Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 26 Nov 2016 17:57:57 +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/2016/Nov/26/t1480183185nctkbnpuf2kf9xt.htm/, Retrieved Fri, 03 May 2024 17:21:42 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Fri, 03 May 2024 17:21:42 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
92,1
93,91
95,46
94,54
95,63
96,32
96,42
96,95
96,52
96,82
96,4
96,69
96,72
98,57
98,6
96,44
97,09
97,36
97,74
96,78
96,45
97,66
98,69
98,21
97,33
99,05
100,09
98,1
97,68
97,44
99,19
98,32
97,83
97,71
97,51
97,62
96,49
98,92
99,69
97,06
97,63
97,97
99,01
97,89
97,23
96,93
96,97
97,68
97,73
99,03
100,35
99,38
99,3
99,77
101,11
101,15
101,59
100,95
99,23
100,41




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

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.713416098012859
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.713416098012859 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.713416098012859[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.713416098012859
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
293.9192.11.81
395.4693.39128313740332.06871686259673
494.5494.8671390494104-0.32713904941042
595.6394.63375278527240.996247214727589
696.3295.34449158585950.97550841414045
796.4296.04043499225430.379565007745668
896.9596.31122277902250.638777220977531
996.5296.7669367315118-0.246936731511767
1096.8296.59076809206060.229231907939408
1196.496.7543058253628-0.354305825362758
1296.6996.50153834592920.18846165407075
1396.7296.63598992380140.0840100761985525
1498.5796.69592406455681.87407593544322
1598.698.03292000580050.567079994199517
1696.4498.4374840025234-1.99748400252345
1797.0997.01244675960010.0775532403999506
1897.3697.06777448975440.292225510245558
1997.7497.27625287301360.463747126986348
2096.7897.6070975388129-0.827097538812922
2196.4597.017032839997-0.567032839996955
2297.6696.61250248384121.04749751615883
2398.6997.35980407449741.33019592550264
2498.2198.3087872612621-0.0987872612620606
2597.3398.2383108387991-0.908310838799096
2699.0597.59030726440031.45969273559975
27100.0998.63167556012951.45832443987047
2898.199.6720676916587-1.57206769165872
2997.6898.5505292932635-0.870529293263459
3097.4497.9294796816576-0.489479681657556
3199.1997.58027699711281.60972300288716
3298.3298.7286793007141-0.408679300714141
3397.8398.43712090866-0.607120908660036
3497.7198.0039910789818-0.293991078981776
3597.5197.794253110564-0.284253110563995
3697.6297.59146236557740.0285376344225909
3796.4997.6118215733737-1.12182157337371
3898.9296.81149600383082.1085039961692
3999.6998.31573669742241.37426330257765
4097.0699.2961582603896-2.23615826038956
4197.6397.7008469597232-0.0708469597232266
4297.9797.65030359816140.319696401838598
4399.0197.87838015770981.13161984229016
4497.8998.6856959700304-0.795695970030422
4597.2398.1180336558868-0.888033655886758
4696.9397.4844961501999-0.554496150199924
4796.9797.0889096703611-0.118909670361148
4897.6897.00407759731610.675922402683909
