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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 10:25:44 -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/26/t1369578371budd22bo7luugpm.htm/, Retrieved Tue, 07 May 2024 14:48:10 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210621, Retrieved Tue, 07 May 2024 14:48:10 +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)
-     [Standard Deviation-Mean Plot] [Standard deviatio...] [2011-12-07 16:21:53] [102faec22d2a25d9aaa52ca244269a51]
- RMP   [Exponential Smoothing] [Inschrijvingen ni...] [2011-12-27 13:51:36] [102faec22d2a25d9aaa52ca244269a51]
- R PD      [Exponential Smoothing] [] [2013-05-26 14:25:44] [c3f863f9a10611e864186291c75f3c4f] [Current]
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Dataseries X:
108,56
108,71
116,73
118,88
119,6
119,62
119,64
119,74
119,74
119,74
119,9
119,9
119,9
119,9
119,9
121,02
122,95
123,62
123,67
123,81
123,83
123,83
123,83
123,83
123,89
123,89
124,44
125,51
125,89
126,12
126,25
126,25
126,3
126,31
126,38
125,51
126,82
126,86
126,86
127,28
128,72
128,77
128,84
128,88
128,88
128,88
128,88
128,88
128,89
128,9
128,92
129,05
129,83
130,54
130,82
130,91
131,04
131,07
131,15
131,2
131,2
131,42
131,45
131,7
134,24
135,17
135,51
135,65
136,02
136,07
136,13
136,07




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210621&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210621&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210621&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0127980485434837
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0127980485434837 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210621&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]0.0127980485434837[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210621&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210621&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
beta0.0127980485434837
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3116.73108.867.87000000000002
4118.88116.9807206420371.89927935796278
5119.6119.1550277114580.444972288541948
6119.62119.880722488407-0.26072248840731
7119.64119.897385749344-0.257385749344309
8119.74119.91409171403-0.1740917140298
9119.74120.011863679823-0.271863679822616
10119.74120.008384355251-0.268384355251044
11119.9120.004949559244-0.104949559244218
12119.9120.16360640969-0.263606409690397
13119.9120.160232762063-0.260232762062813
14119.9120.156902290541-0.256902290541333
15119.9120.153614442556-0.253614442556042
16121.02120.1503686726090.869631327391104
17122.95121.2814982565521.66850174344823
18123.62123.2328518228590.387148177140688
19123.67123.907806564024-0.237806564023884
20123.81123.954763104074-0.144763104073533
21123.83124.09291041884-0.262910418840306
22123.83124.109545678537-0.279545678537403
23123.83124.105968039373-0.275968039373353
24123.83124.102436187009-0.272436187009006
25123.89124.098949535463-0.208949535462651
26123.89124.156275389165-0.266275389164676
27124.44124.1528675838080.287132416191795
28125.51124.7065423184090.80345768159097
29125.89125.7868250088210.10317499117933
30126.12126.168145447366-0.0481454473662524
