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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 12 Dec 2011 07:08:53 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/12/t13236917486zifs7lg7ew5ihl.htm/, Retrieved Fri, 03 May 2024 14:39:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=153932, Retrieved Fri, 03 May 2024 14:39:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Data Series] [Bivariate dataset] [2008-01-05 23:51:08] [74be16979710d4c4e7c6647856088456]
F RMPD  [Univariate Explorative Data Analysis] [Colombia Coffee] [2008-01-07 14:21:11] [74be16979710d4c4e7c6647856088456]
- RMPD    [Univariate Explorative Data Analysis] [paper] [2011-11-24 11:53:20] [74be16979710d4c4e7c6647856088456]
- RMPD      [Decomposition by Loess] [paper] [2011-12-12 12:02:29] [91ce4971c808115c699d50336245df56]
- RMP           [Exponential Smoothing] [Paper] [2011-12-12 12:08:53] [858ef1d716a843f745df26a736207017] [Current]
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Dataseries X:
374.92
375.63
376.51
377.75
378.54
378.21
376.65
374.28
373.12
373.1
374.67
375.97
377.03
377.87
378.88
380.42
380.62
379.66
377.48
376.07
374.1
374.47
376.15
377.51
378.43
379.7
380.91
382.2
382.45
382.14
380.6
378.6
376.72
376.98
378.29
380.07
381.36
382.19
382.65
384.65
384.94
384.01
382.15
380.33
378.81
379.06
380.17
381.85
382.88
383.77
384.42
386.36
386.53
386.01
384.45
381.96
380.81
381.09
382.37
383.84
385.42
385.72
385.96
387.18
388.5
387.88
386.38
384.15
383.07
382.98
384.11
385.54
386.92
387.41
388.77
389.46
390.18
389.43
387.74
385.91
384.77
384.38
385.99
387.26




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153932&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153932&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.420119721396685
beta0.0102379025686814
gamma0.225220858718716

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.420119721396685 \tabularnewline
beta & 0.0102379025686814 \tabularnewline
gamma & 0.225220858718716 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153932&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]0.420119721396685[/C][/ROW]
[ROW][C]beta[/C][C]0.0102379025686814[/C][/ROW]
[ROW][C]gamma[/C][C]0.225220858718716[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153932&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
alpha0.420119721396685
beta0.0102379025686814
gamma0.225220858718716







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13377.03376.017807158121.01219284188039
14377.87377.3192283870040.550771612996414
15378.88378.5929164062080.287083593792374
16380.42380.3045586763470.11544132365259
17380.62380.5837538402890.0362461597110837
18379.66379.662750120666-0.00275012066646241
19377.48378.391601465929-0.911601465929095
20376.07375.603038840680.466961159319567
21374.1374.594812695696-0.494812695696282
22374.47374.3024814589890.167518541010963
23376.15375.891212491750.258787508249782
24377.51377.3002338334720.20976616652797
25378.43378.633839444033-0.203839444032724
26379.7379.3661821019270.333817898073448
27380.91380.5154151931740.39458480682606
28382.2382.251396106812-0.0513961068122057
29382.45382.451030944767-0.00103094476725119
30382.14381.5099874327840.63001256721617
31380.6380.3894134623540.210586537646009
32378.6378.2606083009190.339391699081034