4997.7397.48629152039830.243708479601679
5099.0397.66015707296841.3698429270316
51100.3598.63742506886181.71257493113819
5299.3899.859203593789-0.479203593789052
5399.399.5173320357543-0.217332035754325
5499.7799.36228386283330.40771613716673
55101.1199.65315511850761.45684488149236
56101.15100.6924917092720.457508290728072
57101.59101.0188854888520.571114511148323
58100.95101.426327774914-0.476327774913628
5999.23101.08650787236-1.8565078723596
60100.4199.76204527013070.64795472986934

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 93.91 & 92.1 & 1.81 \tabularnewline
3 & 95.46 & 93.3912831374033 & 2.06871686259673 \tabularnewline
4 & 94.54 & 94.8671390494104 & -0.32713904941042 \tabularnewline
5 & 95.63 & 94.6337527852724 & 0.996247214727589 \tabularnewline
6 & 96.32 & 95.3444915858595 & 0.97550841414045 \tabularnewline
7 & 96.42 & 96.0404349922543 & 0.379565007745668 \tabularnewline
8 & 96.95 & 96.3112227790225 & 0.638777220977531 \tabularnewline
9 & 96.52 & 96.7669367315118 & -0.246936731511767 \tabularnewline
10 & 96.82 & 96.5907680920606 & 0.229231907939408 \tabularnewline
11 & 96.4 & 96.7543058253628 & -0.354305825362758 \tabularnewline
12 & 96.69 & 96.5015383459292 & 0.18846165407075 \tabularnewline
13 & 96.72 & 96.6359899238014 & 0.0840100761985525 \tabularnewline
14 & 98.57 & 96.6959240645568 & 1.87407593544322 \tabularnewline
15 & 98.6 & 98.0329200058005 & 0.567079994199517 \tabularnewline
16 & 96.44 & 98.4374840025234 & -1.99748400252345 \tabularnewline
17 & 97.09 & 97.0124467596001 & 0.0775532403999506 \tabularnewline
18 & 97.36 & 97.0677744897544 & 0.292225510245558 \tabularnewline
19 & 97.74 & 97.2762528730136 & 0.463747126986348 \tabularnewline
20 & 96.78 & 97.6070975388129 & -0.827097538812922 \tabularnewline
21 & 96.45 & 97.017032839997 & -0.567032839996955 \tabularnewline
22 & 97.66 & 96.6125024838412 & 1.04749751615883 \tabularnewline
23 & 98.69 & 97.3598040744974 & 1.33019592550264 \tabularnewline
24 & 98.21 & 98.3087872612621 & -0.0987872612620606 \tabularnewline
25 & 97.33 & 98.2383108387991 & -0.908310838799096 \tabularnewline
26 & 99.05 & 97.5903072644003 & 1.45969273559975 \tabularnewline
27 & 100.09 & 98.6316755601295 & 1.45832443987047 \tabularnewline
28 & 98.1 & 99.6720676916587 & -1.57206769165872 \tabularnewline
29 & 97.68 & 98.5505292932635 & -0.870529293263459 \tabularnewline
30 & 97.44 & 97.9294796816576 & -0.489479681657556 \tabularnewline
31 & 99.19 & 97.5802769971128 & 1.60972300288716 \tabularnewline
32 & 98.32 & 98.7286793007141 & -0.408679300714141 \tabularnewline
33 & 97.83 & 98.43712090866 & -0.607120908660036 \tabularnewline
34 & 97.71 & 98.0039910789818 & -0.293991078981776 \tabularnewline
35 & 97.51 & 97.794253110564 & -0.284253110563995 \tabularnewline
36 & 97.62 & 97.5914623655774 & 0.0285376344225909 \tabularnewline
37 & 96.49 & 97.6118215733737 & -1.12182157337371 \tabularnewline
38 & 98.92 & 96.8114960038308 & 2.1085039961692 \tabularnewline
39 & 99.69 & 98.3157366974224 & 1.37426330257765 \tabularnewline
