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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 14 May 2012 06:09:38 -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/14/t1336990253pbmumdljsk3etr8.htm/, Retrieved Sun, 05 May 2024 20:13:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166441, Retrieved Sun, 05 May 2024 20:13:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2012-05-14 10:09:38] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
15,13
15,25
15,33
15,36
15,4
15,4
15,41
15,47
15,54
15,55
15,59
15,65
15,75
15,86
15,89
15,94
15,93
15,95
15,99
15,99
16,06
16,08
16,07
16,11
16,15
16,18
16,3
16,42
16,49
16,5
16,58
16,64
16,66
16,81
16,91
16,92
16,95
17,11
17,16
17,16
17,27
17,34
17,39
17,43
17,45
17,5
17,56
17,65
17,62
17,7
17,72
17,71
17,74
17,75
17,78
17,8
17,86
17,88
17,89
17,94




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=166441&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=166441&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166441&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
alpha1
beta0.243934263225562
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.243934263225562 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166441&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]0.243934263225562[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166441&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166441&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
beta0.243934263225562
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
315.3315.37-0.0399999999999991
415.3615.440242629471-0.0802426294709768
515.415.4506687027717-0.0506687027716914
615.415.4783088700925-0.078308870092485
715.4115.4592066535624-0.0492066535624485
815.4715.45720346477990.0127965352201027
915.5415.52032497817070.0196750218293449
1015.5515.5951243901245-0.0451243901245402
1115.5915.594117005266-0.00411700526600889
1215.6515.63311272661970.0168872733802523
1315.7515.69723211120960.0527678887903509
1415.8615.81010400728370.0498959927163085
1515.8915.9322753495049-0.0422753495048518
1615.9415.9519629432708-0.0119629432707846
1715.9315.999044771518-0.0690447715180156
1815.9515.9722023860482-0.0222023860481908
1915.9915.98678646336570.00321353663432511
2015.9916.0275703550569-0.0375703550569195
2116.0616.0184056581770.0415943418230107
2216.0816.0985519433039-0.0185519433039367
2316.0716.1140264886827-0.044026488682686
2416.1116.09328691960350.0167130803965314
2516.1516.13736381255620.0126361874437748
2616.1816.1804462116303-0.000446211630301008
2716.316.2103373653250.0896626346749798
2816.4216.35220915405330.0677908459466749
2916.4916.48874566411280.00125433588723212
3016.516.5590516396133-0.0590516396132514
3116.5816.55464692141190.0253530785880649
3216.6416.6408314059578-0.000831405957811171
3316.6616.7006285975581-0.0406285975580545
3416.8116.71071789054680.0992821094531564
3516.9116.88493619876780.0250638012322248
3616.9216.991050118655-0.0710501186549912
3716.9516.9837185603088-0.0337185603087988
3817.1117.00549344814280.104506551857156
3917.1617.1909861768724-0.0309861768723643
4017.1617.2334275866468-0.0734275866468259
