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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 21 May 2014 05:36:00 -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/2014/May/21/t1400664982hfz5bvdh3n2g51s.htm/, Retrieved Tue, 14 May 2024 09:30:41 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235008, Retrieved Tue, 14 May 2024 09:30:41 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-05-21 09:36:00] [3ace99d75142efe6ae27f9378c84deb8] [Current]
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Dataseries X:
55,64
56,13
56,69
56,8
56,93
57
57,01
57,21
57,17
57,36
57,29
57,26
57,29
57,68
58,19
58,34
58,46
58,67
58,72
58,74
58,77
58,84
59,13
59,12
59,12
59,33
59,49
59,67
59,7
59,73
59,74
59,62
59,6
59,98
60,05
60,06
60,1
60,18
60,38
60,52
60,78
60,72
60,72
60,86
60,99
61,11
61,17
61,19
61,19
61,22
61,19
60,82
60,6
60,15
60,14
60,2
60,36
60,38
60,44
60,47




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235008&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235008&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235008&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.517041942355468
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.517041942355468 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235008&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]0.517041942355468[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235008&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235008&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
beta0.517041942355468
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
356.6956.620.0699999999999932
456.857.2161929359649-0.416192935964879
556.9357.111003731959-0.181003731958974
65757.1474172108133-0.147417210813316
757.0157.1411963297978-0.131196329797774
857.2157.08336232460920.126637675390782
957.1757.3488393142687-0.17883931426865
1057.3657.21637188784970.143628112150331
1157.2957.4806336459327-0.190633645932728
1257.2657.3120680553614-0.0520680553613673
1357.2957.25514668688260.0348533131173525
1457.6857.30316731159440.376832688405628
1558.1957.88800561675060.301994383249351
1658.3458.5541493792463-0.214149379246329
1758.4658.5934251682466-0.133425168246596
1858.6758.64443876009730.0255612399027285
1958.7258.8676549932256-0.147654993225594
2058.7458.8413111687297-0.101311168729744
2158.7758.8089290452674-0.038929045267416
2258.8458.81880109608830.0211989039116887
2359.1358.89976181854260.230238181457381
2459.1259.3088046150877-0.18880461508774
2559.1259.2011847101771-0.0811847101770908
2659.3359.15920880993760.170791190062438
2759.4959.45751501858460.032484981415358
2859.6759.6343111164730.0356888835269729
2959.759.8327637661323-0.132763766132307
3059.7359.7941193306168-0.0641193306168404
3159.7459.7909669473722-0.0509669473721672
3259.6259.7746148979069-0.154614897906939
3359.659.5746725107760.0253274892239617
3459.9859.56776788499940.412232115000613
3560.0560.1609091784406-0.1109091784406
3660.0660.1735644813946-0.113564481394619
3760.160.1248468813518-0.0248468813517633
3860.1860.15200000155620.0279999984438319
3960.3860.24647717513750.133522824862489