40 & 97.06 & 99.2961582603896 & -2.23615826038956 \tabularnewline
41 & 97.63 & 97.7008469597232 & -0.0708469597232266 \tabularnewline
42 & 97.97 & 97.6503035981614 & 0.319696401838598 \tabularnewline
43 & 99.01 & 97.8783801577098 & 1.13161984229016 \tabularnewline
44 & 97.89 & 98.6856959700304 & -0.795695970030422 \tabularnewline
45 & 97.23 & 98.1180336558868 & -0.888033655886758 \tabularnewline
46 & 96.93 & 97.4844961501999 & -0.554496150199924 \tabularnewline
47 & 96.97 & 97.0889096703611 & -0.118909670361148 \tabularnewline
48 & 97.68 & 97.0040775973161 & 0.675922402683909 \tabularnewline
49 & 97.73 & 97.4862915203983 & 0.243708479601679 \tabularnewline
50 & 99.03 & 97.6601570729684 & 1.3698429270316 \tabularnewline
51 & 100.35 & 98.6374250688618 & 1.71257493113819 \tabularnewline
52 & 99.38 & 99.859203593789 & -0.479203593789052 \tabularnewline
53 & 99.3 & 99.5173320357543 & -0.217332035754325 \tabularnewline
54 & 99.77 & 99.3622838628333 & 0.40771613716673 \tabularnewline
55 & 101.11 & 99.6531551185076 & 1.45684488149236 \tabularnewline
56 & 101.15 & 100.692491709272 & 0.457508290728072 \tabularnewline
57 & 101.59 & 101.018885488852 & 0.571114511148323 \tabularnewline
58 & 100.95 & 101.426327774914 & -0.476327774913628 \tabularnewline
59 & 99.23 & 101.08650787236 & -1.8565078723596 \tabularnewline
60 & 100.41 & 99.7620452701307 & 0.64795472986934 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2[/C][C]93.91[/C][C]92.1[/C][C]1.81[/C][/ROW]
[ROW][C]3[/C][C]95.46[/C][C]93.3912831374033[/C][C]2.06871686259673[/C][/ROW]
[ROW][C]4[/C][C]94.54[/C][C]94.8671390494104[/C][C]-0.32713904941042[/C][/ROW]
[ROW][C]5[/C][C]95.63[/C][C]94.6337527852724[/C][C]0.996247214727589[/C][/ROW]
[ROW][C]6[/C][C]96.32[/C][C]95.3444915858595[/C][C]0.97550841414045[/C][/ROW]
[ROW][C]7[/C][C]96.42[/C][C]96.0404349922543[/C][C]0.379565007745668[/C][/ROW]
[ROW][C]8[/C][C]96.95[/C][C]96.3112227790225[/C][C]0.638777220977531[/C][/ROW]
[ROW][C]9[/C][C]96.52[/C][C]96.7669367315118[/C][C]-0.246936731511767[/C][/ROW]
[ROW][C]10[/C][C]96.82[/C][C]96.5907680920606[/C][C]0.229231907939408[/C][/ROW]
[ROW][C]11[/C][C]96.4[/C][C]96.7543058253628[/C][C]-0.354305825362758[/C][/ROW]
[ROW][C]12[/C][C]96.69[/C][C]96.5015383459292[/C][C]0.18846165407075[/C][/ROW]
[ROW][C]13[/C][C]96.72[/C][C]96.6359899238014[/C][C]0.0840100761985525[/C][/ROW]
[ROW][C]14[/C][C]98.57[/C][C]96.6959240645568[/C][C]1.87407593544322[/C][/ROW]
[ROW][C]15[/C][C]98.6[/C][C]98.0329200058005[/C][C]0.567079994199517[/C][/ROW]
[ROW][C]16[/C][C]96.44[/C][C]98.4374840025234[/C][C]-1.99748400252345[/C][/ROW]
[ROW][C]17[/C][C]97.09[/C][C]97.0124467596001[/C][C]0.0775532403999506[/C][/ROW]
[ROW][C]18[/C][C]97.36[/C][C]97.0677744897544[/C][C]0.292225510245558[/C][/ROW]
[ROW][C]19[/C][C]97.74[/C][C]97.2762528730136[/C][C]0.463747126986348[/C][/ROW]
[ROW][C]20[/C][C]96.78[/C][C]97.6070975388129[/C][C]-0.827097538812922[/C][/ROW]
[ROW][C]21[/C][C]96.45[/C][C]97.017032839997[/C][C]-0.567032839996955[/C][/ROW]
