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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 21 May 2012 12:27:15 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/21/t1337617675p8xqtjq0xwm3ri7.htm/, Retrieved Thu, 02 May 2024 21:48:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166989, Retrieved Thu, 02 May 2024 21:48:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2012-05-02 16:05:10] [2e3d5d2fadc43e8101372c775eeeade1]
- RMPD    [Exponential Smoothing] [] [2012-05-21 16:27:15] [76c30f62b7052b57088120e90a652e05] [Current]
- R PD      [Exponential Smoothing] [] [2012-05-28 15:17:59] [2e3d5d2fadc43e8101372c775eeeade1]
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Dataseries X:
23,15
23,18
23,32
23,37
23,43
23,65
23,76
23,81
23,85
23,83
23,85
23,71
23,74
23,87
24,13
24,23
24,27
24,41
24,39
24,34
24,31
24,34
24,41
24,39
24,54
24,9
25,63
26,7
27,12
27,68
27,84
27,84
27,77
27,8
27,82
27,72
27,87
27,83
28,07
28,05
28,15
28,3
28,41
28,43
28,43
28,29
28,19
27,53
27,92
27,98
27,92
27,89
27,95
28,02
27,97
27,81
27,78
27,56
27,52
27,18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166989&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166989&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166989&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.916133207303429
beta0.699524991426108
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.916133207303429 \tabularnewline
beta & 0.699524991426108 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166989&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]0.916133207303429[/C][/ROW]
[ROW][C]beta[/C][C]0.699524991426108[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166989&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166989&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
alpha0.916133207303429
beta0.699524991426108
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
323.3223.210.109999999999999
423.3723.4112690409416-0.0412690409416285
523.4323.4475078921467-0.0175078921466678
623.6523.49429504676580.155704953234189
723.7623.7995530174093-0.0395530174093146
823.8123.9005808065984-0.0905808065984424
923.8523.8968109023595-0.0468109023595211
1023.8323.9031409161468-0.0731409161467909
1123.8523.83847618330350.0115238166964851
1223.7123.8587607546785-0.148760754678495
1323.7423.63686877687080.103131223129221
1423.8723.71183588160830.158164118391738
1524.1323.93858120147570.191418798524285
1624.2324.3184645206575-0.0884645206574675
1724.2724.385244234642-0.115244234642045
1824.4124.35363496511280.0563650348872144
1924.3924.5153646337782-0.125364633778236
2024.3424.4302647804782-0.0902647804781758
2124.3124.3194741549919-0.00947415499193482
2224.3424.27662691563170.0633730843683047
2324.4124.34113060410050.0688693958995437
2424.3924.4548051544933-0.0648051544932997
2524.5424.40448510380710.135514896192909
2624.924.62453071901360.275469280986435
2725.6325.14932990649190.480670093508138
2826.726.17016168283430.52983831716568
2927.1227.5755892650754-0.45558926507535
3027.6827.7862658568886-0.106265856888623
3127.8428.2488678906543-0.408867890654253
3227.8428.172219863771-0.332219863771009
3327.7727.9528858575542-0.18288585755424
