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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 12 May 2012 13:33:51 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/May/12/t1336844057z8uhzld2prf3m4o.htm/, Retrieved Sun, 05 May 2024 14:45:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=166428, Retrieved Sun, 05 May 2024 14:45:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact195
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Additief Double e...] [2012-05-12 17:33:51] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
62.11
62.15
62.2
62.22
62.02
62.02
62.02
62.07
62.31
62.71
62.77
62.82
62.82
62.82
62.55
62.6
62.47
62.47
62.47
62.72
63.13
64.09
64.31
64.29
64.29
64.29
64.35
64.42
64.24
64.23
64.23
64.2
65.35
65.83
66.15
66.19
66.19
66.56
66.59
66.48
66.4
66.4
66.4
66.49
66.65
67.69
67.91
68.14
68.14
68.16
67.94
68
68.1
68.12
68.12
68.24
68.42
68.97
69.13
69.2




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

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166428&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166428&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166428&T=0

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0366764843068366
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0366764843068366 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166428&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]0.0366764843068366[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166428&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166428&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
beta0.0366764843068366
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
362.262.190.0100000000000051
462.2262.2403667648431-0.0203667648430752
562.0262.2596197835119-0.239619783511912
662.0262.0508313722823-0.0308313722823357
762.0262.0497005859407-0.0297005859406667
862.0762.04861127286650.0213887271334912
962.3162.09939573618160.210604263818439
1062.7162.34711996015850.362880039841542
1162.7762.7604291242450.00957087575503834
1262.8262.8207801503194-0.000780150319400263
1362.8262.8707515371485-0.0507515371484502
1462.8262.8688901491927-0.0488901491926796
1562.5562.8670970304031-0.317097030403055
1662.662.58546702614370.0145329738562694
1762.4762.6360000445313-0.166000044531309
1862.4762.4999117465031-0.0299117465031173
1962.4762.4988146888019-0.0288146888019085
2062.7262.49775786732030.222242132679746
2163.1362.75590892741180.3740910725882
2264.0963.17962927276490.91037072723509
2364.3164.17301847045580.136981529544244
2464.2964.3980424713744-0.108042471374404
2564.2964.3740798533686-0.0840798533685785
2664.2964.370996099946-0.0809960999459776
2764.3564.3680254477574-0.0180254477574096
2864.4264.4273643377056-0.00736433770559586
2964.2464.4970942396893-0.257094239689309
3064.2364.307664926842-0.0776649268419618
3164.2364.2948164503715-0.0648164503714526
3264.264.2924392108466-0.0924392108465781
3365.3564.25904886558061.09095113441936
3465.8365.44906111774170.38093888225832
3566.1565.94303261667870.206967383321313
3666.1966.2706234526651-0.0806234526651224
3766.1966.3076664678687-0.117666467868673
3866.5666.30335087550640.256649124493563