4060.5260.51551407585320.00448592414679183
4160.7860.65783348678730.122166513212676
4260.7260.9809986980696-0.260998698069599
4360.7260.7860514242674-0.0660514242674424
4460.8660.75190006756890.108099932431138
4560.9960.94779226660160.042207733398449
4661.1161.09961543506030.0103845649396916
4761.1761.2249846906872-0.0549846906872418
4861.1961.2565552994145-0.0665552994145031
4961.1961.2421434181312-0.0521434181311733
5061.2261.21518308393960.00481691606042034
5161.1961.2476736315756-0.057673631575625
5260.8261.1878539450831-0.367853945083063
5360.660.6276580268142-0.0276580268141942
5460.1560.3933576669085-0.243357666908466
5560.1459.8175315461230.322468453876986
5660.259.97426126186390.225738738136066
5760.3660.15097765749470.209022342505314
5860.3860.4190509754593-0.0390509754593182
5960.4460.4188599832570.0211400167430398
6060.4760.4897902585752-0.0197902585752061

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 56.69 & 56.62 & 0.0699999999999932 \tabularnewline
4 & 56.8 & 57.2161929359649 & -0.416192935964879 \tabularnewline
5 & 56.93 & 57.111003731959 & -0.181003731958974 \tabularnewline
6 & 57 & 57.1474172108133 & -0.147417210813316 \tabularnewline
7 & 57.01 & 57.1411963297978 & -0.131196329797774 \tabularnewline
8 & 57.21 & 57.0833623246092 & 0.126637675390782 \tabularnewline
9 & 57.17 & 57.3488393142687 & -0.17883931426865 \tabularnewline
10 & 57.36 & 57.2163718878497 & 0.143628112150331 \tabularnewline
11 & 57.29 & 57.4806336459327 & -0.190633645932728 \tabularnewline
12 & 57.26 & 57.3120680553614 & -0.0520680553613673 \tabularnewline
13 & 57.29 & 57.2551466868826 & 0.0348533131173525 \tabularnewline
14 & 57.68 & 57.3031673115944 & 0.376832688405628 \tabularnewline
15 & 58.19 & 57.8880056167506 & 0.301994383249351 \tabularnewline
16 & 58.34 & 58.5541493792463 & -0.214149379246329 \tabularnewline
17 & 58.46 & 58.5934251682466 & -0.133425168246596 \tabularnewline
18 & 58.67 & 58.6444387600973 & 0.0255612399027285 \tabularnewline
19 & 58.72 & 58.8676549932256 & -0.147654993225594 \tabularnewline
20 & 58.74 & 58.8413111687297 & -0.101311168729744 \tabularnewline
21 & 58.77 & 58.8089290452674 & -0.038929045267416 \tabularnewline
22 & 58.84 & 58.8188010960883 & 0.0211989039116887 \tabularnewline
23 & 59.13 & 58.8997618185426 & 0.230238181457381 \tabularnewline
24 & 59.12 & 59.3088046150877 & -0.18880461508774 \tabularnewline
25 & 59.12 & 59.2011847101771 & -0.0811847101770908 \tabularnewline
26 & 59.33 & 59.1592088099376 & 0.170791190062438 \tabularnewline
27 & 59.49 & 59.4575150185846 & 0.032484981415358 \tabularnewline
28 & 59.67 & 59.634311116473 & 0.0356888835269729 \tabularnewline
29 & 59.7 & 59.8327637661323 & -0.132763766132307 \tabularnewline
30 & 59.73 & 59.7941193306168 & -0.0641193306168404 \tabularnewline
31 & 59.74 & 59.7909669473722 & -0.0509669473721672 \tabularnewline
32 & 59.62 & 59.7746148979069 & -0.154614897906939 \tabularnewline
33 & 59.6 & 59.574672510776 & 0.0253274892239617 \tabularnewline
34 & 59.98 & 59.5677678849994 & 0.412232115000613 \tabularnewline
35 & 60.05 & 60.1609091784406 & -0.1109091784406 \tabularnewline
36 & 60.06 & 60.1735644813946 & -0.113564481394619 \tabularnewline
