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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 10:16:25 -0400
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/May/28/t1338214661tshujsqxyvucbz6.htm/, Retrieved Thu, 02 May 2024 00:00:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167807, Retrieved Thu, 02 May 2024 00:00:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact117

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht 10-oefen...] [2012-05-28 14:16:25] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
6,91
6,87
6,91
6,89
6,88
6,9
6,91
6,85
6,86
6,82
6,8
6,83
6,84
6,89
7,14
7,21
7,25
7,31
7,3
7,48
7,49
7,4
7,44
7,42
7,14
7,24
7,33
7,61
7,66
7,69
7,7
7,68
7,71
7,71
7,72
7,68
7,72
7,74
7,76
7,9
7,97
7,96
7,95
7,97
7,93
7,99
7,96
7,92
7,97
7,98
8
8,04
8,17
8,29
8,26
8,3
8,32
8,28
8,27
8,32
8,31
8,34
8,32
8,36
8,33
8,35
8,34
8,37
8,31
8,33
8,34
8,25
8,27
8,31
8,25
8,3
8,3
8,35
8,78
8,9
8,9
8,9
9
9,05

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167807&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167807&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167807&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.923440651817352
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.923440651817352 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167807&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]0.923440651817352[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167807&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167807&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.923440651817352
beta0
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136.846.687601495726490.152398504273505
146.896.871394824161160.0186051758388368
157.147.121637954177310.0183620458226921
167.217.19373990138620.0162600986137971
177.257.233484158427760.0165158415722377
187.317.29304791224690.0169520877531042
197.37.31759784685697-0.0175978468569742
207.487.278992967330470.201007032669526
217.497.49975672024438-0.0097567202443809
227.47.463392655788-0.0633926557879976
237.447.391665654719050.0483343452809502
247.427.46936190834281-0.0493619083428101
257.147.44767566665799-0.307675666657989
267.247.196374672787210.0436253272127951
277.337.46970381382113-0.139703813821127
287.617.395680396862240.214319603137763
297.667.618340431374230.0416595686257697
307.697.70115632361605-0.0111563236160492
317.77.697104688036350.00289531196365367
327.687.69416027153506-0.0141602715350588
337.717.700093853260880.00990614673911594
347.717.677780947243950.0322190527560462
357.727.702899431010530.0171005689894699
367.687.74427358439965-0.0642735843996469
377.727.689040961893990.0309590381060092
387.747.77734439562511-0.0373443956251132
397.767.96186724348368-0.201867243483685
407.97.857543390561770.0424566094382337
417.977.908279410449150.0617205895508466
427.968.00557691464643-0.0455769146464293
437.957.97081569011058-0.0208156901105756
447.977.944669806043080.0253301939569166
457.937.98891299825955-0.0589129982595509
467.997.904757957668250.0852420423317453
477.967.97768256422724-0.0176825642272407
487.927.98070660626408-0.0607066062640822
