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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 20 Dec 2010 16:11:23 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t1292861461djavx4pet6ay1v4.htm/, Retrieved Fri, 03 May 2024 22:43:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113004, Retrieved Fri, 03 May 2024 22:43:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact86
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opdracht 10 ] [2010-12-20 16:11:23] [3c432a26e3310571299b8b38ea0e36f7] [Current]
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Dataseries X:
108
106,6
122,2
115,8
115,6
124,5
121,7
118,7
113,7
113,4
115,1
143,9
101
103,4
121,5
111,9
117,4
124,3
122
119,7
115
112,2
115,3
142,6
104,1
105,3
124,4
113,9
124,8
131,8
125,6
125
119,7
116,1
120
148,1
109,2
109,4
135,1
114,9
129
138,5
125,6
130,4
120,3
126,2
127,6
150,9
114,6
118,6
131,4
124,5
136,8
136,8
136,6
131
125,8
129,4
124,8
157,1
116,6
114,2
128,4
127,3
133,5
137,2
137,7
131,2
127,7
133,9
124,3
160,6




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113004&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113004&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113004&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.127863990701472
beta0.243685602085768
gamma0.106601253861168

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.127863990701472 \tabularnewline
beta & 0.243685602085768 \tabularnewline
gamma & 0.106601253861168 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113004&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]0.127863990701472[/C][/ROW]
[ROW][C]beta[/C][C]0.243685602085768[/C][/ROW]
[ROW][C]gamma[/C][C]0.106601253861168[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113004&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113004&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
alpha0.127863990701472
beta0.243685602085768
gamma0.106601253861168







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13101101.507665598291-0.507665598290629
14103.4103.738925385997-0.338925385996987
15121.5121.639533858845-0.139533858844715
16111.9111.952956313147-0.0529563131466801
17117.4117.421632205983-0.0216322059831953
18124.3124.2978059612870.00219403871319912
19122120.9020945985251.09790540147485
20119.7118.4348611400591.26513885994113
21115113.7659307918071.23406920819349
22112.2113.860646306122-1.66064630612205
23115.3115.429321839654-0.129321839654168
24142.6144.135602474634-1.53560247463443
25104.1100.9295251386833.1704748613173
26105.3103.7368592164691.56314078353115
27124.4122.0485614546472.35143854535306
28113.9112.9155044169030.984495583096873
29124.8118.7790364917536.0209635082467
30131.8126.8776259142144.92237408578575
31125.6124.8137736694070.786226330592768
32125122.9134001293262.08659987067446
33119.7118.9633767012660.736623298733889
34116.1119.326623284516-3.22662328451649
35120121.389902011815-1.38990201181525
36148.1150.317445691267-2.21744569126702
37109.2107.9536564895241.24634351047625
38109.4110.79751865771-1.39751865770988
39135.1129.1436881145425.95631188545761
40114.9120.796541935946-5.89654193594566
41129126.4861410549382.51385894506188
42138.5134.1625443964784.33745560352173
43125.6131.749518991346-6.14951899134553
