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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 2008 12:17:21 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/21/t121139387504wmsvjjj0bmrr2.htm/, Retrieved Wed, 15 May 2024 23:41:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13006, Retrieved Wed, 15 May 2024 23:41:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact227
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [inschrijvingen ni...] [2008-05-21 12:06:11] [8d57eac511d3a0ef04bba8a22fa0a3ab]
-   PD    [Exponential Smoothing] [verkoopprijzen sc...] [2008-05-21 18:17:21] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
24,65
25,24
25,56
25,9
25,87
25,78
25,78
25,74
25,78
25,73
24,67
24,31
24,56
25
25,38
25,99
26,22
26,19
26,22
26,22
26,61
26,72
25,46
25,48
25,59
25,88
26
26,97
27,2
27,19
27,19
27,19
27,26
26,9
26,11
25,87
26,02
26,31
26,37
26,52
26,86
26,92
26,98
26,98
27,03
26,75
26,39
26,3
26,3
26,52
26,53
26,98
27,22
27,34
27,41
27,47
27,46
27,53
27,21
26,91
26,95
26,91
27,39
27,62
27,79
27,88
27,9
28,09
28,46
28,73
27,93
27,61




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13006&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13006&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13006&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 time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.583291682950799
beta0.000740044920045117
gamma0.982058200741272

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.583291682950799 \tabularnewline
beta & 0.000740044920045117 \tabularnewline
gamma & 0.982058200741272 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13006&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]0.583291682950799[/C][/ROW]
[ROW][C]beta[/C][C]0.000740044920045117[/C][/ROW]
[ROW][C]gamma[/C][C]0.982058200741272[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13006&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13006&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
alpha0.583291682950799
beta0.000740044920045117
gamma0.982058200741272







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1324.5624.28257916666670.277420833333331
142524.90708176318220.092918236817809
1525.3825.34775563894370.0322443610563248
1625.9925.9618028662680.0281971337320037
1726.2226.19516821785420.0248317821458457
1826.1926.15908130678780.0309186932121932
1926.2226.17655818674770.0434418132522794
2026.2226.18344178398700.0365582160130309
2126.6126.59340935033550.0165906496645292
2226.7226.70757049619130.0124295038087467
2325.4625.43430984562290.0256901543771413
2425.4825.44796177837280.0320382216271753
2525.5925.51052641485530.0794735851446724
2625.8825.9442602441533-0.0642602441533242
272626.2685522403264-0.268552240326365
2826.9726.70548991683320.264510083166783
2927.227.0754183040080.124581695991978
3027.1927.10014957057410.0898504294259439
3127.1927.15729506474680.0327049352532427
3227.1927.15526367202910.0347363279708723
3327.2627.5561611249839-0.296161124983875
3426.927.4862228277635-0.58622282776355
3526.1125.86897045508320.241029544916824
3625.8726.0106893720092-0.140689372009174
3726.0225.99170441745690.0282955825430804
3826.3126.3365329129172-0.0265329129172329
3926.3726.5990112736564-0.229011273656408
4026.5227.2769591118058-0.756959111805834
