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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 18 Dec 2013 12:15:19 -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/2013/Dec/18/t1387386950tfv18g7xwo6ll4u.htm/, Retrieved Thu, 28 Mar 2024 10:26:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232442, Retrieved Thu, 28 Mar 2024 10:26:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-18 17:15:19] [f14b00927930a3cd0f0d57b4fa1be6d9] [Current]
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Dataseries X:
3,96
3,97
3,96
3,95
3,94
3,94
3,95
3,93
3,94
3,92
3,95
3,94
3,95
3,92
3,92
3,92
3,92
3,9
3,92
3,94
3,96
3,95
3,96
3,97
3,99
4
4,05
4,08
4,09
4,12
4,14
4,15
4,15
4,15
4,15
4,2
4,22
4,22
4,22
4,23
4,3
4,29
4,32
4,31
4,35
4,34
4,35
4,38
4,39
4,38
4,34
4,33
4,33
4,33
4,33
4,32
4,35
4,35
4,35
4,36
4,38
4,41
4,43
4,42
4,43
4,43
4,42
4,46
4,44
4,41
4,41
4,46
4,5
4,58
4,61
4,65
4,55
4,63
4,69
4,72
4,71
4,74
4,77
4,78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232442&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]6 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=232442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232442&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 time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.828168060312446
beta0.0625593211151414
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.828168060312446 \tabularnewline
beta & 0.0625593211151414 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232442&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]0.828168060312446[/C][/ROW]
[ROW][C]beta[/C][C]0.0625593211151414[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232442&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
alpha0.828168060312446
beta0.0625593211151414
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133.953.96646367521367-0.0164636752136746
143.923.92168463300701-0.00168463300700594
153.923.916974507969060.00302549203093649
163.923.915488574341890.00451142565811002
173.923.915883645452590.00411635454740988
183.93.896164798100580.00383520189941589
193.923.93724514283638-0.0172451428363778
203.943.903307288197320.0366927118026834
213.963.947190077893820.0128099221061753
223.953.941124247984620.00887575201537549
233.963.98142678017134-0.021426780171343
243.973.955940276133570.0140597238664339
253.993.978158671846570.0118413281534271
2643.96243852133660.0375614786634033
274.053.996151529457160.0538484705428353
284.084.044755421075730.0352445789242681
294.094.079871622483040.0101283775169643
304.124.074731710426930.0452682895730652
314.144.15829825239779-0.0182982523977948
324.154.14449684493160.00550315506840349
334.154.16857004709232-0.0185700470923242
344.154.144338961482630.0056610385173661
354.154.18510432322311-0.0351043232231119
364.24.16201169671980.037988303280204
374.224.212528984290190.0074710157098048
384.224.206245797570850.0137542024291513
394.224.2304443327247-0.0104443327247017
404.234.226678576340540.00332142365946542
414.34.233459688607190.0665403113928127
424.294.286417593209240.00358240679075994
434.324.32771982160965-0.00771982160964502
444.314.33049840458677-0.0204984045867693
454.354.33128369919780.018716300802196
