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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 02:40:34 -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/17/t1355730105stkz3mqtcju4lu3.htm/, Retrieved Fri, 26 Apr 2024 12:49:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200676, Retrieved Fri, 26 Apr 2024 12:49:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact120
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [exponential smoot...] [2012-12-17 07:32:15] [6bcbc6a4e55b5452b0dd0259f4dded2d]
-   PD    [Exponential Smoothing] [exponential smoot...] [2012-12-17 07:40:34] [9961cdb39db8ad8fa7b94558bb7b5830] [Current]
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Dataseries X:
2,9
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,1
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3
3,3




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=200676&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=200676&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200676&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
alpha1
beta0.354648862328172
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.354648862328172 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200676&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]0.354648862328172[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200676&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200676&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
beta0.354648862328172
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
333.1-0.1
433.06453511376718-0.064535113767183
533.04164780908943-0.0416478090894321
633.0268774609774-0.0268774609774041
733.0173454000195-0.0173454000194981
833.01119387363596-0.011193873635956
933.00722397908592-0.00722397908591876
1033.00466200312162-0.00466200312161513
1133.00300862901836-0.00300862901836396
1233.00194162215983-0.00194162215983384
1333.00125302806978-0.00125302806977734
1433.00080864309037-0.000808643090365546
1533.00052185873834-0.000521858738337766
1633.00033678213049-0.000336782130490487
1733.00021734273106-0.000217342731059667
1833.00014026237875-0.000140262378753864
1933.0000905184857-9.05184857016295e-05
2033.00005841620773-5.84162077279515e-05
2133.00003769896612-3.76989661154958e-05
2233.00002432907067-2.43290706718469e-05
2333.00001570079344-1.57007934364906e-05
2433.00001013252491-1.01325249066697e-05
2533.00000653903648-6.53903647584997e-06
263.13.000004219974630.0999957800253712
273.13.13546760959824-0.0354676095982449
283.13.12288906220473-0.0228890622047278
293.13.11477148233406-0.0147714823340621
303.13.10953279292939-0.00953279292938625
313.13.10615199876217-0.00615199876216943
323.13.10397019940012-0.00397019940012155
333.13.10256217269965-0.00256217269965253
343.13.10165350106663-0.00165350106663231
353.13.10106708879449-0.00106708879449302
363.13.10068864696752-0.00068864696752291
373.13.10044441910395-0.000444419103945215
383.33.100286806374330.199713193625666
393.33.3711148632856-0.0711148632856022
403.33.34589405792674-0.04589405792674