3427.827.75315781498120.0468421850188356
3527.8227.79391045333050.026089546669521
3627.7227.8323706071786-0.11237060717858
3727.8727.67196920530920.198030794690798
3827.8327.922846468961-0.0928464689609889
3928.0727.84774000285730.22225999714275
4028.0528.2037501478798-0.153750147879798
4128.1528.11675288911920.0332471108808043
4228.328.22237670822850.0776232917715056
4328.4128.4184005335261-0.00840053352606773
4428.4328.5302315261133-0.100231526113308
4528.4328.4936989141543-0.0636989141542799
4628.2928.4498130777207-0.15981307772066
4728.1928.2154563631661-0.0254563631661462
4827.5328.0878743805699-0.557874380569917
4927.9227.11500827100630.804991728993677
5027.9827.90659451053840.073405489461603
5127.9228.0749928026251-0.154992802625117
5227.8927.9348194458681-0.0448194458680753
5327.9527.86685665604020.0831433439598008
5428.0227.96940791054750.0505920894524969
5527.9728.0745602288666-0.104560228866642
5627.8127.9705640892967-0.160564089296692
5727.7827.71236216043190.067637839568107
5827.5627.7065698521649-0.146569852164898
5927.5227.41060429107890.109395708921053
6027.1827.4192444037512-0.239244403751165

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 23.32 & 23.21 & 0.109999999999999 \tabularnewline
4 & 23.37 & 23.4112690409416 & -0.0412690409416285 \tabularnewline
5 & 23.43 & 23.4475078921467 & -0.0175078921466678 \tabularnewline
6 & 23.65 & 23.4942950467658 & 0.155704953234189 \tabularnewline
7 & 23.76 & 23.7995530174093 & -0.0395530174093146 \tabularnewline
8 & 23.81 & 23.9005808065984 & -0.0905808065984424 \tabularnewline
9 & 23.85 & 23.8968109023595 & -0.0468109023595211 \tabularnewline
10 & 23.83 & 23.9031409161468 & -0.0731409161467909 \tabularnewline
11 & 23.85 & 23.8384761833035 & 0.0115238166964851 \tabularnewline
12 & 23.71 & 23.8587607546785 & -0.148760754678495 \tabularnewline
13 & 23.74 & 23.6368687768708 & 0.103131223129221 \tabularnewline
14 & 23.87 & 23.7118358816083 & 0.158164118391738 \tabularnewline
15 & 24.13 & 23.9385812014757 & 0.191418798524285 \tabularnewline
16 & 24.23 & 24.3184645206575 & -0.0884645206574675 \tabularnewline
17 & 24.27 & 24.385244234642 & -0.115244234642045 \tabularnewline
18 & 24.41 & 24.3536349651128 & 0.0563650348872144 \tabularnewline
19 & 24.39 & 24.5153646337782 & -0.125364633778236 \tabularnewline
20 & 24.34 & 24.4302647804782 & -0.0902647804781758 \tabularnewline
21 & 24.31 & 24.3194741549919 & -0.00947415499193482 \tabularnewline
22 & 24.34 & 24.2766269156317 & 0.0633730843683047 \tabularnewline
23 & 24.41 & 24.3411306041005 & 0.0688693958995437 \tabularnewline
24 & 24.39 & 24.4548051544933 & -0.0648051544932997 \tabularnewline
25 & 24.54 & 24.4044851038071 & 0.135514896192909 \tabularnewline
26 & 24.9 & 24.6245307190136 & 0.275469280986435 \tabularnewline
27 & 25.63 & 25.1493299064919 & 0.480670093508138 \tabularnewline
28 & 26.7 & 26.1701616828343 & 0.52983831716568 \tabularnewline
29 & 27.12 & 27.5755892650754 & -0.45558926507535 \tabularnewline
30 & 27.68 & 27.7862658568886 & -0.106265856888623 \tabularnewline
31 & 27.84 & 28.2488678906543 & -0.408867890654253 \tabularnewline
32 & 27.84 & 28.172219863771 & -0.332219863771009 \tabularnewline
33 & 27.77 & 27.9528858575542 & -0.18288585755424 \tabularnewline