464.344.34640974108686-0.0064097410868591
474.354.37386238551718-0.0238623855171838
484.384.37691076919920.00308923080080437
494.394.39574495545361-0.00574495545361486
504.384.38137470165782-0.00137470165782183
514.344.38988038344434-0.0498803834443367
524.334.35477168180775-0.0247716818077457
534.334.34664584782787-0.0166458478278715
544.334.313079451483850.016920548516155
554.334.35736286127262-0.0273628612726204
564.324.33453728110143-0.0145372811014273
574.354.340165913897120.00983408610287739
584.354.336326535700590.0136734642994067
594.354.37116103405593-0.0211610340559334
604.364.37496620169211-0.0149662016921104
614.384.370282477219520.00971752278048221
624.414.363222825656820.0467771743431786
634.434.399520381201470.030479618798533
644.424.43569001916491-0.0156900191649072
654.434.43736439904135-0.00736439904134834
664.434.418616042677060.0113839573229439
674.424.45178173307565-0.0317817330756531
684.464.428348301411740.0316516985882629
694.444.47965785792587-0.0396578579258726
704.414.43616730755773-0.026167307557726
714.414.43063388334194-0.0206338833419437
724.464.434580013507430.0254199864925733
734.54.468316609038370.031683390961633
744.584.48768677988760.0923132201123993
754.614.563124959461790.0468750405382128
764.654.610018350272030.0399816497279719
774.554.66719217097449-0.117192170974493
784.634.562982727123870.0670172728761251
794.694.639960448752450.0500395512475471
804.724.704583352130960.015416647869043
814.714.73874783787902-0.0287478378790187
824.744.71572950831910.0242704916809036
834.774.764649824510550.00535017548945316
844.784.8111068196066-0.0311068196066007

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3.95 & 3.96646367521367 & -0.0164636752136746 \tabularnewline
14 & 3.92 & 3.92168463300701 & -0.00168463300700594 \tabularnewline
15 & 3.92 & 3.91697450796906 & 0.00302549203093649 \tabularnewline
16 & 3.92 & 3.91548857434189 & 0.00451142565811002 \tabularnewline
17 & 3.92 & 3.91588364545259 & 0.00411635454740988 \tabularnewline
18 & 3.9 & 3.89616479810058 & 0.00383520189941589 \tabularnewline
19 & 3.92 & 3.93724514283638 & -0.0172451428363778 \tabularnewline
20 & 3.94 & 3.90330728819732 & 0.0366927118026834 \tabularnewline
21 & 3.96 & 3.94719007789382 & 0.0128099221061753 \tabularnewline
22 & 3.95 & 3.94112424798462 & 0.00887575201537549 \tabularnewline
23 & 3.96 & 3.98142678017134 & -0.021426780171343 \tabularnewline
24 & 3.97 & 3.95594027613357 & 0.0140597238664339 \tabularnewline
25 & 3.99 & 3.97815867184657 & 0.0118413281534271 \tabularnewline
26 & 4 & 3.9624385213366 & 0.0375614786634033 \tabularnewline
27 & 4.05 & 3.99615152945716 & 0.0538484705428353 \tabularnewline
28 & 4.08 & 4.04475542107573 & 0.0352445789242681 \tabularnewline
29 & 4.09 & 4.07987162248304 & 0.0101283775169643 \tabularnewline
30 & 4.12 & 4.07473171042693 & 0.0452682895730652 \tabularnewline
31 & 4.14 & 4.15829825239779 & -0.0182982523977948 \tabularnewline
32 & 4.15 & 4.1444968449316 & 0.00550315506840349 \tabularnewline
33 & 4.15 & 4.16857004709232 & -0.0185700470923242 \tabularnewline
34 & 4.15 & 4.14433896148263 & 0.0056610385173661 \tabularnewline
35 & 4.15 & 4.18510432322311 & -0.0351043232231119 \tabularnewline