497.977.936058823877710.0339411761222914
507.988.0218868187173-0.0418868187173036
5188.18961924644159-0.189619246441588
528.048.11531096681686-0.0753109668168577
538.178.058770457085120.111229542914883
548.298.193571914464710.0964280855352939
558.268.29183958306865-0.0318395830686544
568.38.259046686907910.0409533130920927
578.328.311267298557060.00873270144293592
588.288.30061546293659-0.0206154629365862
598.278.267907105040710.00209289495928644
608.328.285898717384220.0341012826157758
618.318.33604656622893-0.0260465662289295
628.348.36067409931175-0.020674099311746
638.328.5366849160987-0.216684916098703
648.368.44613446422388-0.0861344642238819
658.338.39388051682638-0.0638805168263765
668.358.36584503656959-0.015845036569587
678.348.35061505101421-0.0106150510142093
688.378.342994727250730.0270052727492676
698.318.37986836240823-0.0698683624082292
708.338.294386232816240.0356137671837597
718.348.31534076891270.0246592310873037
728.258.35662159469475-0.106621594694751
738.278.27221533788807-0.00221533788807093
748.318.31926090856889-0.00926090856888884
758.258.49080466928479-0.240804669284788
768.38.38797591430662-0.0879759143066199
778.38.33572524475167-0.0357252447516654
788.358.337367052349740.0126329476502569
798.788.348835199389910.431164800610093
808.98.75205253723590.147947462764101
818.98.893192524809170.00680747519082914
828.98.886591623754780.0134083762452235
8398.88620212702590.113797872974096
849.058.999746423923260.0502535760767433

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6.84 & 6.68760149572649 & 0.152398504273505 \tabularnewline
14 & 6.89 & 6.87139482416116 & 0.0186051758388368 \tabularnewline
15 & 7.14 & 7.12163795417731 & 0.0183620458226921 \tabularnewline
16 & 7.21 & 7.1937399013862 & 0.0162600986137971 \tabularnewline
17 & 7.25 & 7.23348415842776 & 0.0165158415722377 \tabularnewline
18 & 7.31 & 7.2930479122469 & 0.0169520877531042 \tabularnewline
19 & 7.3 & 7.31759784685697 & -0.0175978468569742 \tabularnewline
20 & 7.48 & 7.27899296733047 & 0.201007032669526 \tabularnewline
21 & 7.49 & 7.49975672024438 & -0.0097567202443809 \tabularnewline
22 & 7.4 & 7.463392655788 & -0.0633926557879976 \tabularnewline
23 & 7.44 & 7.39166565471905 & 0.0483343452809502 \tabularnewline
24 & 7.42 & 7.46936190834281 & -0.0493619083428101 \tabularnewline
25 & 7.14 & 7.44767566665799 & -0.307675666657989 \tabularnewline
26 & 7.24 & 7.19637467278721 & 0.0436253272127951 \tabularnewline
27 & 7.33 & 7.46970381382113 & -0.139703813821127 \tabularnewline
28 & 7.61 & 7.39568039686224 & 0.214319603137763 \tabularnewline
29 & 7.66 & 7.61834043137423 & 0.0416595686257697 \tabularnewline
30 & 7.69 & 7.70115632361605 & -0.0111563236160492 \tabularnewline
31 & 7.7 & 7.69710468803635 & 0.00289531196365367 \tabularnewline
32 & 7.68 & 7.69416027153506 & -0.0141602715350588 \tabularnewline
33 & 7.71 & 7.70009385326088 & 0.00990614673911594 \tabularnewline
34 & 7.71 & 7.67778094724395 & 0.0322190527560462 \tabularnewline
35 & 7.72 & 7.70289943101053 & 0.0171005689894699 \tabularnewline
36 & 7.68 & 7.74427358439965 & -0.0642735843996469 \tabularnewline
37 & 7.72 & 7.68904096189399 & 0.0309590381060092 \tabularnewline
