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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 May 2013 03:02:42 -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/2013/May/13/t13684285839p651osj2uf8nl5.htm/, Retrieved Wed, 08 May 2024 02:49:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=208894, Retrieved Wed, 08 May 2024 02:49:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-05-13 07:02:42] [a7b46db3730015db727d65b06ff3f02a] [Current]
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Dataseries X:
10,92
10,98
11,15
11,19
11,33
11,38
11,4
11,45
11,56
11,61
11,82
11,77
11,85
11,82
11,92
11,86
11,87
11,94
11,86
11,92
11,83
11,91
11,93
11,99
11,96
12,12
11,85
12,01
12,1
12,21
12,31
12,31
12,39
12,35
12,41
12,51
12,27
12,51
12,44
12,47
12,51
12,58
12,5
12,52
12,59
12,51
12,67
12,64
12,54
12,6
12,67
12,62
12,72
12,85
12,85
12,82
12,79
12,94
12,71
12,56
12,64
12,7
12,74
12,85
12,84
12,83
12,88
13,07
12,99
13,2
13,23
13,18




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208894&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]3 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=208894&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208894&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 time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.652671177821116
beta0.07053328010691
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.652671177821116 \tabularnewline
beta & 0.07053328010691 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208894&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]0.652671177821116[/C][/ROW]
[ROW][C]beta[/C][C]0.07053328010691[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208894&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208894&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
alpha0.652671177821116
beta0.07053328010691
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
311.1511.040.109999999999999
411.1911.17685768385060.0131423161493505
511.3311.2511041561380.0788958438620071
611.3811.37189803405280.00810196594718882
711.411.4468597626048-0.0468597626048197
811.4511.4837923640485-0.0337923640485229
911.5611.5276980471020.0323019528979565
1011.6111.6162286075058-0.00622860750583598
1111.8211.67932464747930.14067535252069
1211.7711.8447766634099-0.0747766634099314
1311.8511.8661670117226-0.0161670117225921
1411.8211.9250659414185-0.105065941418502
1511.9211.9211063872517-0.0011063872516619
1611.8611.9849473051684-0.124947305168369
1711.8711.9622088712592-0.0922088712591904
1811.9411.9565930305847-0.016593030584696
1911.8611.999565608895-0.139565608895017
2011.9211.9558526214309-0.0358526214308839
2111.8311.9781796348244-0.148179634824386
2211.9111.9203725888166-0.0103725888166366
2311.9311.9520307273081-0.0220307273080795
2411.9911.97506574942820.0149342505717822
2511.9612.0229142460069-0.0629142460068888
2612.1212.01705701286320.102942987136812
2711.8512.1241889998535-0.274188999853463
2812.0111.97255550739830.0374444926016633
2912.112.02603997218980.0739600278102284
3012.2112.10676182711950.103238172880548
3112.3112.21134525679170.0986547432082538
3212.3112.3174787889728-0.00747878897278298