36 & 4.2 & 4.1620116967198 & 0.037988303280204 \tabularnewline
37 & 4.22 & 4.21252898429019 & 0.0074710157098048 \tabularnewline
38 & 4.22 & 4.20624579757085 & 0.0137542024291513 \tabularnewline
39 & 4.22 & 4.2304443327247 & -0.0104443327247017 \tabularnewline
40 & 4.23 & 4.22667857634054 & 0.00332142365946542 \tabularnewline
41 & 4.3 & 4.23345968860719 & 0.0665403113928127 \tabularnewline
42 & 4.29 & 4.28641759320924 & 0.00358240679075994 \tabularnewline
43 & 4.32 & 4.32771982160965 & -0.00771982160964502 \tabularnewline
44 & 4.31 & 4.33049840458677 & -0.0204984045867693 \tabularnewline
45 & 4.35 & 4.3312836991978 & 0.018716300802196 \tabularnewline
46 & 4.34 & 4.34640974108686 & -0.0064097410868591 \tabularnewline
47 & 4.35 & 4.37386238551718 & -0.0238623855171838 \tabularnewline
48 & 4.38 & 4.3769107691992 & 0.00308923080080437 \tabularnewline
49 & 4.39 & 4.39574495545361 & -0.00574495545361486 \tabularnewline
50 & 4.38 & 4.38137470165782 & -0.00137470165782183 \tabularnewline
51 & 4.34 & 4.38988038344434 & -0.0498803834443367 \tabularnewline
52 & 4.33 & 4.35477168180775 & -0.0247716818077457 \tabularnewline
53 & 4.33 & 4.34664584782787 & -0.0166458478278715 \tabularnewline
54 & 4.33 & 4.31307945148385 & 0.016920548516155 \tabularnewline
55 & 4.33 & 4.35736286127262 & -0.0273628612726204 \tabularnewline
56 & 4.32 & 4.33453728110143 & -0.0145372811014273 \tabularnewline
57 & 4.35 & 4.34016591389712 & 0.00983408610287739 \tabularnewline
58 & 4.35 & 4.33632653570059 & 0.0136734642994067 \tabularnewline
59 & 4.35 & 4.37116103405593 & -0.0211610340559334 \tabularnewline
60 & 4.36 & 4.37496620169211 & -0.0149662016921104 \tabularnewline
61 & 4.38 & 4.37028247721952 & 0.00971752278048221 \tabularnewline
62 & 4.41 & 4.36322282565682 & 0.0467771743431786 \tabularnewline
63 & 4.43 & 4.39952038120147 & 0.030479618798533 \tabularnewline
64 & 4.42 & 4.43569001916491 & -0.0156900191649072 \tabularnewline
65 & 4.43 & 4.43736439904135 & -0.00736439904134834 \tabularnewline
66 & 4.43 & 4.41861604267706 & 0.0113839573229439 \tabularnewline
67 & 4.42 & 4.45178173307565 & -0.0317817330756531 \tabularnewline
68 & 4.46 & 4.42834830141174 & 0.0316516985882629 \tabularnewline
69 & 4.44 & 4.47965785792587 & -0.0396578579258726 \tabularnewline
70 & 4.41 & 4.43616730755773 & -0.026167307557726 \tabularnewline
71 & 4.41 & 4.43063388334194 & -0.0206338833419437 \tabularnewline
72 & 4.46 & 4.43458001350743 & 0.0254199864925733 \tabularnewline
73 & 4.5 & 4.46831660903837 & 0.031683390961633 \tabularnewline
74 & 4.58 & 4.4876867798876 & 0.0923132201123993 \tabularnewline
75 & 4.61 & 4.56312495946179 & 0.0468750405382128 \tabularnewline
76 & 4.65 & 4.61001835027203 & 0.0399816497279719 \tabularnewline
77 & 4.55 & 4.66719217097449 & -0.117192170974493 \tabularnewline
78 & 4.63 & 4.56298272712387 & 0.0670172728761251 \tabularnewline
79 & 4.69 & 4.63996044875245 & 0.0500395512475471 \tabularnewline
80 & 4.72 & 4.70458335213096 & 0.015416647869043 \tabularnewline
81 & 4.71 & 4.73874783787902 & -0.0287478378790187 \tabularnewline
82 & 4.74 & 4.7157295083191 & 0.0242704916809036 \tabularnewline
83 & 4.77 & 4.76464982451055 & 0.00535017548945316 \tabularnewline