34 & 27.8 & 27.7531578149812 & 0.0468421850188356 \tabularnewline
35 & 27.82 & 27.7939104533305 & 0.026089546669521 \tabularnewline
36 & 27.72 & 27.8323706071786 & -0.11237060717858 \tabularnewline
37 & 27.87 & 27.6719692053092 & 0.198030794690798 \tabularnewline
38 & 27.83 & 27.922846468961 & -0.0928464689609889 \tabularnewline
39 & 28.07 & 27.8477400028573 & 0.22225999714275 \tabularnewline
40 & 28.05 & 28.2037501478798 & -0.153750147879798 \tabularnewline
41 & 28.15 & 28.1167528891192 & 0.0332471108808043 \tabularnewline
42 & 28.3 & 28.2223767082285 & 0.0776232917715056 \tabularnewline
43 & 28.41 & 28.4184005335261 & -0.00840053352606773 \tabularnewline
44 & 28.43 & 28.5302315261133 & -0.100231526113308 \tabularnewline
45 & 28.43 & 28.4936989141543 & -0.0636989141542799 \tabularnewline
46 & 28.29 & 28.4498130777207 & -0.15981307772066 \tabularnewline
47 & 28.19 & 28.2154563631661 & -0.0254563631661462 \tabularnewline
48 & 27.53 & 28.0878743805699 & -0.557874380569917 \tabularnewline
49 & 27.92 & 27.1150082710063 & 0.804991728993677 \tabularnewline
50 & 27.98 & 27.9065945105384 & 0.073405489461603 \tabularnewline
51 & 27.92 & 28.0749928026251 & -0.154992802625117 \tabularnewline
52 & 27.89 & 27.9348194458681 & -0.0448194458680753 \tabularnewline
53 & 27.95 & 27.8668566560402 & 0.0831433439598008 \tabularnewline
54 & 28.02 & 27.9694079105475 & 0.0505920894524969 \tabularnewline
55 & 27.97 & 28.0745602288666 & -0.104560228866642 \tabularnewline
56 & 27.81 & 27.9705640892967 & -0.160564089296692 \tabularnewline
57 & 27.78 & 27.7123621604319 & 0.067637839568107 \tabularnewline
58 & 27.56 & 27.7065698521649 & -0.146569852164898 \tabularnewline
59 & 27.52 & 27.4106042910789 & 0.109395708921053 \tabularnewline
60 & 27.18 & 27.4192444037512 & -0.239244403751165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166989&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]23.32[/C][C]23.21[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]4[/C][C]23.37[/C][C]23.4112690409416[/C][C]-0.0412690409416285[/C][/ROW]
[ROW][C]5[/C][C]23.43[/C][C]23.4475078921467[/C][C]-0.0175078921466678[/C][/ROW]
[ROW][C]6[/C][C]23.65[/C][C]23.4942950467658[/C][C]0.155704953234189[/C][/ROW]
[ROW][C]7[/C][C]23.76[/C][C]23.7995530174093[/C][C]-0.0395530174093146[/C][/ROW]
[ROW][C]8[/C][C]23.81[/C][C]23.9005808065984[/C][C]-0.0905808065984424[/C][/ROW]
[ROW][C]9[/C][C]23.85[/C][C]23.8968109023595[/C][C]-0.0468109023595211[/C][/ROW]
[ROW][C]10[/C][C]23.83[/C][C]23.9031409161468[/C][C]-0.0731409161467909[/C][/ROW]
[ROW][C]11[/C][C]23.85[/C][C]23.8384761833035[/C][C]0.0115238166964851[/C][/ROW]
[ROW][C]12[/C][C]23.71[/C][C]23.8587607546785[/C][C]-0.148760754678495[/C][/ROW]
[ROW][C]13[/C][C]23.74[/C][C]23.6368687768708[/C][C]0.103131223129221[/C][/ROW]
[ROW][C]14[/C][C]23.87[/C][C]23.7118358816083[/C][C]0.158164118391738[/C][/ROW]
[ROW][C]15[/C][C]24.13[/C][C]23.9385812014757[/C][C]0.191418798524285[/C][/ROW]
[ROW][C]16[/C][C]24.23[/C][C]24.3184645206575[/C][C]-0.0884645206574675[/C][/ROW]
[ROW][C]17[/C][C]24.27[/C][C]24.385244234642[/C][C]-0.115244234642045[/C][/ROW]
[ROW][C]18[/C][C]24.41[/C][C]24.3536349651128[/C][C]0.0563650348872144[/C][/ROW]
