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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 04:23:50 -0500
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/Dec/17/t1355736342i7tmh0s7egr8mzc.htm/, Retrieved Fri, 26 Apr 2024 19:03:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200719, Retrieved Fri, 26 Apr 2024 19:03:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Gemiddelde consum...] [2012-12-17 09:23:50] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
79,57
77,45
75,79
74,88
74,5
74,59
74,59
73,57
73,3
73,23
73
72,31
72,31
71,24
70,82
70,66
69,94
69,87
69,87
68,88
68,09
68,38
66,78
67,2
67,2
66,67
65,86
66,05
66,31
66,39
66,39
65,72
65,52
64,93
65,27
65,04
65,02
64,72
64,68
64,41
64,79
64,71
64,71
64,83
64,77
64,19
64,27
64,23
64,23
63,03
62,85
62,15
61,69
62,1
62,1
61,81
61,28
61,05
61,08
60,98
60,98
61,11
60,58
60,37
59,44
59,29
59,29
59,33
59,06
58,75
58,92
58,73




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200719&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200719&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200719&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.915141113646461
beta0.439774545987717
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.915141113646461 \tabularnewline
beta & 0.439774545987717 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200719&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]0.915141113646461[/C][/ROW]
[ROW][C]beta[/C][C]0.439774545987717[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200719&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200719&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
alpha0.915141113646461
beta0.439774545987717
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
375.7975.330.459999999999994
474.8873.81609456545091.06390543454907
574.573.28302270130681.21697729869317
674.5973.3798127264861.21018727351402
774.5973.95743576876680.632564231233161
873.5774.2610313402108-0.691031340210813
973.373.07524063780930.224759362190667
1073.2372.81798336034420.412016639655761
117372.8979113893630.102088610636955
1272.3172.7352976869297-0.425297686929653
1372.3171.91888759369580.391112406304202
1471.2472.0070133861392-0.767013386139169
1570.8270.72660168993580.0933983100642024
1670.6670.27117680017560.388823199824401
1769.9470.242591512441-0.302591512440998
1869.8769.45948449547260.41051550452741
1969.8769.49418536071720.375814639282765
2068.8869.6483788066886-0.768378806688631
2168.0968.4462353057038-0.356235305703791
2268.3867.47789231372910.902107686270909
2366.7868.0241691702674-1.24416917026741
2467.266.10557677546571.09442322453432
2567.266.76758336830170.432416631698331
2666.6766.9977890780345-0.327789078034471
2765.8666.4003786828955-0.540378682895494
2866.0565.39094028230390.659059717696138
2966.3165.74439966007070.56560033992929
3066.3966.23995963784370.15004036215629
3166.3966.4156082039185-0.0256082039185088
3265.7266.420207376256-0.700207376256017
3365.5265.5256506135473-0.00565061354727447
3464.9365.264437178141-0.334437178140945
3565.2764.56774146856130.702258531438673