38 & 7.74 & 7.77734439562511 & -0.0373443956251132 \tabularnewline
39 & 7.76 & 7.96186724348368 & -0.201867243483685 \tabularnewline
40 & 7.9 & 7.85754339056177 & 0.0424566094382337 \tabularnewline
41 & 7.97 & 7.90827941044915 & 0.0617205895508466 \tabularnewline
42 & 7.96 & 8.00557691464643 & -0.0455769146464293 \tabularnewline
43 & 7.95 & 7.97081569011058 & -0.0208156901105756 \tabularnewline
44 & 7.97 & 7.94466980604308 & 0.0253301939569166 \tabularnewline
45 & 7.93 & 7.98891299825955 & -0.0589129982595509 \tabularnewline
46 & 7.99 & 7.90475795766825 & 0.0852420423317453 \tabularnewline
47 & 7.96 & 7.97768256422724 & -0.0176825642272407 \tabularnewline
48 & 7.92 & 7.98070660626408 & -0.0607066062640822 \tabularnewline
49 & 7.97 & 7.93605882387771 & 0.0339411761222914 \tabularnewline
50 & 7.98 & 8.0218868187173 & -0.0418868187173036 \tabularnewline
51 & 8 & 8.18961924644159 & -0.189619246441588 \tabularnewline
52 & 8.04 & 8.11531096681686 & -0.0753109668168577 \tabularnewline
53 & 8.17 & 8.05877045708512 & 0.111229542914883 \tabularnewline
54 & 8.29 & 8.19357191446471 & 0.0964280855352939 \tabularnewline
55 & 8.26 & 8.29183958306865 & -0.0318395830686544 \tabularnewline
56 & 8.3 & 8.25904668690791 & 0.0409533130920927 \tabularnewline
57 & 8.32 & 8.31126729855706 & 0.00873270144293592 \tabularnewline
58 & 8.28 & 8.30061546293659 & -0.0206154629365862 \tabularnewline
59 & 8.27 & 8.26790710504071 & 0.00209289495928644 \tabularnewline
60 & 8.32 & 8.28589871738422 & 0.0341012826157758 \tabularnewline
61 & 8.31 & 8.33604656622893 & -0.0260465662289295 \tabularnewline
62 & 8.34 & 8.36067409931175 & -0.020674099311746 \tabularnewline
63 & 8.32 & 8.5366849160987 & -0.216684916098703 \tabularnewline
64 & 8.36 & 8.44613446422388 & -0.0861344642238819 \tabularnewline
65 & 8.33 & 8.39388051682638 & -0.0638805168263765 \tabularnewline
66 & 8.35 & 8.36584503656959 & -0.015845036569587 \tabularnewline
67 & 8.34 & 8.35061505101421 & -0.0106150510142093 \tabularnewline
68 & 8.37 & 8.34299472725073 & 0.0270052727492676 \tabularnewline
69 & 8.31 & 8.37986836240823 & -0.0698683624082292 \tabularnewline
70 & 8.33 & 8.29438623281624 & 0.0356137671837597 \tabularnewline
71 & 8.34 & 8.3153407689127 & 0.0246592310873037 \tabularnewline
72 & 8.25 & 8.35662159469475 & -0.106621594694751 \tabularnewline
73 & 8.27 & 8.27221533788807 & -0.00221533788807093 \tabularnewline
74 & 8.31 & 8.31926090856889 & -0.00926090856888884 \tabularnewline
75 & 8.25 & 8.49080466928479 & -0.240804669284788 \tabularnewline
76 & 8.3 & 8.38797591430662 & -0.0879759143066199 \tabularnewline
77 & 8.3 & 8.33572524475167 & -0.0357252447516654 \tabularnewline
78 & 8.35 & 8.33736705234974 & 0.0126329476502569 \tabularnewline
79 & 8.78 & 8.34883519938991 & 0.431164800610093 \tabularnewline
80 & 8.9 & 8.7520525372359 & 0.147947462764101 \tabularnewline
81 & 8.9 & 8.89319252480917 & 0.00680747519082914 \tabularnewline
82 & 8.9 & 8.88659162375478 & 0.0134083762452235 \tabularnewline
83 & 9 & 8.8862021270259 & 0.113797872974096 \tabularnewline