3966.5966.6827638630933-0.0927638630932961
4066.4866.7093616107243-0.229361610724311
4166.466.590949433208-0.19094943320799
4266.466.5039460793175-0.103946079317538
4366.466.5001337025707-0.100133702570702
4466.4966.4964611503998-0.00646115039978667
4566.6566.58622417811850.0637758218814781
4667.6966.74856325104890.941436748951062
4767.9167.82309184119770.086908158802288
4868.1468.04627932692020.0937206730798437
4968.1468.2797166717156-0.13971667171559
5068.1668.274592355398-0.114592355398017
5167.9468.2903895106736-0.35038951067358
526868.0575384552841-0.0575384552840745
5368.168.1154281470318-0.0154281470318125
5468.1268.2148622968393-0.0948622968393096
5568.1268.231383081298-0.111383081297973
5668.2468.22729794146470.0127020585352824
5768.4268.34776380831520.072236191684766
5868.9768.5304131778660.439586822134046
5969.1369.09653567704940.0334643229505502
6069.269.257763030765-0.0577630307649741

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 62.2 & 62.19 & 0.0100000000000051 \tabularnewline
4 & 62.22 & 62.2403667648431 & -0.0203667648430752 \tabularnewline
5 & 62.02 & 62.2596197835119 & -0.239619783511912 \tabularnewline
6 & 62.02 & 62.0508313722823 & -0.0308313722823357 \tabularnewline
7 & 62.02 & 62.0497005859407 & -0.0297005859406667 \tabularnewline
8 & 62.07 & 62.0486112728665 & 0.0213887271334912 \tabularnewline
9 & 62.31 & 62.0993957361816 & 0.210604263818439 \tabularnewline
10 & 62.71 & 62.3471199601585 & 0.362880039841542 \tabularnewline
11 & 62.77 & 62.760429124245 & 0.00957087575503834 \tabularnewline
12 & 62.82 & 62.8207801503194 & -0.000780150319400263 \tabularnewline
13 & 62.82 & 62.8707515371485 & -0.0507515371484502 \tabularnewline
14 & 62.82 & 62.8688901491927 & -0.0488901491926796 \tabularnewline
15 & 62.55 & 62.8670970304031 & -0.317097030403055 \tabularnewline
16 & 62.6 & 62.5854670261437 & 0.0145329738562694 \tabularnewline
17 & 62.47 & 62.6360000445313 & -0.166000044531309 \tabularnewline
18 & 62.47 & 62.4999117465031 & -0.0299117465031173 \tabularnewline
19 & 62.47 & 62.4988146888019 & -0.0288146888019085 \tabularnewline
20 & 62.72 & 62.4977578673203 & 0.222242132679746 \tabularnewline
21 & 63.13 & 62.7559089274118 & 0.3740910725882 \tabularnewline
22 & 64.09 & 63.1796292727649 & 0.91037072723509 \tabularnewline
23 & 64.31 & 64.1730184704558 & 0.136981529544244 \tabularnewline
24 & 64.29 & 64.3980424713744 & -0.108042471374404 \tabularnewline
25 & 64.29 & 64.3740798533686 & -0.0840798533685785 \tabularnewline
26 & 64.29 & 64.370996099946 & -0.0809960999459776 \tabularnewline
27 & 64.35 & 64.3680254477574 & -0.0180254477574096 \tabularnewline
28 & 64.42 & 64.4273643377056 & -0.00736433770559586 \tabularnewline
29 & 64.24 & 64.4970942396893 & -0.257094239689309 \tabularnewline
30 & 64.23 & 64.307664926842 & -0.0776649268419618 \tabularnewline
31 & 64.23 & 64.2948164503715 & -0.0648164503714526 \tabularnewline
32 & 64.2 & 64.2924392108466 & -0.0924392108465781 \tabularnewline
33 & 65.35 & 64.2590488655806 & 1.09095113441936 \tabularnewline
34 & 65.83 & 65.4490611177417 & 0.38093888225832 \tabularnewline
35 & 66.15 & 65.9430326166787 & 0.206967383321313 \tabularnewline