413.33.3296177824954-0.0296177824953983
423.33.31911386962872-0.0191138696287223
433.33.31233515751021-0.0123351575102069
443.33.30796050793257-0.00796050793257308
453.33.30513732285073-0.00513732285073187
463.33.30331537714631-0.00331537714630725
473.33.30213958241318-0.00213958241318046
483.33.30138078194449-0.00138078194448887
493.33.30089108919875-0.000891089198752582
503.33.30057506542818-0.000575065428181976
513.33.30037111912831-0.000371119128312891
523.33.30023950215167-0.000239502151668347
533.33.30015456298605-0.000154562986053985
543.33.30009974739889-9.97473988921804e-05
553.33.30006437209735-6.43720973547701e-05
563.33.30004154260626-4.15426062621016e-05
573.33.30002680956821-2.68095682129932e-05
583.33.30001730158535-1.73015853470737e-05
593.33.30001116559779-1.11655977872438e-05
603.33.30000720573123-7.20573123480506e-06
613.33.30000465022685-4.65022685025573e-06
623.33.30000300102919-3.00102918826539e-06
633.33.3000019367176-1.93671760095881e-06
643.33.30000124986291-1.24986290694906e-06
653.33.30000080660045-8.06600449099193e-07
663.33.30000052054052-5.20540517356949e-07
673.33.30000033593141-3.35931415129664e-07
683.33.30000021679372-2.16793720753117e-07
693.33.30000013990807-1.39908074459072e-07
703.33.30000009028983-9.02898351640147e-08
713.33.30000005826865-5.82686476846561e-08
723.33.30000003760374-3.76037379012928e-08

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3 & 3.1 & -0.1 \tabularnewline
4 & 3 & 3.06453511376718 & -0.064535113767183 \tabularnewline
5 & 3 & 3.04164780908943 & -0.0416478090894321 \tabularnewline
6 & 3 & 3.0268774609774 & -0.0268774609774041 \tabularnewline
7 & 3 & 3.0173454000195 & -0.0173454000194981 \tabularnewline
8 & 3 & 3.01119387363596 & -0.011193873635956 \tabularnewline
9 & 3 & 3.00722397908592 & -0.00722397908591876 \tabularnewline
10 & 3 & 3.00466200312162 & -0.00466200312161513 \tabularnewline
11 & 3 & 3.00300862901836 & -0.00300862901836396 \tabularnewline
12 & 3 & 3.00194162215983 & -0.00194162215983384 \tabularnewline
13 & 3 & 3.00125302806978 & -0.00125302806977734 \tabularnewline
14 & 3 & 3.00080864309037 & -0.000808643090365546 \tabularnewline
15 & 3 & 3.00052185873834 & -0.000521858738337766 \tabularnewline
16 & 3 & 3.00033678213049 & -0.000336782130490487 \tabularnewline
17 & 3 & 3.00021734273106 & -0.000217342731059667 \tabularnewline
18 & 3 & 3.00014026237875 & -0.000140262378753864 \tabularnewline
19 & 3 & 3.0000905184857 & -9.05184857016295e-05 \tabularnewline
20 & 3 & 3.00005841620773 & -5.84162077279515e-05 \tabularnewline
21 & 3 & 3.00003769896612 & -3.76989661154958e-05 \tabularnewline
22 & 3 & 3.00002432907067 & -2.43290706718469e-05 \tabularnewline
23 & 3 & 3.00001570079344 & -1.57007934364906e-05 \tabularnewline
24 & 3 & 3.00001013252491 & -1.01325249066697e-05 \tabularnewline
25 & 3 & 3.00000653903648 & -6.53903647584997e-06 \tabularnewline
26 & 3.1 & 3.00000421997463 & 0.0999957800253712 \tabularnewline
27 & 3.1 & 3.13546760959824 & -0.0354676095982449 \tabularnewline
28 & 3.1 & 3.12288906220473 & -0.0228890622047278 \tabularnewline