31126.25126.397529279594-0.147529279593726
32126.25126.525641192712-0.275641192711888
33126.3126.522113523347-0.222113523346991
34126.31126.569270903693-0.259270903693022
35126.38126.575952742082-0.195952742081658
36125.51126.643444929376-1.13344492937625
37126.82125.7589390461491.06106095385125
38126.86127.082518555744-0.222518555743719
39126.86127.119670752465-0.259670752465482
40127.28127.116347473570.1636525264299
41128.72127.5384419065481.18155809345238
42128.77128.993563544385-0.223563544384547
43128.84129.040702367291-0.200702367291001
44128.88129.108133768652-0.228133768651617
45128.88129.145214101606-0.265214101605977
46128.88129.141819878659-0.261819878659225
47128.88129.138469095142-0.258469095142488
48128.88129.135161195116-0.255161195115875
49128.89129.131895629754-0.241895629754367
50128.9129.138799837742-0.238799837742278
51128.92129.145743665827-0.225743665826712
52129.05129.162854587433-0.112854587433048
53129.83129.2914102689450.538589731055254
54130.54130.0783031664680.461696833532159
55130.82130.7942119849560.0257880150442702
56130.91131.074542021224-0.164542021224094
57131.04131.162436204449-0.122436204449059
58131.07131.290869259961-0.220869259961034
59131.15131.31804256445-0.168042564450275
60131.2131.395891947553-0.195891947553093
61131.2131.443384912899-0.243384912899018
62131.42131.440270060969-0.0202700609689828
63131.45131.660010643745-0.21001064374471
64131.7131.6873229173310.0126770826685743
65134.24131.9374851592512.30251484074921
66135.17134.5069528559550.66304714404518
67135.51135.4454385654910.0645614345091019
68135.65135.786264825864-0.136264825863776
69136.02135.9245209020080.0954790979923814
70136.07136.295742848139-0.225742848138623
71136.13136.34285378021-0.212853780209798
72136.07136.400129667198-0.330129667198008

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 116.73 & 108.86 & 7.87000000000002 \tabularnewline
4 & 118.88 & 116.980720642037 & 1.89927935796278 \tabularnewline
5 & 119.6 & 119.155027711458 & 0.444972288541948 \tabularnewline
6 & 119.62 & 119.880722488407 & -0.26072248840731 \tabularnewline
7 & 119.64 & 119.897385749344 & -0.257385749344309 \tabularnewline
8 & 119.74 & 119.91409171403 & -0.1740917140298 \tabularnewline
9 & 119.74 & 120.011863679823 & -0.271863679822616 \tabularnewline
10 & 119.74 & 120.008384355251 & -0.268384355251044 \tabularnewline
11 & 119.9 & 120.004949559244 & -0.104949559244218 \tabularnewline
12 & 119.9 & 120.16360640969 & -0.263606409690397 \tabularnewline
13 & 119.9 & 120.160232762063 & -0.260232762062813 \tabularnewline
14 & 119.9 & 120.156902290541 & -0.256902290541333 \tabularnewline
15 & 119.9 & 120.153614442556 & -0.253614442556042 \tabularnewline
16 & 121.02 & 120.150368672609 & 0.869631327391104 \tabularnewline
17 & 122.95 & 121.281498256552 & 1.66850174344823 \tabularnewline
18 & 123.62 & 123.232851822859 & 0.387148177140688 \tabularnewline
19 & 123.67 & 123.907806564024 & -0.237806564023884 \tabularnewline
20 & 123.81 & 123.954763104074 & -0.144763104073533 \tabularnewline
21 & 123.83 & 124.09291041884 & -0.262910418840306 \tabularnewline
22 & 123.83 & 124.109545678537 & -0.279545678537403 \tabularnewline
