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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 24 Nov 2015 19:53:24 +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/2015/Nov/24/t1448394885k4pzot38i4top2j.htm/, Retrieved Tue, 14 May 2024 09:57:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284053, Retrieved Tue, 14 May 2024 09:57:36 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-11-24 19:53:24] [64c14b596f7fde091cf1a84a44b2a252] [Current]
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Dataseries X:
91,16
91,17
91,17
91,38
92,68
92,72
92,79
92,81
92,81
92,81
92,81
92,81
92,81
92,82
92,82
92,88
93,38
93,89
94,1
94,18
94,3
94,31
94,36
94,38
94,38
94,5
94,57
94,89
96,71
97,57
97,88
97,97
98,4
98,51
98,46
98,46
98,48
98,6
98,6
98,71
99,13
99,2
99,3
100,18
101,37
101,77
102,28
102,38
102,35
103,23
105,37
106,62
107
107,24
107,31
107,35
107,42
107,58
107,64
107,64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284053&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284053&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284053&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0986002315104745
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0986002315104745 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284053&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0986002315104745[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284053&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284053&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
alpha1
beta0.0986002315104745
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
391.1791.18-0.0100000000000051
491.3891.17901399768490.200986002315091
592.6891.40883126404351.27116873595648
692.7292.8341687956977-0.114168795697722
792.7992.8629117260107-0.0729117260106449
892.8192.9257226129462-0.115722612946172
992.8192.9343123365187-0.124312336518685
1092.8192.9220551113583-0.11205511135833
1192.8192.9110064514365-0.101006451436476
1292.8192.9010471919408-0.0910471919407883
1392.8192.892069917737-0.0820699177370443
1492.8292.8839778048481-0.0639778048481361
1592.8292.8876695784786-0.0676695784785721
1692.8892.8809973423744-0.000997342374361665
1793.3892.94089900418540.439100995814641
1893.8993.48419446402920.405805535970842
1994.194.03420698382410.0657930161758742
2094.1894.2506941904508-0.0706941904508227
2194.394.3237237269059-0.023723726905942
2294.3194.4413845619407-0.131384561940706
2394.3694.4384300137165-0.0784300137164706
2494.3894.4806967962066-0.100696796206648
2594.3894.4907680687883-0.110768068788303
2694.594.47984631156180.0201536884381852
2794.5794.6018334699076-0.0318334699076104
2894.8994.66869468240490.221305317595068
2996.7195.01051543795431.69948456204568
3097.5796.99808500922050.571914990779504
3197.8897.9144759597157-0.0344759597156639
3297.9798.2210766221062-0.251076622106154
3398.498.28632040903960.113679590960388
3498.5198.7275292430263-0.217529243026334
3598.4698.8160808093036-0.356080809303648
3698.4698.7309711590699-0.270971159069859
3798.4898.7042533400529-0.224253340052897
3898.698.7021419088067-0.102141908806701
3998.698.8120706929514-0.212070692951428