33376.72377.080892568552-0.360892568551606
34376.98376.9396146541190.0403853458810204
35378.29378.494597161704-0.204597161703987
36380.07379.7082889442940.361711055706053
37381.36381.058115496580.301884503420297
38382.19382.0817198681480.108280131851927
39382.65383.151744703535-0.501744703534996
40384.65384.4566674372510.193332562749163
41384.94384.7705011138580.169498886141753
42384.01383.9890547697620.0209452302381692
43382.15382.560741621775-0.410741621775117
44380.33380.1879734625120.142026537487538
45378.81378.83328103284-0.0232810328404867
46379.06378.8870980687020.172901931297815
47380.17380.467178722054-0.297178722053616
48381.85381.7169577623610.13304223763862
49382.88382.962941182727-0.0829411827274384
50383.77383.797971116532-0.0279711165320577
51384.42384.728881516429-0.308881516428926
52386.36386.2042346269470.1557653730531
53386.53386.4976381681280.032361831871583
54386.01385.6370520077510.372947992248953
55384.45384.2996328250940.150367174906307
56381.96382.236592551499-0.276592551498652
57380.81380.6844429550170.125557044982884
58381.09380.8270540188550.262945981144924
59382.37382.384600677836-0.014600677836313
60383.84383.8115288728030.0284711271969513
61385.42384.9871676523230.432832347677504
62385.72386.050077212276-0.330077212276024
63385.96386.820094105732-0.860094105731832
64387.18388.124898941668-0.944898941667532
65388.5387.9353845326260.564615467373642
66387.88387.3407883376080.539211662391608
67386.38386.0427643960550.337235603945373
68384.15384.0018874599460.148112540053489
69383.07382.6819304094590.388069590541193
70382.98382.9551447939630.0248552060374436
71384.11384.37776632372-0.26776632372048
72385.54385.704220371936-0.16422037193621
73386.92386.8511473998230.06885260017674
74387.41387.659371219411-0.249371219411273
75388.77388.3922867964270.377713203572512
76389.46390.209580586771-0.749580586771344
77390.18390.303644957407-0.123644957406725
78389.43389.4179963037750.0120036962249515
79387.74387.871253083273-0.13125308327318
80385.91385.6059895733280.304010426671937
81384.77384.3806719514720.38932804852783
82384.38384.604789230156-0.224789230156034
83385.99385.8810501501340.108949849865553
84387.26387.377650266709-0.117650266709461

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 377.03 & 376.01780715812 & 1.01219284188039 \tabularnewline
14 & 377.87 & 377.319228387004 & 0.550771612996414 \tabularnewline
15 & 378.88 & 378.592916406208 & 0.287083593792374 \tabularnewline
16 & 380.42 & 380.304558676347 & 0.11544132365259 \tabularnewline
17 & 380.62 & 380.583753840289 & 0.0362461597110837 \tabularnewline
18 & 379.66 & 379.662750120666 & -0.00275012066646241 \tabularnewline
19 & 377.48 & 378.391601465929 & -0.911601465929095 \tabularnewline
20 & 376.07 & 375.60303884068 & 0.466961159319567 \tabularnewline
21 & 374.1 & 374.594812695696 & -0.494812695696282 \tabularnewline
22 & 374.47 & 374.302481458989 & 0.167518541010963 \tabularnewline
23 & 376.15 & 375.89121249175 & 0.258787508249782 \tabularnewline
24 & 377.51 & 377.300233833472 & 0.20976616652797 \tabularnewline
25 & 378.43 & 378.633839444033 & -0.203839444032724 \tabularnewline
26 & 379.7 & 379.366182101927 & 0.333817898073448 \tabularnewline
27 & 380.91 & 380.515415193174 & 0.39458480682606 \tabularnewline
28 & 382.2 & 382.251396106812 & -0.0513961068122057 \tabularnewline