84 & 4.78 & 4.8111068196066 & -0.0311068196066007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232442&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]3.95[/C][C]3.96646367521367[/C][C]-0.0164636752136746[/C][/ROW]
[ROW][C]14[/C][C]3.92[/C][C]3.92168463300701[/C][C]-0.00168463300700594[/C][/ROW]
[ROW][C]15[/C][C]3.92[/C][C]3.91697450796906[/C][C]0.00302549203093649[/C][/ROW]
[ROW][C]16[/C][C]3.92[/C][C]3.91548857434189[/C][C]0.00451142565811002[/C][/ROW]
[ROW][C]17[/C][C]3.92[/C][C]3.91588364545259[/C][C]0.00411635454740988[/C][/ROW]
[ROW][C]18[/C][C]3.9[/C][C]3.89616479810058[/C][C]0.00383520189941589[/C][/ROW]
[ROW][C]19[/C][C]3.92[/C][C]3.93724514283638[/C][C]-0.0172451428363778[/C][/ROW]
[ROW][C]20[/C][C]3.94[/C][C]3.90330728819732[/C][C]0.0366927118026834[/C][/ROW]
[ROW][C]21[/C][C]3.96[/C][C]3.94719007789382[/C][C]0.0128099221061753[/C][/ROW]
[ROW][C]22[/C][C]3.95[/C][C]3.94112424798462[/C][C]0.00887575201537549[/C][/ROW]
[ROW][C]23[/C][C]3.96[/C][C]3.98142678017134[/C][C]-0.021426780171343[/C][/ROW]
[ROW][C]24[/C][C]3.97[/C][C]3.95594027613357[/C][C]0.0140597238664339[/C][/ROW]
[ROW][C]25[/C][C]3.99[/C][C]3.97815867184657[/C][C]0.0118413281534271[/C][/ROW]
[ROW][C]26[/C][C]4[/C][C]3.9624385213366[/C][C]0.0375614786634033[/C][/ROW]
[ROW][C]27[/C][C]4.05[/C][C]3.99615152945716[/C][C]0.0538484705428353[/C][/ROW]
[ROW][C]28[/C][C]4.08[/C][C]4.04475542107573[/C][C]0.0352445789242681[/C][/ROW]
[ROW][C]29[/C][C]4.09[/C][C]4.07987162248304[/C][C]0.0101283775169643[/C][/ROW]
[ROW][C]30[/C][C]4.12[/C][C]4.07473171042693[/C][C]0.0452682895730652[/C][/ROW]
[ROW][C]31[/C][C]4.14[/C][C]4.15829825239779[/C][C]-0.0182982523977948[/C][/ROW]
[ROW][C]32[/C][C]4.15[/C][C]4.1444968449316[/C][C]0.00550315506840349[/C][/ROW]
[ROW][C]33[/C][C]4.15[/C][C]4.16857004709232[/C][C]-0.0185700470923242[/C][/ROW]
[ROW][C]34[/C][C]4.15[/C][C]4.14433896148263[/C][C]0.0056610385173661[/C][/ROW]
[ROW][C]35[/C][C]4.15[/C][C]4.18510432322311[/C][C]-0.0351043232231119[/C][/ROW]
[ROW][C]36[/C][C]4.2[/C][C]4.1620116967198[/C][C]0.037988303280204[/C][/ROW]
[ROW][C]37[/C][C]4.22[/C][C]4.21252898429019[/C][C]0.0074710157098048[/C][/ROW]
[ROW][C]38[/C][C]4.22[/C][C]4.20624579757085[/C][C]0.0137542024291513[/C][/ROW]
[ROW][C]39[/C][C]4.22[/C][C]4.2304443327247[/C][C]-0.0104443327247017[/C][/ROW]
[ROW][C]40[/C][C]4.23[/C][C]4.22667857634054[/C][C]0.00332142365946542[/C][/ROW]
[ROW][C]41[/C][C]4.3[/C][C]4.23345968860719[/C][C]0.0665403113928127[/C][/ROW]
[ROW][C]42[/C][C]4.29[/C][C]4.28641759320924[/C][C]0.00358240679075994[/C][/ROW]
[ROW][C]43[/C][C]4.32[/C][C]4.32771982160965[/C][C]-0.00771982160964502[/C][/ROW]
[ROW][C]44[/C][C]4.31[/C][C]4.33049840458677[/C][C]-0.0204984045867693[/C][/ROW]
[ROW][C]45[/C][C]4.35[/C][C]4.3312836991978[/C][C]0.018716300802196[/C][/ROW]
[ROW][C]46[/C][C]4.34[/C][C]4.34640974108686[/C][C]-0.0064097410868591[/C][/ROW]
[ROW][C]47[/C][C]4.35[/C][C]4.37386238551718[/C][C]-0.0238623855171838[/C][/ROW]
[ROW][C]48[/C][C]4.38[/C][C]4.3769107691992[/C][C]0.00308923080080437[/C][/ROW]
[ROW][C]49[/C][C]4.39[/C][C]4.39574495545361[/C][C]-0.00574495545361486[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.38137470165782[/C][C]-0.00137470165782183[/C][/ROW]