4098.7198.7911604735298-0.0811604735298346
4199.1398.89315803205030.236841967949715
4299.299.3365107049215-0.13651070492152
4399.399.3930507178126-0.0930507178126163
44100.1899.48387589549410.696124104505941
45101.37100.4325138933580.937486106641614
46101.77101.7149502405110.0550497594888952
47102.28102.1203781595410.159621840458712
48102.38102.646116909965-0.266116909964651
49102.35102.719877721033-0.369877721033291
50103.23102.6534076921090.576592307891175
51105.37103.5902598271541.77974017284593
52106.62105.9057426202250.714257379774835
53107107.226168563229-0.226168563229038
54107.24107.583868290534-0.34386829053426
55107.31107.789962797478-0.479962797478464
56107.35107.812638354531-0.462638354530682
57107.42107.807022105668-0.387022105668322
58107.58107.83886163645-0.258861636449765
59107.64107.973337819167-0.33333781916663
60107.64108.000470633026-0.360470633025599

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 91.17 & 91.18 & -0.0100000000000051 \tabularnewline
4 & 91.38 & 91.1790139976849 & 0.200986002315091 \tabularnewline
5 & 92.68 & 91.4088312640435 & 1.27116873595648 \tabularnewline
6 & 92.72 & 92.8341687956977 & -0.114168795697722 \tabularnewline
7 & 92.79 & 92.8629117260107 & -0.0729117260106449 \tabularnewline
8 & 92.81 & 92.9257226129462 & -0.115722612946172 \tabularnewline
9 & 92.81 & 92.9343123365187 & -0.124312336518685 \tabularnewline
10 & 92.81 & 92.9220551113583 & -0.11205511135833 \tabularnewline
11 & 92.81 & 92.9110064514365 & -0.101006451436476 \tabularnewline
12 & 92.81 & 92.9010471919408 & -0.0910471919407883 \tabularnewline
13 & 92.81 & 92.892069917737 & -0.0820699177370443 \tabularnewline
14 & 92.82 & 92.8839778048481 & -0.0639778048481361 \tabularnewline
15 & 92.82 & 92.8876695784786 & -0.0676695784785721 \tabularnewline
16 & 92.88 & 92.8809973423744 & -0.000997342374361665 \tabularnewline
17 & 93.38 & 92.9408990041854 & 0.439100995814641 \tabularnewline
18 & 93.89 & 93.4841944640292 & 0.405805535970842 \tabularnewline
19 & 94.1 & 94.0342069838241 & 0.0657930161758742 \tabularnewline
20 & 94.18 & 94.2506941904508 & -0.0706941904508227 \tabularnewline
21 & 94.3 & 94.3237237269059 & -0.023723726905942 \tabularnewline
22 & 94.31 & 94.4413845619407 & -0.131384561940706 \tabularnewline
23 & 94.36 & 94.4384300137165 & -0.0784300137164706 \tabularnewline
24 & 94.38 & 94.4806967962066 & -0.100696796206648 \tabularnewline
25 & 94.38 & 94.4907680687883 & -0.110768068788303 \tabularnewline
26 & 94.5 & 94.4798463115618 & 0.0201536884381852 \tabularnewline
27 & 94.57 & 94.6018334699076 & -0.0318334699076104 \tabularnewline
28 & 94.89 & 94.6686946824049 & 0.221305317595068 \tabularnewline
29 & 96.71 & 95.0105154379543 & 1.69948456204568 \tabularnewline
30 & 97.57 & 96.9980850092205 & 0.571914990779504 \tabularnewline
31 & 97.88 & 97.9144759597157 & -0.0344759597156639 \tabularnewline
32 & 97.97 & 98.2210766221062 & -0.251076622106154 \tabularnewline
33 & 98.4 & 98.2863204090396 & 0.113679590960388 \tabularnewline
34 & 98.51 & 98.7275292430263 & -0.217529243026334 \tabularnewline
35 & 98.46 & 98.8160808093036 & -0.356080809303648 \tabularnewline
36 & 98.46 & 98.7309711590699 & -0.270971159069859 \tabularnewline