4117.2717.21551608239770.0544839176022975
4217.3417.33880657669570.0011934233043398
4317.3917.4090976935301-0.0190976935301208
4417.4317.4544391117295-0.0244391117295457
4517.4517.4884775750159-0.0384775750159108
4617.517.49909157610370.000908423896301969
4717.5617.54931317181750.010686828182461
4817.6517.61192005537640.0380799446235542
4917.6217.7112090586119-0.0912090586118595
5017.717.65896004409990.0410399559001178
5117.7217.7489710955052-0.0289710955051845
5217.7117.7619040526683-0.0519040526682879
5317.7417.73924287582220.000757124177766855
5417.7517.7694275643507-0.0194275643507034
5517.7817.77468851575450.00531148424545336
5617.817.8059841687506-0.00598416875059726
5717.8617.82452442495540.0354755750445968
5817.8817.8931781332164-0.0131781332164103
5917.8917.9099635349996-0.0199635349995759
6017.9417.91509374479810.0249062552019232

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 15.33 & 15.37 & -0.0399999999999991 \tabularnewline
4 & 15.36 & 15.440242629471 & -0.0802426294709768 \tabularnewline
5 & 15.4 & 15.4506687027717 & -0.0506687027716914 \tabularnewline
6 & 15.4 & 15.4783088700925 & -0.078308870092485 \tabularnewline
7 & 15.41 & 15.4592066535624 & -0.0492066535624485 \tabularnewline
8 & 15.47 & 15.4572034647799 & 0.0127965352201027 \tabularnewline
9 & 15.54 & 15.5203249781707 & 0.0196750218293449 \tabularnewline
10 & 15.55 & 15.5951243901245 & -0.0451243901245402 \tabularnewline
11 & 15.59 & 15.594117005266 & -0.00411700526600889 \tabularnewline
12 & 15.65 & 15.6331127266197 & 0.0168872733802523 \tabularnewline
13 & 15.75 & 15.6972321112096 & 0.0527678887903509 \tabularnewline
14 & 15.86 & 15.8101040072837 & 0.0498959927163085 \tabularnewline
15 & 15.89 & 15.9322753495049 & -0.0422753495048518 \tabularnewline
16 & 15.94 & 15.9519629432708 & -0.0119629432707846 \tabularnewline
17 & 15.93 & 15.999044771518 & -0.0690447715180156 \tabularnewline
18 & 15.95 & 15.9722023860482 & -0.0222023860481908 \tabularnewline
19 & 15.99 & 15.9867864633657 & 0.00321353663432511 \tabularnewline
20 & 15.99 & 16.0275703550569 & -0.0375703550569195 \tabularnewline
21 & 16.06 & 16.018405658177 & 0.0415943418230107 \tabularnewline
22 & 16.08 & 16.0985519433039 & -0.0185519433039367 \tabularnewline
23 & 16.07 & 16.1140264886827 & -0.044026488682686 \tabularnewline
24 & 16.11 & 16.0932869196035 & 0.0167130803965314 \tabularnewline
25 & 16.15 & 16.1373638125562 & 0.0126361874437748 \tabularnewline
26 & 16.18 & 16.1804462116303 & -0.000446211630301008 \tabularnewline
27 & 16.3 & 16.210337365325 & 0.0896626346749798 \tabularnewline
28 & 16.42 & 16.3522091540533 & 0.0677908459466749 \tabularnewline
29 & 16.49 & 16.4887456641128 & 0.00125433588723212 \tabularnewline
30 & 16.5 & 16.5590516396133 & -0.0590516396132514 \tabularnewline
31 & 16.58 & 16.5546469214119 & 0.0253530785880649 \tabularnewline
32 & 16.64 & 16.6408314059578 & -0.000831405957811171 \tabularnewline
33 & 16.66 & 16.7006285975581 & -0.0406285975580545 \tabularnewline
34 & 16.81 & 16.7107178905468 & 0.0992821094531564 \tabularnewline
35 & 16.91 & 16.8849361987678 & 0.0250638012322248 \tabularnewline
36 & 16.92 & 16.991050118655 & -0.0710501186549912 \tabularnewline
