[/C][/ROW]
[ROW][C]35[/C][C]4.03[/C][C]4.04009867645857[/C][C]-0.010098676458572[/C][/ROW]
[ROW][C]36[/C][C]4.03[/C][C]4.03907517953306[/C][C]-0.00907517953305526[/C][/ROW]
[ROW][C]37[/C][C]4.04[/C][C]4.0381451306866[/C][C]0.00185486931339618[/C][/ROW]
[ROW][C]38[/C][C]4.04[/C][C]4.04832375496764[/C][C]-0.00832375496764026[/C][/ROW]
[ROW][C]39[/C][C]4.05[/C][C]4.04748215934832[/C][C]0.00251784065168259[/C][/ROW]
[ROW][C]40[/C][C]4.05[/C][C]4.05772874080506[/C][C]-0.00772874080506103[/C][/ROW]
[ROW][C]41[/C][C]4.05[/C][C]4.05694812471676[/C][C]-0.00694812471675554[/C][/ROW]
[ROW][C]42[/C][C]4.05[/C][C]4.05623606525827[/C][C]-0.00623606525826848[/C][/ROW]
[ROW][C]43[/C][C]4.06[/C][C]4.05559696747556[/C][C]0.0044030325244373[/C][/ROW]
[ROW][C]44[/C][C]4.06[/C][C]4.06603673806204[/C][C]-0.00603673806203631[/C][/ROW]
[ROW][C]45[/C][C]4.06[/C][C]4.06542952540813[/C][C]-0.00542952540812713[/C][/ROW]
[ROW][C]46[/C][C]4.06[/C][C]4.06487309829689[/C][C]-0.00487309829689142[/C][/ROW]
[ROW][C]47[/C][C]4.07[/C][C]4.06437368301387[/C][C]0.00562631698613281[/C][/ROW]
[ROW][C]48[/C][C]4.07[/C][C]4.07493882085889[/C][C]-0.00493882085888586[/C][/ROW]
[ROW][C]49[/C][C]4.08[/C][C]4.07444412730759[/C][C]0.00555587269241276[/C][/ROW]
[ROW][C]50[/C][C]4.08[/C][C]4.08500205887156[/C][C]-0.0050020588715558[/C][/ROW]
[ROW][C]51[/C][C]4.08[/C][C]4.08450088444186[/C][C]-0.0045008844418577[/C][/ROW]
[ROW][C]52[/C][C]4.09[/C][C]4.08403962830334[/C][C]0.00596037169665742[/C][/ROW]
[ROW][C]53[/C][C]4.09[/C][C]4.09463900147382[/C][C]-0.00463900147382468[/C][/ROW]
[ROW][C]54[/C][C]4.09[/C][C]4.09417503465499[/C][C]-0.00417503465499269[/C][/ROW]
[ROW][C]55[/C][C]4.09[/C][C]4.09374717295231[/C][C]-0.00374717295230553[/C][/ROW]
[ROW][C]56[/C][C]4.1[/C][C]4.09336314716224[/C][C]0.0066368528377625[/C][/ROW]
[ROW][C]57[/C][C]4.1[/C][C]4.10403184890702[/C][C]-0.00403184890702413[/C][/ROW]
[ROW][C]58[/C][C]4.11[/C][C]4.10363010559808[/C][C]0.00636989440192259[/C][/ROW]
[ROW][C]59[/C][C]4.11[/C][C]4.11427146147856[/C][C]-0.00427146147855773[/C][/ROW]
[ROW][C]60[/C][C]4.12[/C][C]4.11384516169587[/C][C]0.00615483830413144[/C][/ROW]
[ROW][C]61[/C][C]4.12[/C][C]4.12446447773669[/C][C]-0.00446447773668979[/C][/ROW]
[ROW][C]62[/C][C]4.12[/C][C]4.12401839684838[/C][C]-0.0040183968483829[/C][/ROW]
[ROW][C]63[/C][C]4.12[/C][C]4.12360658803694[/C][C]-0.00360658803693514[/C][/ROW]
[ROW][C]64[/C][C]4.12[/C][C]4.12323696997131[/C][C]-0.00323696997130618[/C][/ROW]
[ROW][C]65[/C][C]4.15[/C][C]4.12290523188096[/C][C]0.0270947681190385[/C][/ROW]
[ROW][C]66[/C][C]4.15[/C][C]4.15564760467305[/C][C]-0.00564760467304559[/C][/ROW]
[ROW][C]67[/C][C]4.15[/C][C]4.15510318655501[/C][C]-0.00510318655500885[/C][/ROW]
[ROW][C]68[/C][C]4.15[/C][C]4.1545802302851[/C][C]-0.00458023028509658[/C][/ROW]
[ROW][C]69[/C][C]4.16[/C][C]4.15411082935915[/C][C]0.00588917064085415[/C][/ROW]
[ROW][C]70[/C][C]4.16[/C][C]4.16470290553549[/C][C]-0.00470290553548836[/C][/ROW]
[ROW][C]71[/C][C]4.16[/C][C]4.16423238956371[/C][C]-0.00423238956370486[/C][/ROW]
[ROW][C]72[/C][C]4.2[/C][C]4.16379864989241[/C][C]0.0362013501075946[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203315&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203315&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