44130.4128.9772597099781.42274029002158
45120.3124.690208787274-4.39020878727382
46126.2123.7430716382052.45692836179498
47127.6126.5945446334931.00545536650689
48150.9155.716778131472-4.81677813147218
49114.6113.227014797981.37298520202017
50118.6115.729569559072.87043044092972
51131.4135.326432488089-3.92643248808852
52124.5124.3270223707510.172977629248834
53136.8131.4770863343445.32291366565605
54136.8139.672204318251-2.87220431825071
55136.6135.1276941512381.47230584876195
56131134.036829711193-3.03682971119269
57125.8128.503010829938-2.70301082993775
58129.4128.3246449974481.07535500255199
59124.8130.737927693135-5.93792769313471
60157.1158.088116452009-0.988116452008597
61116.6116.4397256579560.160274342043635
62114.2118.665008027763-4.46500802776306
63128.4136.202031686404-7.80203168640415
64127.3124.4774479936252.82255200637461
65133.5131.9168984061131.58310159388662
66137.2138.227202787029-1.02720278702856
67137.7133.7352824235443.96471757645551
68131.2132.03431787576-0.834317875759893
69127.7126.372211655421.32778834458045
70133.9126.7451669715637.15483302843691
71124.3129.157843063896-4.85784306389552
72160.6157.0140550878233.58594491217741

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101 & 101.507665598291 & -0.507665598290629 \tabularnewline
14 & 103.4 & 103.738925385997 & -0.338925385996987 \tabularnewline
15 & 121.5 & 121.639533858845 & -0.139533858844715 \tabularnewline
16 & 111.9 & 111.952956313147 & -0.0529563131466801 \tabularnewline
17 & 117.4 & 117.421632205983 & -0.0216322059831953 \tabularnewline
18 & 124.3 & 124.297805961287 & 0.00219403871319912 \tabularnewline
19 & 122 & 120.902094598525 & 1.09790540147485 \tabularnewline
20 & 119.7 & 118.434861140059 & 1.26513885994113 \tabularnewline
21 & 115 & 113.765930791807 & 1.23406920819349 \tabularnewline
22 & 112.2 & 113.860646306122 & -1.66064630612205 \tabularnewline
23 & 115.3 & 115.429321839654 & -0.129321839654168 \tabularnewline
24 & 142.6 & 144.135602474634 & -1.53560247463443 \tabularnewline
25 & 104.1 & 100.929525138683 & 3.1704748613173 \tabularnewline
26 & 105.3 & 103.736859216469 & 1.56314078353115 \tabularnewline
27 & 124.4 & 122.048561454647 & 2.35143854535306 \tabularnewline
28 & 113.9 & 112.915504416903 & 0.984495583096873 \tabularnewline
29 & 124.8 & 118.779036491753 & 6.0209635082467 \tabularnewline
30 & 131.8 & 126.877625914214 & 4.92237408578575 \tabularnewline
31 & 125.6 & 124.813773669407 & 0.786226330592768 \tabularnewline
32 & 125 & 122.913400129326 & 2.08659987067446 \tabularnewline
33 & 119.7 & 118.963376701266 & 0.736623298733889 \tabularnewline
34 & 116.1 & 119.326623284516 & -3.22662328451649 \tabularnewline
35 & 120 & 121.389902011815 & -1.38990201181525 \tabularnewline
36 & 148.1 & 150.317445691267 & -2.21744569126702 \tabularnewline
37 & 109.2 & 107.953656489524 & 1.24634351047625 \tabularnewline
38 & 109.4 & 110.79751865771 & -1.39751865770988 \tabularnewline
39 & 135.1 & 129.143688114542 & 5.95631188545761 \tabularnewline
40 & 114.9 & 120.796541935946 & -5.89654193594566 \tabularnewline
41 & 129 & 126.486141054938 & 2.51385894506188 \tabularnewline
42 & 138.5 & 134.162544396478 & 4.33745560352173 \tabularnewline
43 & 125.6 & 131.749518991346 & -6.14951899134553 \tabularnewline