37 & 98.48 & 98.7042533400529 & -0.224253340052897 \tabularnewline
38 & 98.6 & 98.7021419088067 & -0.102141908806701 \tabularnewline
39 & 98.6 & 98.8120706929514 & -0.212070692951428 \tabularnewline
40 & 98.71 & 98.7911604735298 & -0.0811604735298346 \tabularnewline
41 & 99.13 & 98.8931580320503 & 0.236841967949715 \tabularnewline
42 & 99.2 & 99.3365107049215 & -0.13651070492152 \tabularnewline
43 & 99.3 & 99.3930507178126 & -0.0930507178126163 \tabularnewline
44 & 100.18 & 99.4838758954941 & 0.696124104505941 \tabularnewline
45 & 101.37 & 100.432513893358 & 0.937486106641614 \tabularnewline
46 & 101.77 & 101.714950240511 & 0.0550497594888952 \tabularnewline
47 & 102.28 & 102.120378159541 & 0.159621840458712 \tabularnewline
48 & 102.38 & 102.646116909965 & -0.266116909964651 \tabularnewline
49 & 102.35 & 102.719877721033 & -0.369877721033291 \tabularnewline
50 & 103.23 & 102.653407692109 & 0.576592307891175 \tabularnewline
51 & 105.37 & 103.590259827154 & 1.77974017284593 \tabularnewline
52 & 106.62 & 105.905742620225 & 0.714257379774835 \tabularnewline
53 & 107 & 107.226168563229 & -0.226168563229038 \tabularnewline
54 & 107.24 & 107.583868290534 & -0.34386829053426 \tabularnewline
55 & 107.31 & 107.789962797478 & -0.479962797478464 \tabularnewline
56 & 107.35 & 107.812638354531 & -0.462638354530682 \tabularnewline
57 & 107.42 & 107.807022105668 & -0.387022105668322 \tabularnewline
58 & 107.58 & 107.83886163645 & -0.258861636449765 \tabularnewline
59 & 107.64 & 107.973337819167 & -0.33333781916663 \tabularnewline
60 & 107.64 & 108.000470633026 & -0.360470633025599 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284053&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]91.17[/C][C]91.18[/C][C]-0.0100000000000051[/C][/ROW]
[ROW][C]4[/C][C]91.38[/C][C]91.1790139976849[/C][C]0.200986002315091[/C][/ROW]
[ROW][C]5[/C][C]92.68[/C][C]91.4088312640435[/C][C]1.27116873595648[/C][/ROW]
[ROW][C]6[/C][C]92.72[/C][C]92.8341687956977[/C][C]-0.114168795697722[/C][/ROW]
[ROW][C]7[/C][C]92.79[/C][C]92.8629117260107[/C][C]-0.0729117260106449[/C][/ROW]
[ROW][C]8[/C][C]92.81[/C][C]92.9257226129462[/C][C]-0.115722612946172[/C][/ROW]
[ROW][C]9[/C][C]92.81[/C][C]92.9343123365187[/C][C]-0.124312336518685[/C][/ROW]
[ROW][C]10[/C][C]92.81[/C][C]92.9220551113583[/C][C]-0.11205511135833[/C][/ROW]
[ROW][C]11[/C][C]92.81[/C][C]92.9110064514365[/C][C]-0.101006451436476[/C][/ROW]
[ROW][C]12[/C][C]92.81[/C][C]92.9010471919408[/C][C]-0.0910471919407883[/C][/ROW]
[ROW][C]13[/C][C]92.81[/C][C]92.892069917737[/C][C]-0.0820699177370443[/C][/ROW]
[ROW][C]14[/C][C]92.82[/C][C]92.8839778048481[/C][C]-0.0639778048481361[/C][/ROW]
[ROW][C]15[/C][C]92.82[/C][C]92.8876695784786[/C][C]-0.0676695784785721[/C][/ROW]
[ROW][C]16[/C][C]92.88[/C][C]92.8809973423744[/C][C]-0.000997342374361665[/C][/ROW]
[ROW][C]17[/C][C]93.38[/C][C]92.9408990041854[/C][C]0.439100995814641[/C][/ROW]
[ROW][C]18[/C][C]93.89[/C][C]93.4841944640292[/C][C]0.405805535970842[/C][/ROW]
[ROW][C]19[/C][C]94.1[/C][C]94.0342069838241[/C][C]0.0657930161758742[/C][/ROW]
[ROW][C]20[/C][C]94.18[/C][C]94.2506941904508[/C][C]-0.0706941904508227[/C][/ROW]