23 & 123.83 & 124.105968039373 & -0.275968039373353 \tabularnewline
24 & 123.83 & 124.102436187009 & -0.272436187009006 \tabularnewline
25 & 123.89 & 124.098949535463 & -0.208949535462651 \tabularnewline
26 & 123.89 & 124.156275389165 & -0.266275389164676 \tabularnewline
27 & 124.44 & 124.152867583808 & 0.287132416191795 \tabularnewline
28 & 125.51 & 124.706542318409 & 0.80345768159097 \tabularnewline
29 & 125.89 & 125.786825008821 & 0.10317499117933 \tabularnewline
30 & 126.12 & 126.168145447366 & -0.0481454473662524 \tabularnewline
31 & 126.25 & 126.397529279594 & -0.147529279593726 \tabularnewline
32 & 126.25 & 126.525641192712 & -0.275641192711888 \tabularnewline
33 & 126.3 & 126.522113523347 & -0.222113523346991 \tabularnewline
34 & 126.31 & 126.569270903693 & -0.259270903693022 \tabularnewline
35 & 126.38 & 126.575952742082 & -0.195952742081658 \tabularnewline
36 & 125.51 & 126.643444929376 & -1.13344492937625 \tabularnewline
37 & 126.82 & 125.758939046149 & 1.06106095385125 \tabularnewline
38 & 126.86 & 127.082518555744 & -0.222518555743719 \tabularnewline
39 & 126.86 & 127.119670752465 & -0.259670752465482 \tabularnewline
40 & 127.28 & 127.11634747357 & 0.1636525264299 \tabularnewline
41 & 128.72 & 127.538441906548 & 1.18155809345238 \tabularnewline
42 & 128.77 & 128.993563544385 & -0.223563544384547 \tabularnewline
43 & 128.84 & 129.040702367291 & -0.200702367291001 \tabularnewline
44 & 128.88 & 129.108133768652 & -0.228133768651617 \tabularnewline
45 & 128.88 & 129.145214101606 & -0.265214101605977 \tabularnewline
46 & 128.88 & 129.141819878659 & -0.261819878659225 \tabularnewline
47 & 128.88 & 129.138469095142 & -0.258469095142488 \tabularnewline
48 & 128.88 & 129.135161195116 & -0.255161195115875 \tabularnewline
49 & 128.89 & 129.131895629754 & -0.241895629754367 \tabularnewline
50 & 128.9 & 129.138799837742 & -0.238799837742278 \tabularnewline
51 & 128.92 & 129.145743665827 & -0.225743665826712 \tabularnewline
52 & 129.05 & 129.162854587433 & -0.112854587433048 \tabularnewline
53 & 129.83 & 129.291410268945 & 0.538589731055254 \tabularnewline
54 & 130.54 & 130.078303166468 & 0.461696833532159 \tabularnewline
55 & 130.82 & 130.794211984956 & 0.0257880150442702 \tabularnewline
56 & 130.91 & 131.074542021224 & -0.164542021224094 \tabularnewline
57 & 131.04 & 131.162436204449 & -0.122436204449059 \tabularnewline
58 & 131.07 & 131.290869259961 & -0.220869259961034 \tabularnewline
59 & 131.15 & 131.31804256445 & -0.168042564450275 \tabularnewline
60 & 131.2 & 131.395891947553 & -0.195891947553093 \tabularnewline
61 & 131.2 & 131.443384912899 & -0.243384912899018 \tabularnewline
62 & 131.42 & 131.440270060969 & -0.0202700609689828 \tabularnewline
63 & 131.45 & 131.660010643745 & -0.21001064374471 \tabularnewline
64 & 131.7 & 131.687322917331 & 0.0126770826685743 \tabularnewline
65 & 134.24 & 131.937485159251 & 2.30251484074921 \tabularnewline
66 & 135.17 & 134.506952855955 & 0.66304714404518 \tabularnewline
67 & 135.51 & 135.445438565491 & 0.0645614345091019 \tabularnewline
68 & 135.65 & 135.786264825864 & -0.136264825863776 \tabularnewline
69 & 136.02 & 135.924520902008 & 0.0954790979923814 \tabularnewline
