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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 09:44:56 -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/2009/Jun/02/t12439575339kyaz6ceny42vfj.htm/, Retrieved Fri, 10 May 2024 16:22:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41289, Retrieved Fri, 10 May 2024 16:22:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponentiol smoot...] [2009-06-02 15:44:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
106.07
106.07
106.07
106.07
106.07
106.2
107.5
108.31
108.53
108.61
108.62
108.62
108.62
108.62
110.1
110.74
110.77
110.77
110.78
110.78
110.78
110.84
110.84
110.84
110.84
110.84
111.01
112.66
114.04
114.16
114.2
114.2
114.23
114.23
114.23
114.23
114.23
114.23
115.97
116.96
117.08
117.08
117.08
117.63
119.12
119.47
119.5
119.52
119.49
119.49
119.5
119.5
119.56
122.35
122.92
122.92
123.04
123.04
123.04
123.06
123.33
128.21
129.57
129.79
131.66
135.01
136.01
136.31
136.37
136.4
136.4
136.4
137.34
142.18
143.79
144.08
144.08
144.09
144.09
144.11
144.11
144.15
144.15
144.16
144.2
144.38
144.38
144.28
144.46
144.53
144.53
145.34
147.98
150.42
150.53
150.64





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=41289&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=41289&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41289&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.912394349585859
beta0.0280522073302993
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.912394349585859 \tabularnewline
beta & 0.0280522073302993 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41289&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]0.912394349585859[/C][/ROW]
[ROW][C]beta[/C][C]0.0280522073302993[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41289&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41289&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
alpha0.912394349585859
beta0.0280522073302993
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13108.62106.5169884203352.10301157966508
14108.62108.5321032689030.0878967310965066
15110.1110.234617744641-0.134617744641417
16110.74110.901450987309-0.161450987309451
17110.77110.930653037448-0.160653037448185
18110.77110.926647260655-0.156647260654680
19110.78110.787947354488-0.00794735448762651
20110.78111.719939359441-0.939939359441027
21110.78111.105905222161-0.325905222160614
22110.84110.8104042216860.029595778314075
23110.84110.7404955589460.0995044410535684
24110.84110.7313802715620.108619728438001
25110.84110.981899150867-0.141899150866962
26110.84110.7207984735410.119201526458681
27111.01112.415447209349-1.40544720934903
28112.66111.8491834016530.810816598347444
29114.04112.7124222068091.32757779319113
30114.16114.0489402795790.111059720421025
31114.2114.1526613251180.0473386748822264
32114.2115.065099160724-0.865099160723517
33114.23114.570732180148-0.34073218014764
34114.23114.282120240736-0.0521202407359311
35114.23114.1273900851900.102609914809790
36114.23114.1053593405240.124640659475560
37114.23114.339315024196-0.10931502419551
38114.23114.1152403379510.114759662049394
39115.97115.7025757893280.267424210672488
40116.96116.9246500960310.035349903969248