3665.0465.1023966216011-0.062396621601053
3765.0264.91217252607990.107827473920082
3864.7264.9211232877065-0.201123287706494
3964.6864.56639727810620.113602721893855
4064.4164.5454100500854-0.135410050085369
4164.7964.24204444093260.547955559067375
4264.7164.7845826715951-0.0745826715951523
4364.7164.7273943462026-0.0173943462026074
4464.8364.71554095364160.114459046358434
4564.7764.8704167249671-0.100416724967147
4664.1964.7882375534827-0.598237553482733
4764.2764.00971792069930.260282079300723
4864.2364.121616924810.108383075190019
4964.2364.13812629887580.0918737011242428
5063.0364.1765023668971-1.14650236689708
5162.8562.62017309059820.229826909401808
5262.1562.4158744862329-0.265874486232882
5361.6961.65093643414340.0390635658565941
5462.161.18078108802490.919218911975136
5562.161.88603703850150.213962961498517
5661.8162.031994900997-0.221994900997046
5761.2861.689646671384-0.409646671384017
5861.0561.01070592599560.0392940740043599
5961.0860.75842344102540.32157655897457
6060.9860.89388960465220.0861103953477595
6160.9860.84852662634410.131473373655915
6261.1160.8975893920590.212410607941017
6360.5861.1062070227941-0.526207022794111
6460.3760.4271102410156-0.0571102410155646
6559.4460.1543188646264-0.714318864626442
6659.2958.99260710943320.297392890566805
6759.2958.87644186067870.41355813932131
6859.3359.03302306551390.296976934486096
6959.0659.2024360969041-0.14243609690412
7058.7558.9123999686596-0.162399968659628
7158.9258.53873527651160.3812647234884
7258.7358.8160426832008-0.0860426832007803

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 75.79 & 75.33 & 0.459999999999994 \tabularnewline
4 & 74.88 & 73.8160945654509 & 1.06390543454907 \tabularnewline
5 & 74.5 & 73.2830227013068 & 1.21697729869317 \tabularnewline
6 & 74.59 & 73.379812726486 & 1.21018727351402 \tabularnewline
7 & 74.59 & 73.9574357687668 & 0.632564231233161 \tabularnewline
8 & 73.57 & 74.2610313402108 & -0.691031340210813 \tabularnewline
9 & 73.3 & 73.0752406378093 & 0.224759362190667 \tabularnewline
10 & 73.23 & 72.8179833603442 & 0.412016639655761 \tabularnewline
11 & 73 & 72.897911389363 & 0.102088610636955 \tabularnewline
12 & 72.31 & 72.7352976869297 & -0.425297686929653 \tabularnewline
13 & 72.31 & 71.9188875936958 & 0.391112406304202 \tabularnewline
14 & 71.24 & 72.0070133861392 & -0.767013386139169 \tabularnewline
15 & 70.82 & 70.7266016899358 & 0.0933983100642024 \tabularnewline
16 & 70.66 & 70.2711768001756 & 0.388823199824401 \tabularnewline
17 & 69.94 & 70.242591512441 & -0.302591512440998 \tabularnewline
18 & 69.87 & 69.4594844954726 & 0.41051550452741 \tabularnewline
19 & 69.87 & 69.4941853607172 & 0.375814639282765 \tabularnewline
20 & 68.88 & 69.6483788066886 & -0.768378806688631 \tabularnewline
21 & 68.09 & 68.4462353057038 & -0.356235305703791 \tabularnewline
22 & 68.38 & 67.4778923137291 & 0.902107686270909 \tabularnewline
23 & 66.78 & 68.0241691702674 & -1.24416917026741 \tabularnewline
24 & 67.2 & 66.1055767754657 & 1.09442322453432 \tabularnewline
25 & 67.2 & 66.7675833683017 & 0.432416631698331 \tabularnewline