[ROW][C]21[/C][C]94.3[/C][C]94.3237237269059[/C][C]-0.023723726905942[/C][/ROW]
[ROW][C]22[/C][C]94.31[/C][C]94.4413845619407[/C][C]-0.131384561940706[/C][/ROW]
[ROW][C]23[/C][C]94.36[/C][C]94.4384300137165[/C][C]-0.0784300137164706[/C][/ROW]
[ROW][C]24[/C][C]94.38[/C][C]94.4806967962066[/C][C]-0.100696796206648[/C][/ROW]
[ROW][C]25[/C][C]94.38[/C][C]94.4907680687883[/C][C]-0.110768068788303[/C][/ROW]
[ROW][C]26[/C][C]94.5[/C][C]94.4798463115618[/C][C]0.0201536884381852[/C][/ROW]
[ROW][C]27[/C][C]94.57[/C][C]94.6018334699076[/C][C]-0.0318334699076104[/C][/ROW]
[ROW][C]28[/C][C]94.89[/C][C]94.6686946824049[/C][C]0.221305317595068[/C][/ROW]
[ROW][C]29[/C][C]96.71[/C][C]95.0105154379543[/C][C]1.69948456204568[/C][/ROW]
[ROW][C]30[/C][C]97.57[/C][C]96.9980850092205[/C][C]0.571914990779504[/C][/ROW]
[ROW][C]31[/C][C]97.88[/C][C]97.9144759597157[/C][C]-0.0344759597156639[/C][/ROW]
[ROW][C]32[/C][C]97.97[/C][C]98.2210766221062[/C][C]-0.251076622106154[/C][/ROW]
[ROW][C]33[/C][C]98.4[/C][C]98.2863204090396[/C][C]0.113679590960388[/C][/ROW]
[ROW][C]34[/C][C]98.51[/C][C]98.7275292430263[/C][C]-0.217529243026334[/C][/ROW]
[ROW][C]35[/C][C]98.46[/C][C]98.8160808093036[/C][C]-0.356080809303648[/C][/ROW]
[ROW][C]36[/C][C]98.46[/C][C]98.7309711590699[/C][C]-0.270971159069859[/C][/ROW]
[ROW][C]37[/C][C]98.48[/C][C]98.7042533400529[/C][C]-0.224253340052897[/C][/ROW]
[ROW][C]38[/C][C]98.6[/C][C]98.7021419088067[/C][C]-0.102141908806701[/C][/ROW]
[ROW][C]39[/C][C]98.6[/C][C]98.8120706929514[/C][C]-0.212070692951428[/C][/ROW]
[ROW][C]40[/C][C]98.71[/C][C]98.7911604735298[/C][C]-0.0811604735298346[/C][/ROW]
[ROW][C]41[/C][C]99.13[/C][C]98.8931580320503[/C][C]0.236841967949715[/C][/ROW]
[ROW][C]42[/C][C]99.2[/C][C]99.3365107049215[/C][C]-0.13651070492152[/C][/ROW]
[ROW][C]43[/C][C]99.3[/C][C]99.3930507178126[/C][C]-0.0930507178126163[/C][/ROW]
[ROW][C]44[/C][C]100.18[/C][C]99.4838758954941[/C][C]0.696124104505941[/C][/ROW]
[ROW][C]45[/C][C]101.37[/C][C]100.432513893358[/C][C]0.937486106641614[/C][/ROW]
[ROW][C]46[/C][C]101.77[/C][C]101.714950240511[/C][C]0.0550497594888952[/C][/ROW]
[ROW][C]47[/C][C]102.28[/C][C]102.120378159541[/C][C]0.159621840458712[/C][/ROW]
[ROW][C]48[/C][C]102.38[/C][C]102.646116909965[/C][C]-0.266116909964651[/C][/ROW]
[ROW][C]49[/C][C]102.35[/C][C]102.719877721033[/C][C]-0.369877721033291[/C][/ROW]
[ROW][C]50[/C][C]103.23[/C][C]102.653407692109[/C][C]0.576592307891175[/C][/ROW]
[ROW][C]51[/C][C]105.37[/C][C]103.590259827154[/C][C]1.77974017284593[/C][/ROW]
[ROW][C]52[/C][C]106.62[/C][C]105.905742620225[/C][C]0.714257379774835[/C][/ROW]
[ROW][C]53[/C][C]107[/C][C]107.226168563229[/C][C]-0.226168563229038[/C][/ROW]
[ROW][C]54[/C][C]107.24[/C][C]107.583868290534[/C][C]-0.34386829053426[/C][/ROW]
[ROW][C]55[/C][C]107.31[/C][C]107.789962797478[/C][C]-0.479962797478464[/C][/ROW]
[ROW][C]56[/C][C]107.35[/C][C]107.812638354531[/C][C]-0.462638354530682[/C][/ROW]
[ROW][C]57[/C][C]107.42[/C][C]107.807022105668[/C][C]-0.387022105668322[/C][/ROW]
[ROW][C]58[/C][C]107.58[/C][C]107.83886163645[/C][C]-0.258861636449765[/C][/ROW]
[ROW][C]59[/C][C]107.64[/C][C]107.973337819167[/C][C]-0.33333781916663[/C][/ROW]