41117.08117.139651691333-0.0596516913332152
42117.08117.080106413129-0.000106413129444149
43117.08117.0499685103640.0300314896364142
44117.63117.858802189427-0.228802189426958
45119.12117.9892398962851.13076010371493
46119.47119.0930612541960.376938745804239
47119.5119.3715384357940.128461564205878
48119.52119.4025290795660.117470920433689
49119.49119.646361181752-0.156361181752075
50119.49119.4252939807280.0647060192721369
51119.5121.079187694063-1.57918769406268
52119.5120.613136997018-1.11313699701826
53119.56119.735993557495-0.175993557494678
54122.35119.5331745217432.8168254782574
55122.92122.0978632660390.82213673396123
56122.92123.685780969789-0.765780969789162
57123.04123.494749552160-0.454749552159853
58123.04123.077507473430-0.0375074734297982
59123.04122.9351853461740.104814653826082
60123.06122.9222637263760.137736273624370
61123.33123.1455903584590.184409641541293
62128.21123.2426466066094.96735339339098
63129.57129.4281535689540.141846431046389
64129.79130.804727386048-1.01472738604818
65131.66130.2696649080331.39033509196744
66135.01131.9623923834153.04760761658491
67136.01134.7294654933541.28053450664638
68136.31136.863746972248-0.553746972247865
69136.37137.152179022137-0.782179022136518
70136.4136.669465768531-0.269465768530750
71136.4136.504127863033-0.104127863033256
72136.4136.472284947038-0.0722849470375877
73137.34136.6934024941460.646597505854146
74142.18137.8374069788834.34259302111724
75143.79143.3180055923030.471994407697025
76144.08145.183920713335-1.10392071333521
77144.08145.008404497298-0.928404497297578
78144.09144.887975793587-0.797975793586716
79144.09143.9974211442780.0925788557218539
80144.11144.925313799889-0.815313799889253
81144.11144.985009562717-0.875009562716826
82144.15144.462951067344-0.312951067344301
83144.15144.261999563211-0.111999563210901
84144.16144.213755672225-0.0537556722247245
85144.2144.519250742944-0.319250742944433
86144.38145.101504902410-0.721504902409691
87144.38145.490871864122-1.11087186412220
88144.28145.595826178109-1.31582617810915
89144.46145.055643725257-0.595643725257219
90144.53145.07194655305-0.541946553050053
91144.53144.3197629524640.210237047535742
92145.34145.1074877269420.232512273057523
93147.98145.9778279979502.00217200205046
94150.42148.0560889055612.36391109443937
95150.53150.2965974087760.233402591223864
96150.64150.5562767927800.083723207220146

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 108.62 & 106.516988420335 & 2.10301157966508 \tabularnewline
14 & 108.62 & 108.532103268903 & 0.0878967310965066 \tabularnewline
15 & 110.1 & 110.234617744641 & -0.134617744641417 \tabularnewline
16 & 110.74 & 110.901450987309 & -0.161450987309451 \tabularnewline
17 & 110.77 & 110.930653037448 & -0.160653037448185 \tabularnewline
18 & 110.77 & 110.926647260655 & -0.156647260654680 \tabularnewline
19 & 110.78 & 110.787947354488 & -0.00794735448762651 \tabularnewline
20 & 110.78 & 111.719939359441 & -0.939939359441027 \tabularnewline
21 & 110.78 & 111.105905222161 & -0.325905222160614 \tabularnewline
22 & 110.84 & 110.810404221686 & 0.029595778314075 \tabularnewline
23 & 110.84 & 110.740495558946 & 0.0995044410535684 \tabularnewline
24 & 110.84 & 110.731380271562 & 0.108619728438001 \tabularnewline