29 & 382.45 & 382.451030944767 & -0.00103094476725119 \tabularnewline
30 & 382.14 & 381.509987432784 & 0.63001256721617 \tabularnewline
31 & 380.6 & 380.389413462354 & 0.210586537646009 \tabularnewline
32 & 378.6 & 378.260608300919 & 0.339391699081034 \tabularnewline
33 & 376.72 & 377.080892568552 & -0.360892568551606 \tabularnewline
34 & 376.98 & 376.939614654119 & 0.0403853458810204 \tabularnewline
35 & 378.29 & 378.494597161704 & -0.204597161703987 \tabularnewline
36 & 380.07 & 379.708288944294 & 0.361711055706053 \tabularnewline
37 & 381.36 & 381.05811549658 & 0.301884503420297 \tabularnewline
38 & 382.19 & 382.081719868148 & 0.108280131851927 \tabularnewline
39 & 382.65 & 383.151744703535 & -0.501744703534996 \tabularnewline
40 & 384.65 & 384.456667437251 & 0.193332562749163 \tabularnewline
41 & 384.94 & 384.770501113858 & 0.169498886141753 \tabularnewline
42 & 384.01 & 383.989054769762 & 0.0209452302381692 \tabularnewline
43 & 382.15 & 382.560741621775 & -0.410741621775117 \tabularnewline
44 & 380.33 & 380.187973462512 & 0.142026537487538 \tabularnewline
45 & 378.81 & 378.83328103284 & -0.0232810328404867 \tabularnewline
46 & 379.06 & 378.887098068702 & 0.172901931297815 \tabularnewline
47 & 380.17 & 380.467178722054 & -0.297178722053616 \tabularnewline
48 & 381.85 & 381.716957762361 & 0.13304223763862 \tabularnewline
49 & 382.88 & 382.962941182727 & -0.0829411827274384 \tabularnewline
50 & 383.77 & 383.797971116532 & -0.0279711165320577 \tabularnewline
51 & 384.42 & 384.728881516429 & -0.308881516428926 \tabularnewline
52 & 386.36 & 386.204234626947 & 0.1557653730531 \tabularnewline
53 & 386.53 & 386.497638168128 & 0.032361831871583 \tabularnewline
54 & 386.01 & 385.637052007751 & 0.372947992248953 \tabularnewline
55 & 384.45 & 384.299632825094 & 0.150367174906307 \tabularnewline
56 & 381.96 & 382.236592551499 & -0.276592551498652 \tabularnewline
57 & 380.81 & 380.684442955017 & 0.125557044982884 \tabularnewline
58 & 381.09 & 380.827054018855 & 0.262945981144924 \tabularnewline
59 & 382.37 & 382.384600677836 & -0.014600677836313 \tabularnewline
60 & 383.84 & 383.811528872803 & 0.0284711271969513 \tabularnewline
61 & 385.42 & 384.987167652323 & 0.432832347677504 \tabularnewline
62 & 385.72 & 386.050077212276 & -0.330077212276024 \tabularnewline
63 & 385.96 & 386.820094105732 & -0.860094105731832 \tabularnewline
64 & 387.18 & 388.124898941668 & -0.944898941667532 \tabularnewline
65 & 388.5 & 387.935384532626 & 0.564615467373642 \tabularnewline
66 & 387.88 & 387.340788337608 & 0.539211662391608 \tabularnewline
67 & 386.38 & 386.042764396055 & 0.337235603945373 \tabularnewline
68 & 384.15 & 384.001887459946 & 0.148112540053489 \tabularnewline
69 & 383.07 & 382.681930409459 & 0.388069590541193 \tabularnewline
70 & 382.98 & 382.955144793963 & 0.0248552060374436 \tabularnewline
71 & 384.11 & 384.37776632372 & -0.26776632372048 \tabularnewline
72 & 385.54 & 385.704220371936 & -0.16422037193621 \tabularnewline
73 & 386.92 & 386.851147399823 & 0.06885260017674 \tabularnewline
74 & 387.41 & 387.659371219411 & -0.249371219411273 \tabularnewline
75 & 388.77 & 388.392286796427 & 0.377713203572512 \tabularnewline
76 & 389.46 & 390.209580586771 & -0.749580586771344 \tabularnewline
77 & 390.18 & 390.303644957407 & -0.123644957406725 \tabularnewline