3312.3912.35399773735690.036002262643148
3412.3512.420552880477-0.0705528804769635
3512.4112.4143146482294-0.00431464822944427
3612.5112.45110957604020.0588904239598236
3712.2712.5318676557248-0.261867655724838
3812.5112.39122109400120.118778905998836
3912.4412.5044795636216-0.0644795636216244
4012.4712.495162192803-0.0251621928029859
4112.5112.5103477941783-0.000347794178296112
4212.5812.54171302761230.0382869723876595
4312.512.600056601913-0.100056601913003
4412.5212.5635012030593-0.0435012030593001
4512.5912.56185530340810.0281446965919248
4612.5112.6082662596736-0.0982662596736059
4712.6712.56764873712710.102351262872933
4812.6412.6626802336909-0.0226802336908918
4912.5412.6750631906851-0.135063190685113
5012.612.6078793915198-0.00787939151983963
5112.6712.62334206425960.0466579357404058
5212.6212.6765475785091-0.0565475785091181
5312.7212.65979065823360.0602093417664218
5412.8512.72200935402960.127990645970396
5512.8512.83435900785390.0156409921460501
5612.8212.8741013144725-0.0541013144724527
5712.7912.8658342715644-0.075834271564446
5812.9412.83989172030440.10010827969556
5912.7112.9333902897645-0.223390289764458
6012.5612.8054668861694-0.245466886169371
6112.6412.6518346467177-0.0118346467176647
6212.712.65014262774270.0498573722573443
6312.7412.69101039753070.0489896024693213
6412.8512.73356703724950.116432962750507
6512.8412.82550201034070.0144979896593078
6612.8312.8515743800027-0.0215743800027237
6712.8812.85311017624570.0268898237542512
6813.0712.88751503552230.182484964477689
6912.9913.0318730610153-0.0418730610152682
7013.213.02787144175910.172128558240894
7113.2313.17146645629060.0585335437093697
7213.1813.2436158728609-0.0636158728609022

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 11.15 & 11.04 & 0.109999999999999 \tabularnewline
4 & 11.19 & 11.1768576838506 & 0.0131423161493505 \tabularnewline
5 & 11.33 & 11.251104156138 & 0.0788958438620071 \tabularnewline
6 & 11.38 & 11.3718980340528 & 0.00810196594718882 \tabularnewline
7 & 11.4 & 11.4468597626048 & -0.0468597626048197 \tabularnewline
8 & 11.45 & 11.4837923640485 & -0.0337923640485229 \tabularnewline
9 & 11.56 & 11.527698047102 & 0.0323019528979565 \tabularnewline
10 & 11.61 & 11.6162286075058 & -0.00622860750583598 \tabularnewline
11 & 11.82 & 11.6793246474793 & 0.14067535252069 \tabularnewline
12 & 11.77 & 11.8447766634099 & -0.0747766634099314 \tabularnewline
13 & 11.85 & 11.8661670117226 & -0.0161670117225921 \tabularnewline
14 & 11.82 & 11.9250659414185 & -0.105065941418502 \tabularnewline
15 & 11.92 & 11.9211063872517 & -0.0011063872516619 \tabularnewline
16 & 11.86 & 11.9849473051684 & -0.124947305168369 \tabularnewline
17 & 11.87 & 11.9622088712592 & -0.0922088712591904 \tabularnewline
18 & 11.94 & 11.9565930305847 & -0.016593030584696 \tabularnewline
19 & 11.86 & 11.999565608895 & -0.139565608895017 \tabularnewline
20 & 11.92 & 11.9558526214309 & -0.0358526214308839 \tabularnewline
21 & 11.83 & 11.9781796348244 & -0.148179634824386 \tabularnewline
22 & 11.91 & 11.9203725888166 & -0.0103725888166366 \tabularnewline
23 & 11.93 & 11.9520307273081 & -0.0220307273080795 \tabularnewline