37 & 16.95 & 16.9837185603088 & -0.0337185603087988 \tabularnewline
38 & 17.11 & 17.0054934481428 & 0.104506551857156 \tabularnewline
39 & 17.16 & 17.1909861768724 & -0.0309861768723643 \tabularnewline
40 & 17.16 & 17.2334275866468 & -0.0734275866468259 \tabularnewline
41 & 17.27 & 17.2155160823977 & 0.0544839176022975 \tabularnewline
42 & 17.34 & 17.3388065766957 & 0.0011934233043398 \tabularnewline
43 & 17.39 & 17.4090976935301 & -0.0190976935301208 \tabularnewline
44 & 17.43 & 17.4544391117295 & -0.0244391117295457 \tabularnewline
45 & 17.45 & 17.4884775750159 & -0.0384775750159108 \tabularnewline
46 & 17.5 & 17.4990915761037 & 0.000908423896301969 \tabularnewline
47 & 17.56 & 17.5493131718175 & 0.010686828182461 \tabularnewline
48 & 17.65 & 17.6119200553764 & 0.0380799446235542 \tabularnewline
49 & 17.62 & 17.7112090586119 & -0.0912090586118595 \tabularnewline
50 & 17.7 & 17.6589600440999 & 0.0410399559001178 \tabularnewline
51 & 17.72 & 17.7489710955052 & -0.0289710955051845 \tabularnewline
52 & 17.71 & 17.7619040526683 & -0.0519040526682879 \tabularnewline
53 & 17.74 & 17.7392428758222 & 0.000757124177766855 \tabularnewline
54 & 17.75 & 17.7694275643507 & -0.0194275643507034 \tabularnewline
55 & 17.78 & 17.7746885157545 & 0.00531148424545336 \tabularnewline
56 & 17.8 & 17.8059841687506 & -0.00598416875059726 \tabularnewline
57 & 17.86 & 17.8245244249554 & 0.0354755750445968 \tabularnewline
58 & 17.88 & 17.8931781332164 & -0.0131781332164103 \tabularnewline
59 & 17.89 & 17.9099635349996 & -0.0199635349995759 \tabularnewline
60 & 17.94 & 17.9150937447981 & 0.0249062552019232 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166441&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]15.33[/C][C]15.37[/C][C]-0.0399999999999991[/C][/ROW]
[ROW][C]4[/C][C]15.36[/C][C]15.440242629471[/C][C]-0.0802426294709768[/C][/ROW]
[ROW][C]5[/C][C]15.4[/C][C]15.4506687027717[/C][C]-0.0506687027716914[/C][/ROW]
[ROW][C]6[/C][C]15.4[/C][C]15.4783088700925[/C][C]-0.078308870092485[/C][/ROW]
[ROW][C]7[/C][C]15.41[/C][C]15.4592066535624[/C][C]-0.0492066535624485[/C][/ROW]
[ROW][C]8[/C][C]15.47[/C][C]15.4572034647799[/C][C]0.0127965352201027[/C][/ROW]
[ROW][C]9[/C][C]15.54[/C][C]15.5203249781707[/C][C]0.0196750218293449[/C][/ROW]
[ROW][C]10[/C][C]15.55[/C][C]15.5951243901245[/C][C]-0.0451243901245402[/C][/ROW]
[ROW][C]11[/C][C]15.59[/C][C]15.594117005266[/C][C]-0.00411700526600889[/C][/ROW]
[ROW][C]12[/C][C]15.65[/C][C]15.6331127266197[/C][C]0.0168872733802523[/C][/ROW]
[ROW][C]13[/C][C]15.75[/C][C]15.6972321112096[/C][C]0.0527678887903509[/C][/ROW]
[ROW][C]14[/C][C]15.86[/C][C]15.8101040072837[/C][C]0.0498959927163085[/C][/ROW]
[ROW][C]15[/C][C]15.89[/C][C]15.9322753495049[/C][C]-0.0422753495048518[/C][/ROW]
[ROW][C]16[/C][C]15.94[/C][C]15.9519629432708[/C][C]-0.0119629432707846[/C][/ROW]
[ROW][C]17[/C][C]15.93[/C][C]15.999044771518[/C][C]-0.0690447715180156[/C][/ROW]
[ROW][C]18[/C][C]15.95[/C][C]15.9722023860482[/C][C]-0.0222023860481908[/C][/ROW]
[ROW][C]19[/C][C]15.99[/C][C]15.9867864633657[/C][C]0.00321353663432511[/C][/ROW]
[ROW][C]20[/C][C]15.99[/C][C]16.0275703550569[/C][C]-0.0375703550569195[/C][/ROW]
