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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 28 May 2012 06:39:57 -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/t1338201810fdzyc6e0jvlru76.htm/, Retrieved Sun, 05 May 2024 17:48:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=167779, Retrieved Sun, 05 May 2024 17:48:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [double exponentia...] [2012-05-28 10:39:57] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
6,94
6,98
7,05
7,07
7,08
7,1
7,12
7,13
7,18
7,2
7,21
7,22
7,26
7,29
7,32
7,36
7,41
7,48
7,48
7,51
7,51
7,51
7,51
7,54
7,58
7,64
7,63
7,71
7,77
7,85
7,88
7,89
7,94
8,02
8,08
8,15
8,17
8,17
8,25
8,33
8,41
8,43
8,48
8,52
8,56
8,63
8,7
8,72
8,73
8,82
8,83
8,81
8,82
8,83
8,84
8,83
8,82
8,87
8,87
8,87




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167779&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167779&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167779&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.193033671532832
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.193033671532832 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167779&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]0.193033671532832[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167779&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167779&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
beta0.193033671532832
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
37.057.020.0299999999999994
47.077.09579101014598-0.0257910101459844
57.087.11081247676497-0.0308124767649653
67.17.114864631246-0.0148646312460041
77.127.13199525690061-0.0119952569006054
87.137.1496797684201-0.0196797684201027
97.187.155880910467050.0241190895329453
107.27.21053670687363-0.0105367068736273
117.217.22850276765995-0.0185027676599461
127.227.23493111048503-0.014931110485028
137.267.242048903408040.0179510965919594
147.297.285514069491230.004485930508773
157.327.316380005127580.00361999487242404
167.367.347078786028730.0129212139712696
177.417.389573015402270.0204269845977336
187.487.443516111237510.036483888762489
197.487.52055873023713-0.0405587302371302
207.517.51272952962675-0.00272952962674733
217.517.54220263850134-0.0322026385013379
227.517.53598644495838-0.0259864449583809
237.517.53097018607798-0.0209701860779781
247.547.526922234066620.0130777659333807
257.587.559446683240190.0205533167598126
267.647.603414165436510.0365858345634882
277.637.67047646340839-0.0404764634083934
287.717.652663143066010.0573368569339925
297.777.743731087074130.0262689129258709
307.857.808801871783390.0411981282166138
317.887.89675449773332-0.0167544977333192
327.897.92352031552117-0.0335203155211685
337.947.927049765945180.0129502340548227
348.027.979549597171990.040450402828009
358.088.067357886944860.0126421130551382
368.158.129798240443830.020201759556171
378.178.20369786026238-0.0336978602623805
388.178.21719303857313-0.0471930385731323
398.258.208083193066570.041916806933429
408.338.296174548207860.0338254517921364
418.418.382703999358560.027296000641444
428.438.46797304658054-0.0379730465805377