29 & 3.1 & 3.11477148233406 & -0.0147714823340621 \tabularnewline
30 & 3.1 & 3.10953279292939 & -0.00953279292938625 \tabularnewline
31 & 3.1 & 3.10615199876217 & -0.00615199876216943 \tabularnewline
32 & 3.1 & 3.10397019940012 & -0.00397019940012155 \tabularnewline
33 & 3.1 & 3.10256217269965 & -0.00256217269965253 \tabularnewline
34 & 3.1 & 3.10165350106663 & -0.00165350106663231 \tabularnewline
35 & 3.1 & 3.10106708879449 & -0.00106708879449302 \tabularnewline
36 & 3.1 & 3.10068864696752 & -0.00068864696752291 \tabularnewline
37 & 3.1 & 3.10044441910395 & -0.000444419103945215 \tabularnewline
38 & 3.3 & 3.10028680637433 & 0.199713193625666 \tabularnewline
39 & 3.3 & 3.3711148632856 & -0.0711148632856022 \tabularnewline
40 & 3.3 & 3.34589405792674 & -0.04589405792674 \tabularnewline
41 & 3.3 & 3.3296177824954 & -0.0296177824953983 \tabularnewline
42 & 3.3 & 3.31911386962872 & -0.0191138696287223 \tabularnewline
43 & 3.3 & 3.31233515751021 & -0.0123351575102069 \tabularnewline
44 & 3.3 & 3.30796050793257 & -0.00796050793257308 \tabularnewline
45 & 3.3 & 3.30513732285073 & -0.00513732285073187 \tabularnewline
46 & 3.3 & 3.30331537714631 & -0.00331537714630725 \tabularnewline
47 & 3.3 & 3.30213958241318 & -0.00213958241318046 \tabularnewline
48 & 3.3 & 3.30138078194449 & -0.00138078194448887 \tabularnewline
49 & 3.3 & 3.30089108919875 & -0.000891089198752582 \tabularnewline
50 & 3.3 & 3.30057506542818 & -0.000575065428181976 \tabularnewline
51 & 3.3 & 3.30037111912831 & -0.000371119128312891 \tabularnewline
52 & 3.3 & 3.30023950215167 & -0.000239502151668347 \tabularnewline
53 & 3.3 & 3.30015456298605 & -0.000154562986053985 \tabularnewline
54 & 3.3 & 3.30009974739889 & -9.97473988921804e-05 \tabularnewline
55 & 3.3 & 3.30006437209735 & -6.43720973547701e-05 \tabularnewline
56 & 3.3 & 3.30004154260626 & -4.15426062621016e-05 \tabularnewline
57 & 3.3 & 3.30002680956821 & -2.68095682129932e-05 \tabularnewline
58 & 3.3 & 3.30001730158535 & -1.73015853470737e-05 \tabularnewline
59 & 3.3 & 3.30001116559779 & -1.11655977872438e-05 \tabularnewline
60 & 3.3 & 3.30000720573123 & -7.20573123480506e-06 \tabularnewline
61 & 3.3 & 3.30000465022685 & -4.65022685025573e-06 \tabularnewline
62 & 3.3 & 3.30000300102919 & -3.00102918826539e-06 \tabularnewline
63 & 3.3 & 3.3000019367176 & -1.93671760095881e-06 \tabularnewline
64 & 3.3 & 3.30000124986291 & -1.24986290694906e-06 \tabularnewline
65 & 3.3 & 3.30000080660045 & -8.06600449099193e-07 \tabularnewline
66 & 3.3 & 3.30000052054052 & -5.20540517356949e-07 \tabularnewline
67 & 3.3 & 3.30000033593141 & -3.35931415129664e-07 \tabularnewline
68 & 3.3 & 3.30000021679372 & -2.16793720753117e-07 \tabularnewline
69 & 3.3 & 3.30000013990807 & -1.39908074459072e-07 \tabularnewline
70 & 3.3 & 3.30000009028983 & -9.02898351640147e-08 \tabularnewline
71 & 3.3 & 3.30000005826865 & -5.82686476846561e-08 \tabularnewline
72 & 3.3 & 3.30000003760374 & -3.76037379012928e-08 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200676&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[/C][C]3.1[/C][C]-0.1[/C][/ROW]