[ROW][C]21[/C][C]16.06[/C][C]16.018405658177[/C][C]0.0415943418230107[/C][/ROW]
[ROW][C]22[/C][C]16.08[/C][C]16.0985519433039[/C][C]-0.0185519433039367[/C][/ROW]
[ROW][C]23[/C][C]16.07[/C][C]16.1140264886827[/C][C]-0.044026488682686[/C][/ROW]
[ROW][C]24[/C][C]16.11[/C][C]16.0932869196035[/C][C]0.0167130803965314[/C][/ROW]
[ROW][C]25[/C][C]16.15[/C][C]16.1373638125562[/C][C]0.0126361874437748[/C][/ROW]
[ROW][C]26[/C][C]16.18[/C][C]16.1804462116303[/C][C]-0.000446211630301008[/C][/ROW]
[ROW][C]27[/C][C]16.3[/C][C]16.210337365325[/C][C]0.0896626346749798[/C][/ROW]
[ROW][C]28[/C][C]16.42[/C][C]16.3522091540533[/C][C]0.0677908459466749[/C][/ROW]
[ROW][C]29[/C][C]16.49[/C][C]16.4887456641128[/C][C]0.00125433588723212[/C][/ROW]
[ROW][C]30[/C][C]16.5[/C][C]16.5590516396133[/C][C]-0.0590516396132514[/C][/ROW]
[ROW][C]31[/C][C]16.58[/C][C]16.5546469214119[/C][C]0.0253530785880649[/C][/ROW]
[ROW][C]32[/C][C]16.64[/C][C]16.6408314059578[/C][C]-0.000831405957811171[/C][/ROW]
[ROW][C]33[/C][C]16.66[/C][C]16.7006285975581[/C][C]-0.0406285975580545[/C][/ROW]
[ROW][C]34[/C][C]16.81[/C][C]16.7107178905468[/C][C]0.0992821094531564[/C][/ROW]
[ROW][C]35[/C][C]16.91[/C][C]16.8849361987678[/C][C]0.0250638012322248[/C][/ROW]
[ROW][C]36[/C][C]16.92[/C][C]16.991050118655[/C][C]-0.0710501186549912[/C][/ROW]
[ROW][C]37[/C][C]16.95[/C][C]16.9837185603088[/C][C]-0.0337185603087988[/C][/ROW]
[ROW][C]38[/C][C]17.11[/C][C]17.0054934481428[/C][C]0.104506551857156[/C][/ROW]
[ROW][C]39[/C][C]17.16[/C][C]17.1909861768724[/C][C]-0.0309861768723643[/C][/ROW]
[ROW][C]40[/C][C]17.16[/C][C]17.2334275866468[/C][C]-0.0734275866468259[/C][/ROW]
[ROW][C]41[/C][C]17.27[/C][C]17.2155160823977[/C][C]0.0544839176022975[/C][/ROW]
[ROW][C]42[/C][C]17.34[/C][C]17.3388065766957[/C][C]0.0011934233043398[/C][/ROW]
[ROW][C]43[/C][C]17.39[/C][C]17.4090976935301[/C][C]-0.0190976935301208[/C][/ROW]
[ROW][C]44[/C][C]17.43[/C][C]17.4544391117295[/C][C]-0.0244391117295457[/C][/ROW]
[ROW][C]45[/C][C]17.45[/C][C]17.4884775750159[/C][C]-0.0384775750159108[/C][/ROW]
[ROW][C]46[/C][C]17.5[/C][C]17.4990915761037[/C][C]0.000908423896301969[/C][/ROW]
[ROW][C]47[/C][C]17.56[/C][C]17.5493131718175[/C][C]0.010686828182461[/C][/ROW]
[ROW][C]48[/C][C]17.65[/C][C]17.6119200553764[/C][C]0.0380799446235542[/C][/ROW]
[ROW][C]49[/C][C]17.62[/C][C]17.7112090586119[/C][C]-0.0912090586118595[/C][/ROW]
[ROW][C]50[/C][C]17.7[/C][C]17.6589600440999[/C][C]0.0410399559001178[/C][/ROW]
[ROW][C]51[/C][C]17.72[/C][C]17.7489710955052[/C][C]-0.0289710955051845[/C][/ROW]
[ROW][C]52[/C][C]17.71[/C][C]17.7619040526683[/C][C]-0.0519040526682879[/C][/ROW]
[ROW][C]53[/C][C]17.74[/C][C]17.7392428758222[/C][C]0.000757124177766855[/C][/ROW]
[ROW][C]54[/C][C]17.75[/C][C]17.7694275643507[/C][C]-0.0194275643507034[/C][/ROW]
[ROW][C]55[/C][C]17.78[/C][C]17.7746885157545[/C][C]0.00531148424545336[/C][/ROW]
[ROW][C]56[/C][C]17.8[/C][C]17.8059841687506[/C][C]-0.00598416875059726[/C][/ROW]
[ROW][C]57[/C][C]17.86[/C][C]17.8245244249554[/C][C]0.0354755750445968[/C][/ROW]
[ROW][C]58[/C][C]17.88[/C][C]17.8931781332164[/C][C]-0.0131781332164103[/C][/ROW]
[ROW][C]59[/C][C]17.89[/C][C]17.9099635349996[/C][C]-0.0199635349995759[/C][/ROW]