44 & 130.4 & 128.977259709978 & 1.42274029002158 \tabularnewline
45 & 120.3 & 124.690208787274 & -4.39020878727382 \tabularnewline
46 & 126.2 & 123.743071638205 & 2.45692836179498 \tabularnewline
47 & 127.6 & 126.594544633493 & 1.00545536650689 \tabularnewline
48 & 150.9 & 155.716778131472 & -4.81677813147218 \tabularnewline
49 & 114.6 & 113.22701479798 & 1.37298520202017 \tabularnewline
50 & 118.6 & 115.72956955907 & 2.87043044092972 \tabularnewline
51 & 131.4 & 135.326432488089 & -3.92643248808852 \tabularnewline
52 & 124.5 & 124.327022370751 & 0.172977629248834 \tabularnewline
53 & 136.8 & 131.477086334344 & 5.32291366565605 \tabularnewline
54 & 136.8 & 139.672204318251 & -2.87220431825071 \tabularnewline
55 & 136.6 & 135.127694151238 & 1.47230584876195 \tabularnewline
56 & 131 & 134.036829711193 & -3.03682971119269 \tabularnewline
57 & 125.8 & 128.503010829938 & -2.70301082993775 \tabularnewline
58 & 129.4 & 128.324644997448 & 1.07535500255199 \tabularnewline
59 & 124.8 & 130.737927693135 & -5.93792769313471 \tabularnewline
60 & 157.1 & 158.088116452009 & -0.988116452008597 \tabularnewline
61 & 116.6 & 116.439725657956 & 0.160274342043635 \tabularnewline
62 & 114.2 & 118.665008027763 & -4.46500802776306 \tabularnewline
63 & 128.4 & 136.202031686404 & -7.80203168640415 \tabularnewline
64 & 127.3 & 124.477447993625 & 2.82255200637461 \tabularnewline
65 & 133.5 & 131.916898406113 & 1.58310159388662 \tabularnewline
66 & 137.2 & 138.227202787029 & -1.02720278702856 \tabularnewline
67 & 137.7 & 133.735282423544 & 3.96471757645551 \tabularnewline
68 & 131.2 & 132.03431787576 & -0.834317875759893 \tabularnewline
69 & 127.7 & 126.37221165542 & 1.32778834458045 \tabularnewline
70 & 133.9 & 126.745166971563 & 7.15483302843691 \tabularnewline
71 & 124.3 & 129.157843063896 & -4.85784306389552 \tabularnewline
72 & 160.6 & 157.014055087823 & 3.58594491217741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113004&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]101[/C][C]101.507665598291[/C][C]-0.507665598290629[/C][/ROW]
[ROW][C]14[/C][C]103.4[/C][C]103.738925385997[/C][C]-0.338925385996987[/C][/ROW]
[ROW][C]15[/C][C]121.5[/C][C]121.639533858845[/C][C]-0.139533858844715[/C][/ROW]
[ROW][C]16[/C][C]111.9[/C][C]111.952956313147[/C][C]-0.0529563131466801[/C][/ROW]
[ROW][C]17[/C][C]117.4[/C][C]117.421632205983[/C][C]-0.0216322059831953[/C][/ROW]
[ROW][C]18[/C][C]124.3[/C][C]124.297805961287[/C][C]0.00219403871319912[/C][/ROW]
[ROW][C]19[/C][C]122[/C][C]120.902094598525[/C][C]1.09790540147485[/C][/ROW]
[ROW][C]20[/C][C]119.7[/C][C]118.434861140059[/C][C]1.26513885994113[/C][/ROW]
[ROW][C]21[/C][C]115[/C][C]113.765930791807[/C][C]1.23406920819349[/C][/ROW]
[ROW][C]22[/C][C]112.2[/C][C]113.860646306122[/C][C]-1.66064630612205[/C][/ROW]
[ROW][C]23[/C][C]115.3[/C][C]115.429321839654[/C][C]-0.129321839654168[/C][/ROW]
[ROW][C]24[/C][C]142.6[/C][C]144.135602474634[/C][C]-1.53560247463443[/C][/ROW]
[ROW][C]25[/C][C]104.1[/C][C]100.929525138683[/C][C]3.1704748613173[/C][/ROW]
[ROW][C]26[/C][C]105.3[/C][C]103.736859216469[/C][C]1.56314078353115[/C][/ROW]
[ROW][C]27[/C][C]124.4[/C][C]122.048561454647[/C][C]2.35143854535306[/C][/ROW]
[ROW][C]28[/C][C]113.9[/C][C]112.915504416903[/C][C]0.984495583096873[/C][/ROW]