70 & 136.07 & 136.295742848139 & -0.225742848138623 \tabularnewline
71 & 136.13 & 136.34285378021 & -0.212853780209798 \tabularnewline
72 & 136.07 & 136.400129667198 & -0.330129667198008 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210621&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]116.73[/C][C]108.86[/C][C]7.87000000000002[/C][/ROW]
[ROW][C]4[/C][C]118.88[/C][C]116.980720642037[/C][C]1.89927935796278[/C][/ROW]
[ROW][C]5[/C][C]119.6[/C][C]119.155027711458[/C][C]0.444972288541948[/C][/ROW]
[ROW][C]6[/C][C]119.62[/C][C]119.880722488407[/C][C]-0.26072248840731[/C][/ROW]
[ROW][C]7[/C][C]119.64[/C][C]119.897385749344[/C][C]-0.257385749344309[/C][/ROW]
[ROW][C]8[/C][C]119.74[/C][C]119.91409171403[/C][C]-0.1740917140298[/C][/ROW]
[ROW][C]9[/C][C]119.74[/C][C]120.011863679823[/C][C]-0.271863679822616[/C][/ROW]
[ROW][C]10[/C][C]119.74[/C][C]120.008384355251[/C][C]-0.268384355251044[/C][/ROW]
[ROW][C]11[/C][C]119.9[/C][C]120.004949559244[/C][C]-0.104949559244218[/C][/ROW]
[ROW][C]12[/C][C]119.9[/C][C]120.16360640969[/C][C]-0.263606409690397[/C][/ROW]
[ROW][C]13[/C][C]119.9[/C][C]120.160232762063[/C][C]-0.260232762062813[/C][/ROW]
[ROW][C]14[/C][C]119.9[/C][C]120.156902290541[/C][C]-0.256902290541333[/C][/ROW]
[ROW][C]15[/C][C]119.9[/C][C]120.153614442556[/C][C]-0.253614442556042[/C][/ROW]
[ROW][C]16[/C][C]121.02[/C][C]120.150368672609[/C][C]0.869631327391104[/C][/ROW]
[ROW][C]17[/C][C]122.95[/C][C]121.281498256552[/C][C]1.66850174344823[/C][/ROW]
[ROW][C]18[/C][C]123.62[/C][C]123.232851822859[/C][C]0.387148177140688[/C][/ROW]
[ROW][C]19[/C][C]123.67[/C][C]123.907806564024[/C][C]-0.237806564023884[/C][/ROW]
[ROW][C]20[/C][C]123.81[/C][C]123.954763104074[/C][C]-0.144763104073533[/C][/ROW]
[ROW][C]21[/C][C]123.83[/C][C]124.09291041884[/C][C]-0.262910418840306[/C][/ROW]
[ROW][C]22[/C][C]123.83[/C][C]124.109545678537[/C][C]-0.279545678537403[/C][/ROW]
[ROW][C]23[/C][C]123.83[/C][C]124.105968039373[/C][C]-0.275968039373353[/C][/ROW]
[ROW][C]24[/C][C]123.83[/C][C]124.102436187009[/C][C]-0.272436187009006[/C][/ROW]
[ROW][C]25[/C][C]123.89[/C][C]124.098949535463[/C][C]-0.208949535462651[/C][/ROW]
[ROW][C]26[/C][C]123.89[/C][C]124.156275389165[/C][C]-0.266275389164676[/C][/ROW]
[ROW][C]27[/C][C]124.44[/C][C]124.152867583808[/C][C]0.287132416191795[/C][/ROW]
[ROW][C]28[/C][C]125.51[/C][C]124.706542318409[/C][C]0.80345768159097[/C][/ROW]
[ROW][C]29[/C][C]125.89[/C][C]125.786825008821[/C][C]0.10317499117933[/C][/ROW]
[ROW][C]30[/C][C]126.12[/C][C]126.168145447366[/C][C]-0.0481454473662524[/C][/ROW]
[ROW][C]31[/C][C]126.25[/C][C]126.397529279594[/C][C]-0.147529279593726[/C][/ROW]
[ROW][C]32[/C][C]126.25[/C][C]126.525641192712[/C][C]-0.275641192711888[/C][/ROW]
[ROW][C]33[/C][C]126.3[/C][C]126.522113523347[/C][C]-0.222113523346991[/C][/ROW]
[ROW][C]34[/C][C]126.31[/C][C]126.569270903693[/C][C]-0.259270903693022[/C][/ROW]
[ROW][C]35[/C][C]126.38[/C][C]126.575952742082[/C][C]-0.195952742081658[/C][/ROW]
[ROW][C]36[/C][C]125.51[/C][C]126.643444929376[/C][C]-1.13344492937625[/C][/ROW]
[ROW][C]37[/C][C]126.82[/C][C]125.758939046149[/C][C]1.06106095385125[/C][/ROW]
[ROW][C]38[/C][C]126.86[/C][C]127.082518555744[/C][C]-0.222518555743719[/C][/ROW]