37 & 60.1 & 60.1248468813518 & -0.0248468813517633 \tabularnewline
38 & 60.18 & 60.1520000015562 & 0.0279999984438319 \tabularnewline
39 & 60.38 & 60.2464771751375 & 0.133522824862489 \tabularnewline
40 & 60.52 & 60.5155140758532 & 0.00448592414679183 \tabularnewline
41 & 60.78 & 60.6578334867873 & 0.122166513212676 \tabularnewline
42 & 60.72 & 60.9809986980696 & -0.260998698069599 \tabularnewline
43 & 60.72 & 60.7860514242674 & -0.0660514242674424 \tabularnewline
44 & 60.86 & 60.7519000675689 & 0.108099932431138 \tabularnewline
45 & 60.99 & 60.9477922666016 & 0.042207733398449 \tabularnewline
46 & 61.11 & 61.0996154350603 & 0.0103845649396916 \tabularnewline
47 & 61.17 & 61.2249846906872 & -0.0549846906872418 \tabularnewline
48 & 61.19 & 61.2565552994145 & -0.0665552994145031 \tabularnewline
49 & 61.19 & 61.2421434181312 & -0.0521434181311733 \tabularnewline
50 & 61.22 & 61.2151830839396 & 0.00481691606042034 \tabularnewline
51 & 61.19 & 61.2476736315756 & -0.057673631575625 \tabularnewline
52 & 60.82 & 61.1878539450831 & -0.367853945083063 \tabularnewline
53 & 60.6 & 60.6276580268142 & -0.0276580268141942 \tabularnewline
54 & 60.15 & 60.3933576669085 & -0.243357666908466 \tabularnewline
55 & 60.14 & 59.817531546123 & 0.322468453876986 \tabularnewline
56 & 60.2 & 59.9742612618639 & 0.225738738136066 \tabularnewline
57 & 60.36 & 60.1509776574947 & 0.209022342505314 \tabularnewline
58 & 60.38 & 60.4190509754593 & -0.0390509754593182 \tabularnewline
59 & 60.44 & 60.418859983257 & 0.0211400167430398 \tabularnewline
60 & 60.47 & 60.4897902585752 & -0.0197902585752061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235008&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]56.69[/C][C]56.62[/C][C]0.0699999999999932[/C][/ROW]
[ROW][C]4[/C][C]56.8[/C][C]57.2161929359649[/C][C]-0.416192935964879[/C][/ROW]
[ROW][C]5[/C][C]56.93[/C][C]57.111003731959[/C][C]-0.181003731958974[/C][/ROW]
[ROW][C]6[/C][C]57[/C][C]57.1474172108133[/C][C]-0.147417210813316[/C][/ROW]
[ROW][C]7[/C][C]57.01[/C][C]57.1411963297978[/C][C]-0.131196329797774[/C][/ROW]
[ROW][C]8[/C][C]57.21[/C][C]57.0833623246092[/C][C]0.126637675390782[/C][/ROW]
[ROW][C]9[/C][C]57.17[/C][C]57.3488393142687[/C][C]-0.17883931426865[/C][/ROW]
[ROW][C]10[/C][C]57.36[/C][C]57.2163718878497[/C][C]0.143628112150331[/C][/ROW]
[ROW][C]11[/C][C]57.29[/C][C]57.4806336459327[/C][C]-0.190633645932728[/C][/ROW]
[ROW][C]12[/C][C]57.26[/C][C]57.3120680553614[/C][C]-0.0520680553613673[/C][/ROW]
[ROW][C]13[/C][C]57.29[/C][C]57.2551466868826[/C][C]0.0348533131173525[/C][/ROW]
[ROW][C]14[/C][C]57.68[/C][C]57.3031673115944[/C][C]0.376832688405628[/C][/ROW]
[ROW][C]15[/C][C]58.19[/C][C]57.8880056167506[/C][C]0.301994383249351[/C][/ROW]
[ROW][C]16[/C][C]58.34[/C][C]58.5541493792463[/C][C]-0.214149379246329[/C][/ROW]
[ROW][C]17[/C][C]58.46[/C][C]58.5934251682466[/C][C]-0.133425168246596[/C][/ROW]
[ROW][C]18[/C][C]58.67[/C][C]58.6444387600973[/C][C]0.0255612399027285[/C][/ROW]
[ROW][C]19[/C][C]58.72[/C][C]58.8676549932256[/C][C]-0.147654993225594[/C][/ROW]
[ROW][C]20[/C][C]58.74[/C][C]58.8413111687297[/C][C]-0.101311168729744[/C][/ROW]