[ROW][C]29[/C][C]124.8[/C][C]118.779036491753[/C][C]6.0209635082467[/C][/ROW]
[ROW][C]30[/C][C]131.8[/C][C]126.877625914214[/C][C]4.92237408578575[/C][/ROW]
[ROW][C]31[/C][C]125.6[/C][C]124.813773669407[/C][C]0.786226330592768[/C][/ROW]
[ROW][C]32[/C][C]125[/C][C]122.913400129326[/C][C]2.08659987067446[/C][/ROW]
[ROW][C]33[/C][C]119.7[/C][C]118.963376701266[/C][C]0.736623298733889[/C][/ROW]
[ROW][C]34[/C][C]116.1[/C][C]119.326623284516[/C][C]-3.22662328451649[/C][/ROW]
[ROW][C]35[/C][C]120[/C][C]121.389902011815[/C][C]-1.38990201181525[/C][/ROW]
[ROW][C]36[/C][C]148.1[/C][C]150.317445691267[/C][C]-2.21744569126702[/C][/ROW]
[ROW][C]37[/C][C]109.2[/C][C]107.953656489524[/C][C]1.24634351047625[/C][/ROW]
[ROW][C]38[/C][C]109.4[/C][C]110.79751865771[/C][C]-1.39751865770988[/C][/ROW]
[ROW][C]39[/C][C]135.1[/C][C]129.143688114542[/C][C]5.95631188545761[/C][/ROW]
[ROW][C]40[/C][C]114.9[/C][C]120.796541935946[/C][C]-5.89654193594566[/C][/ROW]
[ROW][C]41[/C][C]129[/C][C]126.486141054938[/C][C]2.51385894506188[/C][/ROW]
[ROW][C]42[/C][C]138.5[/C][C]134.162544396478[/C][C]4.33745560352173[/C][/ROW]
[ROW][C]43[/C][C]125.6[/C][C]131.749518991346[/C][C]-6.14951899134553[/C][/ROW]
[ROW][C]44[/C][C]130.4[/C][C]128.977259709978[/C][C]1.42274029002158[/C][/ROW]
[ROW][C]45[/C][C]120.3[/C][C]124.690208787274[/C][C]-4.39020878727382[/C][/ROW]
[ROW][C]46[/C][C]126.2[/C][C]123.743071638205[/C][C]2.45692836179498[/C][/ROW]
[ROW][C]47[/C][C]127.6[/C][C]126.594544633493[/C][C]1.00545536650689[/C][/ROW]
[ROW][C]48[/C][C]150.9[/C][C]155.716778131472[/C][C]-4.81677813147218[/C][/ROW]
[ROW][C]49[/C][C]114.6[/C][C]113.22701479798[/C][C]1.37298520202017[/C][/ROW]
[ROW][C]50[/C][C]118.6[/C][C]115.72956955907[/C][C]2.87043044092972[/C][/ROW]
[ROW][C]51[/C][C]131.4[/C][C]135.326432488089[/C][C]-3.92643248808852[/C][/ROW]
[ROW][C]52[/C][C]124.5[/C][C]124.327022370751[/C][C]0.172977629248834[/C][/ROW]
[ROW][C]53[/C][C]136.8[/C][C]131.477086334344[/C][C]5.32291366565605[/C][/ROW]
[ROW][C]54[/C][C]136.8[/C][C]139.672204318251[/C][C]-2.87220431825071[/C][/ROW]
[ROW][C]55[/C][C]136.6[/C][C]135.127694151238[/C][C]1.47230584876195[/C][/ROW]
[ROW][C]56[/C][C]131[/C][C]134.036829711193[/C][C]-3.03682971119269[/C][/ROW]
[ROW][C]57[/C][C]125.8[/C][C]128.503010829938[/C][C]-2.70301082993775[/C][/ROW]
[ROW][C]58[/C][C]129.4[/C][C]128.324644997448[/C][C]1.07535500255199[/C][/ROW]
[ROW][C]59[/C][C]124.8[/C][C]130.737927693135[/C][C]-5.93792769313471[/C][/ROW]
[ROW][C]60[/C][C]157.1[/C][C]158.088116452009[/C][C]-0.988116452008597[/C][/ROW]
[ROW][C]61[/C][C]116.6[/C][C]116.439725657956[/C][C]0.160274342043635[/C][/ROW]
[ROW][C]62[/C][C]114.2[/C][C]118.665008027763[/C][C]-4.46500802776306[/C][/ROW]
[ROW][C]63[/C][C]128.4[/C][C]136.202031686404[/C][C]-7.80203168640415[/C][/ROW]
[ROW][C]64[/C][C]127.3[/C][C]124.477447993625[/C][C]2.82255200637461[/C][/ROW]
[ROW][C]65[/C][C]133.5[/C][C]131.916898406113[/C][C]1.58310159388662[/C][/ROW]
[ROW][C]66[/C][C]137.2[/C][C]138.227202787029[/C][C]-1.02720278702856[/C][/ROW]
[ROW][C]67[/C][C]137.7[/C][C]133.735282423544[/C][C]3.96471757645551[/C][/ROW]
[ROW][C]68[/C][C]131.2[/C][C]132.03431787576[/C][C]-0.834317875759893[/C][/ROW]