[ROW][C]60[/C][C]107.64[/C][C]108.000470633026[/C][C]-0.360470633025599[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284053&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284053&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
391.1791.18-0.0100000000000051
491.3891.17901399768490.200986002315091
592.6891.40883126404351.27116873595648
692.7292.8341687956977-0.114168795697722
792.7992.8629117260107-0.0729117260106449
892.8192.9257226129462-0.115722612946172
992.8192.9343123365187-0.124312336518685
1092.8192.9220551113583-0.11205511135833
1192.8192.9110064514365-0.101006451436476
1292.8192.9010471919408-0.0910471919407883
1392.8192.892069917737-0.0820699177370443
1492.8292.8839778048481-0.0639778048481361
1592.8292.8876695784786-0.0676695784785721
1692.8892.8809973423744-0.000997342374361665
1793.3892.94089900418540.439100995814641
1893.8993.48419446402920.405805535970842
1994.194.03420698382410.0657930161758742
2094.1894.2506941904508-0.0706941904508227
2194.394.3237237269059-0.023723726905942
2294.3194.4413845619407-0.131384561940706
2394.3694.4384300137165-0.0784300137164706
2494.3894.4806967962066-0.100696796206648
2594.3894.4907680687883-0.110768068788303
2694.594.47984631156180.0201536884381852
2794.5794.6018334699076-0.0318334699076104
2894.8994.66869468240490.221305317595068
2996.7195.01051543795431.69948456204568
3097.5796.99808500922050.571914990779504
3197.8897.9144759597157-0.0344759597156639
3297.9798.2210766221062-0.251076622106154
3398.498.28632040903960.113679590960388
3498.5198.7275292430263-0.217529243026334
3598.4698.8160808093036-0.356080809303648
3698.4698.7309711590699-0.270971159069859
3798.4898.7042533400529-0.224253340052897
3898.698.7021419088067-0.102141908806701
3998.698.8120706929514-0.212070692951428
4098.7198.7911604735298-0.0811604735298346
4199.1398.89315803205030.236841967949715
4299.299.3365107049215-0.13651070492152
4399.399.3930507178126-0.0930507178126163
44100.1899.48387589549410.696124104505941
45101.37100.4325138933580.937486106641614
46101.77101.7149502405110.0550497594888952
47102.28102.1203781595410.159621840458712
48102.38102.646116909965-0.266116909964651
49102.35102.719877721033-0.369877721033291
50103.23102.6534076921090.576592307891175
51105.37103.5902598271541.77974017284593
52106.62105.9057426202250.714257379774835
53107107.226168563229-0.226168563229038
54107.24107.583868290534-0.34386829053426
55107.31107.789962797478-0.479962797478464
56107.35107.812638354531-0.462638354530682
57107.42107.807022105668-0.387022105668322
58107.58107.83886163645-0.258861636449765
59107.64107.973337819167-0.33333781916663
60107.64108.000470633026-0.360470633025599







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
61107.964928145157107.048753060864108.881103229449
62108.289856290313106.92881276174109.650899818887
63108.61478443547106.866783017712110.362785853227
64108.939712580626106.826680151577111.052745009675
65109.264640725783106.795440124868111.733841326698
66109.589568870939106.766810203921112.412327537958
67109.914497016096106.737348679629113.091645352562
68110.239425161252106.704996262785113.773854059719
69110.564353306409106.668453461297114.460253151521