[ROW][C]4[/C][C]3[/C][C]3.06453511376718[/C][C]-0.064535113767183[/C][/ROW]
[ROW][C]5[/C][C]3[/C][C]3.04164780908943[/C][C]-0.0416478090894321[/C][/ROW]
[ROW][C]6[/C][C]3[/C][C]3.0268774609774[/C][C]-0.0268774609774041[/C][/ROW]
[ROW][C]7[/C][C]3[/C][C]3.0173454000195[/C][C]-0.0173454000194981[/C][/ROW]
[ROW][C]8[/C][C]3[/C][C]3.01119387363596[/C][C]-0.011193873635956[/C][/ROW]
[ROW][C]9[/C][C]3[/C][C]3.00722397908592[/C][C]-0.00722397908591876[/C][/ROW]
[ROW][C]10[/C][C]3[/C][C]3.00466200312162[/C][C]-0.00466200312161513[/C][/ROW]
[ROW][C]11[/C][C]3[/C][C]3.00300862901836[/C][C]-0.00300862901836396[/C][/ROW]
[ROW][C]12[/C][C]3[/C][C]3.00194162215983[/C][C]-0.00194162215983384[/C][/ROW]
[ROW][C]13[/C][C]3[/C][C]3.00125302806978[/C][C]-0.00125302806977734[/C][/ROW]
[ROW][C]14[/C][C]3[/C][C]3.00080864309037[/C][C]-0.000808643090365546[/C][/ROW]
[ROW][C]15[/C][C]3[/C][C]3.00052185873834[/C][C]-0.000521858738337766[/C][/ROW]
[ROW][C]16[/C][C]3[/C][C]3.00033678213049[/C][C]-0.000336782130490487[/C][/ROW]
[ROW][C]17[/C][C]3[/C][C]3.00021734273106[/C][C]-0.000217342731059667[/C][/ROW]
[ROW][C]18[/C][C]3[/C][C]3.00014026237875[/C][C]-0.000140262378753864[/C][/ROW]
[ROW][C]19[/C][C]3[/C][C]3.0000905184857[/C][C]-9.05184857016295e-05[/C][/ROW]
[ROW][C]20[/C][C]3[/C][C]3.00005841620773[/C][C]-5.84162077279515e-05[/C][/ROW]
[ROW][C]21[/C][C]3[/C][C]3.00003769896612[/C][C]-3.76989661154958e-05[/C][/ROW]
[ROW][C]22[/C][C]3[/C][C]3.00002432907067[/C][C]-2.43290706718469e-05[/C][/ROW]
[ROW][C]23[/C][C]3[/C][C]3.00001570079344[/C][C]-1.57007934364906e-05[/C][/ROW]
[ROW][C]24[/C][C]3[/C][C]3.00001013252491[/C][C]-1.01325249066697e-05[/C][/ROW]
[ROW][C]25[/C][C]3[/C][C]3.00000653903648[/C][C]-6.53903647584997e-06[/C][/ROW]
[ROW][C]26[/C][C]3.1[/C][C]3.00000421997463[/C][C]0.0999957800253712[/C][/ROW]
[ROW][C]27[/C][C]3.1[/C][C]3.13546760959824[/C][C]-0.0354676095982449[/C][/ROW]
[ROW][C]28[/C][C]3.1[/C][C]3.12288906220473[/C][C]-0.0228890622047278[/C][/ROW]
[ROW][C]29[/C][C]3.1[/C][C]3.11477148233406[/C][C]-0.0147714823340621[/C][/ROW]
[ROW][C]30[/C][C]3.1[/C][C]3.10953279292939[/C][C]-0.00953279292938625[/C][/ROW]
[ROW][C]31[/C][C]3.1[/C][C]3.10615199876217[/C][C]-0.00615199876216943[/C][/ROW]
[ROW][C]32[/C][C]3.1[/C][C]3.10397019940012[/C][C]-0.00397019940012155[/C][/ROW]
[ROW][C]33[/C][C]3.1[/C][C]3.10256217269965[/C][C]-0.00256217269965253[/C][/ROW]
[ROW][C]34[/C][C]3.1[/C][C]3.10165350106663[/C][C]-0.00165350106663231[/C][/ROW]
[ROW][C]35[/C][C]3.1[/C][C]3.10106708879449[/C][C]-0.00106708879449302[/C][/ROW]
[ROW][C]36[/C][C]3.1[/C][C]3.10068864696752[/C][C]-0.00068864696752291[/C][/ROW]
[ROW][C]37[/C][C]3.1[/C][C]3.10044441910395[/C][C]-0.000444419103945215[/C][/ROW]
[ROW][C]38[/C][C]3.3[/C][C]3.10028680637433[/C][C]0.199713193625666[/C][/ROW]
[ROW][C]39[/C][C]3.3[/C][C]3.3711148632856[/C][C]-0.0711148632856022[/C][/ROW]
[ROW][C]40[/C][C]3.3[/C][C]3.34589405792674[/C][C]-0.04589405792674[/C][/ROW]
[ROW][C]41[/C][C]3.3[/C][C]3.3296177824954[/C][C]-0.0296177824953983[/C][/ROW]