24 & 11.99 & 11.9750657494282 & 0.0149342505717822 \tabularnewline
25 & 11.96 & 12.0229142460069 & -0.0629142460068888 \tabularnewline
26 & 12.12 & 12.0170570128632 & 0.102942987136812 \tabularnewline
27 & 11.85 & 12.1241889998535 & -0.274188999853463 \tabularnewline
28 & 12.01 & 11.9725555073983 & 0.0374444926016633 \tabularnewline
29 & 12.1 & 12.0260399721898 & 0.0739600278102284 \tabularnewline
30 & 12.21 & 12.1067618271195 & 0.103238172880548 \tabularnewline
31 & 12.31 & 12.2113452567917 & 0.0986547432082538 \tabularnewline
32 & 12.31 & 12.3174787889728 & -0.00747878897278298 \tabularnewline
33 & 12.39 & 12.3539977373569 & 0.036002262643148 \tabularnewline
34 & 12.35 & 12.420552880477 & -0.0705528804769635 \tabularnewline
35 & 12.41 & 12.4143146482294 & -0.00431464822944427 \tabularnewline
36 & 12.51 & 12.4511095760402 & 0.0588904239598236 \tabularnewline
37 & 12.27 & 12.5318676557248 & -0.261867655724838 \tabularnewline
38 & 12.51 & 12.3912210940012 & 0.118778905998836 \tabularnewline
39 & 12.44 & 12.5044795636216 & -0.0644795636216244 \tabularnewline
40 & 12.47 & 12.495162192803 & -0.0251621928029859 \tabularnewline
41 & 12.51 & 12.5103477941783 & -0.000347794178296112 \tabularnewline
42 & 12.58 & 12.5417130276123 & 0.0382869723876595 \tabularnewline
43 & 12.5 & 12.600056601913 & -0.100056601913003 \tabularnewline
44 & 12.52 & 12.5635012030593 & -0.0435012030593001 \tabularnewline
45 & 12.59 & 12.5618553034081 & 0.0281446965919248 \tabularnewline
46 & 12.51 & 12.6082662596736 & -0.0982662596736059 \tabularnewline
47 & 12.67 & 12.5676487371271 & 0.102351262872933 \tabularnewline
48 & 12.64 & 12.6626802336909 & -0.0226802336908918 \tabularnewline
49 & 12.54 & 12.6750631906851 & -0.135063190685113 \tabularnewline
50 & 12.6 & 12.6078793915198 & -0.00787939151983963 \tabularnewline
51 & 12.67 & 12.6233420642596 & 0.0466579357404058 \tabularnewline
52 & 12.62 & 12.6765475785091 & -0.0565475785091181 \tabularnewline
53 & 12.72 & 12.6597906582336 & 0.0602093417664218 \tabularnewline
54 & 12.85 & 12.7220093540296 & 0.127990645970396 \tabularnewline
55 & 12.85 & 12.8343590078539 & 0.0156409921460501 \tabularnewline
56 & 12.82 & 12.8741013144725 & -0.0541013144724527 \tabularnewline
57 & 12.79 & 12.8658342715644 & -0.075834271564446 \tabularnewline
58 & 12.94 & 12.8398917203044 & 0.10010827969556 \tabularnewline
59 & 12.71 & 12.9333902897645 & -0.223390289764458 \tabularnewline
60 & 12.56 & 12.8054668861694 & -0.245466886169371 \tabularnewline
61 & 12.64 & 12.6518346467177 & -0.0118346467176647 \tabularnewline
62 & 12.7 & 12.6501426277427 & 0.0498573722573443 \tabularnewline
63 & 12.74 & 12.6910103975307 & 0.0489896024693213 \tabularnewline
64 & 12.85 & 12.7335670372495 & 0.116432962750507 \tabularnewline
65 & 12.84 & 12.8255020103407 & 0.0144979896593078 \tabularnewline
66 & 12.83 & 12.8515743800027 & -0.0215743800027237 \tabularnewline
67 & 12.88 & 12.8531101762457 & 0.0268898237542512 \tabularnewline
68 & 13.07 & 12.8875150355223 & 0.182484964477689 \tabularnewline
69 & 12.99 & 13.0318730610153 & -0.0418730610152682 \tabularnewline
70 & 13.2 & 13.0278714417591 & 0.172128558240894 \tabularnewline