78 & 389.43 & 389.417996303775 & 0.0120036962249515 \tabularnewline
79 & 387.74 & 387.871253083273 & -0.13125308327318 \tabularnewline
80 & 385.91 & 385.605989573328 & 0.304010426671937 \tabularnewline
81 & 384.77 & 384.380671951472 & 0.38932804852783 \tabularnewline
82 & 384.38 & 384.604789230156 & -0.224789230156034 \tabularnewline
83 & 385.99 & 385.881050150134 & 0.108949849865553 \tabularnewline
84 & 387.26 & 387.377650266709 & -0.117650266709461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153932&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]377.03[/C][C]376.01780715812[/C][C]1.01219284188039[/C][/ROW]
[ROW][C]14[/C][C]377.87[/C][C]377.319228387004[/C][C]0.550771612996414[/C][/ROW]
[ROW][C]15[/C][C]378.88[/C][C]378.592916406208[/C][C]0.287083593792374[/C][/ROW]
[ROW][C]16[/C][C]380.42[/C][C]380.304558676347[/C][C]0.11544132365259[/C][/ROW]
[ROW][C]17[/C][C]380.62[/C][C]380.583753840289[/C][C]0.0362461597110837[/C][/ROW]
[ROW][C]18[/C][C]379.66[/C][C]379.662750120666[/C][C]-0.00275012066646241[/C][/ROW]
[ROW][C]19[/C][C]377.48[/C][C]378.391601465929[/C][C]-0.911601465929095[/C][/ROW]
[ROW][C]20[/C][C]376.07[/C][C]375.60303884068[/C][C]0.466961159319567[/C][/ROW]
[ROW][C]21[/C][C]374.1[/C][C]374.594812695696[/C][C]-0.494812695696282[/C][/ROW]
[ROW][C]22[/C][C]374.47[/C][C]374.302481458989[/C][C]0.167518541010963[/C][/ROW]
[ROW][C]23[/C][C]376.15[/C][C]375.89121249175[/C][C]0.258787508249782[/C][/ROW]
[ROW][C]24[/C][C]377.51[/C][C]377.300233833472[/C][C]0.20976616652797[/C][/ROW]
[ROW][C]25[/C][C]378.43[/C][C]378.633839444033[/C][C]-0.203839444032724[/C][/ROW]
[ROW][C]26[/C][C]379.7[/C][C]379.366182101927[/C][C]0.333817898073448[/C][/ROW]
[ROW][C]27[/C][C]380.91[/C][C]380.515415193174[/C][C]0.39458480682606[/C][/ROW]
[ROW][C]28[/C][C]382.2[/C][C]382.251396106812[/C][C]-0.0513961068122057[/C][/ROW]
[ROW][C]29[/C][C]382.45[/C][C]382.451030944767[/C][C]-0.00103094476725119[/C][/ROW]
[ROW][C]30[/C][C]382.14[/C][C]381.509987432784[/C][C]0.63001256721617[/C][/ROW]
[ROW][C]31[/C][C]380.6[/C][C]380.389413462354[/C][C]0.210586537646009[/C][/ROW]
[ROW][C]32[/C][C]378.6[/C][C]378.260608300919[/C][C]0.339391699081034[/C][/ROW]
[ROW][C]33[/C][C]376.72[/C][C]377.080892568552[/C][C]-0.360892568551606[/C][/ROW]
[ROW][C]34[/C][C]376.98[/C][C]376.939614654119[/C][C]0.0403853458810204[/C][/ROW]
[ROW][C]35[/C][C]378.29[/C][C]378.494597161704[/C][C]-0.204597161703987[/C][/ROW]
[ROW][C]36[/C][C]380.07[/C][C]379.708288944294[/C][C]0.361711055706053[/C][/ROW]
[ROW][C]37[/C][C]381.36[/C][C]381.05811549658[/C][C]0.301884503420297[/C][/ROW]
[ROW][C]38[/C][C]382.19[/C][C]382.081719868148[/C][C]0.108280131851927[/C][/ROW]
[ROW][C]39[/C][C]382.65[/C][C]383.151744703535[/C][C]-0.501744703534996[/C][/ROW]
[ROW][C]40[/C][C]384.65[/C][C]384.456667437251[/C][C]0.193332562749163[/C][/ROW]
[ROW][C]41[/C][C]384.94[/C][C]384.770501113858[/C][C]0.169498886141753[/C][/ROW]
[ROW][C]42[/C][C]384.01[/C][C]383.989054769762[/C][C]0.0209452302381692[/C][/ROW]
[ROW][C]43[/C][C]382.15[/C][C]382.560741621775[/C][C]-0.410741621775117[/C][/ROW]
[ROW][C]44[/C][C]380.33[/C][C]380.187973462512[/C][C]0.142026537487538[/C][/ROW]
[ROW][C]45[/C][C]378.81[/C][C]378.83328103284[/C][C]-0.0232810328404867[/C][/ROW]