25 & 110.84 & 110.981899150867 & -0.141899150866962 \tabularnewline
26 & 110.84 & 110.720798473541 & 0.119201526458681 \tabularnewline
27 & 111.01 & 112.415447209349 & -1.40544720934903 \tabularnewline
28 & 112.66 & 111.849183401653 & 0.810816598347444 \tabularnewline
29 & 114.04 & 112.712422206809 & 1.32757779319113 \tabularnewline
30 & 114.16 & 114.048940279579 & 0.111059720421025 \tabularnewline
31 & 114.2 & 114.152661325118 & 0.0473386748822264 \tabularnewline
32 & 114.2 & 115.065099160724 & -0.865099160723517 \tabularnewline
33 & 114.23 & 114.570732180148 & -0.34073218014764 \tabularnewline
34 & 114.23 & 114.282120240736 & -0.0521202407359311 \tabularnewline
35 & 114.23 & 114.127390085190 & 0.102609914809790 \tabularnewline
36 & 114.23 & 114.105359340524 & 0.124640659475560 \tabularnewline
37 & 114.23 & 114.339315024196 & -0.10931502419551 \tabularnewline
38 & 114.23 & 114.115240337951 & 0.114759662049394 \tabularnewline
39 & 115.97 & 115.702575789328 & 0.267424210672488 \tabularnewline
40 & 116.96 & 116.924650096031 & 0.035349903969248 \tabularnewline
41 & 117.08 & 117.139651691333 & -0.0596516913332152 \tabularnewline
42 & 117.08 & 117.080106413129 & -0.000106413129444149 \tabularnewline
43 & 117.08 & 117.049968510364 & 0.0300314896364142 \tabularnewline
44 & 117.63 & 117.858802189427 & -0.228802189426958 \tabularnewline
45 & 119.12 & 117.989239896285 & 1.13076010371493 \tabularnewline
46 & 119.47 & 119.093061254196 & 0.376938745804239 \tabularnewline
47 & 119.5 & 119.371538435794 & 0.128461564205878 \tabularnewline
48 & 119.52 & 119.402529079566 & 0.117470920433689 \tabularnewline
49 & 119.49 & 119.646361181752 & -0.156361181752075 \tabularnewline
50 & 119.49 & 119.425293980728 & 0.0647060192721369 \tabularnewline
51 & 119.5 & 121.079187694063 & -1.57918769406268 \tabularnewline
52 & 119.5 & 120.613136997018 & -1.11313699701826 \tabularnewline
53 & 119.56 & 119.735993557495 & -0.175993557494678 \tabularnewline
54 & 122.35 & 119.533174521743 & 2.8168254782574 \tabularnewline
55 & 122.92 & 122.097863266039 & 0.82213673396123 \tabularnewline
56 & 122.92 & 123.685780969789 & -0.765780969789162 \tabularnewline
57 & 123.04 & 123.494749552160 & -0.454749552159853 \tabularnewline
58 & 123.04 & 123.077507473430 & -0.0375074734297982 \tabularnewline
59 & 123.04 & 122.935185346174 & 0.104814653826082 \tabularnewline
60 & 123.06 & 122.922263726376 & 0.137736273624370 \tabularnewline
61 & 123.33 & 123.145590358459 & 0.184409641541293 \tabularnewline
62 & 128.21 & 123.242646606609 & 4.96735339339098 \tabularnewline
63 & 129.57 & 129.428153568954 & 0.141846431046389 \tabularnewline
64 & 129.79 & 130.804727386048 & -1.01472738604818 \tabularnewline
65 & 131.66 & 130.269664908033 & 1.39033509196744 \tabularnewline
66 & 135.01 & 131.962392383415 & 3.04760761658491 \tabularnewline
67 & 136.01 & 134.729465493354 & 1.28053450664638 \tabularnewline
68 & 136.31 & 136.863746972248 & -0.553746972247865 \tabularnewline
69 & 136.37 & 137.152179022137 & -0.782179022136518 \tabularnewline
70 & 136.4 & 136.669465768531 & -0.269465768530750 \tabularnewline
71 & 136.4 & 136.504127863033 & -0.104127863033256 \tabularnewline