4126.8626.9931691149069-0.133169114906909
4226.9226.85259132683680.0674086731631718
4326.9826.87249927845220.107500721547826
4426.9826.91419754465220.0658024553478072
4527.0327.1970858427777-0.167085842777727
4626.7527.0830733208619-0.333073320861899
4726.3925.951467934550.438532065449984
4826.326.05171114659240.248288853407583
4926.326.3284701280868-0.0284701280868163
5026.5226.6174277398632-0.097427739863214
5126.5326.7553401951758-0.225340195175807
5226.9827.2190249184114-0.239024918411378
5327.2227.4924885473967-0.272488547396666
5427.3427.3525417702348-0.0125417702347832
5527.4127.34199978740110.0680002125988608
5627.4727.34335397931960.126646020680386
5727.4627.5662132862382-0.106213286238241
5827.5327.41959290416780.110407095832219
5927.2126.86243590841190.347564091588133
6026.9126.83172988986930.07827011013066
6126.9526.89595158801140.0540484119886422
6226.9127.2047493663155-0.294749366315539
6327.3927.17506217228500.214937827715033
6427.6227.8899894927051-0.269989492705083
6527.7928.1317163074545-0.341716307454469
6627.8828.0577571095773-0.177757109577311
6727.927.9837244816603-0.0837244816602905
6828.0927.92043090433160.169569095668415
6928.4628.07290422639950.38709577360051
7028.7328.30275859256970.427241407430287
7127.9328.027681093299-0.0976810932989913
7227.6127.6270918885627-0.0170918885627245

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 24.56 & 24.2825791666667 & 0.277420833333331 \tabularnewline
14 & 25 & 24.9070817631822 & 0.092918236817809 \tabularnewline
15 & 25.38 & 25.3477556389437 & 0.0322443610563248 \tabularnewline
16 & 25.99 & 25.961802866268 & 0.0281971337320037 \tabularnewline
17 & 26.22 & 26.1951682178542 & 0.0248317821458457 \tabularnewline
18 & 26.19 & 26.1590813067878 & 0.0309186932121932 \tabularnewline
19 & 26.22 & 26.1765581867477 & 0.0434418132522794 \tabularnewline
20 & 26.22 & 26.1834417839870 & 0.0365582160130309 \tabularnewline
21 & 26.61 & 26.5934093503355 & 0.0165906496645292 \tabularnewline
22 & 26.72 & 26.7075704961913 & 0.0124295038087467 \tabularnewline
23 & 25.46 & 25.4343098456229 & 0.0256901543771413 \tabularnewline
24 & 25.48 & 25.4479617783728 & 0.0320382216271753 \tabularnewline
25 & 25.59 & 25.5105264148553 & 0.0794735851446724 \tabularnewline
26 & 25.88 & 25.9442602441533 & -0.0642602441533242 \tabularnewline
27 & 26 & 26.2685522403264 & -0.268552240326365 \tabularnewline
28 & 26.97 & 26.7054899168332 & 0.264510083166783 \tabularnewline
29 & 27.2 & 27.075418304008 & 0.124581695991978 \tabularnewline
30 & 27.19 & 27.1001495705741 & 0.0898504294259439 \tabularnewline
31 & 27.19 & 27.1572950647468 & 0.0327049352532427 \tabularnewline
32 & 27.19 & 27.1552636720291 & 0.0347363279708723 \tabularnewline
33 & 27.26 & 27.5561611249839 & -0.296161124983875 \tabularnewline
34 & 26.9 & 27.4862228277635 & -0.58622282776355 \tabularnewline
35 & 26.11 & 25.8689704550832 & 0.241029544916824 \tabularnewline
36 & 25.87 & 26.0106893720092 & -0.140689372009174 \tabularnewline
37 & 26.02 & 25.9917044174569 & 0.0282955825430804 \tabularnewline
38 & 26.31 & 26.3365329129172 & -0.0265329129172329 \tabularnewline
39 & 26.37 & 26.5990112736564 & -0.229011273656408 \tabularnewline
40 & 26.52 & 27.2769591118058 & -0.756959111805834 \tabularnewline
41 & 26.86 & 26.9931691149069 & -0.133169114906909 \tabularnewline