26 & 66.67 & 66.9977890780345 & -0.327789078034471 \tabularnewline
27 & 65.86 & 66.4003786828955 & -0.540378682895494 \tabularnewline
28 & 66.05 & 65.3909402823039 & 0.659059717696138 \tabularnewline
29 & 66.31 & 65.7443996600707 & 0.56560033992929 \tabularnewline
30 & 66.39 & 66.2399596378437 & 0.15004036215629 \tabularnewline
31 & 66.39 & 66.4156082039185 & -0.0256082039185088 \tabularnewline
32 & 65.72 & 66.420207376256 & -0.700207376256017 \tabularnewline
33 & 65.52 & 65.5256506135473 & -0.00565061354727447 \tabularnewline
34 & 64.93 & 65.264437178141 & -0.334437178140945 \tabularnewline
35 & 65.27 & 64.5677414685613 & 0.702258531438673 \tabularnewline
36 & 65.04 & 65.1023966216011 & -0.062396621601053 \tabularnewline
37 & 65.02 & 64.9121725260799 & 0.107827473920082 \tabularnewline
38 & 64.72 & 64.9211232877065 & -0.201123287706494 \tabularnewline
39 & 64.68 & 64.5663972781062 & 0.113602721893855 \tabularnewline
40 & 64.41 & 64.5454100500854 & -0.135410050085369 \tabularnewline
41 & 64.79 & 64.2420444409326 & 0.547955559067375 \tabularnewline
42 & 64.71 & 64.7845826715951 & -0.0745826715951523 \tabularnewline
43 & 64.71 & 64.7273943462026 & -0.0173943462026074 \tabularnewline
44 & 64.83 & 64.7155409536416 & 0.114459046358434 \tabularnewline
45 & 64.77 & 64.8704167249671 & -0.100416724967147 \tabularnewline
46 & 64.19 & 64.7882375534827 & -0.598237553482733 \tabularnewline
47 & 64.27 & 64.0097179206993 & 0.260282079300723 \tabularnewline
48 & 64.23 & 64.12161692481 & 0.108383075190019 \tabularnewline
49 & 64.23 & 64.1381262988758 & 0.0918737011242428 \tabularnewline
50 & 63.03 & 64.1765023668971 & -1.14650236689708 \tabularnewline
51 & 62.85 & 62.6201730905982 & 0.229826909401808 \tabularnewline
52 & 62.15 & 62.4158744862329 & -0.265874486232882 \tabularnewline
53 & 61.69 & 61.6509364341434 & 0.0390635658565941 \tabularnewline
54 & 62.1 & 61.1807810880249 & 0.919218911975136 \tabularnewline
55 & 62.1 & 61.8860370385015 & 0.213962961498517 \tabularnewline
56 & 61.81 & 62.031994900997 & -0.221994900997046 \tabularnewline
57 & 61.28 & 61.689646671384 & -0.409646671384017 \tabularnewline
58 & 61.05 & 61.0107059259956 & 0.0392940740043599 \tabularnewline
59 & 61.08 & 60.7584234410254 & 0.32157655897457 \tabularnewline
60 & 60.98 & 60.8938896046522 & 0.0861103953477595 \tabularnewline
61 & 60.98 & 60.8485266263441 & 0.131473373655915 \tabularnewline
62 & 61.11 & 60.897589392059 & 0.212410607941017 \tabularnewline
63 & 60.58 & 61.1062070227941 & -0.526207022794111 \tabularnewline
64 & 60.37 & 60.4271102410156 & -0.0571102410155646 \tabularnewline
65 & 59.44 & 60.1543188646264 & -0.714318864626442 \tabularnewline
66 & 59.29 & 58.9926071094332 & 0.297392890566805 \tabularnewline
67 & 59.29 & 58.8764418606787 & 0.41355813932131 \tabularnewline
68 & 59.33 & 59.0330230655139 & 0.296976934486096 \tabularnewline
69 & 59.06 & 59.2024360969041 & -0.14243609690412 \tabularnewline
70 & 58.75 & 58.9123999686596 & -0.162399968659628 \tabularnewline
71 & 58.92 & 58.5387352765116 & 0.3812647234884 \tabularnewline