84 & 9.05 & 8.99974642392326 & 0.0502535760767433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167807&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]6.84[/C][C]6.68760149572649[/C][C]0.152398504273505[/C][/ROW]
[ROW][C]14[/C][C]6.89[/C][C]6.87139482416116[/C][C]0.0186051758388368[/C][/ROW]
[ROW][C]15[/C][C]7.14[/C][C]7.12163795417731[/C][C]0.0183620458226921[/C][/ROW]
[ROW][C]16[/C][C]7.21[/C][C]7.1937399013862[/C][C]0.0162600986137971[/C][/ROW]
[ROW][C]17[/C][C]7.25[/C][C]7.23348415842776[/C][C]0.0165158415722377[/C][/ROW]
[ROW][C]18[/C][C]7.31[/C][C]7.2930479122469[/C][C]0.0169520877531042[/C][/ROW]
[ROW][C]19[/C][C]7.3[/C][C]7.31759784685697[/C][C]-0.0175978468569742[/C][/ROW]
[ROW][C]20[/C][C]7.48[/C][C]7.27899296733047[/C][C]0.201007032669526[/C][/ROW]
[ROW][C]21[/C][C]7.49[/C][C]7.49975672024438[/C][C]-0.0097567202443809[/C][/ROW]
[ROW][C]22[/C][C]7.4[/C][C]7.463392655788[/C][C]-0.0633926557879976[/C][/ROW]
[ROW][C]23[/C][C]7.44[/C][C]7.39166565471905[/C][C]0.0483343452809502[/C][/ROW]
[ROW][C]24[/C][C]7.42[/C][C]7.46936190834281[/C][C]-0.0493619083428101[/C][/ROW]
[ROW][C]25[/C][C]7.14[/C][C]7.44767566665799[/C][C]-0.307675666657989[/C][/ROW]
[ROW][C]26[/C][C]7.24[/C][C]7.19637467278721[/C][C]0.0436253272127951[/C][/ROW]
[ROW][C]27[/C][C]7.33[/C][C]7.46970381382113[/C][C]-0.139703813821127[/C][/ROW]
[ROW][C]28[/C][C]7.61[/C][C]7.39568039686224[/C][C]0.214319603137763[/C][/ROW]
[ROW][C]29[/C][C]7.66[/C][C]7.61834043137423[/C][C]0.0416595686257697[/C][/ROW]
[ROW][C]30[/C][C]7.69[/C][C]7.70115632361605[/C][C]-0.0111563236160492[/C][/ROW]
[ROW][C]31[/C][C]7.7[/C][C]7.69710468803635[/C][C]0.00289531196365367[/C][/ROW]
[ROW][C]32[/C][C]7.68[/C][C]7.69416027153506[/C][C]-0.0141602715350588[/C][/ROW]
[ROW][C]33[/C][C]7.71[/C][C]7.70009385326088[/C][C]0.00990614673911594[/C][/ROW]
[ROW][C]34[/C][C]7.71[/C][C]7.67778094724395[/C][C]0.0322190527560462[/C][/ROW]
[ROW][C]35[/C][C]7.72[/C][C]7.70289943101053[/C][C]0.0171005689894699[/C][/ROW]
[ROW][C]36[/C][C]7.68[/C][C]7.74427358439965[/C][C]-0.0642735843996469[/C][/ROW]
[ROW][C]37[/C][C]7.72[/C][C]7.68904096189399[/C][C]0.0309590381060092[/C][/ROW]
[ROW][C]38[/C][C]7.74[/C][C]7.77734439562511[/C][C]-0.0373443956251132[/C][/ROW]
[ROW][C]39[/C][C]7.76[/C][C]7.96186724348368[/C][C]-0.201867243483685[/C][/ROW]
[ROW][C]40[/C][C]7.9[/C][C]7.85754339056177[/C][C]0.0424566094382337[/C][/ROW]
[ROW][C]41[/C][C]7.97[/C][C]7.90827941044915[/C][C]0.0617205895508466[/C][/ROW]
[ROW][C]42[/C][C]7.96[/C][C]8.00557691464643[/C][C]-0.0455769146464293[/C][/ROW]
[ROW][C]43[/C][C]7.95[/C][C]7.97081569011058[/C][C]-0.0208156901105756[/C][/ROW]
[ROW][C]44[/C][C]7.97[/C][C]7.94466980604308[/C][C]0.0253301939569166[/C][/ROW]
[ROW][C]45[/C][C]7.93[/C][C]7.98891299825955[/C][C]-0.0589129982595509[/C][/ROW]
[ROW][C]46[/C][C]7.99[/C][C]7.90475795766825[/C][C]0.0852420423317453[/C][/ROW]
[ROW][C]47[/C][C]7.96[/C][C]7.97768256422724[/C][C]-0.0176825642272407[/C][/ROW]
[ROW][C]48[/C][C]7.92[/C][C]7.98070660626408[/C][C]-0.0607066062640822[/C][/ROW]
[ROW][C]49[/C][C]7.97[/C][C]7.93605882387771[/C][C]0.0339411761222914[/C][/ROW]
[ROW][C]50[/C][C]7.98[/C][C]8.0218868187173[/C][C]-0.0418868187173036[/C][/ROW]
[ROW][C]51[/C][C]8[/C][C]8.18961924644159[/C][C]-0.189619246441588[/C][/ROW]