[ROW][C]69[/C][C]127.7[/C][C]126.37221165542[/C][C]1.32778834458045[/C][/ROW]
[ROW][C]70[/C][C]133.9[/C][C]126.745166971563[/C][C]7.15483302843691[/C][/ROW]
[ROW][C]71[/C][C]124.3[/C][C]129.157843063896[/C][C]-4.85784306389552[/C][/ROW]
[ROW][C]72[/C][C]160.6[/C][C]157.014055087823[/C][C]3.58594491217741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113004&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113004&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
13101101.507665598291-0.507665598290629
14103.4103.738925385997-0.338925385996987
15121.5121.639533858845-0.139533858844715
16111.9111.952956313147-0.0529563131466801
17117.4117.421632205983-0.0216322059831953
18124.3124.2978059612870.00219403871319912
19122120.9020945985251.09790540147485
20119.7118.4348611400591.26513885994113
21115113.7659307918071.23406920819349
22112.2113.860646306122-1.66064630612205
23115.3115.429321839654-0.129321839654168
24142.6144.135602474634-1.53560247463443
25104.1100.9295251386833.1704748613173
26105.3103.7368592164691.56314078353115
27124.4122.0485614546472.35143854535306
28113.9112.9155044169030.984495583096873
29124.8118.7790364917536.0209635082467
30131.8126.8776259142144.92237408578575
31125.6124.8137736694070.786226330592768
32125122.9134001293262.08659987067446
33119.7118.9633767012660.736623298733889
34116.1119.326623284516-3.22662328451649
35120121.389902011815-1.38990201181525
36148.1150.317445691267-2.21744569126702
37109.2107.9536564895241.24634351047625
38109.4110.79751865771-1.39751865770988
39135.1129.1436881145425.95631188545761
40114.9120.796541935946-5.89654193594566
41129126.4861410549382.51385894506188
42138.5134.1625443964784.33745560352173
43125.6131.749518991346-6.14951899134553
44130.4128.9772597099781.42274029002158
45120.3124.690208787274-4.39020878727382
46126.2123.7430716382052.45692836179498
47127.6126.5945446334931.00545536650689
48150.9155.716778131472-4.81677813147218
49114.6113.227014797981.37298520202017
50118.6115.729569559072.87043044092972
51131.4135.326432488089-3.92643248808852
52124.5124.3270223707510.172977629248834
53136.8131.4770863343445.32291366565605
54136.8139.672204318251-2.87220431825071
55136.6135.1276941512381.47230584876195
56131134.036829711193-3.03682971119269
57125.8128.503010829938-2.70301082993775
58129.4128.3246449974481.07535500255199
59124.8130.737927693135-5.93792769313471
60157.1158.088116452009-0.988116452008597
61116.6116.4397256579560.160274342043635
62114.2118.665008027763-4.46500802776306
63128.4136.202031686404-7.80203168640415
64127.3124.4774479936252.82255200637461
65133.5131.9168984061131.58310159388662
66137.2138.227202787029-1.02720278702856
67137.7133.7352824235443.96471757645551
68131.2132.03431787576-0.834317875759893
69127.7126.372211655421.32778834458045
70133.9126.7451669715637.15483302843691
71124.3129.157843063896-4.85784306389552
72160.6157.0140550878233.58594491217741







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73116.107541707836109.77325483888122.441828576792
74117.927573541166111.513695389819124.341451692512
75135.909647617774129.383619391048142.4356758445
76126.597921690166119.922988544297133.272854836035
77133.900772741499127.036895911734140.764649571263
78140.056182207149132.961031028382147.151333385917