[ROW][C]39[/C][C]126.86[/C][C]127.119670752465[/C][C]-0.259670752465482[/C][/ROW]
[ROW][C]40[/C][C]127.28[/C][C]127.11634747357[/C][C]0.1636525264299[/C][/ROW]
[ROW][C]41[/C][C]128.72[/C][C]127.538441906548[/C][C]1.18155809345238[/C][/ROW]
[ROW][C]42[/C][C]128.77[/C][C]128.993563544385[/C][C]-0.223563544384547[/C][/ROW]
[ROW][C]43[/C][C]128.84[/C][C]129.040702367291[/C][C]-0.200702367291001[/C][/ROW]
[ROW][C]44[/C][C]128.88[/C][C]129.108133768652[/C][C]-0.228133768651617[/C][/ROW]
[ROW][C]45[/C][C]128.88[/C][C]129.145214101606[/C][C]-0.265214101605977[/C][/ROW]
[ROW][C]46[/C][C]128.88[/C][C]129.141819878659[/C][C]-0.261819878659225[/C][/ROW]
[ROW][C]47[/C][C]128.88[/C][C]129.138469095142[/C][C]-0.258469095142488[/C][/ROW]
[ROW][C]48[/C][C]128.88[/C][C]129.135161195116[/C][C]-0.255161195115875[/C][/ROW]
[ROW][C]49[/C][C]128.89[/C][C]129.131895629754[/C][C]-0.241895629754367[/C][/ROW]
[ROW][C]50[/C][C]128.9[/C][C]129.138799837742[/C][C]-0.238799837742278[/C][/ROW]
[ROW][C]51[/C][C]128.92[/C][C]129.145743665827[/C][C]-0.225743665826712[/C][/ROW]
[ROW][C]52[/C][C]129.05[/C][C]129.162854587433[/C][C]-0.112854587433048[/C][/ROW]
[ROW][C]53[/C][C]129.83[/C][C]129.291410268945[/C][C]0.538589731055254[/C][/ROW]
[ROW][C]54[/C][C]130.54[/C][C]130.078303166468[/C][C]0.461696833532159[/C][/ROW]
[ROW][C]55[/C][C]130.82[/C][C]130.794211984956[/C][C]0.0257880150442702[/C][/ROW]
[ROW][C]56[/C][C]130.91[/C][C]131.074542021224[/C][C]-0.164542021224094[/C][/ROW]
[ROW][C]57[/C][C]131.04[/C][C]131.162436204449[/C][C]-0.122436204449059[/C][/ROW]
[ROW][C]58[/C][C]131.07[/C][C]131.290869259961[/C][C]-0.220869259961034[/C][/ROW]
[ROW][C]59[/C][C]131.15[/C][C]131.31804256445[/C][C]-0.168042564450275[/C][/ROW]
[ROW][C]60[/C][C]131.2[/C][C]131.395891947553[/C][C]-0.195891947553093[/C][/ROW]
[ROW][C]61[/C][C]131.2[/C][C]131.443384912899[/C][C]-0.243384912899018[/C][/ROW]
[ROW][C]62[/C][C]131.42[/C][C]131.440270060969[/C][C]-0.0202700609689828[/C][/ROW]
[ROW][C]63[/C][C]131.45[/C][C]131.660010643745[/C][C]-0.21001064374471[/C][/ROW]
[ROW][C]64[/C][C]131.7[/C][C]131.687322917331[/C][C]0.0126770826685743[/C][/ROW]
[ROW][C]65[/C][C]134.24[/C][C]131.937485159251[/C][C]2.30251484074921[/C][/ROW]
[ROW][C]66[/C][C]135.17[/C][C]134.506952855955[/C][C]0.66304714404518[/C][/ROW]
[ROW][C]67[/C][C]135.51[/C][C]135.445438565491[/C][C]0.0645614345091019[/C][/ROW]
[ROW][C]68[/C][C]135.65[/C][C]135.786264825864[/C][C]-0.136264825863776[/C][/ROW]
[ROW][C]69[/C][C]136.02[/C][C]135.924520902008[/C][C]0.0954790979923814[/C][/ROW]
[ROW][C]70[/C][C]136.07[/C][C]136.295742848139[/C][C]-0.225742848138623[/C][/ROW]
[ROW][C]71[/C][C]136.13[/C][C]136.34285378021[/C][C]-0.212853780209798[/C][/ROW]
[ROW][C]72[/C][C]136.07[/C][C]136.400129667198[/C][C]-0.330129667198008[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210621&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210621&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
3116.73108.867.87000000000002
4118.88116.9807206420371.89927935796278
5119.6119.1550277114580.444972288541948
6119.62119.880722488407-0.26072248840731
7119.64119.897385749344-0.257385749344309
8119.74119.91409171403-0.1740917140298