[ROW][C]46[/C][C]379.06[/C][C]378.887098068702[/C][C]0.172901931297815[/C][/ROW]
[ROW][C]47[/C][C]380.17[/C][C]380.467178722054[/C][C]-0.297178722053616[/C][/ROW]
[ROW][C]48[/C][C]381.85[/C][C]381.716957762361[/C][C]0.13304223763862[/C][/ROW]
[ROW][C]49[/C][C]382.88[/C][C]382.962941182727[/C][C]-0.0829411827274384[/C][/ROW]
[ROW][C]50[/C][C]383.77[/C][C]383.797971116532[/C][C]-0.0279711165320577[/C][/ROW]
[ROW][C]51[/C][C]384.42[/C][C]384.728881516429[/C][C]-0.308881516428926[/C][/ROW]
[ROW][C]52[/C][C]386.36[/C][C]386.204234626947[/C][C]0.1557653730531[/C][/ROW]
[ROW][C]53[/C][C]386.53[/C][C]386.497638168128[/C][C]0.032361831871583[/C][/ROW]
[ROW][C]54[/C][C]386.01[/C][C]385.637052007751[/C][C]0.372947992248953[/C][/ROW]
[ROW][C]55[/C][C]384.45[/C][C]384.299632825094[/C][C]0.150367174906307[/C][/ROW]
[ROW][C]56[/C][C]381.96[/C][C]382.236592551499[/C][C]-0.276592551498652[/C][/ROW]
[ROW][C]57[/C][C]380.81[/C][C]380.684442955017[/C][C]0.125557044982884[/C][/ROW]
[ROW][C]58[/C][C]381.09[/C][C]380.827054018855[/C][C]0.262945981144924[/C][/ROW]
[ROW][C]59[/C][C]382.37[/C][C]382.384600677836[/C][C]-0.014600677836313[/C][/ROW]
[ROW][C]60[/C][C]383.84[/C][C]383.811528872803[/C][C]0.0284711271969513[/C][/ROW]
[ROW][C]61[/C][C]385.42[/C][C]384.987167652323[/C][C]0.432832347677504[/C][/ROW]
[ROW][C]62[/C][C]385.72[/C][C]386.050077212276[/C][C]-0.330077212276024[/C][/ROW]
[ROW][C]63[/C][C]385.96[/C][C]386.820094105732[/C][C]-0.860094105731832[/C][/ROW]
[ROW][C]64[/C][C]387.18[/C][C]388.124898941668[/C][C]-0.944898941667532[/C][/ROW]
[ROW][C]65[/C][C]388.5[/C][C]387.935384532626[/C][C]0.564615467373642[/C][/ROW]
[ROW][C]66[/C][C]387.88[/C][C]387.340788337608[/C][C]0.539211662391608[/C][/ROW]
[ROW][C]67[/C][C]386.38[/C][C]386.042764396055[/C][C]0.337235603945373[/C][/ROW]
[ROW][C]68[/C][C]384.15[/C][C]384.001887459946[/C][C]0.148112540053489[/C][/ROW]
[ROW][C]69[/C][C]383.07[/C][C]382.681930409459[/C][C]0.388069590541193[/C][/ROW]
[ROW][C]70[/C][C]382.98[/C][C]382.955144793963[/C][C]0.0248552060374436[/C][/ROW]
[ROW][C]71[/C][C]384.11[/C][C]384.37776632372[/C][C]-0.26776632372048[/C][/ROW]
[ROW][C]72[/C][C]385.54[/C][C]385.704220371936[/C][C]-0.16422037193621[/C][/ROW]
[ROW][C]73[/C][C]386.92[/C][C]386.851147399823[/C][C]0.06885260017674[/C][/ROW]
[ROW][C]74[/C][C]387.41[/C][C]387.659371219411[/C][C]-0.249371219411273[/C][/ROW]
[ROW][C]75[/C][C]388.77[/C][C]388.392286796427[/C][C]0.377713203572512[/C][/ROW]
[ROW][C]76[/C][C]389.46[/C][C]390.209580586771[/C][C]-0.749580586771344[/C][/ROW]
[ROW][C]77[/C][C]390.18[/C][C]390.303644957407[/C][C]-0.123644957406725[/C][/ROW]
[ROW][C]78[/C][C]389.43[/C][C]389.417996303775[/C][C]0.0120036962249515[/C][/ROW]
[ROW][C]79[/C][C]387.74[/C][C]387.871253083273[/C][C]-0.13125308327318[/C][/ROW]
[ROW][C]80[/C][C]385.91[/C][C]385.605989573328[/C][C]0.304010426671937[/C][/ROW]
[ROW][C]81[/C][C]384.77[/C][C]384.380671951472[/C][C]0.38932804852783[/C][/ROW]
[ROW][C]82[/C][C]384.38[/C][C]384.604789230156[/C][C]-0.224789230156034[/C][/ROW]
[ROW][C]83[/C][C]385.99[/C][C]385.881050150134[/C][C]0.108949849865553[/C][/ROW]
[ROW][C]84[/C][C]387.26[/C][C]387.377650266709[/C][C]-0.117650266709461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153932&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
13377.03376.017807158121.01219284188039