[ROW][C]22[/C][C]97.66[/C][C]96.6125024838412[/C][C]1.04749751615883[/C][/ROW]
[ROW][C]23[/C][C]98.69[/C][C]97.3598040744974[/C][C]1.33019592550264[/C][/ROW]
[ROW][C]24[/C][C]98.21[/C][C]98.3087872612621[/C][C]-0.0987872612620606[/C][/ROW]
[ROW][C]25[/C][C]97.33[/C][C]98.2383108387991[/C][C]-0.908310838799096[/C][/ROW]
[ROW][C]26[/C][C]99.05[/C][C]97.5903072644003[/C][C]1.45969273559975[/C][/ROW]
[ROW][C]27[/C][C]100.09[/C][C]98.6316755601295[/C][C]1.45832443987047[/C][/ROW]
[ROW][C]28[/C][C]98.1[/C][C]99.6720676916587[/C][C]-1.57206769165872[/C][/ROW]
[ROW][C]29[/C][C]97.68[/C][C]98.5505292932635[/C][C]-0.870529293263459[/C][/ROW]
[ROW][C]30[/C][C]97.44[/C][C]97.9294796816576[/C][C]-0.489479681657556[/C][/ROW]
[ROW][C]31[/C][C]99.19[/C][C]97.5802769971128[/C][C]1.60972300288716[/C][/ROW]
[ROW][C]32[/C][C]98.32[/C][C]98.7286793007141[/C][C]-0.408679300714141[/C][/ROW]
[ROW][C]33[/C][C]97.83[/C][C]98.43712090866[/C][C]-0.607120908660036[/C][/ROW]
[ROW][C]34[/C][C]97.71[/C][C]98.0039910789818[/C][C]-0.293991078981776[/C][/ROW]
[ROW][C]35[/C][C]97.51[/C][C]97.794253110564[/C][C]-0.284253110563995[/C][/ROW]
[ROW][C]36[/C][C]97.62[/C][C]97.5914623655774[/C][C]0.0285376344225909[/C][/ROW]
[ROW][C]37[/C][C]96.49[/C][C]97.6118215733737[/C][C]-1.12182157337371[/C][/ROW]
[ROW][C]38[/C][C]98.92[/C][C]96.8114960038308[/C][C]2.1085039961692[/C][/ROW]
[ROW][C]39[/C][C]99.69[/C][C]98.3157366974224[/C][C]1.37426330257765[/C][/ROW]
[ROW][C]40[/C][C]97.06[/C][C]99.2961582603896[/C][C]-2.23615826038956[/C][/ROW]
[ROW][C]41[/C][C]97.63[/C][C]97.7008469597232[/C][C]-0.0708469597232266[/C][/ROW]
[ROW][C]42[/C][C]97.97[/C][C]97.6503035981614[/C][C]0.319696401838598[/C][/ROW]
[ROW][C]43[/C][C]99.01[/C][C]97.8783801577098[/C][C]1.13161984229016[/C][/ROW]
[ROW][C]44[/C][C]97.89[/C][C]98.6856959700304[/C][C]-0.795695970030422[/C][/ROW]
[ROW][C]45[/C][C]97.23[/C][C]98.1180336558868[/C][C]-0.888033655886758[/C][/ROW]
[ROW][C]46[/C][C]96.93[/C][C]97.4844961501999[/C][C]-0.554496150199924[/C][/ROW]
[ROW][C]47[/C][C]96.97[/C][C]97.0889096703611[/C][C]-0.118909670361148[/C][/ROW]
[ROW][C]48[/C][C]97.68[/C][C]97.0040775973161[/C][C]0.675922402683909[/C][/ROW]
[ROW][C]49[/C][C]97.73[/C][C]97.4862915203983[/C][C]0.243708479601679[/C][/ROW]
[ROW][C]50[/C][C]99.03[/C][C]97.6601570729684[/C][C]1.3698429270316[/C][/ROW]
[ROW][C]51[/C][C]100.35[/C][C]98.6374250688618[/C][C]1.71257493113819[/C][/ROW]
[ROW][C]52[/C][C]99.38[/C][C]99.859203593789[/C][C]-0.479203593789052[/C][/ROW]
[ROW][C]53[/C][C]99.3[/C][C]99.5173320357543[/C][C]-0.217332035754325[/C][/ROW]
[ROW][C]54[/C][C]99.77[/C][C]99.3622838628333[/C][C]0.40771613716673[/C][/ROW]
[ROW][C]55[/C][C]101.11[/C][C]99.6531551185076[/C][C]1.45684488149236[/C][/ROW]
[ROW][C]56[/C][C]101.15[/C][C]100.692491709272[/C][C]0.457508290728072[/C][/ROW]
[ROW][C]57[/C][C]101.59[/C][C]101.018885488852[/C][C]0.571114511148323[/C][/ROW]
[ROW][C]58[/C][C]100.95[/C][C]101.426327774914[/C][C]-0.476327774913628[/C][/ROW]