72 & 136.4 & 136.472284947038 & -0.0722849470375877 \tabularnewline
73 & 137.34 & 136.693402494146 & 0.646597505854146 \tabularnewline
74 & 142.18 & 137.837406978883 & 4.34259302111724 \tabularnewline
75 & 143.79 & 143.318005592303 & 0.471994407697025 \tabularnewline
76 & 144.08 & 145.183920713335 & -1.10392071333521 \tabularnewline
77 & 144.08 & 145.008404497298 & -0.928404497297578 \tabularnewline
78 & 144.09 & 144.887975793587 & -0.797975793586716 \tabularnewline
79 & 144.09 & 143.997421144278 & 0.0925788557218539 \tabularnewline
80 & 144.11 & 144.925313799889 & -0.815313799889253 \tabularnewline
81 & 144.11 & 144.985009562717 & -0.875009562716826 \tabularnewline
82 & 144.15 & 144.462951067344 & -0.312951067344301 \tabularnewline
83 & 144.15 & 144.261999563211 & -0.111999563210901 \tabularnewline
84 & 144.16 & 144.213755672225 & -0.0537556722247245 \tabularnewline
85 & 144.2 & 144.519250742944 & -0.319250742944433 \tabularnewline
86 & 144.38 & 145.101504902410 & -0.721504902409691 \tabularnewline
87 & 144.38 & 145.490871864122 & -1.11087186412220 \tabularnewline
88 & 144.28 & 145.595826178109 & -1.31582617810915 \tabularnewline
89 & 144.46 & 145.055643725257 & -0.595643725257219 \tabularnewline
90 & 144.53 & 145.07194655305 & -0.541946553050053 \tabularnewline
91 & 144.53 & 144.319762952464 & 0.210237047535742 \tabularnewline
92 & 145.34 & 145.107487726942 & 0.232512273057523 \tabularnewline
93 & 147.98 & 145.977827997950 & 2.00217200205046 \tabularnewline
94 & 150.42 & 148.056088905561 & 2.36391109443937 \tabularnewline
95 & 150.53 & 150.296597408776 & 0.233402591223864 \tabularnewline
96 & 150.64 & 150.556276792780 & 0.083723207220146 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41289&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]108.62[/C][C]106.516988420335[/C][C]2.10301157966508[/C][/ROW]
[ROW][C]14[/C][C]108.62[/C][C]108.532103268903[/C][C]0.0878967310965066[/C][/ROW]
[ROW][C]15[/C][C]110.1[/C][C]110.234617744641[/C][C]-0.134617744641417[/C][/ROW]
[ROW][C]16[/C][C]110.74[/C][C]110.901450987309[/C][C]-0.161450987309451[/C][/ROW]
[ROW][C]17[/C][C]110.77[/C][C]110.930653037448[/C][C]-0.160653037448185[/C][/ROW]
[ROW][C]18[/C][C]110.77[/C][C]110.926647260655[/C][C]-0.156647260654680[/C][/ROW]
[ROW][C]19[/C][C]110.78[/C][C]110.787947354488[/C][C]-0.00794735448762651[/C][/ROW]
[ROW][C]20[/C][C]110.78[/C][C]111.719939359441[/C][C]-0.939939359441027[/C][/ROW]
[ROW][C]21[/C][C]110.78[/C][C]111.105905222161[/C][C]-0.325905222160614[/C][/ROW]
[ROW][C]22[/C][C]110.84[/C][C]110.810404221686[/C][C]0.029595778314075[/C][/ROW]
[ROW][C]23[/C][C]110.84[/C][C]110.740495558946[/C][C]0.0995044410535684[/C][/ROW]
[ROW][C]24[/C][C]110.84[/C][C]110.731380271562[/C][C]0.108619728438001[/C][/ROW]
[ROW][C]25[/C][C]110.84[/C][C]110.981899150867[/C][C]-0.141899150866962[/C][/ROW]
[ROW][C]26[/C][C]110.84[/C][C]110.720798473541[/C][C]0.119201526458681[/C][/ROW]
[ROW][C]27[/C][C]111.01[/C][C]112.415447209349[/C][C]-1.40544720934903[/C][/ROW]
[ROW][C]28[/C][C]112.66[/C][C]111.849183401653[/C][C]0.810816598347444[/C][/ROW]
[ROW][C]29[/C][C]114.04[/C][C]112.712422206809[/C][C]1.32757779319113[/C][/ROW]
[ROW][C]30[/C][C]114.16[/C][C]114.048940279579[/C][C]0.111059720421025[/C][/ROW]