14377.87377.3192283870040.550771612996414
15378.88378.5929164062080.287083593792374
16380.42380.3045586763470.11544132365259
17380.62380.5837538402890.0362461597110837
18379.66379.662750120666-0.00275012066646241
19377.48378.391601465929-0.911601465929095
20376.07375.603038840680.466961159319567
21374.1374.594812695696-0.494812695696282
22374.47374.3024814589890.167518541010963
23376.15375.891212491750.258787508249782
24377.51377.3002338334720.20976616652797
25378.43378.633839444033-0.203839444032724
26379.7379.3661821019270.333817898073448
27380.91380.5154151931740.39458480682606
28382.2382.251396106812-0.0513961068122057
29382.45382.451030944767-0.00103094476725119
30382.14381.5099874327840.63001256721617
31380.6380.3894134623540.210586537646009
32378.6378.2606083009190.339391699081034
33376.72377.080892568552-0.360892568551606
34376.98376.9396146541190.0403853458810204
35378.29378.494597161704-0.204597161703987
36380.07379.7082889442940.361711055706053
37381.36381.058115496580.301884503420297
38382.19382.0817198681480.108280131851927
39382.65383.151744703535-0.501744703534996
40384.65384.4566674372510.193332562749163
41384.94384.7705011138580.169498886141753
42384.01383.9890547697620.0209452302381692
43382.15382.560741621775-0.410741621775117
44380.33380.1879734625120.142026537487538
45378.81378.83328103284-0.0232810328404867
46379.06378.8870980687020.172901931297815
47380.17380.467178722054-0.297178722053616
48381.85381.7169577623610.13304223763862
49382.88382.962941182727-0.0829411827274384
50383.77383.797971116532-0.0279711165320577
51384.42384.728881516429-0.308881516428926
52386.36386.2042346269470.1557653730531
53386.53386.4976381681280.032361831871583
54386.01385.6370520077510.372947992248953
55384.45384.2996328250940.150367174906307
56381.96382.236592551499-0.276592551498652
57380.81380.6844429550170.125557044982884
58381.09380.8270540188550.262945981144924
59382.37382.384600677836-0.014600677836313
60383.84383.8115288728030.0284711271969513
61385.42384.9871676523230.432832347677504
62385.72386.050077212276-0.330077212276024
63385.96386.820094105732-0.860094105731832
64387.18388.124898941668-0.944898941667532
65388.5387.9353845326260.564615467373642
66387.88387.3407883376080.539211662391608
67386.38386.0427643960550.337235603945373
68384.15384.0018874599460.148112540053489
69383.07382.6819304094590.388069590541193
70382.98382.9551447939630.0248552060374436
71384.11384.37776632372-0.26776632372048
72385.54385.704220371936-0.16422037193621
73386.92386.8511473998230.06885260017674
74387.41387.659371219411-0.249371219411273
75388.77388.3922867964270.377713203572512
76389.46390.209580586771-0.749580586771344
77390.18390.303644957407-0.123644957406725
78389.43389.4179963037750.0120036962249515
79387.74387.871253083273-0.13125308327318
80385.91385.6059895733280.304010426671937
81384.77384.3806719514720.38932804852783
82384.38384.604789230156-0.224789230156034
83385.99385.8810501501340.108949849865553
84387.26387.377650266709-0.117650266709461







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85388.573139169239387.86990394068389.276374397797
86389.309137377298388.545185312368390.073089442228
87390.228050355674389.406758423626391.049342287721
88391.737142630475390.861213909111392.61307135184
89392.228801644228391.300451970276393.15715131818