36 & 66.19 & 66.2706234526651 & -0.0806234526651224 \tabularnewline
37 & 66.19 & 66.3076664678687 & -0.117666467868673 \tabularnewline
38 & 66.56 & 66.3033508755064 & 0.256649124493563 \tabularnewline
39 & 66.59 & 66.6827638630933 & -0.0927638630932961 \tabularnewline
40 & 66.48 & 66.7093616107243 & -0.229361610724311 \tabularnewline
41 & 66.4 & 66.590949433208 & -0.19094943320799 \tabularnewline
42 & 66.4 & 66.5039460793175 & -0.103946079317538 \tabularnewline
43 & 66.4 & 66.5001337025707 & -0.100133702570702 \tabularnewline
44 & 66.49 & 66.4964611503998 & -0.00646115039978667 \tabularnewline
45 & 66.65 & 66.5862241781185 & 0.0637758218814781 \tabularnewline
46 & 67.69 & 66.7485632510489 & 0.941436748951062 \tabularnewline
47 & 67.91 & 67.8230918411977 & 0.086908158802288 \tabularnewline
48 & 68.14 & 68.0462793269202 & 0.0937206730798437 \tabularnewline
49 & 68.14 & 68.2797166717156 & -0.13971667171559 \tabularnewline
50 & 68.16 & 68.274592355398 & -0.114592355398017 \tabularnewline
51 & 67.94 & 68.2903895106736 & -0.35038951067358 \tabularnewline
52 & 68 & 68.0575384552841 & -0.0575384552840745 \tabularnewline
53 & 68.1 & 68.1154281470318 & -0.0154281470318125 \tabularnewline
54 & 68.12 & 68.2148622968393 & -0.0948622968393096 \tabularnewline
55 & 68.12 & 68.231383081298 & -0.111383081297973 \tabularnewline
56 & 68.24 & 68.2272979414647 & 0.0127020585352824 \tabularnewline
57 & 68.42 & 68.3477638083152 & 0.072236191684766 \tabularnewline
58 & 68.97 & 68.530413177866 & 0.439586822134046 \tabularnewline
59 & 69.13 & 69.0965356770494 & 0.0334643229505502 \tabularnewline
60 & 69.2 & 69.257763030765 & -0.0577630307649741 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166428&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]62.2[/C][C]62.19[/C][C]0.0100000000000051[/C][/ROW]
[ROW][C]4[/C][C]62.22[/C][C]62.2403667648431[/C][C]-0.0203667648430752[/C][/ROW]
[ROW][C]5[/C][C]62.02[/C][C]62.2596197835119[/C][C]-0.239619783511912[/C][/ROW]
[ROW][C]6[/C][C]62.02[/C][C]62.0508313722823[/C][C]-0.0308313722823357[/C][/ROW]
[ROW][C]7[/C][C]62.02[/C][C]62.0497005859407[/C][C]-0.0297005859406667[/C][/ROW]
[ROW][C]8[/C][C]62.07[/C][C]62.0486112728665[/C][C]0.0213887271334912[/C][/ROW]
[ROW][C]9[/C][C]62.31[/C][C]62.0993957361816[/C][C]0.210604263818439[/C][/ROW]
[ROW][C]10[/C][C]62.71[/C][C]62.3471199601585[/C][C]0.362880039841542[/C][/ROW]
[ROW][C]11[/C][C]62.77[/C][C]62.760429124245[/C][C]0.00957087575503834[/C][/ROW]
[ROW][C]12[/C][C]62.82[/C][C]62.8207801503194[/C][C]-0.000780150319400263[/C][/ROW]
[ROW][C]13[/C][C]62.82[/C][C]62.8707515371485[/C][C]-0.0507515371484502[/C][/ROW]
[ROW][C]14[/C][C]62.82[/C][C]62.8688901491927[/C][C]-0.0488901491926796[/C][/ROW]
[ROW][C]15[/C][C]62.55[/C][C]62.8670970304031[/C][C]-0.317097030403055[/C][/ROW]
[ROW][C]16[/C][C]62.6[/C][C]62.5854670261437[/C][C]0.0145329738562694[/C][/ROW]
[ROW][C]17[/C][C]62.47[/C][C]62.6360000445313[/C][C]-0.166000044531309[/C][/ROW]
[ROW][C]18[/C][C]62.47[/C][C]62.4999117465031[/C][C]-0.0299117465031173[/C][/ROW]
[ROW][C]19[/C][C]62.47[/C][C]62.4988146888019[/C][C]-0.0288146888019085[/C][/ROW]