42 & 26.92 & 26.8525913268368 & 0.0674086731631718 \tabularnewline
43 & 26.98 & 26.8724992784522 & 0.107500721547826 \tabularnewline
44 & 26.98 & 26.9141975446522 & 0.0658024553478072 \tabularnewline
45 & 27.03 & 27.1970858427777 & -0.167085842777727 \tabularnewline
46 & 26.75 & 27.0830733208619 & -0.333073320861899 \tabularnewline
47 & 26.39 & 25.95146793455 & 0.438532065449984 \tabularnewline
48 & 26.3 & 26.0517111465924 & 0.248288853407583 \tabularnewline
49 & 26.3 & 26.3284701280868 & -0.0284701280868163 \tabularnewline
50 & 26.52 & 26.6174277398632 & -0.097427739863214 \tabularnewline
51 & 26.53 & 26.7553401951758 & -0.225340195175807 \tabularnewline
52 & 26.98 & 27.2190249184114 & -0.239024918411378 \tabularnewline
53 & 27.22 & 27.4924885473967 & -0.272488547396666 \tabularnewline
54 & 27.34 & 27.3525417702348 & -0.0125417702347832 \tabularnewline
55 & 27.41 & 27.3419997874011 & 0.0680002125988608 \tabularnewline
56 & 27.47 & 27.3433539793196 & 0.126646020680386 \tabularnewline
57 & 27.46 & 27.5662132862382 & -0.106213286238241 \tabularnewline
58 & 27.53 & 27.4195929041678 & 0.110407095832219 \tabularnewline
59 & 27.21 & 26.8624359084119 & 0.347564091588133 \tabularnewline
60 & 26.91 & 26.8317298898693 & 0.07827011013066 \tabularnewline
61 & 26.95 & 26.8959515880114 & 0.0540484119886422 \tabularnewline
62 & 26.91 & 27.2047493663155 & -0.294749366315539 \tabularnewline
63 & 27.39 & 27.1750621722850 & 0.214937827715033 \tabularnewline
64 & 27.62 & 27.8899894927051 & -0.269989492705083 \tabularnewline
65 & 27.79 & 28.1317163074545 & -0.341716307454469 \tabularnewline
66 & 27.88 & 28.0577571095773 & -0.177757109577311 \tabularnewline
67 & 27.9 & 27.9837244816603 & -0.0837244816602905 \tabularnewline
68 & 28.09 & 27.9204309043316 & 0.169569095668415 \tabularnewline
69 & 28.46 & 28.0729042263995 & 0.38709577360051 \tabularnewline
70 & 28.73 & 28.3027585925697 & 0.427241407430287 \tabularnewline
71 & 27.93 & 28.027681093299 & -0.0976810932989913 \tabularnewline
72 & 27.61 & 27.6270918885627 & -0.0170918885627245 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13006&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]24.56[/C][C]24.2825791666667[/C][C]0.277420833333331[/C][/ROW]
[ROW][C]14[/C][C]25[/C][C]24.9070817631822[/C][C]0.092918236817809[/C][/ROW]
[ROW][C]15[/C][C]25.38[/C][C]25.3477556389437[/C][C]0.0322443610563248[/C][/ROW]
[ROW][C]16[/C][C]25.99[/C][C]25.961802866268[/C][C]0.0281971337320037[/C][/ROW]
[ROW][C]17[/C][C]26.22[/C][C]26.1951682178542[/C][C]0.0248317821458457[/C][/ROW]
[ROW][C]18[/C][C]26.19[/C][C]26.1590813067878[/C][C]0.0309186932121932[/C][/ROW]
[ROW][C]19[/C][C]26.22[/C][C]26.1765581867477[/C][C]0.0434418132522794[/C][/ROW]
[ROW][C]20[/C][C]26.22[/C][C]26.1834417839870[/C][C]0.0365582160130309[/C][/ROW]
[ROW][C]21[/C][C]26.61[/C][C]26.5934093503355[/C][C]0.0165906496645292[/C][/ROW]
[ROW][C]22[/C][C]26.72[/C][C]26.7075704961913[/C][C]0.0124295038087467[/C][/ROW]
[ROW][C]23[/C][C]25.46[/C][C]25.4343098456229[/C][C]0.0256901543771413[/C][/ROW]
[ROW][C]24[/C][C]25.48[/C][C]25.4479617783728[/C][C]0.0320382216271753[/C][/ROW]
[ROW][C]25[/C][C]25.59[/C][C]25.5105264148553[/C][C]0.0794735851446724[/C][/ROW]
[ROW][C]26[/C][C]25.88[/C][C]25.9442602441533[/C][C]-0.0642602441533242[/C][/ROW]
[ROW][C]27[/C][C]26[/C][C]26.2685522403264[/C][C]-0.268552240326365[/C][/ROW]