[ROW][C]21[/C][C]58.77[/C][C]58.8089290452674[/C][C]-0.038929045267416[/C][/ROW]
[ROW][C]22[/C][C]58.84[/C][C]58.8188010960883[/C][C]0.0211989039116887[/C][/ROW]
[ROW][C]23[/C][C]59.13[/C][C]58.8997618185426[/C][C]0.230238181457381[/C][/ROW]
[ROW][C]24[/C][C]59.12[/C][C]59.3088046150877[/C][C]-0.18880461508774[/C][/ROW]
[ROW][C]25[/C][C]59.12[/C][C]59.2011847101771[/C][C]-0.0811847101770908[/C][/ROW]
[ROW][C]26[/C][C]59.33[/C][C]59.1592088099376[/C][C]0.170791190062438[/C][/ROW]
[ROW][C]27[/C][C]59.49[/C][C]59.4575150185846[/C][C]0.032484981415358[/C][/ROW]
[ROW][C]28[/C][C]59.67[/C][C]59.634311116473[/C][C]0.0356888835269729[/C][/ROW]
[ROW][C]29[/C][C]59.7[/C][C]59.8327637661323[/C][C]-0.132763766132307[/C][/ROW]
[ROW][C]30[/C][C]59.73[/C][C]59.7941193306168[/C][C]-0.0641193306168404[/C][/ROW]
[ROW][C]31[/C][C]59.74[/C][C]59.7909669473722[/C][C]-0.0509669473721672[/C][/ROW]
[ROW][C]32[/C][C]59.62[/C][C]59.7746148979069[/C][C]-0.154614897906939[/C][/ROW]
[ROW][C]33[/C][C]59.6[/C][C]59.574672510776[/C][C]0.0253274892239617[/C][/ROW]
[ROW][C]34[/C][C]59.98[/C][C]59.5677678849994[/C][C]0.412232115000613[/C][/ROW]
[ROW][C]35[/C][C]60.05[/C][C]60.1609091784406[/C][C]-0.1109091784406[/C][/ROW]
[ROW][C]36[/C][C]60.06[/C][C]60.1735644813946[/C][C]-0.113564481394619[/C][/ROW]
[ROW][C]37[/C][C]60.1[/C][C]60.1248468813518[/C][C]-0.0248468813517633[/C][/ROW]
[ROW][C]38[/C][C]60.18[/C][C]60.1520000015562[/C][C]0.0279999984438319[/C][/ROW]
[ROW][C]39[/C][C]60.38[/C][C]60.2464771751375[/C][C]0.133522824862489[/C][/ROW]
[ROW][C]40[/C][C]60.52[/C][C]60.5155140758532[/C][C]0.00448592414679183[/C][/ROW]
[ROW][C]41[/C][C]60.78[/C][C]60.6578334867873[/C][C]0.122166513212676[/C][/ROW]
[ROW][C]42[/C][C]60.72[/C][C]60.9809986980696[/C][C]-0.260998698069599[/C][/ROW]
[ROW][C]43[/C][C]60.72[/C][C]60.7860514242674[/C][C]-0.0660514242674424[/C][/ROW]
[ROW][C]44[/C][C]60.86[/C][C]60.7519000675689[/C][C]0.108099932431138[/C][/ROW]
[ROW][C]45[/C][C]60.99[/C][C]60.9477922666016[/C][C]0.042207733398449[/C][/ROW]
[ROW][C]46[/C][C]61.11[/C][C]61.0996154350603[/C][C]0.0103845649396916[/C][/ROW]
[ROW][C]47[/C][C]61.17[/C][C]61.2249846906872[/C][C]-0.0549846906872418[/C][/ROW]
[ROW][C]48[/C][C]61.19[/C][C]61.2565552994145[/C][C]-0.0665552994145031[/C][/ROW]
[ROW][C]49[/C][C]61.19[/C][C]61.2421434181312[/C][C]-0.0521434181311733[/C][/ROW]
[ROW][C]50[/C][C]61.22[/C][C]61.2151830839396[/C][C]0.00481691606042034[/C][/ROW]
[ROW][C]51[/C][C]61.19[/C][C]61.2476736315756[/C][C]-0.057673631575625[/C][/ROW]
[ROW][C]52[/C][C]60.82[/C][C]61.1878539450831[/C][C]-0.367853945083063[/C][/ROW]
[ROW][C]53[/C][C]60.6[/C][C]60.6276580268142[/C][C]-0.0276580268141942[/C][/ROW]
[ROW][C]54[/C][C]60.15[/C][C]60.3933576669085[/C][C]-0.243357666908466[/C][/ROW]
[ROW][C]55[/C][C]60.14[/C][C]59.817531546123[/C][C]0.322468453876986[/C][/ROW]
[ROW][C]56[/C][C]60.2[/C][C]59.9742612618639[/C][C]0.225738738136066[/C][/ROW]
[ROW][C]57[/C][C]60.36[/C][C]60.1509776574947[/C][C]0.209022342505314[/C][/ROW]
[ROW][C]58[/C][C]60.38[/C][C]60.4190509754593[/C][C]-0.0390509754593182[/C][/ROW]
[ROW][C]59[/C][C]60.44[/C][C]60.418859983257[/C][C]0.0211400167430398[/C][/ROW]