79136.481921934605129.111865233028143.851978636183
80134.026522598103126.337542842938141.715502353268
81128.896784457177120.845256660625136.94831225373
82129.825012511221121.368316095308138.281708927133
83130.166384504849121.2633422805139.069426729198
84159.540498457592150.151656807631168.929340107554

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 116.107541707836 & 109.77325483888 & 122.441828576792 \tabularnewline
74 & 117.927573541166 & 111.513695389819 & 124.341451692512 \tabularnewline
75 & 135.909647617774 & 129.383619391048 & 142.4356758445 \tabularnewline
76 & 126.597921690166 & 119.922988544297 & 133.272854836035 \tabularnewline
77 & 133.900772741499 & 127.036895911734 & 140.764649571263 \tabularnewline
78 & 140.056182207149 & 132.961031028382 & 147.151333385917 \tabularnewline
79 & 136.481921934605 & 129.111865233028 & 143.851978636183 \tabularnewline
80 & 134.026522598103 & 126.337542842938 & 141.715502353268 \tabularnewline
81 & 128.896784457177 & 120.845256660625 & 136.94831225373 \tabularnewline
82 & 129.825012511221 & 121.368316095308 & 138.281708927133 \tabularnewline
83 & 130.166384504849 & 121.2633422805 & 139.069426729198 \tabularnewline
84 & 159.540498457592 & 150.151656807631 & 168.929340107554 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113004&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]73[/C][C]116.107541707836[/C][C]109.77325483888[/C][C]122.441828576792[/C][/ROW]
[ROW][C]74[/C][C]117.927573541166[/C][C]111.513695389819[/C][C]124.341451692512[/C][/ROW]
[ROW][C]75[/C][C]135.909647617774[/C][C]129.383619391048[/C][C]142.4356758445[/C][/ROW]
[ROW][C]76[/C][C]126.597921690166[/C][C]119.922988544297[/C][C]133.272854836035[/C][/ROW]
[ROW][C]77[/C][C]133.900772741499[/C][C]127.036895911734[/C][C]140.764649571263[/C][/ROW]
[ROW][C]78[/C][C]140.056182207149[/C][C]132.961031028382[/C][C]147.151333385917[/C][/ROW]
[ROW][C]79[/C][C]136.481921934605[/C][C]129.111865233028[/C][C]143.851978636183[/C][/ROW]
[ROW][C]80[/C][C]134.026522598103[/C][C]126.337542842938[/C][C]141.715502353268[/C][/ROW]
[ROW][C]81[/C][C]128.896784457177[/C][C]120.845256660625[/C][C]136.94831225373[/C][/ROW]
[ROW][C]82[/C][C]129.825012511221[/C][C]121.368316095308[/C][C]138.281708927133[/C][/ROW]
[ROW][C]83[/C][C]130.166384504849[/C][C]121.2633422805[/C][C]139.069426729198[/C][/ROW]
[ROW][C]84[/C][C]159.540498457592[/C][C]150.151656807631[/C][C]168.929340107554[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113004&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113004&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
73116.107541707836109.77325483888122.441828576792
74117.927573541166111.513695389819124.341451692512
75135.909647617774129.383619391048142.4356758445
76126.597921690166119.922988544297133.272854836035
77133.900772741499127.036895911734140.764649571263
78140.056182207149132.961031028382147.151333385917
79136.481921934605129.111865233028143.851978636183
80134.026522598103126.337542842938141.715502353268
81128.896784457177120.845256660625136.94831225373
82129.825012511221121.368316095308138.281708927133
83130.166384504849121.2633422805139.069426729198
84159.540498457592150.151656807631168.929340107554



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')