[ROW][C]42[/C][C]3.3[/C][C]3.31911386962872[/C][C]-0.0191138696287223[/C][/ROW]
[ROW][C]43[/C][C]3.3[/C][C]3.31233515751021[/C][C]-0.0123351575102069[/C][/ROW]
[ROW][C]44[/C][C]3.3[/C][C]3.30796050793257[/C][C]-0.00796050793257308[/C][/ROW]
[ROW][C]45[/C][C]3.3[/C][C]3.30513732285073[/C][C]-0.00513732285073187[/C][/ROW]
[ROW][C]46[/C][C]3.3[/C][C]3.30331537714631[/C][C]-0.00331537714630725[/C][/ROW]
[ROW][C]47[/C][C]3.3[/C][C]3.30213958241318[/C][C]-0.00213958241318046[/C][/ROW]
[ROW][C]48[/C][C]3.3[/C][C]3.30138078194449[/C][C]-0.00138078194448887[/C][/ROW]
[ROW][C]49[/C][C]3.3[/C][C]3.30089108919875[/C][C]-0.000891089198752582[/C][/ROW]
[ROW][C]50[/C][C]3.3[/C][C]3.30057506542818[/C][C]-0.000575065428181976[/C][/ROW]
[ROW][C]51[/C][C]3.3[/C][C]3.30037111912831[/C][C]-0.000371119128312891[/C][/ROW]
[ROW][C]52[/C][C]3.3[/C][C]3.30023950215167[/C][C]-0.000239502151668347[/C][/ROW]
[ROW][C]53[/C][C]3.3[/C][C]3.30015456298605[/C][C]-0.000154562986053985[/C][/ROW]
[ROW][C]54[/C][C]3.3[/C][C]3.30009974739889[/C][C]-9.97473988921804e-05[/C][/ROW]
[ROW][C]55[/C][C]3.3[/C][C]3.30006437209735[/C][C]-6.43720973547701e-05[/C][/ROW]
[ROW][C]56[/C][C]3.3[/C][C]3.30004154260626[/C][C]-4.15426062621016e-05[/C][/ROW]
[ROW][C]57[/C][C]3.3[/C][C]3.30002680956821[/C][C]-2.68095682129932e-05[/C][/ROW]
[ROW][C]58[/C][C]3.3[/C][C]3.30001730158535[/C][C]-1.73015853470737e-05[/C][/ROW]
[ROW][C]59[/C][C]3.3[/C][C]3.30001116559779[/C][C]-1.11655977872438e-05[/C][/ROW]
[ROW][C]60[/C][C]3.3[/C][C]3.30000720573123[/C][C]-7.20573123480506e-06[/C][/ROW]
[ROW][C]61[/C][C]3.3[/C][C]3.30000465022685[/C][C]-4.65022685025573e-06[/C][/ROW]
[ROW][C]62[/C][C]3.3[/C][C]3.30000300102919[/C][C]-3.00102918826539e-06[/C][/ROW]
[ROW][C]63[/C][C]3.3[/C][C]3.3000019367176[/C][C]-1.93671760095881e-06[/C][/ROW]
[ROW][C]64[/C][C]3.3[/C][C]3.30000124986291[/C][C]-1.24986290694906e-06[/C][/ROW]
[ROW][C]65[/C][C]3.3[/C][C]3.30000080660045[/C][C]-8.06600449099193e-07[/C][/ROW]
[ROW][C]66[/C][C]3.3[/C][C]3.30000052054052[/C][C]-5.20540517356949e-07[/C][/ROW]
[ROW][C]67[/C][C]3.3[/C][C]3.30000033593141[/C][C]-3.35931415129664e-07[/C][/ROW]
[ROW][C]68[/C][C]3.3[/C][C]3.30000021679372[/C][C]-2.16793720753117e-07[/C][/ROW]
[ROW][C]69[/C][C]3.3[/C][C]3.30000013990807[/C][C]-1.39908074459072e-07[/C][/ROW]
[ROW][C]70[/C][C]3.3[/C][C]3.30000009028983[/C][C]-9.02898351640147e-08[/C][/ROW]
[ROW][C]71[/C][C]3.3[/C][C]3.30000005826865[/C][C]-5.82686476846561e-08[/C][/ROW]
[ROW][C]72[/C][C]3.3[/C][C]3.30000003760374[/C][C]-3.76037379012928e-08[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200676&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200676&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
333.1-0.1
433.06453511376718-0.064535113767183
533.04164780908943-0.0416478090894321
633.0268774609774-0.0268774609774041
733.0173454000195-0.0173454000194981
833.01119387363596-0.011193873635956
933.00722397908592-0.00722397908591876
1033.00466200312162-0.00466200312161513
1133.00300862901836-0.00300862901836396
1233.00194162215983-0.00194162215983384