90391.414279511192390.435359334612392.393199687771
91389.845197141148388.817274864081390.873119418216
92387.693899424484386.618320556301388.769478292667
93386.35267388859385.230604331075387.474743446104
94386.332018090029385.164476623454387.499559556604
95387.746266679412386.53414987303388.958383485795
96389.166994552328387.911096221192390.422892883464

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 388.573139169239 & 387.86990394068 & 389.276374397797 \tabularnewline
86 & 389.309137377298 & 388.545185312368 & 390.073089442228 \tabularnewline
87 & 390.228050355674 & 389.406758423626 & 391.049342287721 \tabularnewline
88 & 391.737142630475 & 390.861213909111 & 392.61307135184 \tabularnewline
89 & 392.228801644228 & 391.300451970276 & 393.15715131818 \tabularnewline
90 & 391.414279511192 & 390.435359334612 & 392.393199687771 \tabularnewline
91 & 389.845197141148 & 388.817274864081 & 390.873119418216 \tabularnewline
92 & 387.693899424484 & 386.618320556301 & 388.769478292667 \tabularnewline
93 & 386.35267388859 & 385.230604331075 & 387.474743446104 \tabularnewline
94 & 386.332018090029 & 385.164476623454 & 387.499559556604 \tabularnewline
95 & 387.746266679412 & 386.53414987303 & 388.958383485795 \tabularnewline
96 & 389.166994552328 & 387.911096221192 & 390.422892883464 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=153932&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]388.573139169239[/C][C]387.86990394068[/C][C]389.276374397797[/C][/ROW]
[ROW][C]86[/C][C]389.309137377298[/C][C]388.545185312368[/C][C]390.073089442228[/C][/ROW]
[ROW][C]87[/C][C]390.228050355674[/C][C]389.406758423626[/C][C]391.049342287721[/C][/ROW]
[ROW][C]88[/C][C]391.737142630475[/C][C]390.861213909111[/C][C]392.61307135184[/C][/ROW]
[ROW][C]89[/C][C]392.228801644228[/C][C]391.300451970276[/C][C]393.15715131818[/C][/ROW]
[ROW][C]90[/C][C]391.414279511192[/C][C]390.435359334612[/C][C]392.393199687771[/C][/ROW]
[ROW][C]91[/C][C]389.845197141148[/C][C]388.817274864081[/C][C]390.873119418216[/C][/ROW]
[ROW][C]92[/C][C]387.693899424484[/C][C]386.618320556301[/C][C]388.769478292667[/C][/ROW]
[ROW][C]93[/C][C]386.35267388859[/C][C]385.230604331075[/C][C]387.474743446104[/C][/ROW]
[ROW][C]94[/C][C]386.332018090029[/C][C]385.164476623454[/C][C]387.499559556604[/C][/ROW]
[ROW][C]95[/C][C]387.746266679412[/C][C]386.53414987303[/C][C]388.958383485795[/C][/ROW]
[ROW][C]96[/C][C]389.166994552328[/C][C]387.911096221192[/C][C]390.422892883464[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=153932&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=153932&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
85388.573139169239387.86990394068389.276374397797
86389.309137377298388.545185312368390.073089442228
87390.228050355674389.406758423626391.049342287721
88391.737142630475390.861213909111392.61307135184
89392.228801644228391.300451970276393.15715131818
90391.414279511192390.435359334612392.393199687771
91389.845197141148388.817274864081390.873119418216
92387.693899424484386.618320556301388.769478292667
93386.35267388859385.230604331075387.474743446104
94386.332018090029385.164476623454387.499559556604
95387.746266679412386.53414987303388.958383485795
96389.166994552328387.911096221192390.422892883464



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')