[ROW][C]60[/C][C]60.47[/C][C]60.4897902585752[/C][C]-0.0197902585752061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235008&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235008&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
356.6956.620.0699999999999932
456.857.2161929359649-0.416192935964879
556.9357.111003731959-0.181003731958974
65757.1474172108133-0.147417210813316
757.0157.1411963297978-0.131196329797774
857.2157.08336232460920.126637675390782
957.1757.3488393142687-0.17883931426865
1057.3657.21637188784970.143628112150331
1157.2957.4806336459327-0.190633645932728
1257.2657.3120680553614-0.0520680553613673
1357.2957.25514668688260.0348533131173525
1457.6857.30316731159440.376832688405628
1558.1957.88800561675060.301994383249351
1658.3458.5541493792463-0.214149379246329
1758.4658.5934251682466-0.133425168246596
1858.6758.64443876009730.0255612399027285
1958.7258.8676549932256-0.147654993225594
2058.7458.8413111687297-0.101311168729744
2158.7758.8089290452674-0.038929045267416
2258.8458.81880109608830.0211989039116887
2359.1358.89976181854260.230238181457381
2459.1259.3088046150877-0.18880461508774
2559.1259.2011847101771-0.0811847101770908
2659.3359.15920880993760.170791190062438
2759.4959.45751501858460.032484981415358
2859.6759.6343111164730.0356888835269729
2959.759.8327637661323-0.132763766132307
3059.7359.7941193306168-0.0641193306168404
3159.7459.7909669473722-0.0509669473721672
3259.6259.7746148979069-0.154614897906939
3359.659.5746725107760.0253274892239617
3459.9859.56776788499940.412232115000613
3560.0560.1609091784406-0.1109091784406
3660.0660.1735644813946-0.113564481394619
3760.160.1248468813518-0.0248468813517633
3860.1860.15200000155620.0279999984438319
3960.3860.24647717513750.133522824862489
4060.5260.51551407585320.00448592414679183
4160.7860.65783348678730.122166513212676
4260.7260.9809986980696-0.260998698069599
4360.7260.7860514242674-0.0660514242674424
4460.8660.75190006756890.108099932431138
4560.9960.94779226660160.042207733398449
4661.1161.09961543506030.0103845649396916
4761.1761.2249846906872-0.0549846906872418
4861.1961.2565552994145-0.0665552994145031
4961.1961.2421434181312-0.0521434181311733
5061.2261.21518308393960.00481691606042034
5161.1961.2476736315756-0.057673631575625
5260.8261.1878539450831-0.367853945083063
5360.660.6276580268142-0.0276580268141942
5460.1560.3933576669085-0.243357666908466
5560.1459.8175315461230.322468453876986
5660.259.97426126186390.225738738136066
5760.3660.15097765749470.209022342505314
5860.3860.4190509754593-0.0390509754593182
5960.4460.4188599832570.0211400167430398
6060.4760.4897902585752-0.0197902585752061







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6160.509557864841860.183445569150360.8356701605332
6260.549115729683559.956576216539261.1416552428279
6360.588673594525359.699222798343561.4781243907071
6460.628231459367159.410336001992261.8461269167419
6560.667789324208859.091590054904762.243988593513
6660.707347189050658.744851768334962.6698426097663
6760.746905053892458.371808645840863.1220014619439
6860.786462918734157.97392859302363.5989972444452