[ROW][C]60[/C][C]17.94[/C][C]17.9150937447981[/C][C]0.0249062552019232[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166441&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166441&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
315.3315.37-0.0399999999999991
415.3615.440242629471-0.0802426294709768
515.415.4506687027717-0.0506687027716914
615.415.4783088700925-0.078308870092485
715.4115.4592066535624-0.0492066535624485
815.4715.45720346477990.0127965352201027
915.5415.52032497817070.0196750218293449
1015.5515.5951243901245-0.0451243901245402
1115.5915.594117005266-0.00411700526600889
1215.6515.63311272661970.0168872733802523
1315.7515.69723211120960.0527678887903509
1415.8615.81010400728370.0498959927163085
1515.8915.9322753495049-0.0422753495048518
1615.9415.9519629432708-0.0119629432707846
1715.9315.999044771518-0.0690447715180156
1815.9515.9722023860482-0.0222023860481908
1915.9915.98678646336570.00321353663432511
2015.9916.0275703550569-0.0375703550569195
2116.0616.0184056581770.0415943418230107
2216.0816.0985519433039-0.0185519433039367
2316.0716.1140264886827-0.044026488682686
2416.1116.09328691960350.0167130803965314
2516.1516.13736381255620.0126361874437748
2616.1816.1804462116303-0.000446211630301008
2716.316.2103373653250.0896626346749798
2816.4216.35220915405330.0677908459466749
2916.4916.48874566411280.00125433588723212
3016.516.5590516396133-0.0590516396132514
3116.5816.55464692141190.0253530785880649
3216.6416.6408314059578-0.000831405957811171
3316.6616.7006285975581-0.0406285975580545
3416.8116.71071789054680.0992821094531564
3516.9116.88493619876780.0250638012322248
3616.9216.991050118655-0.0710501186549912
3716.9516.9837185603088-0.0337185603087988
3817.1117.00549344814280.104506551857156
3917.1617.1909861768724-0.0309861768723643
4017.1617.2334275866468-0.0734275866468259
4117.2717.21551608239770.0544839176022975
4217.3417.33880657669570.0011934233043398
4317.3917.4090976935301-0.0190976935301208
4417.4317.4544391117295-0.0244391117295457
4517.4517.4884775750159-0.0384775750159108
4617.517.49909157610370.000908423896301969
4717.5617.54931317181750.010686828182461
4817.6517.61192005537640.0380799446235542
4917.6217.7112090586119-0.0912090586118595
5017.717.65896004409990.0410399559001178
5117.7217.7489710955052-0.0289710955051845
5217.7117.7619040526683-0.0519040526682879
5317.7417.73924287582220.000757124177766855
5417.7517.7694275643507-0.0194275643507034
5517.7817.77468851575450.00531148424545336
5617.817.8059841687506-0.00598416875059726
5717.8617.82452442495540.0354755750445968
5817.8817.8931781332164-0.0131781332164103
5917.8917.9099635349996-0.0199635349995759
6017.9417.91509374479810.0249062552019232







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6117.971169233810517.883567185359118.0587712822618
6218.002338467620917.862521304671818.14215563057
6318.033507701431417.842360007557218.2246553953056
6418.064676935241917.820641682185218.3087121882985
6518.095846169052317.796664934639718.395027403465
6618.127015402862817.770197045528318.4838337601973
6718.158184636673317.741175916812718.5751933565338
6818.189353870483717.709610722186918.6690970187806