[ROW][C]20[/C][C]62.72[/C][C]62.4977578673203[/C][C]0.222242132679746[/C][/ROW]
[ROW][C]21[/C][C]63.13[/C][C]62.7559089274118[/C][C]0.3740910725882[/C][/ROW]
[ROW][C]22[/C][C]64.09[/C][C]63.1796292727649[/C][C]0.91037072723509[/C][/ROW]
[ROW][C]23[/C][C]64.31[/C][C]64.1730184704558[/C][C]0.136981529544244[/C][/ROW]
[ROW][C]24[/C][C]64.29[/C][C]64.3980424713744[/C][C]-0.108042471374404[/C][/ROW]
[ROW][C]25[/C][C]64.29[/C][C]64.3740798533686[/C][C]-0.0840798533685785[/C][/ROW]
[ROW][C]26[/C][C]64.29[/C][C]64.370996099946[/C][C]-0.0809960999459776[/C][/ROW]
[ROW][C]27[/C][C]64.35[/C][C]64.3680254477574[/C][C]-0.0180254477574096[/C][/ROW]
[ROW][C]28[/C][C]64.42[/C][C]64.4273643377056[/C][C]-0.00736433770559586[/C][/ROW]
[ROW][C]29[/C][C]64.24[/C][C]64.4970942396893[/C][C]-0.257094239689309[/C][/ROW]
[ROW][C]30[/C][C]64.23[/C][C]64.307664926842[/C][C]-0.0776649268419618[/C][/ROW]
[ROW][C]31[/C][C]64.23[/C][C]64.2948164503715[/C][C]-0.0648164503714526[/C][/ROW]
[ROW][C]32[/C][C]64.2[/C][C]64.2924392108466[/C][C]-0.0924392108465781[/C][/ROW]
[ROW][C]33[/C][C]65.35[/C][C]64.2590488655806[/C][C]1.09095113441936[/C][/ROW]
[ROW][C]34[/C][C]65.83[/C][C]65.4490611177417[/C][C]0.38093888225832[/C][/ROW]
[ROW][C]35[/C][C]66.15[/C][C]65.9430326166787[/C][C]0.206967383321313[/C][/ROW]
[ROW][C]36[/C][C]66.19[/C][C]66.2706234526651[/C][C]-0.0806234526651224[/C][/ROW]
[ROW][C]37[/C][C]66.19[/C][C]66.3076664678687[/C][C]-0.117666467868673[/C][/ROW]
[ROW][C]38[/C][C]66.56[/C][C]66.3033508755064[/C][C]0.256649124493563[/C][/ROW]
[ROW][C]39[/C][C]66.59[/C][C]66.6827638630933[/C][C]-0.0927638630932961[/C][/ROW]
[ROW][C]40[/C][C]66.48[/C][C]66.7093616107243[/C][C]-0.229361610724311[/C][/ROW]
[ROW][C]41[/C][C]66.4[/C][C]66.590949433208[/C][C]-0.19094943320799[/C][/ROW]
[ROW][C]42[/C][C]66.4[/C][C]66.5039460793175[/C][C]-0.103946079317538[/C][/ROW]
[ROW][C]43[/C][C]66.4[/C][C]66.5001337025707[/C][C]-0.100133702570702[/C][/ROW]
[ROW][C]44[/C][C]66.49[/C][C]66.4964611503998[/C][C]-0.00646115039978667[/C][/ROW]
[ROW][C]45[/C][C]66.65[/C][C]66.5862241781185[/C][C]0.0637758218814781[/C][/ROW]
[ROW][C]46[/C][C]67.69[/C][C]66.7485632510489[/C][C]0.941436748951062[/C][/ROW]
[ROW][C]47[/C][C]67.91[/C][C]67.8230918411977[/C][C]0.086908158802288[/C][/ROW]
[ROW][C]48[/C][C]68.14[/C][C]68.0462793269202[/C][C]0.0937206730798437[/C][/ROW]
[ROW][C]49[/C][C]68.14[/C][C]68.2797166717156[/C][C]-0.13971667171559[/C][/ROW]
[ROW][C]50[/C][C]68.16[/C][C]68.274592355398[/C][C]-0.114592355398017[/C][/ROW]
[ROW][C]51[/C][C]67.94[/C][C]68.2903895106736[/C][C]-0.35038951067358[/C][/ROW]
[ROW][C]52[/C][C]68[/C][C]68.0575384552841[/C][C]-0.0575384552840745[/C][/ROW]
[ROW][C]53[/C][C]68.1[/C][C]68.1154281470318[/C][C]-0.0154281470318125[/C][/ROW]
[ROW][C]54[/C][C]68.12[/C][C]68.2148622968393[/C][C]-0.0948622968393096[/C][/ROW]
[ROW][C]55[/C][C]68.12[/C][C]68.231383081298[/C][C]-0.111383081297973[/C][/ROW]
[ROW][C]56[/C][C]68.24[/C][C]68.2272979414647[/C][C]0.0127020585352824[/C][/ROW]
[ROW][C]57[/C][C]68.42[/C][C]68.3477638083152[/C][C]0.072236191684766[/C][/ROW]
[ROW][C]58[/C][C]68.97[/C][C]68.530413177866[/C][C]0.439586822134046[/C][/ROW]