438.488.48064296997981-0.000642969979807617
448.528.53051885512392-0.0105188551239213
458.568.56848836189903-0.00848836189902791
468.638.606849822236360.0231501777636414
478.78.681318586046710.0186814139532849
488.728.75492472797154-0.0349247279715392
498.738.76818307950391-0.0381830795039093
508.828.770812459476840.0491875405231603
518.838.8703073110177-0.0403073110176955
528.818.87252664278233-0.0625266427823323
538.828.84045689535744-0.0204568953574373
548.838.84650802573843-0.0165080257384282
558.848.85332142092038-0.0133214209203807
568.838.86074993813009-0.0307499381300858
578.828.84481416467343-0.0248141646734279
588.878.83002419536050.0399758046395036
598.878.88774087170254-0.0177408717025376
608.878.8843162861016-0.0143162861016037

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 7.05 & 7.02 & 0.0299999999999994 \tabularnewline
4 & 7.07 & 7.09579101014598 & -0.0257910101459844 \tabularnewline
5 & 7.08 & 7.11081247676497 & -0.0308124767649653 \tabularnewline
6 & 7.1 & 7.114864631246 & -0.0148646312460041 \tabularnewline
7 & 7.12 & 7.13199525690061 & -0.0119952569006054 \tabularnewline
8 & 7.13 & 7.1496797684201 & -0.0196797684201027 \tabularnewline
9 & 7.18 & 7.15588091046705 & 0.0241190895329453 \tabularnewline
10 & 7.2 & 7.21053670687363 & -0.0105367068736273 \tabularnewline
11 & 7.21 & 7.22850276765995 & -0.0185027676599461 \tabularnewline
12 & 7.22 & 7.23493111048503 & -0.014931110485028 \tabularnewline
13 & 7.26 & 7.24204890340804 & 0.0179510965919594 \tabularnewline
14 & 7.29 & 7.28551406949123 & 0.004485930508773 \tabularnewline
15 & 7.32 & 7.31638000512758 & 0.00361999487242404 \tabularnewline
16 & 7.36 & 7.34707878602873 & 0.0129212139712696 \tabularnewline
17 & 7.41 & 7.38957301540227 & 0.0204269845977336 \tabularnewline
18 & 7.48 & 7.44351611123751 & 0.036483888762489 \tabularnewline
19 & 7.48 & 7.52055873023713 & -0.0405587302371302 \tabularnewline
20 & 7.51 & 7.51272952962675 & -0.00272952962674733 \tabularnewline
21 & 7.51 & 7.54220263850134 & -0.0322026385013379 \tabularnewline
22 & 7.51 & 7.53598644495838 & -0.0259864449583809 \tabularnewline
23 & 7.51 & 7.53097018607798 & -0.0209701860779781 \tabularnewline
24 & 7.54 & 7.52692223406662 & 0.0130777659333807 \tabularnewline
25 & 7.58 & 7.55944668324019 & 0.0205533167598126 \tabularnewline
26 & 7.64 & 7.60341416543651 & 0.0365858345634882 \tabularnewline
27 & 7.63 & 7.67047646340839 & -0.0404764634083934 \tabularnewline
28 & 7.71 & 7.65266314306601 & 0.0573368569339925 \tabularnewline
29 & 7.77 & 7.74373108707413 & 0.0262689129258709 \tabularnewline
30 & 7.85 & 7.80880187178339 & 0.0411981282166138 \tabularnewline
31 & 7.88 & 7.89675449773332 & -0.0167544977333192 \tabularnewline
32 & 7.89 & 7.92352031552117 & -0.0335203155211685 \tabularnewline
33 & 7.94 & 7.92704976594518 & 0.0129502340548227 \tabularnewline
34 & 8.02 & 7.97954959717199 & 0.040450402828009 \tabularnewline
35 & 8.08 & 8.06735788694486 & 0.0126421130551382 \tabularnewline
36 & 8.15 & 8.12979824044383 & 0.020201759556171 \tabularnewline
37 & 8.17 & 8.20369786026238 & -0.0336978602623805 \tabularnewline