[ROW][C]28[/C][C]26.97[/C][C]26.7054899168332[/C][C]0.264510083166783[/C][/ROW]
[ROW][C]29[/C][C]27.2[/C][C]27.075418304008[/C][C]0.124581695991978[/C][/ROW]
[ROW][C]30[/C][C]27.19[/C][C]27.1001495705741[/C][C]0.0898504294259439[/C][/ROW]
[ROW][C]31[/C][C]27.19[/C][C]27.1572950647468[/C][C]0.0327049352532427[/C][/ROW]
[ROW][C]32[/C][C]27.19[/C][C]27.1552636720291[/C][C]0.0347363279708723[/C][/ROW]
[ROW][C]33[/C][C]27.26[/C][C]27.5561611249839[/C][C]-0.296161124983875[/C][/ROW]
[ROW][C]34[/C][C]26.9[/C][C]27.4862228277635[/C][C]-0.58622282776355[/C][/ROW]
[ROW][C]35[/C][C]26.11[/C][C]25.8689704550832[/C][C]0.241029544916824[/C][/ROW]
[ROW][C]36[/C][C]25.87[/C][C]26.0106893720092[/C][C]-0.140689372009174[/C][/ROW]
[ROW][C]37[/C][C]26.02[/C][C]25.9917044174569[/C][C]0.0282955825430804[/C][/ROW]
[ROW][C]38[/C][C]26.31[/C][C]26.3365329129172[/C][C]-0.0265329129172329[/C][/ROW]
[ROW][C]39[/C][C]26.37[/C][C]26.5990112736564[/C][C]-0.229011273656408[/C][/ROW]
[ROW][C]40[/C][C]26.52[/C][C]27.2769591118058[/C][C]-0.756959111805834[/C][/ROW]
[ROW][C]41[/C][C]26.86[/C][C]26.9931691149069[/C][C]-0.133169114906909[/C][/ROW]
[ROW][C]42[/C][C]26.92[/C][C]26.8525913268368[/C][C]0.0674086731631718[/C][/ROW]
[ROW][C]43[/C][C]26.98[/C][C]26.8724992784522[/C][C]0.107500721547826[/C][/ROW]
[ROW][C]44[/C][C]26.98[/C][C]26.9141975446522[/C][C]0.0658024553478072[/C][/ROW]
[ROW][C]45[/C][C]27.03[/C][C]27.1970858427777[/C][C]-0.167085842777727[/C][/ROW]
[ROW][C]46[/C][C]26.75[/C][C]27.0830733208619[/C][C]-0.333073320861899[/C][/ROW]
[ROW][C]47[/C][C]26.39[/C][C]25.95146793455[/C][C]0.438532065449984[/C][/ROW]
[ROW][C]48[/C][C]26.3[/C][C]26.0517111465924[/C][C]0.248288853407583[/C][/ROW]
[ROW][C]49[/C][C]26.3[/C][C]26.3284701280868[/C][C]-0.0284701280868163[/C][/ROW]
[ROW][C]50[/C][C]26.52[/C][C]26.6174277398632[/C][C]-0.097427739863214[/C][/ROW]
[ROW][C]51[/C][C]26.53[/C][C]26.7553401951758[/C][C]-0.225340195175807[/C][/ROW]
[ROW][C]52[/C][C]26.98[/C][C]27.2190249184114[/C][C]-0.239024918411378[/C][/ROW]
[ROW][C]53[/C][C]27.22[/C][C]27.4924885473967[/C][C]-0.272488547396666[/C][/ROW]
[ROW][C]54[/C][C]27.34[/C][C]27.3525417702348[/C][C]-0.0125417702347832[/C][/ROW]
[ROW][C]55[/C][C]27.41[/C][C]27.3419997874011[/C][C]0.0680002125988608[/C][/ROW]
[ROW][C]56[/C][C]27.47[/C][C]27.3433539793196[/C][C]0.126646020680386[/C][/ROW]
[ROW][C]57[/C][C]27.46[/C][C]27.5662132862382[/C][C]-0.106213286238241[/C][/ROW]
[ROW][C]58[/C][C]27.53[/C][C]27.4195929041678[/C][C]0.110407095832219[/C][/ROW]
[ROW][C]59[/C][C]27.21[/C][C]26.8624359084119[/C][C]0.347564091588133[/C][/ROW]
[ROW][C]60[/C][C]26.91[/C][C]26.8317298898693[/C][C]0.07827011013066[/C][/ROW]
[ROW][C]61[/C][C]26.95[/C][C]26.8959515880114[/C][C]0.0540484119886422[/C][/ROW]
[ROW][C]62[/C][C]26.91[/C][C]27.2047493663155[/C][C]-0.294749366315539[/C][/ROW]
[ROW][C]63[/C][C]27.39[/C][C]27.1750621722850[/C][C]0.214937827715033[/C][/ROW]
[ROW][C]64[/C][C]27.62[/C][C]27.8899894927051[/C][C]-0.269989492705083[/C][/ROW]
[ROW][C]65[/C][C]27.79[/C][C]28.1317163074545[/C][C]-0.341716307454469[/C][/ROW]
[ROW][C]66[/C][C]27.88[/C][C]28.0577571095773[/C][C]-0.177757109577311[/C][/ROW]
[ROW][C]67[/C][C]27.9[/C][C]27.9837244816603[/C][C]-0.0837244816602905[/C][/ROW]
[ROW][C]68[/C][C]28.09[/C][C]27.9204309043316[/C][C]0.169569095668415[/C][/ROW]