[ROW][C]31[/C][C]114.2[/C][C]114.152661325118[/C][C]0.0473386748822264[/C][/ROW]
[ROW][C]32[/C][C]114.2[/C][C]115.065099160724[/C][C]-0.865099160723517[/C][/ROW]
[ROW][C]33[/C][C]114.23[/C][C]114.570732180148[/C][C]-0.34073218014764[/C][/ROW]
[ROW][C]34[/C][C]114.23[/C][C]114.282120240736[/C][C]-0.0521202407359311[/C][/ROW]
[ROW][C]35[/C][C]114.23[/C][C]114.127390085190[/C][C]0.102609914809790[/C][/ROW]
[ROW][C]36[/C][C]114.23[/C][C]114.105359340524[/C][C]0.124640659475560[/C][/ROW]
[ROW][C]37[/C][C]114.23[/C][C]114.339315024196[/C][C]-0.10931502419551[/C][/ROW]
[ROW][C]38[/C][C]114.23[/C][C]114.115240337951[/C][C]0.114759662049394[/C][/ROW]
[ROW][C]39[/C][C]115.97[/C][C]115.702575789328[/C][C]0.267424210672488[/C][/ROW]
[ROW][C]40[/C][C]116.96[/C][C]116.924650096031[/C][C]0.035349903969248[/C][/ROW]
[ROW][C]41[/C][C]117.08[/C][C]117.139651691333[/C][C]-0.0596516913332152[/C][/ROW]
[ROW][C]42[/C][C]117.08[/C][C]117.080106413129[/C][C]-0.000106413129444149[/C][/ROW]
[ROW][C]43[/C][C]117.08[/C][C]117.049968510364[/C][C]0.0300314896364142[/C][/ROW]
[ROW][C]44[/C][C]117.63[/C][C]117.858802189427[/C][C]-0.228802189426958[/C][/ROW]
[ROW][C]45[/C][C]119.12[/C][C]117.989239896285[/C][C]1.13076010371493[/C][/ROW]
[ROW][C]46[/C][C]119.47[/C][C]119.093061254196[/C][C]0.376938745804239[/C][/ROW]
[ROW][C]47[/C][C]119.5[/C][C]119.371538435794[/C][C]0.128461564205878[/C][/ROW]
[ROW][C]48[/C][C]119.52[/C][C]119.402529079566[/C][C]0.117470920433689[/C][/ROW]
[ROW][C]49[/C][C]119.49[/C][C]119.646361181752[/C][C]-0.156361181752075[/C][/ROW]
[ROW][C]50[/C][C]119.49[/C][C]119.425293980728[/C][C]0.0647060192721369[/C][/ROW]
[ROW][C]51[/C][C]119.5[/C][C]121.079187694063[/C][C]-1.57918769406268[/C][/ROW]
[ROW][C]52[/C][C]119.5[/C][C]120.613136997018[/C][C]-1.11313699701826[/C][/ROW]
[ROW][C]53[/C][C]119.56[/C][C]119.735993557495[/C][C]-0.175993557494678[/C][/ROW]
[ROW][C]54[/C][C]122.35[/C][C]119.533174521743[/C][C]2.8168254782574[/C][/ROW]
[ROW][C]55[/C][C]122.92[/C][C]122.097863266039[/C][C]0.82213673396123[/C][/ROW]
[ROW][C]56[/C][C]122.92[/C][C]123.685780969789[/C][C]-0.765780969789162[/C][/ROW]
[ROW][C]57[/C][C]123.04[/C][C]123.494749552160[/C][C]-0.454749552159853[/C][/ROW]
[ROW][C]58[/C][C]123.04[/C][C]123.077507473430[/C][C]-0.0375074734297982[/C][/ROW]
[ROW][C]59[/C][C]123.04[/C][C]122.935185346174[/C][C]0.104814653826082[/C][/ROW]
[ROW][C]60[/C][C]123.06[/C][C]122.922263726376[/C][C]0.137736273624370[/C][/ROW]
[ROW][C]61[/C][C]123.33[/C][C]123.145590358459[/C][C]0.184409641541293[/C][/ROW]
[ROW][C]62[/C][C]128.21[/C][C]123.242646606609[/C][C]4.96735339339098[/C][/ROW]
[ROW][C]63[/C][C]129.57[/C][C]129.428153568954[/C][C]0.141846431046389[/C][/ROW]
[ROW][C]64[/C][C]129.79[/C][C]130.804727386048[/C][C]-1.01472738604818[/C][/ROW]
[ROW][C]65[/C][C]131.66[/C][C]130.269664908033[/C][C]1.39033509196744[/C][/ROW]
[ROW][C]66[/C][C]135.01[/C][C]131.962392383415[/C][C]3.04760761658491[/C][/ROW]
[ROW][C]67[/C][C]136.01[/C][C]134.729465493354[/C][C]1.28053450664638[/C][/ROW]
[ROW][C]68[/C][C]136.31[/C][C]136.863746972248[/C][C]-0.553746972247865[/C][/ROW]
[ROW][C]69[/C][C]136.37[/C][C]137.152179022137[/C][C]-0.782179022136518[/C][/ROW]