[ROW][C]52[/C][C]8.04[/C][C]8.11531096681686[/C][C]-0.0753109668168577[/C][/ROW]
[ROW][C]53[/C][C]8.17[/C][C]8.05877045708512[/C][C]0.111229542914883[/C][/ROW]
[ROW][C]54[/C][C]8.29[/C][C]8.19357191446471[/C][C]0.0964280855352939[/C][/ROW]
[ROW][C]55[/C][C]8.26[/C][C]8.29183958306865[/C][C]-0.0318395830686544[/C][/ROW]
[ROW][C]56[/C][C]8.3[/C][C]8.25904668690791[/C][C]0.0409533130920927[/C][/ROW]
[ROW][C]57[/C][C]8.32[/C][C]8.31126729855706[/C][C]0.00873270144293592[/C][/ROW]
[ROW][C]58[/C][C]8.28[/C][C]8.30061546293659[/C][C]-0.0206154629365862[/C][/ROW]
[ROW][C]59[/C][C]8.27[/C][C]8.26790710504071[/C][C]0.00209289495928644[/C][/ROW]
[ROW][C]60[/C][C]8.32[/C][C]8.28589871738422[/C][C]0.0341012826157758[/C][/ROW]
[ROW][C]61[/C][C]8.31[/C][C]8.33604656622893[/C][C]-0.0260465662289295[/C][/ROW]
[ROW][C]62[/C][C]8.34[/C][C]8.36067409931175[/C][C]-0.020674099311746[/C][/ROW]
[ROW][C]63[/C][C]8.32[/C][C]8.5366849160987[/C][C]-0.216684916098703[/C][/ROW]
[ROW][C]64[/C][C]8.36[/C][C]8.44613446422388[/C][C]-0.0861344642238819[/C][/ROW]
[ROW][C]65[/C][C]8.33[/C][C]8.39388051682638[/C][C]-0.0638805168263765[/C][/ROW]
[ROW][C]66[/C][C]8.35[/C][C]8.36584503656959[/C][C]-0.015845036569587[/C][/ROW]
[ROW][C]67[/C][C]8.34[/C][C]8.35061505101421[/C][C]-0.0106150510142093[/C][/ROW]
[ROW][C]68[/C][C]8.37[/C][C]8.34299472725073[/C][C]0.0270052727492676[/C][/ROW]
[ROW][C]69[/C][C]8.31[/C][C]8.37986836240823[/C][C]-0.0698683624082292[/C][/ROW]
[ROW][C]70[/C][C]8.33[/C][C]8.29438623281624[/C][C]0.0356137671837597[/C][/ROW]
[ROW][C]71[/C][C]8.34[/C][C]8.3153407689127[/C][C]0.0246592310873037[/C][/ROW]
[ROW][C]72[/C][C]8.25[/C][C]8.35662159469475[/C][C]-0.106621594694751[/C][/ROW]
[ROW][C]73[/C][C]8.27[/C][C]8.27221533788807[/C][C]-0.00221533788807093[/C][/ROW]
[ROW][C]74[/C][C]8.31[/C][C]8.31926090856889[/C][C]-0.00926090856888884[/C][/ROW]
[ROW][C]75[/C][C]8.25[/C][C]8.49080466928479[/C][C]-0.240804669284788[/C][/ROW]
[ROW][C]76[/C][C]8.3[/C][C]8.38797591430662[/C][C]-0.0879759143066199[/C][/ROW]
[ROW][C]77[/C][C]8.3[/C][C]8.33572524475167[/C][C]-0.0357252447516654[/C][/ROW]
[ROW][C]78[/C][C]8.35[/C][C]8.33736705234974[/C][C]0.0126329476502569[/C][/ROW]
[ROW][C]79[/C][C]8.78[/C][C]8.34883519938991[/C][C]0.431164800610093[/C][/ROW]
[ROW][C]80[/C][C]8.9[/C][C]8.7520525372359[/C][C]0.147947462764101[/C][/ROW]
[ROW][C]81[/C][C]8.9[/C][C]8.89319252480917[/C][C]0.00680747519082914[/C][/ROW]
[ROW][C]82[/C][C]8.9[/C][C]8.88659162375478[/C][C]0.0134083762452235[/C][/ROW]
[ROW][C]83[/C][C]9[/C][C]8.8862021270259[/C][C]0.113797872974096[/C][/ROW]
[ROW][C]84[/C][C]9.05[/C][C]8.99974642392326[/C][C]0.0502535760767433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167807&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167807&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136.846.687601495726490.152398504273505
146.896.871394824161160.0186051758388368
157.147.121637954177310.0183620458226921
167.217.19373990138620.0162600986137971
177.257.233484158427760.0165158415722377
187.317.29304791224690.0169520877531042
197.37.31759784685697-0.0175978468569742
207.487.278992967330470.201007032669526