6960.826020783575957.552483153313964.0995584138379
7060.865578648417657.108579582544364.622577714291
7160.905136513259456.643189703511765.1670833230071
7260.944694378101256.157173549499265.7322152067032

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 60.5095578648418 & 60.1834455691503 & 60.8356701605332 \tabularnewline
62 & 60.5491157296835 & 59.9565762165392 & 61.1416552428279 \tabularnewline
63 & 60.5886735945253 & 59.6992227983435 & 61.4781243907071 \tabularnewline
64 & 60.6282314593671 & 59.4103360019922 & 61.8461269167419 \tabularnewline
65 & 60.6677893242088 & 59.0915900549047 & 62.243988593513 \tabularnewline
66 & 60.7073471890506 & 58.7448517683349 & 62.6698426097663 \tabularnewline
67 & 60.7469050538924 & 58.3718086458408 & 63.1220014619439 \tabularnewline
68 & 60.7864629187341 & 57.973928593023 & 63.5989972444452 \tabularnewline
69 & 60.8260207835759 & 57.5524831533139 & 64.0995584138379 \tabularnewline
70 & 60.8655786484176 & 57.1085795825443 & 64.622577714291 \tabularnewline
71 & 60.9051365132594 & 56.6431897035117 & 65.1670833230071 \tabularnewline
72 & 60.9446943781012 & 56.1571735494992 & 65.7322152067032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235008&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]60.5095578648418[/C][C]60.1834455691503[/C][C]60.8356701605332[/C][/ROW]
[ROW][C]62[/C][C]60.5491157296835[/C][C]59.9565762165392[/C][C]61.1416552428279[/C][/ROW]
[ROW][C]63[/C][C]60.5886735945253[/C][C]59.6992227983435[/C][C]61.4781243907071[/C][/ROW]
[ROW][C]64[/C][C]60.6282314593671[/C][C]59.4103360019922[/C][C]61.8461269167419[/C][/ROW]
[ROW][C]65[/C][C]60.6677893242088[/C][C]59.0915900549047[/C][C]62.243988593513[/C][/ROW]
[ROW][C]66[/C][C]60.7073471890506[/C][C]58.7448517683349[/C][C]62.6698426097663[/C][/ROW]
[ROW][C]67[/C][C]60.7469050538924[/C][C]58.3718086458408[/C][C]63.1220014619439[/C][/ROW]
[ROW][C]68[/C][C]60.7864629187341[/C][C]57.973928593023[/C][C]63.5989972444452[/C][/ROW]
[ROW][C]69[/C][C]60.8260207835759[/C][C]57.5524831533139[/C][C]64.0995584138379[/C][/ROW]
[ROW][C]70[/C][C]60.8655786484176[/C][C]57.1085795825443[/C][C]64.622577714291[/C][/ROW]
[ROW][C]71[/C][C]60.9051365132594[/C][C]56.6431897035117[/C][C]65.1670833230071[/C][/ROW]
[ROW][C]72[/C][C]60.9446943781012[/C][C]56.1571735494992[/C][C]65.7322152067032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235008&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235008&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
6160.509557864841860.183445569150360.8356701605332
6260.549115729683559.956576216539261.1416552428279
6360.588673594525359.699222798343561.4781243907071
6460.628231459367159.410336001992261.8461269167419
6560.667789324208859.091590054904762.243988593513
6660.707347189050658.744851768334962.6698426097663
6760.746905053892458.371808645840863.1220014619439
6860.786462918734157.97392859302363.5989972444452
6960.826020783575957.552483153313964.0995584138379
7060.865578648417657.108579582544364.622577714291
7160.905136513259456.643189703511765.1670833230071
7260.944694378101256.157173549499265.7322152067032



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')