72 & 58.73 & 58.8160426832008 & -0.0860426832007803 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200719&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]75.79[/C][C]75.33[/C][C]0.459999999999994[/C][/ROW]
[ROW][C]4[/C][C]74.88[/C][C]73.8160945654509[/C][C]1.06390543454907[/C][/ROW]
[ROW][C]5[/C][C]74.5[/C][C]73.2830227013068[/C][C]1.21697729869317[/C][/ROW]
[ROW][C]6[/C][C]74.59[/C][C]73.379812726486[/C][C]1.21018727351402[/C][/ROW]
[ROW][C]7[/C][C]74.59[/C][C]73.9574357687668[/C][C]0.632564231233161[/C][/ROW]
[ROW][C]8[/C][C]73.57[/C][C]74.2610313402108[/C][C]-0.691031340210813[/C][/ROW]
[ROW][C]9[/C][C]73.3[/C][C]73.0752406378093[/C][C]0.224759362190667[/C][/ROW]
[ROW][C]10[/C][C]73.23[/C][C]72.8179833603442[/C][C]0.412016639655761[/C][/ROW]
[ROW][C]11[/C][C]73[/C][C]72.897911389363[/C][C]0.102088610636955[/C][/ROW]
[ROW][C]12[/C][C]72.31[/C][C]72.7352976869297[/C][C]-0.425297686929653[/C][/ROW]
[ROW][C]13[/C][C]72.31[/C][C]71.9188875936958[/C][C]0.391112406304202[/C][/ROW]
[ROW][C]14[/C][C]71.24[/C][C]72.0070133861392[/C][C]-0.767013386139169[/C][/ROW]
[ROW][C]15[/C][C]70.82[/C][C]70.7266016899358[/C][C]0.0933983100642024[/C][/ROW]
[ROW][C]16[/C][C]70.66[/C][C]70.2711768001756[/C][C]0.388823199824401[/C][/ROW]
[ROW][C]17[/C][C]69.94[/C][C]70.242591512441[/C][C]-0.302591512440998[/C][/ROW]
[ROW][C]18[/C][C]69.87[/C][C]69.4594844954726[/C][C]0.41051550452741[/C][/ROW]
[ROW][C]19[/C][C]69.87[/C][C]69.4941853607172[/C][C]0.375814639282765[/C][/ROW]
[ROW][C]20[/C][C]68.88[/C][C]69.6483788066886[/C][C]-0.768378806688631[/C][/ROW]
[ROW][C]21[/C][C]68.09[/C][C]68.4462353057038[/C][C]-0.356235305703791[/C][/ROW]
[ROW][C]22[/C][C]68.38[/C][C]67.4778923137291[/C][C]0.902107686270909[/C][/ROW]
[ROW][C]23[/C][C]66.78[/C][C]68.0241691702674[/C][C]-1.24416917026741[/C][/ROW]
[ROW][C]24[/C][C]67.2[/C][C]66.1055767754657[/C][C]1.09442322453432[/C][/ROW]
[ROW][C]25[/C][C]67.2[/C][C]66.7675833683017[/C][C]0.432416631698331[/C][/ROW]
[ROW][C]26[/C][C]66.67[/C][C]66.9977890780345[/C][C]-0.327789078034471[/C][/ROW]
[ROW][C]27[/C][C]65.86[/C][C]66.4003786828955[/C][C]-0.540378682895494[/C][/ROW]
[ROW][C]28[/C][C]66.05[/C][C]65.3909402823039[/C][C]0.659059717696138[/C][/ROW]
[ROW][C]29[/C][C]66.31[/C][C]65.7443996600707[/C][C]0.56560033992929[/C][/ROW]
[ROW][C]30[/C][C]66.39[/C][C]66.2399596378437[/C][C]0.15004036215629[/C][/ROW]
[ROW][C]31[/C][C]66.39[/C][C]66.4156082039185[/C][C]-0.0256082039185088[/C][/ROW]
[ROW][C]32[/C][C]65.72[/C][C]66.420207376256[/C][C]-0.700207376256017[/C][/ROW]
[ROW][C]33[/C][C]65.52[/C][C]65.5256506135473[/C][C]-0.00565061354727447[/C][/ROW]
[ROW][C]34[/C][C]64.93[/C][C]65.264437178141[/C][C]-0.334437178140945[/C][/ROW]
[ROW][C]35[/C][C]65.27[/C][C]64.5677414685613[/C][C]0.702258531438673[/C][/ROW]
[ROW][C]36[/C][C]65.04[/C][C]65.1023966216011[/C][C]-0.062396621601053[/C][/ROW]
[ROW][C]37[/C][C]65.02[/C][C]64.9121725260799[/C][C]0.107827473920082[/C][/ROW]
[ROW][C]38[/C][C]64.72[/C][C]64.9211232877065[/C][C]-0.201123287706494[/C][/ROW]
[ROW][C]39[/C][C]64.68[/C][C]64.5663972781062[/C][C]0.113602721893855[/C][/ROW]