[ROW][C]69[/C][C]28.46[/C][C]28.0729042263995[/C][C]0.38709577360051[/C][/ROW]
[ROW][C]70[/C][C]28.73[/C][C]28.3027585925697[/C][C]0.427241407430287[/C][/ROW]
[ROW][C]71[/C][C]27.93[/C][C]28.027681093299[/C][C]-0.0976810932989913[/C][/ROW]
[ROW][C]72[/C][C]27.61[/C][C]27.6270918885627[/C][C]-0.0170918885627245[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13006&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13006&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
1324.5624.28257916666670.277420833333331
142524.90708176318220.092918236817809
1525.3825.34775563894370.0322443610563248
1625.9925.9618028662680.0281971337320037
1726.2226.19516821785420.0248317821458457
1826.1926.15908130678780.0309186932121932
1926.2226.17655818674770.0434418132522794
2026.2226.18344178398700.0365582160130309
2126.6126.59340935033550.0165906496645292
2226.7226.70757049619130.0124295038087467
2325.4625.43430984562290.0256901543771413
2425.4825.44796177837280.0320382216271753
2525.5925.51052641485530.0794735851446724
2625.8825.9442602441533-0.0642602441533242
272626.2685522403264-0.268552240326365
2826.9726.70548991683320.264510083166783
2927.227.0754183040080.124581695991978
3027.1927.10014957057410.0898504294259439
3127.1927.15729506474680.0327049352532427
3227.1927.15526367202910.0347363279708723
3327.2627.5561611249839-0.296161124983875
3426.927.4862228277635-0.58622282776355
3526.1125.86897045508320.241029544916824
3625.8726.0106893720092-0.140689372009174
3726.0225.99170441745690.0282955825430804
3826.3126.3365329129172-0.0265329129172329
3926.3726.5990112736564-0.229011273656408
4026.5227.2769591118058-0.756959111805834
4126.8626.9931691149069-0.133169114906909
4226.9226.85259132683680.0674086731631718
4326.9826.87249927845220.107500721547826
4426.9826.91419754465220.0658024553478072
4527.0327.1970858427777-0.167085842777727
4626.7527.0830733208619-0.333073320861899
4726.3925.951467934550.438532065449984
4826.326.05171114659240.248288853407583
4926.326.3284701280868-0.0284701280868163
5026.5226.6174277398632-0.097427739863214
5126.5326.7553401951758-0.225340195175807
5226.9827.2190249184114-0.239024918411378
5327.2227.4924885473967-0.272488547396666
5427.3427.3525417702348-0.0125417702347832
5527.4127.34199978740110.0680002125988608
5627.4727.34335397931960.126646020680386
5727.4627.5662132862382-0.106213286238241
5827.5327.41959290416780.110407095832219
5927.2126.86243590841190.347564091588133
6026.9126.83172988986930.07827011013066
6126.9526.89595158801140.0540484119886422
6226.9127.2047493663155-0.294749366315539
6327.3927.17506217228500.214937827715033
6427.6227.8899894927051-0.269989492705083
6527.7928.1317163074545-0.341716307454469
6627.8828.0577571095773-0.177757109577311
6727.927.9837244816603-0.0837244816602905
6828.0927.92043090433160.169569095668415
6928.4628.07290422639950.38709577360051
7028.7328.30275859256970.427241407430287
7127.9328.027681093299-0.0976810932989913
7227.6127.6270918885627-0.0170918885627245







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7327.625764565417827.189140367419928.0623887634156
7427.760261003266927.254693743819228.2658282627146
7528.111169911748427.54490855439828.6774312690989
7628.502276344971527.881146910528829.1234057794142
7728.872247684569228.200646706771829.5438486623666