38 & 8.17 & 8.21719303857313 & -0.0471930385731323 \tabularnewline
39 & 8.25 & 8.20808319306657 & 0.041916806933429 \tabularnewline
40 & 8.33 & 8.29617454820786 & 0.0338254517921364 \tabularnewline
41 & 8.41 & 8.38270399935856 & 0.027296000641444 \tabularnewline
42 & 8.43 & 8.46797304658054 & -0.0379730465805377 \tabularnewline
43 & 8.48 & 8.48064296997981 & -0.000642969979807617 \tabularnewline
44 & 8.52 & 8.53051885512392 & -0.0105188551239213 \tabularnewline
45 & 8.56 & 8.56848836189903 & -0.00848836189902791 \tabularnewline
46 & 8.63 & 8.60684982223636 & 0.0231501777636414 \tabularnewline
47 & 8.7 & 8.68131858604671 & 0.0186814139532849 \tabularnewline
48 & 8.72 & 8.75492472797154 & -0.0349247279715392 \tabularnewline
49 & 8.73 & 8.76818307950391 & -0.0381830795039093 \tabularnewline
50 & 8.82 & 8.77081245947684 & 0.0491875405231603 \tabularnewline
51 & 8.83 & 8.8703073110177 & -0.0403073110176955 \tabularnewline
52 & 8.81 & 8.87252664278233 & -0.0625266427823323 \tabularnewline
53 & 8.82 & 8.84045689535744 & -0.0204568953574373 \tabularnewline
54 & 8.83 & 8.84650802573843 & -0.0165080257384282 \tabularnewline
55 & 8.84 & 8.85332142092038 & -0.0133214209203807 \tabularnewline
56 & 8.83 & 8.86074993813009 & -0.0307499381300858 \tabularnewline
57 & 8.82 & 8.84481416467343 & -0.0248141646734279 \tabularnewline
58 & 8.87 & 8.8300241953605 & 0.0399758046395036 \tabularnewline
59 & 8.87 & 8.88774087170254 & -0.0177408717025376 \tabularnewline
60 & 8.87 & 8.8843162861016 & -0.0143162861016037 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167779&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]7.05[/C][C]7.02[/C][C]0.0299999999999994[/C][/ROW]
[ROW][C]4[/C][C]7.07[/C][C]7.09579101014598[/C][C]-0.0257910101459844[/C][/ROW]
[ROW][C]5[/C][C]7.08[/C][C]7.11081247676497[/C][C]-0.0308124767649653[/C][/ROW]
[ROW][C]6[/C][C]7.1[/C][C]7.114864631246[/C][C]-0.0148646312460041[/C][/ROW]
[ROW][C]7[/C][C]7.12[/C][C]7.13199525690061[/C][C]-0.0119952569006054[/C][/ROW]
[ROW][C]8[/C][C]7.13[/C][C]7.1496797684201[/C][C]-0.0196797684201027[/C][/ROW]
[ROW][C]9[/C][C]7.18[/C][C]7.15588091046705[/C][C]0.0241190895329453[/C][/ROW]
[ROW][C]10[/C][C]7.2[/C][C]7.21053670687363[/C][C]-0.0105367068736273[/C][/ROW]
[ROW][C]11[/C][C]7.21[/C][C]7.22850276765995[/C][C]-0.0185027676599461[/C][/ROW]
[ROW][C]12[/C][C]7.22[/C][C]7.23493111048503[/C][C]-0.014931110485028[/C][/ROW]
[ROW][C]13[/C][C]7.26[/C][C]7.24204890340804[/C][C]0.0179510965919594[/C][/ROW]
[ROW][C]14[/C][C]7.29[/C][C]7.28551406949123[/C][C]0.004485930508773[/C][/ROW]
[ROW][C]15[/C][C]7.32[/C][C]7.31638000512758[/C][C]0.00361999487242404[/C][/ROW]
[ROW][C]16[/C][C]7.36[/C][C]7.34707878602873[/C][C]0.0129212139712696[/C][/ROW]
[ROW][C]17[/C][C]7.41[/C][C]7.38957301540227[/C][C]0.0204269845977336[/C][/ROW]
[ROW][C]18[/C][C]7.48[/C][C]7.44351611123751[/C][C]0.036483888762489[/C][/ROW]
[ROW][C]19[/C][C]7.48[/C][C]7.52055873023713[/C][C]-0.0405587302371302[/C][/ROW]
[ROW][C]20[/C][C]7.51[/C][C]7.51272952962675[/C][C]-0.00272952962674733[/C][/ROW]
[ROW][C]21[/C][C]7.51[/C][C]7.54220263850134[/C][C]-0.0322026385013379[/C][/ROW]