[ROW][C]40[/C][C]64.41[/C][C]64.5454100500854[/C][C]-0.135410050085369[/C][/ROW]
[ROW][C]41[/C][C]64.79[/C][C]64.2420444409326[/C][C]0.547955559067375[/C][/ROW]
[ROW][C]42[/C][C]64.71[/C][C]64.7845826715951[/C][C]-0.0745826715951523[/C][/ROW]
[ROW][C]43[/C][C]64.71[/C][C]64.7273943462026[/C][C]-0.0173943462026074[/C][/ROW]
[ROW][C]44[/C][C]64.83[/C][C]64.7155409536416[/C][C]0.114459046358434[/C][/ROW]
[ROW][C]45[/C][C]64.77[/C][C]64.8704167249671[/C][C]-0.100416724967147[/C][/ROW]
[ROW][C]46[/C][C]64.19[/C][C]64.7882375534827[/C][C]-0.598237553482733[/C][/ROW]
[ROW][C]47[/C][C]64.27[/C][C]64.0097179206993[/C][C]0.260282079300723[/C][/ROW]
[ROW][C]48[/C][C]64.23[/C][C]64.12161692481[/C][C]0.108383075190019[/C][/ROW]
[ROW][C]49[/C][C]64.23[/C][C]64.1381262988758[/C][C]0.0918737011242428[/C][/ROW]
[ROW][C]50[/C][C]63.03[/C][C]64.1765023668971[/C][C]-1.14650236689708[/C][/ROW]
[ROW][C]51[/C][C]62.85[/C][C]62.6201730905982[/C][C]0.229826909401808[/C][/ROW]
[ROW][C]52[/C][C]62.15[/C][C]62.4158744862329[/C][C]-0.265874486232882[/C][/ROW]
[ROW][C]53[/C][C]61.69[/C][C]61.6509364341434[/C][C]0.0390635658565941[/C][/ROW]
[ROW][C]54[/C][C]62.1[/C][C]61.1807810880249[/C][C]0.919218911975136[/C][/ROW]
[ROW][C]55[/C][C]62.1[/C][C]61.8860370385015[/C][C]0.213962961498517[/C][/ROW]
[ROW][C]56[/C][C]61.81[/C][C]62.031994900997[/C][C]-0.221994900997046[/C][/ROW]
[ROW][C]57[/C][C]61.28[/C][C]61.689646671384[/C][C]-0.409646671384017[/C][/ROW]
[ROW][C]58[/C][C]61.05[/C][C]61.0107059259956[/C][C]0.0392940740043599[/C][/ROW]
[ROW][C]59[/C][C]61.08[/C][C]60.7584234410254[/C][C]0.32157655897457[/C][/ROW]
[ROW][C]60[/C][C]60.98[/C][C]60.8938896046522[/C][C]0.0861103953477595[/C][/ROW]
[ROW][C]61[/C][C]60.98[/C][C]60.8485266263441[/C][C]0.131473373655915[/C][/ROW]
[ROW][C]62[/C][C]61.11[/C][C]60.897589392059[/C][C]0.212410607941017[/C][/ROW]
[ROW][C]63[/C][C]60.58[/C][C]61.1062070227941[/C][C]-0.526207022794111[/C][/ROW]
[ROW][C]64[/C][C]60.37[/C][C]60.4271102410156[/C][C]-0.0571102410155646[/C][/ROW]
[ROW][C]65[/C][C]59.44[/C][C]60.1543188646264[/C][C]-0.714318864626442[/C][/ROW]
[ROW][C]66[/C][C]59.29[/C][C]58.9926071094332[/C][C]0.297392890566805[/C][/ROW]
[ROW][C]67[/C][C]59.29[/C][C]58.8764418606787[/C][C]0.41355813932131[/C][/ROW]
[ROW][C]68[/C][C]59.33[/C][C]59.0330230655139[/C][C]0.296976934486096[/C][/ROW]
[ROW][C]69[/C][C]59.06[/C][C]59.2024360969041[/C][C]-0.14243609690412[/C][/ROW]
[ROW][C]70[/C][C]58.75[/C][C]58.9123999686596[/C][C]-0.162399968659628[/C][/ROW]
[ROW][C]71[/C][C]58.92[/C][C]58.5387352765116[/C][C]0.3812647234884[/C][/ROW]
[ROW][C]72[/C][C]58.73[/C][C]58.8160426832008[/C][C]-0.0860426832007803[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200719&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200719&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
375.7975.330.459999999999994
474.8873.81609456545091.06390543454907
574.573.28302270130681.21697729869317
674.5973.3798127264861.21018727351402
774.5973.95743576876680.632564231233161
873.5774.2610313402108-0.691031340210813
973.373.07524063780930.224759362190667
1073.2372.81798336034420.412016639655761