[ROW][C]70[/C][C]136.4[/C][C]136.669465768531[/C][C]-0.269465768530750[/C][/ROW]
[ROW][C]71[/C][C]136.4[/C][C]136.504127863033[/C][C]-0.104127863033256[/C][/ROW]
[ROW][C]72[/C][C]136.4[/C][C]136.472284947038[/C][C]-0.0722849470375877[/C][/ROW]
[ROW][C]73[/C][C]137.34[/C][C]136.693402494146[/C][C]0.646597505854146[/C][/ROW]
[ROW][C]74[/C][C]142.18[/C][C]137.837406978883[/C][C]4.34259302111724[/C][/ROW]
[ROW][C]75[/C][C]143.79[/C][C]143.318005592303[/C][C]0.471994407697025[/C][/ROW]
[ROW][C]76[/C][C]144.08[/C][C]145.183920713335[/C][C]-1.10392071333521[/C][/ROW]
[ROW][C]77[/C][C]144.08[/C][C]145.008404497298[/C][C]-0.928404497297578[/C][/ROW]
[ROW][C]78[/C][C]144.09[/C][C]144.887975793587[/C][C]-0.797975793586716[/C][/ROW]
[ROW][C]79[/C][C]144.09[/C][C]143.997421144278[/C][C]0.0925788557218539[/C][/ROW]
[ROW][C]80[/C][C]144.11[/C][C]144.925313799889[/C][C]-0.815313799889253[/C][/ROW]
[ROW][C]81[/C][C]144.11[/C][C]144.985009562717[/C][C]-0.875009562716826[/C][/ROW]
[ROW][C]82[/C][C]144.15[/C][C]144.462951067344[/C][C]-0.312951067344301[/C][/ROW]
[ROW][C]83[/C][C]144.15[/C][C]144.261999563211[/C][C]-0.111999563210901[/C][/ROW]
[ROW][C]84[/C][C]144.16[/C][C]144.213755672225[/C][C]-0.0537556722247245[/C][/ROW]
[ROW][C]85[/C][C]144.2[/C][C]144.519250742944[/C][C]-0.319250742944433[/C][/ROW]
[ROW][C]86[/C][C]144.38[/C][C]145.101504902410[/C][C]-0.721504902409691[/C][/ROW]
[ROW][C]87[/C][C]144.38[/C][C]145.490871864122[/C][C]-1.11087186412220[/C][/ROW]
[ROW][C]88[/C][C]144.28[/C][C]145.595826178109[/C][C]-1.31582617810915[/C][/ROW]
[ROW][C]89[/C][C]144.46[/C][C]145.055643725257[/C][C]-0.595643725257219[/C][/ROW]
[ROW][C]90[/C][C]144.53[/C][C]145.07194655305[/C][C]-0.541946553050053[/C][/ROW]
[ROW][C]91[/C][C]144.53[/C][C]144.319762952464[/C][C]0.210237047535742[/C][/ROW]
[ROW][C]92[/C][C]145.34[/C][C]145.107487726942[/C][C]0.232512273057523[/C][/ROW]
[ROW][C]93[/C][C]147.98[/C][C]145.977827997950[/C][C]2.00217200205046[/C][/ROW]
[ROW][C]94[/C][C]150.42[/C][C]148.056088905561[/C][C]2.36391109443937[/C][/ROW]
[ROW][C]95[/C][C]150.53[/C][C]150.296597408776[/C][C]0.233402591223864[/C][/ROW]
[ROW][C]96[/C][C]150.64[/C][C]150.556276792780[/C][C]0.083723207220146[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41289&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41289&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
13108.62106.5169884203352.10301157966508
14108.62108.5321032689030.0878967310965066
15110.1110.234617744641-0.134617744641417
16110.74110.901450987309-0.161450987309451
17110.77110.930653037448-0.160653037448185
18110.77110.926647260655-0.156647260654680
19110.78110.787947354488-0.00794735448762651
20110.78111.719939359441-0.939939359441027
21110.78111.105905222161-0.325905222160614
22110.84110.8104042216860.029595778314075
23110.84110.7404955589460.0995044410535684
24110.84110.7313802715620.108619728438001
25110.84110.981899150867-0.141899150866962
26110.84110.7207984735410.119201526458681
27111.01112.415447209349-1.40544720934903
28112.66111.8491834016530.810816598347444
29114.04112.7124222068091.32757779319113
30114.16114.0489402795790.111059720421025
31114.2114.1526613251180.0473386748822264
32114.2115.065099160724-0.865099160723517