217.497.49975672024438-0.0097567202443809
227.47.463392655788-0.0633926557879976
237.447.391665654719050.0483343452809502
247.427.46936190834281-0.0493619083428101
257.147.44767566665799-0.307675666657989
267.247.196374672787210.0436253272127951
277.337.46970381382113-0.139703813821127
287.617.395680396862240.214319603137763
297.667.618340431374230.0416595686257697
307.697.70115632361605-0.0111563236160492
317.77.697104688036350.00289531196365367
327.687.69416027153506-0.0141602715350588
337.717.700093853260880.00990614673911594
347.717.677780947243950.0322190527560462
357.727.702899431010530.0171005689894699
367.687.74427358439965-0.0642735843996469
377.727.689040961893990.0309590381060092
387.747.77734439562511-0.0373443956251132
397.767.96186724348368-0.201867243483685
407.97.857543390561770.0424566094382337
417.977.908279410449150.0617205895508466
427.968.00557691464643-0.0455769146464293
437.957.97081569011058-0.0208156901105756
447.977.944669806043080.0253301939569166
457.937.98891299825955-0.0589129982595509
467.997.904757957668250.0852420423317453
477.967.97768256422724-0.0176825642272407
487.927.98070660626408-0.0607066062640822
497.977.936058823877710.0339411761222914
507.988.0218868187173-0.0418868187173036
5188.18961924644159-0.189619246441588
528.048.11531096681686-0.0753109668168577
538.178.058770457085120.111229542914883
548.298.193571914464710.0964280855352939
558.268.29183958306865-0.0318395830686544
568.38.259046686907910.0409533130920927
578.328.311267298557060.00873270144293592
588.288.30061546293659-0.0206154629365862
598.278.267907105040710.00209289495928644
608.328.285898717384220.0341012826157758
618.318.33604656622893-0.0260465662289295
628.348.36067409931175-0.020674099311746
638.328.5366849160987-0.216684916098703
648.368.44613446422388-0.0861344642238819
658.338.39388051682638-0.0638805168263765
668.358.36584503656959-0.015845036569587
678.348.35061505101421-0.0106150510142093
688.378.342994727250730.0270052727492676
698.318.37986836240823-0.0698683624082292
708.338.294386232816240.0356137671837597
718.348.31534076891270.0246592310873037
728.258.35662159469475-0.106621594694751
738.278.27221533788807-0.00221533788807093
748.318.31926090856889-0.00926090856888884
758.258.49080466928479-0.240804669284788
768.38.38797591430662-0.0879759143066199
778.38.33572524475167-0.0357252447516654
788.358.337367052349740.0126329476502569
798.788.348835199389910.431164800610093
808.98.75205253723590.147947462764101
818.98.893192524809170.00680747519082914
828.98.886591623754780.0134083762452235
8398.88620212702590.113797872974096
849.058.999746423923260.0502535760767433






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
859.068198352035078.866730543973399.26966616009676
869.116750251480358.84252135914819.3909791438126
879.279119072245368.947737580465329.6105005640254
889.410359607896899.030325529426359.79039368636744
899.443349751196719.020220800989399.86647870140403
909.481683973784189.019460741775949.94390720579242
919.513528869268099.0152693747145710.0117883638216
929.496908167818498.9650484761541110.0287678594829
939.490621868491048.9271620746087110.0540816623734