[ROW][C]22[/C][C]7.51[/C][C]7.53598644495838[/C][C]-0.0259864449583809[/C][/ROW]
[ROW][C]23[/C][C]7.51[/C][C]7.53097018607798[/C][C]-0.0209701860779781[/C][/ROW]
[ROW][C]24[/C][C]7.54[/C][C]7.52692223406662[/C][C]0.0130777659333807[/C][/ROW]
[ROW][C]25[/C][C]7.58[/C][C]7.55944668324019[/C][C]0.0205533167598126[/C][/ROW]
[ROW][C]26[/C][C]7.64[/C][C]7.60341416543651[/C][C]0.0365858345634882[/C][/ROW]
[ROW][C]27[/C][C]7.63[/C][C]7.67047646340839[/C][C]-0.0404764634083934[/C][/ROW]
[ROW][C]28[/C][C]7.71[/C][C]7.65266314306601[/C][C]0.0573368569339925[/C][/ROW]
[ROW][C]29[/C][C]7.77[/C][C]7.74373108707413[/C][C]0.0262689129258709[/C][/ROW]
[ROW][C]30[/C][C]7.85[/C][C]7.80880187178339[/C][C]0.0411981282166138[/C][/ROW]
[ROW][C]31[/C][C]7.88[/C][C]7.89675449773332[/C][C]-0.0167544977333192[/C][/ROW]
[ROW][C]32[/C][C]7.89[/C][C]7.92352031552117[/C][C]-0.0335203155211685[/C][/ROW]
[ROW][C]33[/C][C]7.94[/C][C]7.92704976594518[/C][C]0.0129502340548227[/C][/ROW]
[ROW][C]34[/C][C]8.02[/C][C]7.97954959717199[/C][C]0.040450402828009[/C][/ROW]
[ROW][C]35[/C][C]8.08[/C][C]8.06735788694486[/C][C]0.0126421130551382[/C][/ROW]
[ROW][C]36[/C][C]8.15[/C][C]8.12979824044383[/C][C]0.020201759556171[/C][/ROW]
[ROW][C]37[/C][C]8.17[/C][C]8.20369786026238[/C][C]-0.0336978602623805[/C][/ROW]
[ROW][C]38[/C][C]8.17[/C][C]8.21719303857313[/C][C]-0.0471930385731323[/C][/ROW]
[ROW][C]39[/C][C]8.25[/C][C]8.20808319306657[/C][C]0.041916806933429[/C][/ROW]
[ROW][C]40[/C][C]8.33[/C][C]8.29617454820786[/C][C]0.0338254517921364[/C][/ROW]
[ROW][C]41[/C][C]8.41[/C][C]8.38270399935856[/C][C]0.027296000641444[/C][/ROW]
[ROW][C]42[/C][C]8.43[/C][C]8.46797304658054[/C][C]-0.0379730465805377[/C][/ROW]
[ROW][C]43[/C][C]8.48[/C][C]8.48064296997981[/C][C]-0.000642969979807617[/C][/ROW]
[ROW][C]44[/C][C]8.52[/C][C]8.53051885512392[/C][C]-0.0105188551239213[/C][/ROW]
[ROW][C]45[/C][C]8.56[/C][C]8.56848836189903[/C][C]-0.00848836189902791[/C][/ROW]
[ROW][C]46[/C][C]8.63[/C][C]8.60684982223636[/C][C]0.0231501777636414[/C][/ROW]
[ROW][C]47[/C][C]8.7[/C][C]8.68131858604671[/C][C]0.0186814139532849[/C][/ROW]
[ROW][C]48[/C][C]8.72[/C][C]8.75492472797154[/C][C]-0.0349247279715392[/C][/ROW]
[ROW][C]49[/C][C]8.73[/C][C]8.76818307950391[/C][C]-0.0381830795039093[/C][/ROW]
[ROW][C]50[/C][C]8.82[/C][C]8.77081245947684[/C][C]0.0491875405231603[/C][/ROW]
[ROW][C]51[/C][C]8.83[/C][C]8.8703073110177[/C][C]-0.0403073110176955[/C][/ROW]
[ROW][C]52[/C][C]8.81[/C][C]8.87252664278233[/C][C]-0.0625266427823323[/C][/ROW]
[ROW][C]53[/C][C]8.82[/C][C]8.84045689535744[/C][C]-0.0204568953574373[/C][/ROW]
[ROW][C]54[/C][C]8.83[/C][C]8.84650802573843[/C][C]-0.0165080257384282[/C][/ROW]
[ROW][C]55[/C][C]8.84[/C][C]8.85332142092038[/C][C]-0.0133214209203807[/C][/ROW]
[ROW][C]56[/C][C]8.83[/C][C]8.86074993813009[/C][C]-0.0307499381300858[/C][/ROW]
[ROW][C]57[/C][C]8.82[/C][C]8.84481416467343[/C][C]-0.0248141646734279[/C][/ROW]
[ROW][C]58[/C][C]8.87[/C][C]8.8300241953605[/C][C]0.0399758046395036[/C][/ROW]
[ROW][C]59[/C][C]8.87[/C][C]8.88774087170254[/C][C]-0.0177408717025376[/C][/ROW]