33.693.670.0199999999999996
43.73.70202674199258-0.00202674199258013
53.73.71184194761267-0.0118419476126652
63.713.71063983247953-0.000639832479527147
73.713.72056280255977-0.0105628025597748
83.713.71949174008406-0.00949174008406439
93.723.718519000386950.00148099961305448
103.723.7286593089525-0.00865930895250289
113.733.727783324370930.00221667562907113
123.743.737999041188710.00200095881128659
133.783.748204094593780.0317959054062165
143.783.79142825939234-0.0114282593923436
153.793.79030288625912-0.000302886259118562
163.793.80026042737945-0.0102604273794493
173.83.799220353609860.000779646390139277
183.813.809288797719060.000711202280942569
193.833.819361671532660.0106383284673424
203.843.8404404610592-0.000440461059196817
213.883.85040677805260.0295932219474011
223.913.893405215883710.016594784116287
233.963.925117349064560.0348826509354438
243.963.97866933988154-0.0186693398815376
253.973.9768133544232-0.00681335442320163
263.983.98610368897154-0.00610368897154423
273.993.9954781445623-0.00547814456229601
283.994.00491672160178-0.0149167216017805
2944.0033994646104-0.00339946461040075
3044.01303961612919-0.013039616129185
314.024.011714719539750.0082852804602469
324.024.0325409016929-0.0125409016928959
334.024.03127857269176-0.0112785726917579
344.034.03012272412982-0.000122724129818508
354.034.04009867645857-0.010098676458572
364.034.03907517953306-0.00907517953305526
374.044.03814513068660.00185486931339618
384.044.04832375496764-0.00832375496764026
394.054.047482159348320.00251784065168259
404.054.05772874080506-0.00772874080506103
414.054.05694812471676-0.00694812471675554
424.054.05623606525827-0.00623606525826848
434.064.055596967475560.0044030325244373
444.064.06603673806204-0.00603673806203631
454.064.06542952540813-0.00542952540812713
464.064.06487309829689-0.00487309829689142
474.074.064373683013870.00562631698613281
484.074.07493882085889-0.00493882085888586
494.084.074444127307590.00555587269241276
504.084.08500205887156-0.0050020588715558
514.084.08450088444186-0.0045008844418577
524.094.084039628303340.00596037169665742
534.094.09463900147382-0.00463900147382468
544.094.09417503465499-0.00417503465499269
554.094.09374717295231-0.00374717295230553
564.14.093363147162240.0066368528377625
574.14.10403184890702-0.00403184890702413
584.114.103630105598080.00636989440192259
594.114.11427146147856-0.00427146147855773
604.124.113845161695870.00615483830413144
614.124.12446447773669-0.00446447773668979
624.124.12401839684838-0.0040183968483829
634.124.12360658803694-0.00360658803693514
644.124.12323696997131-0.00323696997130618
654.154.122905231880960.0270947681190385
664.154.15564760467305-0.00564760467304559
674.154.15510318655501-0.00510318655500885
684.154.1545802302851-0.00458023028509658
694.164.154110829359150.00588917064085415
704.164.16470290553549-0.00470290553548836
714.164.16423238956371-0.00423238956370486
724.24.163798649892410.0362013501075946







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734.207462832517464.185168463421284.22975720161363
744.214962933918144.181797908029814.24812795980648
754.222463035318834.179800641205394.26512542943227
764.229963136719524.17831104536424.28161522807483
774.23746323812024.177015642536384.29791083370402
784.244963339520894.175764954113544.31416172492824