[ROW][C]51[/C][C]4.34[/C][C]4.38988038344434[/C][C]-0.0498803834443367[/C][/ROW]
[ROW][C]52[/C][C]4.33[/C][C]4.35477168180775[/C][C]-0.0247716818077457[/C][/ROW]
[ROW][C]53[/C][C]4.33[/C][C]4.34664584782787[/C][C]-0.0166458478278715[/C][/ROW]
[ROW][C]54[/C][C]4.33[/C][C]4.31307945148385[/C][C]0.016920548516155[/C][/ROW]
[ROW][C]55[/C][C]4.33[/C][C]4.35736286127262[/C][C]-0.0273628612726204[/C][/ROW]
[ROW][C]56[/C][C]4.32[/C][C]4.33453728110143[/C][C]-0.0145372811014273[/C][/ROW]
[ROW][C]57[/C][C]4.35[/C][C]4.34016591389712[/C][C]0.00983408610287739[/C][/ROW]
[ROW][C]58[/C][C]4.35[/C][C]4.33632653570059[/C][C]0.0136734642994067[/C][/ROW]
[ROW][C]59[/C][C]4.35[/C][C]4.37116103405593[/C][C]-0.0211610340559334[/C][/ROW]
[ROW][C]60[/C][C]4.36[/C][C]4.37496620169211[/C][C]-0.0149662016921104[/C][/ROW]
[ROW][C]61[/C][C]4.38[/C][C]4.37028247721952[/C][C]0.00971752278048221[/C][/ROW]
[ROW][C]62[/C][C]4.41[/C][C]4.36322282565682[/C][C]0.0467771743431786[/C][/ROW]
[ROW][C]63[/C][C]4.43[/C][C]4.39952038120147[/C][C]0.030479618798533[/C][/ROW]
[ROW][C]64[/C][C]4.42[/C][C]4.43569001916491[/C][C]-0.0156900191649072[/C][/ROW]
[ROW][C]65[/C][C]4.43[/C][C]4.43736439904135[/C][C]-0.00736439904134834[/C][/ROW]
[ROW][C]66[/C][C]4.43[/C][C]4.41861604267706[/C][C]0.0113839573229439[/C][/ROW]
[ROW][C]67[/C][C]4.42[/C][C]4.45178173307565[/C][C]-0.0317817330756531[/C][/ROW]
[ROW][C]68[/C][C]4.46[/C][C]4.42834830141174[/C][C]0.0316516985882629[/C][/ROW]
[ROW][C]69[/C][C]4.44[/C][C]4.47965785792587[/C][C]-0.0396578579258726[/C][/ROW]
[ROW][C]70[/C][C]4.41[/C][C]4.43616730755773[/C][C]-0.026167307557726[/C][/ROW]
[ROW][C]71[/C][C]4.41[/C][C]4.43063388334194[/C][C]-0.0206338833419437[/C][/ROW]
[ROW][C]72[/C][C]4.46[/C][C]4.43458001350743[/C][C]0.0254199864925733[/C][/ROW]
[ROW][C]73[/C][C]4.5[/C][C]4.46831660903837[/C][C]0.031683390961633[/C][/ROW]
[ROW][C]74[/C][C]4.58[/C][C]4.4876867798876[/C][C]0.0923132201123993[/C][/ROW]
[ROW][C]75[/C][C]4.61[/C][C]4.56312495946179[/C][C]0.0468750405382128[/C][/ROW]
[ROW][C]76[/C][C]4.65[/C][C]4.61001835027203[/C][C]0.0399816497279719[/C][/ROW]
[ROW][C]77[/C][C]4.55[/C][C]4.66719217097449[/C][C]-0.117192170974493[/C][/ROW]
[ROW][C]78[/C][C]4.63[/C][C]4.56298272712387[/C][C]0.0670172728761251[/C][/ROW]
[ROW][C]79[/C][C]4.69[/C][C]4.63996044875245[/C][C]0.0500395512475471[/C][/ROW]
[ROW][C]80[/C][C]4.72[/C][C]4.70458335213096[/C][C]0.015416647869043[/C][/ROW]
[ROW][C]81[/C][C]4.71[/C][C]4.73874783787902[/C][C]-0.0287478378790187[/C][/ROW]
[ROW][C]82[/C][C]4.74[/C][C]4.7157295083191[/C][C]0.0242704916809036[/C][/ROW]
[ROW][C]83[/C][C]4.77[/C][C]4.76464982451055[/C][C]0.00535017548945316[/C][/ROW]
[ROW][C]84[/C][C]4.78[/C][C]4.8111068196066[/C][C]-0.0311068196066007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232442&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232442&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
133.953.96646367521367-0.0164636752136746
143.923.92168463300701-0.00168463300700594
153.923.916974507969060.00302549203093649
163.923.915488574341890.00451142565811002
173.923.915883645452590.00411635454740988