[ROW][C]60[/C][C]8.87[/C][C]8.8843162861016[/C][C]-0.0143162861016037[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167779&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167779&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
37.057.020.0299999999999994
47.077.09579101014598-0.0257910101459844
57.087.11081247676497-0.0308124767649653
67.17.114864631246-0.0148646312460041
77.127.13199525690061-0.0119952569006054
87.137.1496797684201-0.0196797684201027
97.187.155880910467050.0241190895329453
107.27.21053670687363-0.0105367068736273
117.217.22850276765995-0.0185027676599461
127.227.23493111048503-0.014931110485028
137.267.242048903408040.0179510965919594
147.297.285514069491230.004485930508773
157.327.316380005127580.00361999487242404
167.367.347078786028730.0129212139712696
177.417.389573015402270.0204269845977336
187.487.443516111237510.036483888762489
197.487.52055873023713-0.0405587302371302
207.517.51272952962675-0.00272952962674733
217.517.54220263850134-0.0322026385013379
227.517.53598644495838-0.0259864449583809
237.517.53097018607798-0.0209701860779781
247.547.526922234066620.0130777659333807
257.587.559446683240190.0205533167598126
267.647.603414165436510.0365858345634882
277.637.67047646340839-0.0404764634083934
287.717.652663143066010.0573368569339925
297.777.743731087074130.0262689129258709
307.857.808801871783390.0411981282166138
317.887.89675449773332-0.0167544977333192
327.897.92352031552117-0.0335203155211685
337.947.927049765945180.0129502340548227
348.027.979549597171990.040450402828009
358.088.067357886944860.0126421130551382
368.158.129798240443830.020201759556171
378.178.20369786026238-0.0336978602623805
388.178.21719303857313-0.0471930385731323
398.258.208083193066570.041916806933429
408.338.296174548207860.0338254517921364
418.418.382703999358560.027296000641444
428.438.46797304658054-0.0379730465805377
438.488.48064296997981-0.000642969979807617
448.528.53051885512392-0.0105188551239213
458.568.56848836189903-0.00848836189902791
468.638.606849822236360.0231501777636414
478.78.681318586046710.0186814139532849
488.728.75492472797154-0.0349247279715392
498.738.76818307950391-0.0381830795039093
508.828.770812459476840.0491875405231603
518.838.8703073110177-0.0403073110176955
528.818.87252664278233-0.0625266427823323
538.828.84045689535744-0.0204568953574373
548.838.84650802573843-0.0165080257384282
558.848.85332142092038-0.0133214209203807
568.838.86074993813009-0.0307499381300858
578.828.84481416467343-0.0248141646734279
588.878.83002419536050.0399758046395036
598.878.88774087170254-0.0177408717025376
608.878.8843162861016-0.0143162861016037







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
618.88155276083278.824709155710868.93839636595454
628.893105521665398.804616817722718.98159422560808
638.904658282498098.786176353727739.02314021126845
648.916211043330798.767566678483569.06485540817801
658.927763804163488.74820158210379.10732602622327
668.939316564996188.727842920741639.15079020925073
678.950869325828888.706387259678599.19535139197917
688.962422086661588.683792352867779.24105182045539
698.973974847494278.660046436120749.2879032588678