71 & 13.23 & 13.1714664562906 & 0.0585335437093697 \tabularnewline
72 & 13.18 & 13.2436158728609 & -0.0636158728609022 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208894&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]11.15[/C][C]11.04[/C][C]0.109999999999999[/C][/ROW]
[ROW][C]4[/C][C]11.19[/C][C]11.1768576838506[/C][C]0.0131423161493505[/C][/ROW]
[ROW][C]5[/C][C]11.33[/C][C]11.251104156138[/C][C]0.0788958438620071[/C][/ROW]
[ROW][C]6[/C][C]11.38[/C][C]11.3718980340528[/C][C]0.00810196594718882[/C][/ROW]
[ROW][C]7[/C][C]11.4[/C][C]11.4468597626048[/C][C]-0.0468597626048197[/C][/ROW]
[ROW][C]8[/C][C]11.45[/C][C]11.4837923640485[/C][C]-0.0337923640485229[/C][/ROW]
[ROW][C]9[/C][C]11.56[/C][C]11.527698047102[/C][C]0.0323019528979565[/C][/ROW]
[ROW][C]10[/C][C]11.61[/C][C]11.6162286075058[/C][C]-0.00622860750583598[/C][/ROW]
[ROW][C]11[/C][C]11.82[/C][C]11.6793246474793[/C][C]0.14067535252069[/C][/ROW]
[ROW][C]12[/C][C]11.77[/C][C]11.8447766634099[/C][C]-0.0747766634099314[/C][/ROW]
[ROW][C]13[/C][C]11.85[/C][C]11.8661670117226[/C][C]-0.0161670117225921[/C][/ROW]
[ROW][C]14[/C][C]11.82[/C][C]11.9250659414185[/C][C]-0.105065941418502[/C][/ROW]
[ROW][C]15[/C][C]11.92[/C][C]11.9211063872517[/C][C]-0.0011063872516619[/C][/ROW]
[ROW][C]16[/C][C]11.86[/C][C]11.9849473051684[/C][C]-0.124947305168369[/C][/ROW]
[ROW][C]17[/C][C]11.87[/C][C]11.9622088712592[/C][C]-0.0922088712591904[/C][/ROW]
[ROW][C]18[/C][C]11.94[/C][C]11.9565930305847[/C][C]-0.016593030584696[/C][/ROW]
[ROW][C]19[/C][C]11.86[/C][C]11.999565608895[/C][C]-0.139565608895017[/C][/ROW]
[ROW][C]20[/C][C]11.92[/C][C]11.9558526214309[/C][C]-0.0358526214308839[/C][/ROW]
[ROW][C]21[/C][C]11.83[/C][C]11.9781796348244[/C][C]-0.148179634824386[/C][/ROW]
[ROW][C]22[/C][C]11.91[/C][C]11.9203725888166[/C][C]-0.0103725888166366[/C][/ROW]
[ROW][C]23[/C][C]11.93[/C][C]11.9520307273081[/C][C]-0.0220307273080795[/C][/ROW]
[ROW][C]24[/C][C]11.99[/C][C]11.9750657494282[/C][C]0.0149342505717822[/C][/ROW]
[ROW][C]25[/C][C]11.96[/C][C]12.0229142460069[/C][C]-0.0629142460068888[/C][/ROW]
[ROW][C]26[/C][C]12.12[/C][C]12.0170570128632[/C][C]0.102942987136812[/C][/ROW]
[ROW][C]27[/C][C]11.85[/C][C]12.1241889998535[/C][C]-0.274188999853463[/C][/ROW]
[ROW][C]28[/C][C]12.01[/C][C]11.9725555073983[/C][C]0.0374444926016633[/C][/ROW]
[ROW][C]29[/C][C]12.1[/C][C]12.0260399721898[/C][C]0.0739600278102284[/C][/ROW]
[ROW][C]30[/C][C]12.21[/C][C]12.1067618271195[/C][C]0.103238172880548[/C][/ROW]
[ROW][C]31[/C][C]12.31[/C][C]12.2113452567917[/C][C]0.0986547432082538[/C][/ROW]
[ROW][C]32[/C][C]12.31[/C][C]12.3174787889728[/C][C]-0.00747878897278298[/C][/ROW]
[ROW][C]33[/C][C]12.39[/C][C]12.3539977373569[/C][C]0.036002262643148[/C][/ROW]
[ROW][C]34[/C][C]12.35[/C][C]12.420552880477[/C][C]-0.0705528804769635[/C][/ROW]
[ROW][C]35[/C][C]12.41[/C][C]12.4143146482294[/C][C]-0.00431464822944427[/C][/ROW]
[ROW][C]36[/C][C]12.51[/C][C]12.4511095760402[/C][C]0.0588904239598236[/C][/ROW]
[ROW][C]37[/C][C]12.27[/C][C]12.5318676557248[/C][C]-0.261867655724838[/C][/ROW]
[ROW][C]38[/C][C]12.51[/C][C]12.3912210940012[/C][C]0.118778905998836[/C][/ROW]