70110.889281451566106.626871769462115.15169113367
71111.214209596722106.579685826704115.84873336674
72111.539137741879106.526515744844116.551759738913

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 107.964928145157 & 107.048753060864 & 108.881103229449 \tabularnewline
62 & 108.289856290313 & 106.92881276174 & 109.650899818887 \tabularnewline
63 & 108.61478443547 & 106.866783017712 & 110.362785853227 \tabularnewline
64 & 108.939712580626 & 106.826680151577 & 111.052745009675 \tabularnewline
65 & 109.264640725783 & 106.795440124868 & 111.733841326698 \tabularnewline
66 & 109.589568870939 & 106.766810203921 & 112.412327537958 \tabularnewline
67 & 109.914497016096 & 106.737348679629 & 113.091645352562 \tabularnewline
68 & 110.239425161252 & 106.704996262785 & 113.773854059719 \tabularnewline
69 & 110.564353306409 & 106.668453461297 & 114.460253151521 \tabularnewline
70 & 110.889281451566 & 106.626871769462 & 115.15169113367 \tabularnewline
71 & 111.214209596722 & 106.579685826704 & 115.84873336674 \tabularnewline
72 & 111.539137741879 & 106.526515744844 & 116.551759738913 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284053&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]107.964928145157[/C][C]107.048753060864[/C][C]108.881103229449[/C][/ROW]
[ROW][C]62[/C][C]108.289856290313[/C][C]106.92881276174[/C][C]109.650899818887[/C][/ROW]
[ROW][C]63[/C][C]108.61478443547[/C][C]106.866783017712[/C][C]110.362785853227[/C][/ROW]
[ROW][C]64[/C][C]108.939712580626[/C][C]106.826680151577[/C][C]111.052745009675[/C][/ROW]
[ROW][C]65[/C][C]109.264640725783[/C][C]106.795440124868[/C][C]111.733841326698[/C][/ROW]
[ROW][C]66[/C][C]109.589568870939[/C][C]106.766810203921[/C][C]112.412327537958[/C][/ROW]
[ROW][C]67[/C][C]109.914497016096[/C][C]106.737348679629[/C][C]113.091645352562[/C][/ROW]
[ROW][C]68[/C][C]110.239425161252[/C][C]106.704996262785[/C][C]113.773854059719[/C][/ROW]
[ROW][C]69[/C][C]110.564353306409[/C][C]106.668453461297[/C][C]114.460253151521[/C][/ROW]
[ROW][C]70[/C][C]110.889281451566[/C][C]106.626871769462[/C][C]115.15169113367[/C][/ROW]
[ROW][C]71[/C][C]111.214209596722[/C][C]106.579685826704[/C][C]115.84873336674[/C][/ROW]
[ROW][C]72[/C][C]111.539137741879[/C][C]106.526515744844[/C][C]116.551759738913[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284053&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284053&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
61107.964928145157107.048753060864108.881103229449
62108.289856290313106.92881276174109.650899818887
63108.61478443547106.866783017712110.362785853227
64108.939712580626106.826680151577111.052745009675
65109.264640725783106.795440124868111.733841326698
66109.589568870939106.766810203921112.412327537958
67109.914497016096106.737348679629113.091645352562
68110.239425161252106.704996262785113.773854059719
69110.564353306409106.668453461297114.460253151521
70110.889281451566106.626871769462115.15169113367
71111.214209596722106.579685826704115.84873336674
72111.539137741879106.526515744844116.551759738913



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
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')