1333.00125302806978-0.00125302806977734
1433.00080864309037-0.000808643090365546
1533.00052185873834-0.000521858738337766
1633.00033678213049-0.000336782130490487
1733.00021734273106-0.000217342731059667
1833.00014026237875-0.000140262378753864
1933.0000905184857-9.05184857016295e-05
2033.00005841620773-5.84162077279515e-05
2133.00003769896612-3.76989661154958e-05
2233.00002432907067-2.43290706718469e-05
2333.00001570079344-1.57007934364906e-05
2433.00001013252491-1.01325249066697e-05
2533.00000653903648-6.53903647584997e-06
263.13.000004219974630.0999957800253712
273.13.13546760959824-0.0354676095982449
283.13.12288906220473-0.0228890622047278
293.13.11477148233406-0.0147714823340621
303.13.10953279292939-0.00953279292938625
313.13.10615199876217-0.00615199876216943
323.13.10397019940012-0.00397019940012155
333.13.10256217269965-0.00256217269965253
343.13.10165350106663-0.00165350106663231
353.13.10106708879449-0.00106708879449302
363.13.10068864696752-0.00068864696752291
373.13.10044441910395-0.000444419103945215
383.33.100286806374330.199713193625666
393.33.3711148632856-0.0711148632856022
403.33.34589405792674-0.04589405792674
413.33.3296177824954-0.0296177824953983
423.33.31911386962872-0.0191138696287223
433.33.31233515751021-0.0123351575102069
443.33.30796050793257-0.00796050793257308
453.33.30513732285073-0.00513732285073187
463.33.30331537714631-0.00331537714630725
473.33.30213958241318-0.00213958241318046
483.33.30138078194449-0.00138078194448887
493.33.30089108919875-0.000891089198752582
503.33.30057506542818-0.000575065428181976
513.33.30037111912831-0.000371119128312891
523.33.30023950215167-0.000239502151668347
533.33.30015456298605-0.000154562986053985
543.33.30009974739889-9.97473988921804e-05
553.33.30006437209735-6.43720973547701e-05
563.33.30004154260626-4.15426062621016e-05
573.33.30002680956821-2.68095682129932e-05
583.33.30001730158535-1.73015853470737e-05
593.33.30001116559779-1.11655977872438e-05
603.33.30000720573123-7.20573123480506e-06
613.33.30000465022685-4.65022685025573e-06
623.33.30000300102919-3.00102918826539e-06
633.33.3000019367176-1.93671760095881e-06
643.33.30000124986291-1.24986290694906e-06
653.33.30000080660045-8.06600449099193e-07
663.33.30000052054052-5.20540517356949e-07
673.33.30000033593141-3.35931415129664e-07
683.33.30000021679372-2.16793720753117e-07
693.33.30000013990807-1.39908074459072e-07
703.33.30000009028983-9.02898351640147e-08
713.33.30000005826865-5.82686476846561e-08
723.33.30000003760374-3.76037379012928e-08







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
733.300000024267613.234650038944073.36535000959116
743.300000048535233.189965856523443.41003424054703
753.300000072802853.143204058622423.45679608698327
763.300000097070463.093173352889523.5068268412514
773.300000121338083.039695028952793.56030521372336
783.300000145605692.982819457864933.61718083334646
793.300000169873312.922659307596733.67734103214988
803.300000194140922.85934087482653.74065951345534
813.300000218408542.792987991421923.80701244539515
823.300000242676152.723716722381993.87628376297031