9119.74120.011863679823-0.271863679822616
10119.74120.008384355251-0.268384355251044
11119.9120.004949559244-0.104949559244218
12119.9120.16360640969-0.263606409690397
13119.9120.160232762063-0.260232762062813
14119.9120.156902290541-0.256902290541333
15119.9120.153614442556-0.253614442556042
16121.02120.1503686726090.869631327391104
17122.95121.2814982565521.66850174344823
18123.62123.2328518228590.387148177140688
19123.67123.907806564024-0.237806564023884
20123.81123.954763104074-0.144763104073533
21123.83124.09291041884-0.262910418840306
22123.83124.109545678537-0.279545678537403
23123.83124.105968039373-0.275968039373353
24123.83124.102436187009-0.272436187009006
25123.89124.098949535463-0.208949535462651
26123.89124.156275389165-0.266275389164676
27124.44124.1528675838080.287132416191795
28125.51124.7065423184090.80345768159097
29125.89125.7868250088210.10317499117933
30126.12126.168145447366-0.0481454473662524
31126.25126.397529279594-0.147529279593726
32126.25126.525641192712-0.275641192711888
33126.3126.522113523347-0.222113523346991
34126.31126.569270903693-0.259270903693022
35126.38126.575952742082-0.195952742081658
36125.51126.643444929376-1.13344492937625
37126.82125.7589390461491.06106095385125
38126.86127.082518555744-0.222518555743719
39126.86127.119670752465-0.259670752465482
40127.28127.116347473570.1636525264299
41128.72127.5384419065481.18155809345238
42128.77128.993563544385-0.223563544384547
43128.84129.040702367291-0.200702367291001
44128.88129.108133768652-0.228133768651617
45128.88129.145214101606-0.265214101605977
46128.88129.141819878659-0.261819878659225
47128.88129.138469095142-0.258469095142488
48128.88129.135161195116-0.255161195115875
49128.89129.131895629754-0.241895629754367
50128.9129.138799837742-0.238799837742278
51128.92129.145743665827-0.225743665826712
52129.05129.162854587433-0.112854587433048
53129.83129.2914102689450.538589731055254
54130.54130.0783031664680.461696833532159
55130.82130.7942119849560.0257880150442702
56130.91131.074542021224-0.164542021224094
57131.04131.162436204449-0.122436204449059
58131.07131.290869259961-0.220869259961034
59131.15131.31804256445-0.168042564450275
60131.2131.395891947553-0.195891947553093
61131.2131.443384912899-0.243384912899018
62131.42131.440270060969-0.0202700609689828
63131.45131.660010643745-0.21001064374471
64131.7131.6873229173310.0126770826685743
65134.24131.9374851592512.30251484074921
66135.17134.5069528559550.66304714404518
67135.51135.4454385654910.0645614345091019
68135.65135.786264825864-0.136264825863776
69136.02135.9245209020080.0954790979923814
70136.07136.295742848139-0.225742848138623
71136.13136.34285378021-0.212853780209798
72136.07136.400129667198-0.330129667198008







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73136.335904651692134.204236289098138.467573014285
74136.601809303383133.567822948585139.635795658182
75136.867713955075133.128104602978140.607323307171
76137.133618606766132.788010104973141.47922710856
77137.399523258458132.510201509786142.28884500713
78137.665427910149132.275657194522143.055198625777
79137.931332561841132.073151496605143.789513627077
80138.197237213533131.895417891511144.499056535554