183.93.896164798100580.00383520189941589
193.923.93724514283638-0.0172451428363778
203.943.903307288197320.0366927118026834
213.963.947190077893820.0128099221061753
223.953.941124247984620.00887575201537549
233.963.98142678017134-0.021426780171343
243.973.955940276133570.0140597238664339
253.993.978158671846570.0118413281534271
2643.96243852133660.0375614786634033
274.053.996151529457160.0538484705428353
284.084.044755421075730.0352445789242681
294.094.079871622483040.0101283775169643
304.124.074731710426930.0452682895730652
314.144.15829825239779-0.0182982523977948
324.154.14449684493160.00550315506840349
334.154.16857004709232-0.0185700470923242
344.154.144338961482630.0056610385173661
354.154.18510432322311-0.0351043232231119
364.24.16201169671980.037988303280204
374.224.212528984290190.0074710157098048
384.224.206245797570850.0137542024291513
394.224.2304443327247-0.0104443327247017
404.234.226678576340540.00332142365946542
414.34.233459688607190.0665403113928127
424.294.286417593209240.00358240679075994
434.324.32771982160965-0.00771982160964502
444.314.33049840458677-0.0204984045867693
454.354.33128369919780.018716300802196
464.344.34640974108686-0.0064097410868591
474.354.37386238551718-0.0238623855171838
484.384.37691076919920.00308923080080437
494.394.39574495545361-0.00574495545361486
504.384.38137470165782-0.00137470165782183
514.344.38988038344434-0.0498803834443367
524.334.35477168180775-0.0247716818077457
534.334.34664584782787-0.0166458478278715
544.334.313079451483850.016920548516155
554.334.35736286127262-0.0273628612726204
564.324.33453728110143-0.0145372811014273
574.354.340165913897120.00983408610287739
584.354.336326535700590.0136734642994067
594.354.37116103405593-0.0211610340559334
604.364.37496620169211-0.0149662016921104
614.384.370282477219520.00971752278048221
624.414.363222825656820.0467771743431786
634.434.399520381201470.030479618798533
644.424.43569001916491-0.0156900191649072
654.434.43736439904135-0.00736439904134834
664.434.418616042677060.0113839573229439
674.424.45178173307565-0.0317817330756531
684.464.428348301411740.0316516985882629
694.444.47965785792587-0.0396578579258726
704.414.43616730755773-0.026167307557726
714.414.43063388334194-0.0206338833419437
724.464.434580013507430.0254199864925733
734.54.468316609038370.031683390961633
744.584.48768677988760.0923132201123993
754.614.563124959461790.0468750405382128
764.654.610018350272030.0399816497279719
774.554.66719217097449-0.117192170974493
784.634.562982727123870.0670172728761251
794.694.639960448752450.0500395512475471
804.724.704583352130960.015416647869043
814.714.73874783787902-0.0287478378790187
824.744.71572950831910.0242704916809036
834.774.764649824510550.00535017548945316
844.784.8111068196066-0.0311068196066007







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
854.809255511258264.747609032910084.87090198960643
864.821312684546864.73919641124584.90342895784793
874.816217592949654.71600483135384.91643035454549
884.824402808866164.707273667376464.94153195035586
894.820682928461674.68729102955044.95407482737294
904.850478353459394.701195105672724.99976160124606
914.870862045026734.7058896059175.03583448413645