117372.8979113893630.102088610636955
1272.3172.7352976869297-0.425297686929653
1372.3171.91888759369580.391112406304202
1471.2472.0070133861392-0.767013386139169
1570.8270.72660168993580.0933983100642024
1670.6670.27117680017560.388823199824401
1769.9470.242591512441-0.302591512440998
1869.8769.45948449547260.41051550452741
1969.8769.49418536071720.375814639282765
2068.8869.6483788066886-0.768378806688631
2168.0968.4462353057038-0.356235305703791
2268.3867.47789231372910.902107686270909
2366.7868.0241691702674-1.24416917026741
2467.266.10557677546571.09442322453432
2567.266.76758336830170.432416631698331
2666.6766.9977890780345-0.327789078034471
2765.8666.4003786828955-0.540378682895494
2866.0565.39094028230390.659059717696138
2966.3165.74439966007070.56560033992929
3066.3966.23995963784370.15004036215629
3166.3966.4156082039185-0.0256082039185088
3265.7266.420207376256-0.700207376256017
3365.5265.5256506135473-0.00565061354727447
3464.9365.264437178141-0.334437178140945
3565.2764.56774146856130.702258531438673
3665.0465.1023966216011-0.062396621601053
3765.0264.91217252607990.107827473920082
3864.7264.9211232877065-0.201123287706494
3964.6864.56639727810620.113602721893855
4064.4164.5454100500854-0.135410050085369
4164.7964.24204444093260.547955559067375
4264.7164.7845826715951-0.0745826715951523
4364.7164.7273943462026-0.0173943462026074
4464.8364.71554095364160.114459046358434
4564.7764.8704167249671-0.100416724967147
4664.1964.7882375534827-0.598237553482733
4764.2764.00971792069930.260282079300723
4864.2364.121616924810.108383075190019
4964.2364.13812629887580.0918737011242428
5063.0364.1765023668971-1.14650236689708
5162.8562.62017309059820.229826909401808
5262.1562.4158744862329-0.265874486232882
5361.6961.65093643414340.0390635658565941
5462.161.18078108802490.919218911975136
5562.161.88603703850150.213962961498517
5661.8162.031994900997-0.221994900997046
5761.2861.689646671384-0.409646671384017
5861.0561.01070592599560.0392940740043599
5961.0860.75842344102540.32157655897457
6060.9860.89388960465220.0861103953477595
6160.9860.84852662634410.131473373655915
6261.1160.8975893920590.212410607941017
6360.5861.1062070227941-0.526207022794111
6460.3760.4271102410156-0.0571102410155646
6559.4460.1543188646264-0.714318864626442
6659.2958.99260710943320.297392890566805
6759.2958.87644186067870.41355813932131
6859.3359.03302306551390.296976934486096
6959.0659.2024360969041-0.14243609690412
7058.7558.9123999686596-0.162399968659628
7158.9258.53873527651160.3812647234884
7258.7358.8160426832008-0.0860426832007803







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7358.631069495188757.62498572887559.6371532615024
7458.524837504102256.860669866005760.1890051421987
7558.418605513015656.017742505773560.8194685202578
7658.312373521929155.099249318536461.5254977253218
7758.206141530842654.110116546255762.3021665154294
7858.09990953975653.054931976935763.1448871025763
7957.993677548669551.937672611629964.049682485709
8057.887445557582950.761752111703965.013139003462
8157.781213566496449.530115014366166.0323121186267