[ROW][C]19[/C][C]24.39[/C][C]24.5153646337782[/C][C]-0.125364633778236[/C][/ROW]
[ROW][C]20[/C][C]24.34[/C][C]24.4302647804782[/C][C]-0.0902647804781758[/C][/ROW]
[ROW][C]21[/C][C]24.31[/C][C]24.3194741549919[/C][C]-0.00947415499193482[/C][/ROW]
[ROW][C]22[/C][C]24.34[/C][C]24.2766269156317[/C][C]0.0633730843683047[/C][/ROW]
[ROW][C]23[/C][C]24.41[/C][C]24.3411306041005[/C][C]0.0688693958995437[/C][/ROW]
[ROW][C]24[/C][C]24.39[/C][C]24.4548051544933[/C][C]-0.0648051544932997[/C][/ROW]
[ROW][C]25[/C][C]24.54[/C][C]24.4044851038071[/C][C]0.135514896192909[/C][/ROW]
[ROW][C]26[/C][C]24.9[/C][C]24.6245307190136[/C][C]0.275469280986435[/C][/ROW]
[ROW][C]27[/C][C]25.63[/C][C]25.1493299064919[/C][C]0.480670093508138[/C][/ROW]
[ROW][C]28[/C][C]26.7[/C][C]26.1701616828343[/C][C]0.52983831716568[/C][/ROW]
[ROW][C]29[/C][C]27.12[/C][C]27.5755892650754[/C][C]-0.45558926507535[/C][/ROW]
[ROW][C]30[/C][C]27.68[/C][C]27.7862658568886[/C][C]-0.106265856888623[/C][/ROW]
[ROW][C]31[/C][C]27.84[/C][C]28.2488678906543[/C][C]-0.408867890654253[/C][/ROW]
[ROW][C]32[/C][C]27.84[/C][C]28.172219863771[/C][C]-0.332219863771009[/C][/ROW]
[ROW][C]33[/C][C]27.77[/C][C]27.9528858575542[/C][C]-0.18288585755424[/C][/ROW]
[ROW][C]34[/C][C]27.8[/C][C]27.7531578149812[/C][C]0.0468421850188356[/C][/ROW]
[ROW][C]35[/C][C]27.82[/C][C]27.7939104533305[/C][C]0.026089546669521[/C][/ROW]
[ROW][C]36[/C][C]27.72[/C][C]27.8323706071786[/C][C]-0.11237060717858[/C][/ROW]
[ROW][C]37[/C][C]27.87[/C][C]27.6719692053092[/C][C]0.198030794690798[/C][/ROW]
[ROW][C]38[/C][C]27.83[/C][C]27.922846468961[/C][C]-0.0928464689609889[/C][/ROW]
[ROW][C]39[/C][C]28.07[/C][C]27.8477400028573[/C][C]0.22225999714275[/C][/ROW]
[ROW][C]40[/C][C]28.05[/C][C]28.2037501478798[/C][C]-0.153750147879798[/C][/ROW]
[ROW][C]41[/C][C]28.15[/C][C]28.1167528891192[/C][C]0.0332471108808043[/C][/ROW]
[ROW][C]42[/C][C]28.3[/C][C]28.2223767082285[/C][C]0.0776232917715056[/C][/ROW]
[ROW][C]43[/C][C]28.41[/C][C]28.4184005335261[/C][C]-0.00840053352606773[/C][/ROW]
[ROW][C]44[/C][C]28.43[/C][C]28.5302315261133[/C][C]-0.100231526113308[/C][/ROW]
[ROW][C]45[/C][C]28.43[/C][C]28.4936989141543[/C][C]-0.0636989141542799[/C][/ROW]
[ROW][C]46[/C][C]28.29[/C][C]28.4498130777207[/C][C]-0.15981307772066[/C][/ROW]
[ROW][C]47[/C][C]28.19[/C][C]28.2154563631661[/C][C]-0.0254563631661462[/C][/ROW]
[ROW][C]48[/C][C]27.53[/C][C]28.0878743805699[/C][C]-0.557874380569917[/C][/ROW]
[ROW][C]49[/C][C]27.92[/C][C]27.1150082710063[/C][C]0.804991728993677[/C][/ROW]
[ROW][C]50[/C][C]27.98[/C][C]27.9065945105384[/C][C]0.073405489461603[/C][/ROW]
[ROW][C]51[/C][C]27.92[/C][C]28.0749928026251[/C][C]-0.154992802625117[/C][/ROW]
[ROW][C]52[/C][C]27.89[/C][C]27.9348194458681[/C][C]-0.0448194458680753[/C][/ROW]
[ROW][C]53[/C][C]27.95[/C][C]27.8668566560402[/C][C]0.0831433439598008[/C][/ROW]
[ROW][C]54[/C][C]28.02[/C][C]27.9694079105475[/C][C]0.0505920894524969[/C][/ROW]
[ROW][C]55[/C][C]27.97[/C][C]28.0745602288666[/C][C]-0.104560228866642[/C][/ROW]
[ROW][C]56[/C][C]27.81[/C][C]27.9705640892967[/C][C]-0.160564089296692[/C][/ROW]
[ROW][C]57[/C][C]27.78[/C][C]27.7123621604319[/C][C]0.067637839568107[/C][/ROW]
[ROW][C]58[/C][C]27.56[/C][C]27.7065698521649[/C][C]-0.146569852164898[/C][/ROW]