7829.064968387902428.346365373007829.783571402797
7929.133440178232128.370662947130329.8962174093339
8029.223013358235828.418423786939630.0276029295321
8129.365899250754128.521508235930530.2102902655776
8229.386527623238128.50407388600330.2689813604732
8328.647379230888927.728385386176029.5663730756019
8428.336738884468527.382552570513129.290925198424

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 27.6257645654178 & 27.1891403674199 & 28.0623887634156 \tabularnewline
74 & 27.7602610032669 & 27.2546937438192 & 28.2658282627146 \tabularnewline
75 & 28.1111699117484 & 27.544908554398 & 28.6774312690989 \tabularnewline
76 & 28.5022763449715 & 27.8811469105288 & 29.1234057794142 \tabularnewline
77 & 28.8722476845692 & 28.2006467067718 & 29.5438486623666 \tabularnewline
78 & 29.0649683879024 & 28.3463653730078 & 29.783571402797 \tabularnewline
79 & 29.1334401782321 & 28.3706629471303 & 29.8962174093339 \tabularnewline
80 & 29.2230133582358 & 28.4184237869396 & 30.0276029295321 \tabularnewline
81 & 29.3658992507541 & 28.5215082359305 & 30.2102902655776 \tabularnewline
82 & 29.3865276232381 & 28.504073886003 & 30.2689813604732 \tabularnewline
83 & 28.6473792308889 & 27.7283853861760 & 29.5663730756019 \tabularnewline
84 & 28.3367388844685 & 27.3825525705131 & 29.290925198424 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13006&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]27.6257645654178[/C][C]27.1891403674199[/C][C]28.0623887634156[/C][/ROW]
[ROW][C]74[/C][C]27.7602610032669[/C][C]27.2546937438192[/C][C]28.2658282627146[/C][/ROW]
[ROW][C]75[/C][C]28.1111699117484[/C][C]27.544908554398[/C][C]28.6774312690989[/C][/ROW]
[ROW][C]76[/C][C]28.5022763449715[/C][C]27.8811469105288[/C][C]29.1234057794142[/C][/ROW]
[ROW][C]77[/C][C]28.8722476845692[/C][C]28.2006467067718[/C][C]29.5438486623666[/C][/ROW]
[ROW][C]78[/C][C]29.0649683879024[/C][C]28.3463653730078[/C][C]29.783571402797[/C][/ROW]
[ROW][C]79[/C][C]29.1334401782321[/C][C]28.3706629471303[/C][C]29.8962174093339[/C][/ROW]
[ROW][C]80[/C][C]29.2230133582358[/C][C]28.4184237869396[/C][C]30.0276029295321[/C][/ROW]
[ROW][C]81[/C][C]29.3658992507541[/C][C]28.5215082359305[/C][C]30.2102902655776[/C][/ROW]
[ROW][C]82[/C][C]29.3865276232381[/C][C]28.504073886003[/C][C]30.2689813604732[/C][/ROW]
[ROW][C]83[/C][C]28.6473792308889[/C][C]27.7283853861760[/C][C]29.5663730756019[/C][/ROW]
[ROW][C]84[/C][C]28.3367388844685[/C][C]27.3825525705131[/C][C]29.290925198424[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13006&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13006&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
7327.625764565417827.189140367419928.0623887634156
7427.760261003266927.254693743819228.2658282627146
7528.111169911748427.54490855439828.6774312690989
7628.502276344971527.881146910528829.1234057794142
7728.872247684569228.200646706771829.5438486623666
7829.064968387902428.346365373007829.783571402797
7929.133440178232128.370662947130329.8962174093339
8029.223013358235828.418423786939630.0276029295321
8129.365899250754128.521508235930530.2102902655776
8229.386527623238128.50407388600330.2689813604732
8328.647379230888927.728385386176029.5663730756019
8428.336738884468527.382552570513129.290925198424



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')