[ROW][C]59[/C][C]69.13[/C][C]69.0965356770494[/C][C]0.0334643229505502[/C][/ROW]
[ROW][C]60[/C][C]69.2[/C][C]69.257763030765[/C][C]-0.0577630307649741[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166428&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166428&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
362.262.190.0100000000000051
462.2262.2403667648431-0.0203667648430752
562.0262.2596197835119-0.239619783511912
662.0262.0508313722823-0.0308313722823357
762.0262.0497005859407-0.0297005859406667
862.0762.04861127286650.0213887271334912
962.3162.09939573618160.210604263818439
1062.7162.34711996015850.362880039841542
1162.7762.7604291242450.00957087575503834
1262.8262.8207801503194-0.000780150319400263
1362.8262.8707515371485-0.0507515371484502
1462.8262.8688901491927-0.0488901491926796
1562.5562.8670970304031-0.317097030403055
1662.662.58546702614370.0145329738562694
1762.4762.6360000445313-0.166000044531309
1862.4762.4999117465031-0.0299117465031173
1962.4762.4988146888019-0.0288146888019085
2062.7262.49775786732030.222242132679746
2163.1362.75590892741180.3740910725882
2264.0963.17962927276490.91037072723509
2364.3164.17301847045580.136981529544244
2464.2964.3980424713744-0.108042471374404
2564.2964.3740798533686-0.0840798533685785
2664.2964.370996099946-0.0809960999459776
2764.3564.3680254477574-0.0180254477574096
2864.4264.4273643377056-0.00736433770559586
2964.2464.4970942396893-0.257094239689309
3064.2364.307664926842-0.0776649268419618
3164.2364.2948164503715-0.0648164503714526
3264.264.2924392108466-0.0924392108465781
3365.3564.25904886558061.09095113441936
3465.8365.44906111774170.38093888225832
3566.1565.94303261667870.206967383321313
3666.1966.2706234526651-0.0806234526651224
3766.1966.3076664678687-0.117666467868673
3866.5666.30335087550640.256649124493563
3966.5966.6827638630933-0.0927638630932961
4066.4866.7093616107243-0.229361610724311
4166.466.590949433208-0.19094943320799
4266.466.5039460793175-0.103946079317538
4366.466.5001337025707-0.100133702570702
4466.4966.4964611503998-0.00646115039978667
4566.6566.58622417811850.0637758218814781
4667.6966.74856325104890.941436748951062
4767.9167.82309184119770.086908158802288
4868.1468.04627932692020.0937206730798437
4968.1468.2797166717156-0.13971667171559
5068.1668.274592355398-0.114592355398017
5167.9468.2903895106736-0.35038951067358
526868.0575384552841-0.0575384552840745
5368.168.1154281470318-0.0154281470318125
5468.1268.2148622968393-0.0948622968393096
5568.1268.231383081298-0.111383081297973
5668.2468.22729794146470.0127020585352824
5768.4268.34776380831520.072236191684766
5868.9768.5304131778660.439586822134046
5969.1369.09653567704940.0334643229505502
6069.269.257763030765-0.0577630307649741







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6169.325644485873668.787455489389169.8638334823581
6269.451288971747268.676091634540870.2264863089537
6369.576933457620868.610170925343870.5436959898979
6469.702577943494468.566125881445670.8390300055433
6569.828222429368168.535012993521671.1214318652145
6669.953866915241768.512336094382671.3953977361007
6770.079511401115368.495477334657971.6635454675727
6870.205155886988968.482765588483771.927546185494