[ROW][C]59[/C][C]27.52[/C][C]27.4106042910789[/C][C]0.109395708921053[/C][/ROW]
[ROW][C]60[/C][C]27.18[/C][C]27.4192444037512[/C][C]-0.239244403751165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166989&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166989&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
323.3223.210.109999999999999
423.3723.4112690409416-0.0412690409416285
523.4323.4475078921467-0.0175078921466678
623.6523.49429504676580.155704953234189
723.7623.7995530174093-0.0395530174093146
823.8123.9005808065984-0.0905808065984424
923.8523.8968109023595-0.0468109023595211
1023.8323.9031409161468-0.0731409161467909
1123.8523.83847618330350.0115238166964851
1223.7123.8587607546785-0.148760754678495
1323.7423.63686877687080.103131223129221
1423.8723.71183588160830.158164118391738
1524.1323.93858120147570.191418798524285
1624.2324.3184645206575-0.0884645206574675
1724.2724.385244234642-0.115244234642045
1824.4124.35363496511280.0563650348872144
1924.3924.5153646337782-0.125364633778236
2024.3424.4302647804782-0.0902647804781758
2124.3124.3194741549919-0.00947415499193482
2224.3424.27662691563170.0633730843683047
2324.4124.34113060410050.0688693958995437
2424.3924.4548051544933-0.0648051544932997
2524.5424.40448510380710.135514896192909
2624.924.62453071901360.275469280986435
2725.6325.14932990649190.480670093508138
2826.726.17016168283430.52983831716568
2927.1227.5755892650754-0.45558926507535
3027.6827.7862658568886-0.106265856888623
3127.8428.2488678906543-0.408867890654253
3227.8428.172219863771-0.332219863771009
3327.7727.9528858575542-0.18288585755424
3427.827.75315781498120.0468421850188356
3527.8227.79391045333050.026089546669521
3627.7227.8323706071786-0.11237060717858
3727.8727.67196920530920.198030794690798
3827.8327.922846468961-0.0928464689609889
3928.0727.84774000285730.22225999714275
4028.0528.2037501478798-0.153750147879798
4128.1528.11675288911920.0332471108808043
4228.328.22237670822850.0776232917715056
4328.4128.4184005335261-0.00840053352606773
4428.4328.5302315261133-0.100231526113308
4528.4328.4936989141543-0.0636989141542799
4628.2928.4498130777207-0.15981307772066
4728.1928.2154563631661-0.0254563631661462
4827.5328.0878743805699-0.557874380569917
4927.9227.11500827100630.804991728993677
5027.9827.90659451053840.073405489461603
5127.9228.0749928026251-0.154992802625117
5227.8927.9348194458681-0.0448194458680753
5327.9527.86685665604020.0831433439598008
5428.0227.96940791054750.0505920894524969
5527.9728.0745602288666-0.104560228866642
5627.8127.9705640892967-0.160564089296692
5727.7827.71236216043190.067637839568107
5827.5627.7065698521649-0.146569852164898
5927.5227.41060429107890.109395708921053
6027.1827.4192444037512-0.239244403751165







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6126.955162024006926.531754789881427.3785692581324
6226.710259387200625.926758989993727.4937597844075
6326.465356750394325.248861002854227.6818524979344
6426.22045411358824.510338371159427.9305698560166
6525.975551476781723.718334209637928.2327687439255
6625.730648839975422.87780485684828.5834928231027
6725.485746203169121.992493001934528.9789994044037
6825.240843566362821.065369668562229.4163174641634