[ROW][C]39[/C][C]12.44[/C][C]12.5044795636216[/C][C]-0.0644795636216244[/C][/ROW]
[ROW][C]40[/C][C]12.47[/C][C]12.495162192803[/C][C]-0.0251621928029859[/C][/ROW]
[ROW][C]41[/C][C]12.51[/C][C]12.5103477941783[/C][C]-0.000347794178296112[/C][/ROW]
[ROW][C]42[/C][C]12.58[/C][C]12.5417130276123[/C][C]0.0382869723876595[/C][/ROW]
[ROW][C]43[/C][C]12.5[/C][C]12.600056601913[/C][C]-0.100056601913003[/C][/ROW]
[ROW][C]44[/C][C]12.52[/C][C]12.5635012030593[/C][C]-0.0435012030593001[/C][/ROW]
[ROW][C]45[/C][C]12.59[/C][C]12.5618553034081[/C][C]0.0281446965919248[/C][/ROW]
[ROW][C]46[/C][C]12.51[/C][C]12.6082662596736[/C][C]-0.0982662596736059[/C][/ROW]
[ROW][C]47[/C][C]12.67[/C][C]12.5676487371271[/C][C]0.102351262872933[/C][/ROW]
[ROW][C]48[/C][C]12.64[/C][C]12.6626802336909[/C][C]-0.0226802336908918[/C][/ROW]
[ROW][C]49[/C][C]12.54[/C][C]12.6750631906851[/C][C]-0.135063190685113[/C][/ROW]
[ROW][C]50[/C][C]12.6[/C][C]12.6078793915198[/C][C]-0.00787939151983963[/C][/ROW]
[ROW][C]51[/C][C]12.67[/C][C]12.6233420642596[/C][C]0.0466579357404058[/C][/ROW]
[ROW][C]52[/C][C]12.62[/C][C]12.6765475785091[/C][C]-0.0565475785091181[/C][/ROW]
[ROW][C]53[/C][C]12.72[/C][C]12.6597906582336[/C][C]0.0602093417664218[/C][/ROW]
[ROW][C]54[/C][C]12.85[/C][C]12.7220093540296[/C][C]0.127990645970396[/C][/ROW]
[ROW][C]55[/C][C]12.85[/C][C]12.8343590078539[/C][C]0.0156409921460501[/C][/ROW]
[ROW][C]56[/C][C]12.82[/C][C]12.8741013144725[/C][C]-0.0541013144724527[/C][/ROW]
[ROW][C]57[/C][C]12.79[/C][C]12.8658342715644[/C][C]-0.075834271564446[/C][/ROW]
[ROW][C]58[/C][C]12.94[/C][C]12.8398917203044[/C][C]0.10010827969556[/C][/ROW]
[ROW][C]59[/C][C]12.71[/C][C]12.9333902897645[/C][C]-0.223390289764458[/C][/ROW]
[ROW][C]60[/C][C]12.56[/C][C]12.8054668861694[/C][C]-0.245466886169371[/C][/ROW]
[ROW][C]61[/C][C]12.64[/C][C]12.6518346467177[/C][C]-0.0118346467176647[/C][/ROW]
[ROW][C]62[/C][C]12.7[/C][C]12.6501426277427[/C][C]0.0498573722573443[/C][/ROW]
[ROW][C]63[/C][C]12.74[/C][C]12.6910103975307[/C][C]0.0489896024693213[/C][/ROW]
[ROW][C]64[/C][C]12.85[/C][C]12.7335670372495[/C][C]0.116432962750507[/C][/ROW]
[ROW][C]65[/C][C]12.84[/C][C]12.8255020103407[/C][C]0.0144979896593078[/C][/ROW]
[ROW][C]66[/C][C]12.83[/C][C]12.8515743800027[/C][C]-0.0215743800027237[/C][/ROW]
[ROW][C]67[/C][C]12.88[/C][C]12.8531101762457[/C][C]0.0268898237542512[/C][/ROW]
[ROW][C]68[/C][C]13.07[/C][C]12.8875150355223[/C][C]0.182484964477689[/C][/ROW]
[ROW][C]69[/C][C]12.99[/C][C]13.0318730610153[/C][C]-0.0418730610152682[/C][/ROW]
[ROW][C]70[/C][C]13.2[/C][C]13.0278714417591[/C][C]0.172128558240894[/C][/ROW]
[ROW][C]71[/C][C]13.23[/C][C]13.1714664562906[/C][C]0.0585335437093697[/C][/ROW]
[ROW][C]72[/C][C]13.18[/C][C]13.2436158728609[/C][C]-0.0636158728609022[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208894&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208894&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
311.1511.040.109999999999999
411.1911.17685768385060.0131423161493505
511.3311.2511041561380.0788958438620071
611.3811.37189803405280.00810196594718882
711.411.4468597626048-0.0468597626048197
811.4511.4837923640485-0.0337923640485229
911.5611.5276980471020.0323019528979565