6918.220523104294217.675542124615418.765504083973
7018.251692338104717.639024489716918.8643601864924
7118.282861571915117.60011737279418.9656057710363
7218.314030805725617.558881287050719.0691803244005

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 17.9711692338105 & 17.8835671853591 & 18.0587712822618 \tabularnewline
62 & 18.0023384676209 & 17.8625213046718 & 18.14215563057 \tabularnewline
63 & 18.0335077014314 & 17.8423600075572 & 18.2246553953056 \tabularnewline
64 & 18.0646769352419 & 17.8206416821852 & 18.3087121882985 \tabularnewline
65 & 18.0958461690523 & 17.7966649346397 & 18.395027403465 \tabularnewline
66 & 18.1270154028628 & 17.7701970455283 & 18.4838337601973 \tabularnewline
67 & 18.1581846366733 & 17.7411759168127 & 18.5751933565338 \tabularnewline
68 & 18.1893538704837 & 17.7096107221869 & 18.6690970187806 \tabularnewline
69 & 18.2205231042942 & 17.6755421246154 & 18.765504083973 \tabularnewline
70 & 18.2516923381047 & 17.6390244897169 & 18.8643601864924 \tabularnewline
71 & 18.2828615719151 & 17.600117372794 & 18.9656057710363 \tabularnewline
72 & 18.3140308057256 & 17.5588812870507 & 19.0691803244005 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166441&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]17.9711692338105[/C][C]17.8835671853591[/C][C]18.0587712822618[/C][/ROW]
[ROW][C]62[/C][C]18.0023384676209[/C][C]17.8625213046718[/C][C]18.14215563057[/C][/ROW]
[ROW][C]63[/C][C]18.0335077014314[/C][C]17.8423600075572[/C][C]18.2246553953056[/C][/ROW]
[ROW][C]64[/C][C]18.0646769352419[/C][C]17.8206416821852[/C][C]18.3087121882985[/C][/ROW]
[ROW][C]65[/C][C]18.0958461690523[/C][C]17.7966649346397[/C][C]18.395027403465[/C][/ROW]
[ROW][C]66[/C][C]18.1270154028628[/C][C]17.7701970455283[/C][C]18.4838337601973[/C][/ROW]
[ROW][C]67[/C][C]18.1581846366733[/C][C]17.7411759168127[/C][C]18.5751933565338[/C][/ROW]
[ROW][C]68[/C][C]18.1893538704837[/C][C]17.7096107221869[/C][C]18.6690970187806[/C][/ROW]
[ROW][C]69[/C][C]18.2205231042942[/C][C]17.6755421246154[/C][C]18.765504083973[/C][/ROW]
[ROW][C]70[/C][C]18.2516923381047[/C][C]17.6390244897169[/C][C]18.8643601864924[/C][/ROW]
[ROW][C]71[/C][C]18.2828615719151[/C][C]17.600117372794[/C][C]18.9656057710363[/C][/ROW]
[ROW][C]72[/C][C]18.3140308057256[/C][C]17.5588812870507[/C][C]19.0691803244005[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166441&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166441&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
6117.971169233810517.883567185359118.0587712822618
6218.002338467620917.862521304671818.14215563057
6318.033507701431417.842360007557218.2246553953056
6418.064676935241917.820641682185218.3087121882985
6518.095846169052317.796664934639718.395027403465
6618.127015402862817.770197045528318.4838337601973
6718.158184636673317.741175916812718.5751933565338
6818.189353870483717.709610722186918.6690970187806
6918.220523104294217.675542124615418.765504083973
7018.251692338104717.639024489716918.8643601864924
7118.282861571915117.60011737279418.9656057710363
7218.314030805725617.558881287050719.0691803244005



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')