6924.995940929556520.098873756807729.8930081023052
7024.751038292750119.095056780223230.4070198052771
7124.506135655943818.055676969104230.9565943427835
7224.261233019137516.982263781074931.5402022572002

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 26.9551620240069 & 26.5317547898814 & 27.3785692581324 \tabularnewline
62 & 26.7102593872006 & 25.9267589899937 & 27.4937597844075 \tabularnewline
63 & 26.4653567503943 & 25.2488610028542 & 27.6818524979344 \tabularnewline
64 & 26.220454113588 & 24.5103383711594 & 27.9305698560166 \tabularnewline
65 & 25.9755514767817 & 23.7183342096379 & 28.2327687439255 \tabularnewline
66 & 25.7306488399754 & 22.877804856848 & 28.5834928231027 \tabularnewline
67 & 25.4857462031691 & 21.9924930019345 & 28.9789994044037 \tabularnewline
68 & 25.2408435663628 & 21.0653696685622 & 29.4163174641634 \tabularnewline
69 & 24.9959409295565 & 20.0988737568077 & 29.8930081023052 \tabularnewline
70 & 24.7510382927501 & 19.0950567802232 & 30.4070198052771 \tabularnewline
71 & 24.5061356559438 & 18.0556769691042 & 30.9565943427835 \tabularnewline
72 & 24.2612330191375 & 16.9822637810749 & 31.5402022572002 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166989&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]26.9551620240069[/C][C]26.5317547898814[/C][C]27.3785692581324[/C][/ROW]
[ROW][C]62[/C][C]26.7102593872006[/C][C]25.9267589899937[/C][C]27.4937597844075[/C][/ROW]
[ROW][C]63[/C][C]26.4653567503943[/C][C]25.2488610028542[/C][C]27.6818524979344[/C][/ROW]
[ROW][C]64[/C][C]26.220454113588[/C][C]24.5103383711594[/C][C]27.9305698560166[/C][/ROW]
[ROW][C]65[/C][C]25.9755514767817[/C][C]23.7183342096379[/C][C]28.2327687439255[/C][/ROW]
[ROW][C]66[/C][C]25.7306488399754[/C][C]22.877804856848[/C][C]28.5834928231027[/C][/ROW]
[ROW][C]67[/C][C]25.4857462031691[/C][C]21.9924930019345[/C][C]28.9789994044037[/C][/ROW]
[ROW][C]68[/C][C]25.2408435663628[/C][C]21.0653696685622[/C][C]29.4163174641634[/C][/ROW]
[ROW][C]69[/C][C]24.9959409295565[/C][C]20.0988737568077[/C][C]29.8930081023052[/C][/ROW]
[ROW][C]70[/C][C]24.7510382927501[/C][C]19.0950567802232[/C][C]30.4070198052771[/C][/ROW]
[ROW][C]71[/C][C]24.5061356559438[/C][C]18.0556769691042[/C][C]30.9565943427835[/C][/ROW]
[ROW][C]72[/C][C]24.2612330191375[/C][C]16.9822637810749[/C][C]31.5402022572002[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166989&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166989&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
6126.955162024006926.531754789881427.3785692581324
6226.710259387200625.926758989993727.4937597844075
6326.465356750394325.248861002854227.6818524979344
6426.22045411358824.510338371159427.9305698560166
6525.975551476781723.718334209637928.2327687439255
6625.730648839975422.87780485684828.5834928231027
6725.485746203169121.992493001934528.9789994044037
6825.240843566362821.065369668562229.4163174641634
6924.995940929556520.098873756807729.8930081023052
7024.751038292750119.095056780223230.4070198052771
7124.506135655943818.055676969104230.9565943427835
7224.261233019137516.982263781074931.5402022572002



Parameters (Session):
par1 = 0.1 ; par2 = 0.9 ; par3 = 0.1 ;
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')