1011.6111.6162286075058-0.00622860750583598
1111.8211.67932464747930.14067535252069
1211.7711.8447766634099-0.0747766634099314
1311.8511.8661670117226-0.0161670117225921
1411.8211.9250659414185-0.105065941418502
1511.9211.9211063872517-0.0011063872516619
1611.8611.9849473051684-0.124947305168369
1711.8711.9622088712592-0.0922088712591904
1811.9411.9565930305847-0.016593030584696
1911.8611.999565608895-0.139565608895017
2011.9211.9558526214309-0.0358526214308839
2111.8311.9781796348244-0.148179634824386
2211.9111.9203725888166-0.0103725888166366
2311.9311.9520307273081-0.0220307273080795
2411.9911.97506574942820.0149342505717822
2511.9612.0229142460069-0.0629142460068888
2612.1212.01705701286320.102942987136812
2711.8512.1241889998535-0.274188999853463
2812.0111.97255550739830.0374444926016633
2912.112.02603997218980.0739600278102284
3012.2112.10676182711950.103238172880548
3112.3112.21134525679170.0986547432082538
3212.3112.3174787889728-0.00747878897278298
3312.3912.35399773735690.036002262643148
3412.3512.420552880477-0.0705528804769635
3512.4112.4143146482294-0.00431464822944427
3612.5112.45110957604020.0588904239598236
3712.2712.5318676557248-0.261867655724838
3812.5112.39122109400120.118778905998836
3912.4412.5044795636216-0.0644795636216244
4012.4712.495162192803-0.0251621928029859
4112.5112.5103477941783-0.000347794178296112
4212.5812.54171302761230.0382869723876595
4312.512.600056601913-0.100056601913003
4412.5212.5635012030593-0.0435012030593001
4512.5912.56185530340810.0281446965919248
4612.5112.6082662596736-0.0982662596736059
4712.6712.56764873712710.102351262872933
4812.6412.6626802336909-0.0226802336908918
4912.5412.6750631906851-0.135063190685113
5012.612.6078793915198-0.00787939151983963
5112.6712.62334206425960.0466579357404058
5212.6212.6765475785091-0.0565475785091181
5312.7212.65979065823360.0602093417664218
5412.8512.72200935402960.127990645970396
5512.8512.83435900785390.0156409921460501
5612.8212.8741013144725-0.0541013144724527
5712.7912.8658342715644-0.075834271564446
5812.9412.83989172030440.10010827969556
5912.7112.9333902897645-0.223390289764458
6012.5612.8054668861694-0.245466886169371
6112.6412.6518346467177-0.0118346467176647
6212.712.65014262774270.0498573722573443
6312.7412.69101039753070.0489896024693213
6412.8512.73356703724950.116432962750507
6512.8412.82550201034070.0144979896593078
6612.8312.8515743800027-0.0215743800027237
6712.8812.85311017624570.0268898237542512
6813.0712.88751503552230.182484964477689
6912.9913.0318730610153-0.0418730610152682
7013.213.02787144175910.172128558240894
7113.2313.17146645629060.0585335437093697
7213.1813.2436158728609-0.0636158728609022







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7313.233113326659713.044949956695613.4212766966239
7413.264131027126813.034587881622313.4936741726313
7513.295148727593913.026211336759213.5640861184286
7613.32616642806113.018811077283613.6335217788384
7713.35718412852813.011843580274113.7025246767819
7813.388201828995113.004984224660513.7714194333297
7913.419219529462212.998025643116313.8404134158081
8013.450237229929212.990829098339813.9096453615187