[ROW][C]59[/C][C]99.23[/C][C]101.08650787236[/C][C]-1.8565078723596[/C][/ROW]
[ROW][C]60[/C][C]100.41[/C][C]99.7620452701307[/C][C]0.64795472986934[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
293.9192.11.81
395.4693.39128313740332.06871686259673
494.5494.8671390494104-0.32713904941042
595.6394.63375278527240.996247214727589
696.3295.34449158585950.97550841414045
796.4296.04043499225430.379565007745668
896.9596.31122277902250.638777220977531
996.5296.7669367315118-0.246936731511767
1096.8296.59076809206060.229231907939408
1196.496.7543058253628-0.354305825362758
1296.6996.50153834592920.18846165407075
1396.7296.63598992380140.0840100761985525
1498.5796.69592406455681.87407593544322
1598.698.03292000580050.567079994199517
1696.4498.4374840025234-1.99748400252345
1797.0997.01244675960010.0775532403999506
1897.3697.06777448975440.292225510245558
1997.7497.27625287301360.463747126986348
2096.7897.6070975388129-0.827097538812922
2196.4597.017032839997-0.567032839996955
2297.6696.61250248384121.04749751615883
2398.6997.35980407449741.33019592550264
2498.2198.3087872612621-0.0987872612620606
2597.3398.2383108387991-0.908310838799096
2699.0597.59030726440031.45969273559975
27100.0998.63167556012951.45832443987047
2898.199.6720676916587-1.57206769165872
2997.6898.5505292932635-0.870529293263459
3097.4497.9294796816576-0.489479681657556
3199.1997.58027699711281.60972300288716
3298.3298.7286793007141-0.408679300714141
3397.8398.43712090866-0.607120908660036
3497.7198.0039910789818-0.293991078981776
3597.5197.794253110564-0.284253110563995
3697.6297.59146236557740.0285376344225909
3796.4997.6118215733737-1.12182157337371
3898.9296.81149600383082.1085039961692
3999.6998.31573669742241.37426330257765
4097.0699.2961582603896-2.23615826038956
4197.6397.7008469597232-0.0708469597232266
4297.9797.65030359816140.319696401838598
4399.0197.87838015770981.13161984229016
4497.8998.6856959700304-0.795695970030422
4597.2398.1180336558868-0.888033655886758
4696.9397.4844961501999-0.554496150199924
4796.9797.0889096703611-0.118909670361148
4897.6897.00407759731610.675922402683909
4997.7397.48629152039830.243708479601679
5099.0397.66015707296841.3698429270316
51100.3598.63742506886181.71257493113819
5299.3899.859203593789-0.479203593789052
5399.399.5173320357543-0.217332035754325
5499.7799.36228386283330.40771613716673
55101.1199.65315511850761.45684488149236
56101.15100.6924917092720.457508290728072
57101.59101.0188854888520.571114511148323
58100.95101.426327774914-0.476327774913628
5999.23101.08650787236-1.8565078723596
60100.4199.76204527013070.64795472986934







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61100.22430660520398.2251093769579102.223503833448
62100.22430660520397.7684960102944102.680117200112
63100.22430660520397.384373190718103.064240019688
64100.22430660520397.0463453217147103.402267888691
65100.22430660520396.7409671098346103.707646100571
66100.22430660520396.4602834702268103.988329740179
67100.22430660520396.1991250836715104.249488126735