6970.330800372862568.47306422250772.188536523218
7070.456444858736168.465563405121572.4473263123507
7170.582089344609768.459665338620172.7045133505993
7270.707733830483368.454916272914572.9605513880521

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 69.3256444858736 & 68.7874554893891 & 69.8638334823581 \tabularnewline
62 & 69.4512889717472 & 68.6760916345408 & 70.2264863089537 \tabularnewline
63 & 69.5769334576208 & 68.6101709253438 & 70.5436959898979 \tabularnewline
64 & 69.7025779434944 & 68.5661258814456 & 70.8390300055433 \tabularnewline
65 & 69.8282224293681 & 68.5350129935216 & 71.1214318652145 \tabularnewline
66 & 69.9538669152417 & 68.5123360943826 & 71.3953977361007 \tabularnewline
67 & 70.0795114011153 & 68.4954773346579 & 71.6635454675727 \tabularnewline
68 & 70.2051558869889 & 68.4827655884837 & 71.927546185494 \tabularnewline
69 & 70.3308003728625 & 68.473064222507 & 72.188536523218 \tabularnewline
70 & 70.4564448587361 & 68.4655634051215 & 72.4473263123507 \tabularnewline
71 & 70.5820893446097 & 68.4596653386201 & 72.7045133505993 \tabularnewline
72 & 70.7077338304833 & 68.4549162729145 & 72.9605513880521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=166428&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]69.3256444858736[/C][C]68.7874554893891[/C][C]69.8638334823581[/C][/ROW]
[ROW][C]62[/C][C]69.4512889717472[/C][C]68.6760916345408[/C][C]70.2264863089537[/C][/ROW]
[ROW][C]63[/C][C]69.5769334576208[/C][C]68.6101709253438[/C][C]70.5436959898979[/C][/ROW]
[ROW][C]64[/C][C]69.7025779434944[/C][C]68.5661258814456[/C][C]70.8390300055433[/C][/ROW]
[ROW][C]65[/C][C]69.8282224293681[/C][C]68.5350129935216[/C][C]71.1214318652145[/C][/ROW]
[ROW][C]66[/C][C]69.9538669152417[/C][C]68.5123360943826[/C][C]71.3953977361007[/C][/ROW]
[ROW][C]67[/C][C]70.0795114011153[/C][C]68.4954773346579[/C][C]71.6635454675727[/C][/ROW]
[ROW][C]68[/C][C]70.2051558869889[/C][C]68.4827655884837[/C][C]71.927546185494[/C][/ROW]
[ROW][C]69[/C][C]70.3308003728625[/C][C]68.473064222507[/C][C]72.188536523218[/C][/ROW]
[ROW][C]70[/C][C]70.4564448587361[/C][C]68.4655634051215[/C][C]72.4473263123507[/C][/ROW]
[ROW][C]71[/C][C]70.5820893446097[/C][C]68.4596653386201[/C][C]72.7045133505993[/C][/ROW]
[ROW][C]72[/C][C]70.7077338304833[/C][C]68.4549162729145[/C][C]72.9605513880521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=166428&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=166428&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
6169.325644485873668.787455489389169.8638334823581
6269.451288971747268.676091634540870.2264863089537
6369.576933457620868.610170925343870.5436959898979
6469.702577943494468.566125881445670.8390300055433
6569.828222429368168.535012993521671.1214318652145
6669.953866915241768.512336094382671.3953977361007
6770.079511401115368.495477334657971.6635454675727
6870.205155886988968.482765588483771.927546185494
6970.330800372862568.47306422250772.188536523218
7070.456444858736168.465563405121572.4473263123507
7170.582089344609768.459665338620172.7045133505993
7270.707733830483368.454916272914572.9605513880521



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')