924.887326788610744.706758094648215.06789548257327
934.899568417844474.703422215877035.09571461981192
944.909391374816024.697634095501895.12114865413014
954.933626088115054.706186220492655.16106595573744
964.967776129706374.724554053350395.21099820606235

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 4.80925551125826 & 4.74760903291008 & 4.87090198960643 \tabularnewline
86 & 4.82131268454686 & 4.7391964112458 & 4.90342895784793 \tabularnewline
87 & 4.81621759294965 & 4.7160048313538 & 4.91643035454549 \tabularnewline
88 & 4.82440280886616 & 4.70727366737646 & 4.94153195035586 \tabularnewline
89 & 4.82068292846167 & 4.6872910295504 & 4.95407482737294 \tabularnewline
90 & 4.85047835345939 & 4.70119510567272 & 4.99976160124606 \tabularnewline
91 & 4.87086204502673 & 4.705889605917 & 5.03583448413645 \tabularnewline
92 & 4.88732678861074 & 4.70675809464821 & 5.06789548257327 \tabularnewline
93 & 4.89956841784447 & 4.70342221587703 & 5.09571461981192 \tabularnewline
94 & 4.90939137481602 & 4.69763409550189 & 5.12114865413014 \tabularnewline
95 & 4.93362608811505 & 4.70618622049265 & 5.16106595573744 \tabularnewline
96 & 4.96777612970637 & 4.72455405335039 & 5.21099820606235 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232442&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]85[/C][C]4.80925551125826[/C][C]4.74760903291008[/C][C]4.87090198960643[/C][/ROW]
[ROW][C]86[/C][C]4.82131268454686[/C][C]4.7391964112458[/C][C]4.90342895784793[/C][/ROW]
[ROW][C]87[/C][C]4.81621759294965[/C][C]4.7160048313538[/C][C]4.91643035454549[/C][/ROW]
[ROW][C]88[/C][C]4.82440280886616[/C][C]4.70727366737646[/C][C]4.94153195035586[/C][/ROW]
[ROW][C]89[/C][C]4.82068292846167[/C][C]4.6872910295504[/C][C]4.95407482737294[/C][/ROW]
[ROW][C]90[/C][C]4.85047835345939[/C][C]4.70119510567272[/C][C]4.99976160124606[/C][/ROW]
[ROW][C]91[/C][C]4.87086204502673[/C][C]4.705889605917[/C][C]5.03583448413645[/C][/ROW]
[ROW][C]92[/C][C]4.88732678861074[/C][C]4.70675809464821[/C][C]5.06789548257327[/C][/ROW]
[ROW][C]93[/C][C]4.89956841784447[/C][C]4.70342221587703[/C][C]5.09571461981192[/C][/ROW]
[ROW][C]94[/C][C]4.90939137481602[/C][C]4.69763409550189[/C][C]5.12114865413014[/C][/ROW]
[ROW][C]95[/C][C]4.93362608811505[/C][C]4.70618622049265[/C][C]5.16106595573744[/C][/ROW]
[ROW][C]96[/C][C]4.96777612970637[/C][C]4.72455405335039[/C][C]5.21099820606235[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232442&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232442&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
854.809255511258264.747609032910084.87090198960643
864.821312684546864.73919641124584.90342895784793
874.816217592949654.71600483135384.91643035454549
884.824402808866164.707273667376464.94153195035586
894.820682928461674.68729102955044.95407482737294
904.850478353459394.701195105672724.99976160124606
914.870862045026734.7058896059175.03583448413645
924.887326788610744.706758094648215.06789548257327
934.899568417844474.703422215877035.09571461981192
944.909391374816024.697634095501895.12114865413014
954.933626088115054.706186220492655.16106595573744
964.967776129706374.724554053350395.21099820606235



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')