794.252463440921584.174477098561114.33044978328204
804.259963542322264.173103379835454.34682370480908
814.267463643722954.171613301519964.36331398592594
824.274963745123634.169987141661834.37994034858544
834.282463846524324.168211922211834.39671577083681
844.289963947925014.166279067019334.41364882883069

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.20746283251746 & 4.18516846342128 & 4.22975720161363 \tabularnewline
74 & 4.21496293391814 & 4.18179790802981 & 4.24812795980648 \tabularnewline
75 & 4.22246303531883 & 4.17980064120539 & 4.26512542943227 \tabularnewline
76 & 4.22996313671952 & 4.1783110453642 & 4.28161522807483 \tabularnewline
77 & 4.2374632381202 & 4.17701564253638 & 4.29791083370402 \tabularnewline
78 & 4.24496333952089 & 4.17576495411354 & 4.31416172492824 \tabularnewline
79 & 4.25246344092158 & 4.17447709856111 & 4.33044978328204 \tabularnewline
80 & 4.25996354232226 & 4.17310337983545 & 4.34682370480908 \tabularnewline
81 & 4.26746364372295 & 4.17161330151996 & 4.36331398592594 \tabularnewline
82 & 4.27496374512363 & 4.16998714166183 & 4.37994034858544 \tabularnewline
83 & 4.28246384652432 & 4.16821192221183 & 4.39671577083681 \tabularnewline
84 & 4.28996394792501 & 4.16627906701933 & 4.41364882883069 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203315&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]4.20746283251746[/C][C]4.18516846342128[/C][C]4.22975720161363[/C][/ROW]
[ROW][C]74[/C][C]4.21496293391814[/C][C]4.18179790802981[/C][C]4.24812795980648[/C][/ROW]
[ROW][C]75[/C][C]4.22246303531883[/C][C]4.17980064120539[/C][C]4.26512542943227[/C][/ROW]
[ROW][C]76[/C][C]4.22996313671952[/C][C]4.1783110453642[/C][C]4.28161522807483[/C][/ROW]
[ROW][C]77[/C][C]4.2374632381202[/C][C]4.17701564253638[/C][C]4.29791083370402[/C][/ROW]
[ROW][C]78[/C][C]4.24496333952089[/C][C]4.17576495411354[/C][C]4.31416172492824[/C][/ROW]
[ROW][C]79[/C][C]4.25246344092158[/C][C]4.17447709856111[/C][C]4.33044978328204[/C][/ROW]
[ROW][C]80[/C][C]4.25996354232226[/C][C]4.17310337983545[/C][C]4.34682370480908[/C][/ROW]
[ROW][C]81[/C][C]4.26746364372295[/C][C]4.17161330151996[/C][C]4.36331398592594[/C][/ROW]
[ROW][C]82[/C][C]4.27496374512363[/C][C]4.16998714166183[/C][C]4.37994034858544[/C][/ROW]
[ROW][C]83[/C][C]4.28246384652432[/C][C]4.16821192221183[/C][C]4.39671577083681[/C][/ROW]
[ROW][C]84[/C][C]4.28996394792501[/C][C]4.16627906701933[/C][C]4.41364882883069[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203315&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203315&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
734.207462832517464.185168463421284.22975720161363
744.214962933918144.181797908029814.24812795980648
754.222463035318834.179800641205394.26512542943227
764.229963136719524.17831104536424.28161522807483
774.23746323812024.177015642536384.29791083370402
784.244963339520894.175764954113544.31416172492824
794.252463440921584.174477098561114.33044978328204
804.259963542322264.173103379835454.34682370480908
814.267463643722954.171613301519964.36331398592594
824.274963745123634.169987141661834.37994034858544
834.282463846524324.168211922211834.39671577083681
844.289963947925014.166279067019334.41364882883069



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')