33114.23114.570732180148-0.34073218014764
34114.23114.282120240736-0.0521202407359311
35114.23114.1273900851900.102609914809790
36114.23114.1053593405240.124640659475560
37114.23114.339315024196-0.10931502419551
38114.23114.1152403379510.114759662049394
39115.97115.7025757893280.267424210672488
40116.96116.9246500960310.035349903969248
41117.08117.139651691333-0.0596516913332152
42117.08117.080106413129-0.000106413129444149
43117.08117.0499685103640.0300314896364142
44117.63117.858802189427-0.228802189426958
45119.12117.9892398962851.13076010371493
46119.47119.0930612541960.376938745804239
47119.5119.3715384357940.128461564205878
48119.52119.4025290795660.117470920433689
49119.49119.646361181752-0.156361181752075
50119.49119.4252939807280.0647060192721369
51119.5121.079187694063-1.57918769406268
52119.5120.613136997018-1.11313699701826
53119.56119.735993557495-0.175993557494678
54122.35119.5331745217432.8168254782574
55122.92122.0978632660390.82213673396123
56122.92123.685780969789-0.765780969789162
57123.04123.494749552160-0.454749552159853
58123.04123.077507473430-0.0375074734297982
59123.04122.9351853461740.104814653826082
60123.06122.9222637263760.137736273624370
61123.33123.1455903584590.184409641541293
62128.21123.2426466066094.96735339339098
63129.57129.4281535689540.141846431046389
64129.79130.804727386048-1.01472738604818
65131.66130.2696649080331.39033509196744
66135.01131.9623923834153.04760761658491
67136.01134.7294654933541.28053450664638
68136.31136.863746972248-0.553746972247865
69136.37137.152179022137-0.782179022136518
70136.4136.669465768531-0.269465768530750
71136.4136.504127863033-0.104127863033256
72136.4136.472284947038-0.0722849470375877
73137.34136.6934024941460.646597505854146
74142.18137.8374069788834.34259302111724
75143.79143.3180055923030.471994407697025
76144.08145.183920713335-1.10392071333521
77144.08145.008404497298-0.928404497297578
78144.09144.887975793587-0.797975793586716
79144.09143.9974211442780.0925788557218539
80144.11144.925313799889-0.815313799889253
81144.11144.985009562717-0.875009562716826
82144.15144.462951067344-0.312951067344301
83144.15144.261999563211-0.111999563210901
84144.16144.213755672225-0.0537556722247245
85144.2144.519250742944-0.319250742944433
86144.38145.101504902410-0.721504902409691
87144.38145.490871864122-1.11087186412220
88144.28145.595826178109-1.31582617810915
89144.46145.055643725257-0.595643725257219
90144.53145.07194655305-0.541946553050053
91144.53144.3197629524640.210237047535742
92145.34145.1074877269420.232512273057523
93147.98145.9778279979502.00217200205046
94150.42148.0560889055612.36391109443937
95150.53150.2965974087760.233402591223864
96150.64150.5562767927800.083723207220146







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97150.967001580134148.798316128932153.135687031336
98151.839994870281148.863773277691154.816216462871
99152.917718259413149.273165210047156.562271308780
100154.121148005582149.878767475583158.363528535581
101154.964054812409150.177147464209159.750962160608
102155.653990657130150.357425393060160.950555921199
103155.544544249315149.785820313667161.303268184963
104156.279732299861150.047437889816162.512026709906