833.300000266943772.651634005006963.94836652888058
843.300000291211382.576837777350944.02316280507182

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 3.30000002426761 & 3.23465003894407 & 3.36535000959116 \tabularnewline
74 & 3.30000004853523 & 3.18996585652344 & 3.41003424054703 \tabularnewline
75 & 3.30000007280285 & 3.14320405862242 & 3.45679608698327 \tabularnewline
76 & 3.30000009707046 & 3.09317335288952 & 3.5068268412514 \tabularnewline
77 & 3.30000012133808 & 3.03969502895279 & 3.56030521372336 \tabularnewline
78 & 3.30000014560569 & 2.98281945786493 & 3.61718083334646 \tabularnewline
79 & 3.30000016987331 & 2.92265930759673 & 3.67734103214988 \tabularnewline
80 & 3.30000019414092 & 2.8593408748265 & 3.74065951345534 \tabularnewline
81 & 3.30000021840854 & 2.79298799142192 & 3.80701244539515 \tabularnewline
82 & 3.30000024267615 & 2.72371672238199 & 3.87628376297031 \tabularnewline
83 & 3.30000026694377 & 2.65163400500696 & 3.94836652888058 \tabularnewline
84 & 3.30000029121138 & 2.57683777735094 & 4.02316280507182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200676&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]3.30000002426761[/C][C]3.23465003894407[/C][C]3.36535000959116[/C][/ROW]
[ROW][C]74[/C][C]3.30000004853523[/C][C]3.18996585652344[/C][C]3.41003424054703[/C][/ROW]
[ROW][C]75[/C][C]3.30000007280285[/C][C]3.14320405862242[/C][C]3.45679608698327[/C][/ROW]
[ROW][C]76[/C][C]3.30000009707046[/C][C]3.09317335288952[/C][C]3.5068268412514[/C][/ROW]
[ROW][C]77[/C][C]3.30000012133808[/C][C]3.03969502895279[/C][C]3.56030521372336[/C][/ROW]
[ROW][C]78[/C][C]3.30000014560569[/C][C]2.98281945786493[/C][C]3.61718083334646[/C][/ROW]
[ROW][C]79[/C][C]3.30000016987331[/C][C]2.92265930759673[/C][C]3.67734103214988[/C][/ROW]
[ROW][C]80[/C][C]3.30000019414092[/C][C]2.8593408748265[/C][C]3.74065951345534[/C][/ROW]
[ROW][C]81[/C][C]3.30000021840854[/C][C]2.79298799142192[/C][C]3.80701244539515[/C][/ROW]
[ROW][C]82[/C][C]3.30000024267615[/C][C]2.72371672238199[/C][C]3.87628376297031[/C][/ROW]
[ROW][C]83[/C][C]3.30000026694377[/C][C]2.65163400500696[/C][C]3.94836652888058[/C][/ROW]
[ROW][C]84[/C][C]3.30000029121138[/C][C]2.57683777735094[/C][C]4.02316280507182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200676&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200676&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
733.300000024267613.234650038944073.36535000959116
743.300000048535233.189965856523443.41003424054703
753.300000072802853.143204058622423.45679608698327
763.300000097070463.093173352889523.5068268412514
773.300000121338083.039695028952793.56030521372336
783.300000145605692.982819457864933.61718083334646
793.300000169873312.922659307596733.67734103214988
803.300000194140922.85934087482653.74065951345534
813.300000218408542.792987991421923.80701244539515
823.300000242676152.723716722381993.87628376297031
833.300000266943772.651634005006963.94836652888058
843.300000291211382.576837777350944.02316280507182



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')