81138.463141865224131.73744182603145.188841904418
82138.729046516916131.595595972492145.862497061339
83138.994951168607131.467159842316146.522742494898
84139.260855820299131.350033720682147.171677919916

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 136.335904651692 & 134.204236289098 & 138.467573014285 \tabularnewline
74 & 136.601809303383 & 133.567822948585 & 139.635795658182 \tabularnewline
75 & 136.867713955075 & 133.128104602978 & 140.607323307171 \tabularnewline
76 & 137.133618606766 & 132.788010104973 & 141.47922710856 \tabularnewline
77 & 137.399523258458 & 132.510201509786 & 142.28884500713 \tabularnewline
78 & 137.665427910149 & 132.275657194522 & 143.055198625777 \tabularnewline
79 & 137.931332561841 & 132.073151496605 & 143.789513627077 \tabularnewline
80 & 138.197237213533 & 131.895417891511 & 144.499056535554 \tabularnewline
81 & 138.463141865224 & 131.73744182603 & 145.188841904418 \tabularnewline
82 & 138.729046516916 & 131.595595972492 & 145.862497061339 \tabularnewline
83 & 138.994951168607 & 131.467159842316 & 146.522742494898 \tabularnewline
84 & 139.260855820299 & 131.350033720682 & 147.171677919916 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210621&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]136.335904651692[/C][C]134.204236289098[/C][C]138.467573014285[/C][/ROW]
[ROW][C]74[/C][C]136.601809303383[/C][C]133.567822948585[/C][C]139.635795658182[/C][/ROW]
[ROW][C]75[/C][C]136.867713955075[/C][C]133.128104602978[/C][C]140.607323307171[/C][/ROW]
[ROW][C]76[/C][C]137.133618606766[/C][C]132.788010104973[/C][C]141.47922710856[/C][/ROW]
[ROW][C]77[/C][C]137.399523258458[/C][C]132.510201509786[/C][C]142.28884500713[/C][/ROW]
[ROW][C]78[/C][C]137.665427910149[/C][C]132.275657194522[/C][C]143.055198625777[/C][/ROW]
[ROW][C]79[/C][C]137.931332561841[/C][C]132.073151496605[/C][C]143.789513627077[/C][/ROW]
[ROW][C]80[/C][C]138.197237213533[/C][C]131.895417891511[/C][C]144.499056535554[/C][/ROW]
[ROW][C]81[/C][C]138.463141865224[/C][C]131.73744182603[/C][C]145.188841904418[/C][/ROW]
[ROW][C]82[/C][C]138.729046516916[/C][C]131.595595972492[/C][C]145.862497061339[/C][/ROW]
[ROW][C]83[/C][C]138.994951168607[/C][C]131.467159842316[/C][C]146.522742494898[/C][/ROW]
[ROW][C]84[/C][C]139.260855820299[/C][C]131.350033720682[/C][C]147.171677919916[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210621&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210621&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
73136.335904651692134.204236289098138.467573014285
74136.601809303383133.567822948585139.635795658182
75136.867713955075133.128104602978140.607323307171
76137.133618606766132.788010104973141.47922710856
77137.399523258458132.510201509786142.28884500713
78137.665427910149132.275657194522143.055198625777
79137.931332561841132.073151496605143.789513627077
80138.197237213533131.895417891511144.499056535554
81138.463141865224131.73744182603145.188841904418
82138.729046516916131.595595972492145.862497061339
83138.994951168607131.467159842316146.522742494898
84139.260855820299131.350033720682147.171677919916



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')