105157.237873790305150.53597825365163.939769326959
106157.572832559082150.436017864066164.709647254098
107157.446350755637149.903141624874164.9895598864
108157.457640068931148.927131069726165.988149068137

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 150.967001580134 & 148.798316128932 & 153.135687031336 \tabularnewline
98 & 151.839994870281 & 148.863773277691 & 154.816216462871 \tabularnewline
99 & 152.917718259413 & 149.273165210047 & 156.562271308780 \tabularnewline
100 & 154.121148005582 & 149.878767475583 & 158.363528535581 \tabularnewline
101 & 154.964054812409 & 150.177147464209 & 159.750962160608 \tabularnewline
102 & 155.653990657130 & 150.357425393060 & 160.950555921199 \tabularnewline
103 & 155.544544249315 & 149.785820313667 & 161.303268184963 \tabularnewline
104 & 156.279732299861 & 150.047437889816 & 162.512026709906 \tabularnewline
105 & 157.237873790305 & 150.53597825365 & 163.939769326959 \tabularnewline
106 & 157.572832559082 & 150.436017864066 & 164.709647254098 \tabularnewline
107 & 157.446350755637 & 149.903141624874 & 164.9895598864 \tabularnewline
108 & 157.457640068931 & 148.927131069726 & 165.988149068137 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41289&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]97[/C][C]150.967001580134[/C][C]148.798316128932[/C][C]153.135687031336[/C][/ROW]
[ROW][C]98[/C][C]151.839994870281[/C][C]148.863773277691[/C][C]154.816216462871[/C][/ROW]
[ROW][C]99[/C][C]152.917718259413[/C][C]149.273165210047[/C][C]156.562271308780[/C][/ROW]
[ROW][C]100[/C][C]154.121148005582[/C][C]149.878767475583[/C][C]158.363528535581[/C][/ROW]
[ROW][C]101[/C][C]154.964054812409[/C][C]150.177147464209[/C][C]159.750962160608[/C][/ROW]
[ROW][C]102[/C][C]155.653990657130[/C][C]150.357425393060[/C][C]160.950555921199[/C][/ROW]
[ROW][C]103[/C][C]155.544544249315[/C][C]149.785820313667[/C][C]161.303268184963[/C][/ROW]
[ROW][C]104[/C][C]156.279732299861[/C][C]150.047437889816[/C][C]162.512026709906[/C][/ROW]
[ROW][C]105[/C][C]157.237873790305[/C][C]150.53597825365[/C][C]163.939769326959[/C][/ROW]
[ROW][C]106[/C][C]157.572832559082[/C][C]150.436017864066[/C][C]164.709647254098[/C][/ROW]
[ROW][C]107[/C][C]157.446350755637[/C][C]149.903141624874[/C][C]164.9895598864[/C][/ROW]
[ROW][C]108[/C][C]157.457640068931[/C][C]148.927131069726[/C][C]165.988149068137[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41289&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41289&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
97150.967001580134148.798316128932153.135687031336
98151.839994870281148.863773277691154.816216462871
99152.917718259413149.273165210047156.562271308780
100154.121148005582149.878767475583158.363528535581
101154.964054812409150.177147464209159.750962160608
102155.653990657130150.357425393060160.950555921199
103155.544544249315149.785820313667161.303268184963
104156.279732299861150.047437889816162.512026709906
105157.237873790305150.53597825365163.939769326959
106157.572832559082150.436017864066164.709647254098
107157.446350755637149.903141624874164.9895598864
108157.457640068931148.927131069726165.988149068137



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