708.985527608326978.635153752270159.3359014643838
718.997080369159678.609127144177089.38503359414226
729.008633129992378.581984039562289.43528222042245

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 8.8815527608327 & 8.82470915571086 & 8.93839636595454 \tabularnewline
62 & 8.89310552166539 & 8.80461681772271 & 8.98159422560808 \tabularnewline
63 & 8.90465828249809 & 8.78617635372773 & 9.02314021126845 \tabularnewline
64 & 8.91621104333079 & 8.76756667848356 & 9.06485540817801 \tabularnewline
65 & 8.92776380416348 & 8.7482015821037 & 9.10732602622327 \tabularnewline
66 & 8.93931656499618 & 8.72784292074163 & 9.15079020925073 \tabularnewline
67 & 8.95086932582888 & 8.70638725967859 & 9.19535139197917 \tabularnewline
68 & 8.96242208666158 & 8.68379235286777 & 9.24105182045539 \tabularnewline
69 & 8.97397484749427 & 8.66004643612074 & 9.2879032588678 \tabularnewline
70 & 8.98552760832697 & 8.63515375227015 & 9.3359014643838 \tabularnewline
71 & 8.99708036915967 & 8.60912714417708 & 9.38503359414226 \tabularnewline
72 & 9.00863312999237 & 8.58198403956228 & 9.43528222042245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=167779&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]61[/C][C]8.8815527608327[/C][C]8.82470915571086[/C][C]8.93839636595454[/C][/ROW]
[ROW][C]62[/C][C]8.89310552166539[/C][C]8.80461681772271[/C][C]8.98159422560808[/C][/ROW]
[ROW][C]63[/C][C]8.90465828249809[/C][C]8.78617635372773[/C][C]9.02314021126845[/C][/ROW]
[ROW][C]64[/C][C]8.91621104333079[/C][C]8.76756667848356[/C][C]9.06485540817801[/C][/ROW]
[ROW][C]65[/C][C]8.92776380416348[/C][C]8.7482015821037[/C][C]9.10732602622327[/C][/ROW]
[ROW][C]66[/C][C]8.93931656499618[/C][C]8.72784292074163[/C][C]9.15079020925073[/C][/ROW]
[ROW][C]67[/C][C]8.95086932582888[/C][C]8.70638725967859[/C][C]9.19535139197917[/C][/ROW]
[ROW][C]68[/C][C]8.96242208666158[/C][C]8.68379235286777[/C][C]9.24105182045539[/C][/ROW]
[ROW][C]69[/C][C]8.97397484749427[/C][C]8.66004643612074[/C][C]9.2879032588678[/C][/ROW]
[ROW][C]70[/C][C]8.98552760832697[/C][C]8.63515375227015[/C][C]9.3359014643838[/C][/ROW]
[ROW][C]71[/C][C]8.99708036915967[/C][C]8.60912714417708[/C][C]9.38503359414226[/C][/ROW]
[ROW][C]72[/C][C]9.00863312999237[/C][C]8.58198403956228[/C][C]9.43528222042245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=167779&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=167779&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
618.88155276083278.824709155710868.93839636595454
628.893105521665398.804616817722718.98159422560808
638.904658282498098.786176353727739.02314021126845
648.916211043330798.767566678483569.06485540817801
658.927763804163488.74820158210379.10732602622327
668.939316564996188.727842920741639.15079020925073
678.950869325828888.706387259678599.19535139197917
688.962422086661588.683792352867779.24105182045539
698.973974847494278.660046436120749.2879032588678
708.985527608326978.635153752270159.3359014643838
718.997080369159678.609127144177089.38503359414226
729.008633129992378.581984039562289.43528222042245



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')