8113.481254930396312.983298686404413.9792111743882
8213.512272630863412.975366565701314.0491786960255
8313.543290331330512.966983988110814.1195966745501
8413.574308031797512.958115593962514.1905004696326

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 13.2331133266597 & 13.0449499566956 & 13.4212766966239 \tabularnewline
74 & 13.2641310271268 & 13.0345878816223 & 13.4936741726313 \tabularnewline
75 & 13.2951487275939 & 13.0262113367592 & 13.5640861184286 \tabularnewline
76 & 13.326166428061 & 13.0188110772836 & 13.6335217788384 \tabularnewline
77 & 13.357184128528 & 13.0118435802741 & 13.7025246767819 \tabularnewline
78 & 13.3882018289951 & 13.0049842246605 & 13.7714194333297 \tabularnewline
79 & 13.4192195294622 & 12.9980256431163 & 13.8404134158081 \tabularnewline
80 & 13.4502372299292 & 12.9908290983398 & 13.9096453615187 \tabularnewline
81 & 13.4812549303963 & 12.9832986864044 & 13.9792111743882 \tabularnewline
82 & 13.5122726308634 & 12.9753665657013 & 14.0491786960255 \tabularnewline
83 & 13.5432903313305 & 12.9669839881108 & 14.1195966745501 \tabularnewline
84 & 13.5743080317975 & 12.9581155939625 & 14.1905004696326 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=208894&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]13.2331133266597[/C][C]13.0449499566956[/C][C]13.4212766966239[/C][/ROW]
[ROW][C]74[/C][C]13.2641310271268[/C][C]13.0345878816223[/C][C]13.4936741726313[/C][/ROW]
[ROW][C]75[/C][C]13.2951487275939[/C][C]13.0262113367592[/C][C]13.5640861184286[/C][/ROW]
[ROW][C]76[/C][C]13.326166428061[/C][C]13.0188110772836[/C][C]13.6335217788384[/C][/ROW]
[ROW][C]77[/C][C]13.357184128528[/C][C]13.0118435802741[/C][C]13.7025246767819[/C][/ROW]
[ROW][C]78[/C][C]13.3882018289951[/C][C]13.0049842246605[/C][C]13.7714194333297[/C][/ROW]
[ROW][C]79[/C][C]13.4192195294622[/C][C]12.9980256431163[/C][C]13.8404134158081[/C][/ROW]
[ROW][C]80[/C][C]13.4502372299292[/C][C]12.9908290983398[/C][C]13.9096453615187[/C][/ROW]
[ROW][C]81[/C][C]13.4812549303963[/C][C]12.9832986864044[/C][C]13.9792111743882[/C][/ROW]
[ROW][C]82[/C][C]13.5122726308634[/C][C]12.9753665657013[/C][C]14.0491786960255[/C][/ROW]
[ROW][C]83[/C][C]13.5432903313305[/C][C]12.9669839881108[/C][C]14.1195966745501[/C][/ROW]
[ROW][C]84[/C][C]13.5743080317975[/C][C]12.9581155939625[/C][C]14.1905004696326[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=208894&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=208894&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
7313.233113326659713.044949956695613.4212766966239
7413.264131027126813.034587881622313.4936741726313
7513.295148727593913.026211336759213.5640861184286
7613.32616642806113.018811077283613.6335217788384
7713.35718412852813.011843580274113.7025246767819
7813.388201828995113.004984224660513.7714194333297
7913.419219529462212.998025643116313.8404134158081
8013.450237229929212.990829098339813.9096453615187
8113.481254930396312.983298686404413.9792111743882
8213.512272630863412.975366565701314.0491786960255
8313.543290331330512.966983988110814.1195966745501
8413.574308031797512.958115593962514.1905004696326



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')