68100.22430660520395.9539082160686104.494704994337
69100.22430660520395.722027346587104.726585863819
70100.22430660520395.5015177423374104.947095468069
71100.22430660520395.2908543895786105.157758820827
72100.22430660520395.088825431594105.359787778812

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 100.224306605203 & 98.2251093769579 & 102.223503833448 \tabularnewline
62 & 100.224306605203 & 97.7684960102944 & 102.680117200112 \tabularnewline
63 & 100.224306605203 & 97.384373190718 & 103.064240019688 \tabularnewline
64 & 100.224306605203 & 97.0463453217147 & 103.402267888691 \tabularnewline
65 & 100.224306605203 & 96.7409671098346 & 103.707646100571 \tabularnewline
66 & 100.224306605203 & 96.4602834702268 & 103.988329740179 \tabularnewline
67 & 100.224306605203 & 96.1991250836715 & 104.249488126735 \tabularnewline
68 & 100.224306605203 & 95.9539082160686 & 104.494704994337 \tabularnewline
69 & 100.224306605203 & 95.722027346587 & 104.726585863819 \tabularnewline
70 & 100.224306605203 & 95.5015177423374 & 104.947095468069 \tabularnewline
71 & 100.224306605203 & 95.2908543895786 & 105.157758820827 \tabularnewline
72 & 100.224306605203 & 95.088825431594 & 105.359787778812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]100.224306605203[/C][C]98.2251093769579[/C][C]102.223503833448[/C][/ROW]
[ROW][C]62[/C][C]100.224306605203[/C][C]97.7684960102944[/C][C]102.680117200112[/C][/ROW]
[ROW][C]63[/C][C]100.224306605203[/C][C]97.384373190718[/C][C]103.064240019688[/C][/ROW]
[ROW][C]64[/C][C]100.224306605203[/C][C]97.0463453217147[/C][C]103.402267888691[/C][/ROW]
[ROW][C]65[/C][C]100.224306605203[/C][C]96.7409671098346[/C][C]103.707646100571[/C][/ROW]
[ROW][C]66[/C][C]100.224306605203[/C][C]96.4602834702268[/C][C]103.988329740179[/C][/ROW]
[ROW][C]67[/C][C]100.224306605203[/C][C]96.1991250836715[/C][C]104.249488126735[/C][/ROW]
[ROW][C]68[/C][C]100.224306605203[/C][C]95.9539082160686[/C][C]104.494704994337[/C][/ROW]
[ROW][C]69[/C][C]100.224306605203[/C][C]95.722027346587[/C][C]104.726585863819[/C][/ROW]
[ROW][C]70[/C][C]100.224306605203[/C][C]95.5015177423374[/C][C]104.947095468069[/C][/ROW]
[ROW][C]71[/C][C]100.224306605203[/C][C]95.2908543895786[/C][C]105.157758820827[/C][/ROW]
[ROW][C]72[/C][C]100.224306605203[/C][C]95.088825431594[/C][C]105.359787778812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
61100.22430660520398.2251093769579102.223503833448
62100.22430660520397.7684960102944102.680117200112
63100.22430660520397.384373190718103.064240019688
64100.22430660520397.0463453217147103.402267888691
65100.22430660520396.7409671098346103.707646100571
66100.22430660520396.4602834702268103.988329740179
67100.22430660520396.1991250836715104.249488126735
68100.22430660520395.9539082160686104.494704994337
69100.22430660520395.722027346587104.726585863819
70100.22430660520395.5015177423374104.947095468069
71100.22430660520395.2908543895786105.157758820827
72100.22430660520395.088825431594105.359787778812



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')