949.478240028791348.8848605995670810.0716194580156
959.473154446796718.8512932446534210.09501564894
969.476748251748258.8276538345517310.1258426689448

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 9.06819835203507 & 8.86673054397339 & 9.26966616009676 \tabularnewline
86 & 9.11675025148035 & 8.8425213591481 & 9.3909791438126 \tabularnewline
87 & 9.27911907224536 & 8.94773758046532 & 9.6105005640254 \tabularnewline
88 & 9.41035960789689 & 9.03032552942635 & 9.79039368636744 \tabularnewline
89 & 9.44334975119671 & 9.02022080098939 & 9.86647870140403 \tabularnewline
90 & 9.48168397378418 & 9.01946074177594 & 9.94390720579242 \tabularnewline
91 & 9.51352886926809 & 9.01526937471457 & 10.0117883638216 \tabularnewline
92 & 9.49690816781849 & 8.96504847615411 & 10.0287678594829 \tabularnewline
93 & 9.49062186849104 & 8.92716207460871 & 10.0540816623734 \tabularnewline
94 & 9.47824002879134 & 8.88486059956708 & 10.0716194580156 \tabularnewline
95 & 9.47315444679671 & 8.85129324465342 & 10.09501564894 \tabularnewline
96 & 9.47674825174825 & 8.82765383455173 & 10.1258426689448 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167807&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]9.06819835203507[/C][C]8.86673054397339[/C][C]9.26966616009676[/C][/ROW]
[ROW][C]86[/C][C]9.11675025148035[/C][C]8.8425213591481[/C][C]9.3909791438126[/C][/ROW]
[ROW][C]87[/C][C]9.27911907224536[/C][C]8.94773758046532[/C][C]9.6105005640254[/C][/ROW]
[ROW][C]88[/C][C]9.41035960789689[/C][C]9.03032552942635[/C][C]9.79039368636744[/C][/ROW]
[ROW][C]89[/C][C]9.44334975119671[/C][C]9.02022080098939[/C][C]9.86647870140403[/C][/ROW]
[ROW][C]90[/C][C]9.48168397378418[/C][C]9.01946074177594[/C][C]9.94390720579242[/C][/ROW]
[ROW][C]91[/C][C]9.51352886926809[/C][C]9.01526937471457[/C][C]10.0117883638216[/C][/ROW]
[ROW][C]92[/C][C]9.49690816781849[/C][C]8.96504847615411[/C][C]10.0287678594829[/C][/ROW]
[ROW][C]93[/C][C]9.49062186849104[/C][C]8.92716207460871[/C][C]10.0540816623734[/C][/ROW]
[ROW][C]94[/C][C]9.47824002879134[/C][C]8.88486059956708[/C][C]10.0716194580156[/C][/ROW]
[ROW][C]95[/C][C]9.47315444679671[/C][C]8.85129324465342[/C][C]10.09501564894[/C][/ROW]
[ROW][C]96[/C][C]9.47674825174825[/C][C]8.82765383455173[/C][C]10.1258426689448[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167807&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167807&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
859.068198352035078.866730543973399.26966616009676
869.116750251480358.84252135914819.3909791438126
879.279119072245368.947737580465329.6105005640254
889.410359607896899.030325529426359.79039368636744
899.443349751196719.020220800989399.86647870140403
909.481683973784189.019460741775949.94390720579242
919.513528869268099.0152693747145710.0117883638216
929.496908167818498.9650484761541110.0287678594829
939.490621868491048.9271620746087110.0540816623734
949.478240028791348.8848605995670810.0716194580156
959.473154446796718.8512932446534210.09501564894
969.476748251748258.8276538345517310.1258426689448


Figures (Output of Computation)

Input Parameters & R Code

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')