8257.674981575409848.245323504173267.1046396466465
8357.568749584323346.909627950667168.2278712179795
8457.462517593236745.525022456278469.4000127301951

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 58.6310694951887 & 57.624985728875 & 59.6371532615024 \tabularnewline
74 & 58.5248375041022 & 56.8606698660057 & 60.1890051421987 \tabularnewline
75 & 58.4186055130156 & 56.0177425057735 & 60.8194685202578 \tabularnewline
76 & 58.3123735219291 & 55.0992493185364 & 61.5254977253218 \tabularnewline
77 & 58.2061415308426 & 54.1101165462557 & 62.3021665154294 \tabularnewline
78 & 58.099909539756 & 53.0549319769357 & 63.1448871025763 \tabularnewline
79 & 57.9936775486695 & 51.9376726116299 & 64.049682485709 \tabularnewline
80 & 57.8874455575829 & 50.7617521117039 & 65.013139003462 \tabularnewline
81 & 57.7812135664964 & 49.5301150143661 & 66.0323121186267 \tabularnewline
82 & 57.6749815754098 & 48.2453235041732 & 67.1046396466465 \tabularnewline
83 & 57.5687495843233 & 46.9096279506671 & 68.2278712179795 \tabularnewline
84 & 57.4625175932367 & 45.5250224562784 & 69.4000127301951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200719&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]58.6310694951887[/C][C]57.624985728875[/C][C]59.6371532615024[/C][/ROW]
[ROW][C]74[/C][C]58.5248375041022[/C][C]56.8606698660057[/C][C]60.1890051421987[/C][/ROW]
[ROW][C]75[/C][C]58.4186055130156[/C][C]56.0177425057735[/C][C]60.8194685202578[/C][/ROW]
[ROW][C]76[/C][C]58.3123735219291[/C][C]55.0992493185364[/C][C]61.5254977253218[/C][/ROW]
[ROW][C]77[/C][C]58.2061415308426[/C][C]54.1101165462557[/C][C]62.3021665154294[/C][/ROW]
[ROW][C]78[/C][C]58.099909539756[/C][C]53.0549319769357[/C][C]63.1448871025763[/C][/ROW]
[ROW][C]79[/C][C]57.9936775486695[/C][C]51.9376726116299[/C][C]64.049682485709[/C][/ROW]
[ROW][C]80[/C][C]57.8874455575829[/C][C]50.7617521117039[/C][C]65.013139003462[/C][/ROW]
[ROW][C]81[/C][C]57.7812135664964[/C][C]49.5301150143661[/C][C]66.0323121186267[/C][/ROW]
[ROW][C]82[/C][C]57.6749815754098[/C][C]48.2453235041732[/C][C]67.1046396466465[/C][/ROW]
[ROW][C]83[/C][C]57.5687495843233[/C][C]46.9096279506671[/C][C]68.2278712179795[/C][/ROW]
[ROW][C]84[/C][C]57.4625175932367[/C][C]45.5250224562784[/C][C]69.4000127301951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200719&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200719&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
7358.631069495188757.62498572887559.6371532615024
7458.524837504102256.860669866005760.1890051421987
7558.418605513015656.017742505773560.8194685202578
7658.312373521929155.099249318536461.5254977253218
7758.206141530842654.110116546255762.3021665154294
7858.09990953975653.054931976935763.1448871025763
7957.993677548669551.937672611629964.049682485709
8057.887445557582950.761752111703965.013139003462
8157.781213566496449.530115014366166.0323121186267
8257.674981575409848.245323504173267.1046396466465
8357.568749584323346.909627950667168.2278712179795
8457.462517593236745.525022456278469.4000127301951



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')