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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 Nov 2014 08:38:00 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/30/t1417336701i897o2h2ygnf321.htm/, Retrieved Sun, 19 May 2024 14:59:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261302, Retrieved Sun, 19 May 2024 14:59:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact112
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-30 08:38:00] [823d84bc2f1aa2ddbab319cc794dd4cf] [Current]
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Dataseries X:
104,31
104,76
105,68
106,22
106,69
107,17
107,46
107,16
107,35
107,65
107,75
108,22
108,68
109,35
109,54
109,46
108,86
108,63
107,55
106,8
106,07
106,44
106,38
107,07
106,54
107,83
108,06
108,49
107,9
108,02
108,46
108,31
107,69
107,71
107,74
108,15
107,39
109,16
109,65
110,4
110,26
110,5
110,31
109,85
109,4
109,75
109,79
110,27
109,19
111,78
111,58
111,71
111,59
112,14
111,73
111,32
111,29
112,45
112,61
114,3
113,32
114,85
115,35
114,9
115,49
115,55
115,44
114,81
113,83
113,64
113,26
114,68




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261302&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261302&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.930241284041313
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.930241284041313 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261302&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]0.930241284041313[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261302&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
alpha0.930241284041313
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2104.76104.310.450000000000003
3105.68104.7286085778190.951391422181416
4106.22105.6136321560150.606367843985467
5106.69106.1777005578050.512299442195058
6107.17106.6542626487260.515737351273884
7107.46107.1340228246030.325977175396787
8107.16107.437260250812-0.277260250812475
9107.35107.1793413190830.170658680916944
10107.65107.3380950695520.31190493044798
11107.75107.6282419125510.121758087449237
12108.22107.7415063121620.478493687838039
13108.68108.1866208947420.493379105257929
14109.35108.6455825071360.704417492863627
15109.54109.3008607401990.239139259801007
16109.46109.523317952301-0.0633179523009773
17108.86109.46441697905-0.604416979049645
18108.63108.902163352362-0.272163352362142
19107.55108.648985765992-1.09898576599178
20106.8107.626663835892-0.826663835892461
21106.07106.857667007721-0.787667007721339
22106.44106.1249466390620.315053360938336
23106.38106.418022282082-0.0380222820824798
24107.07106.3826523855760.687347614424112
25106.54107.022051513001-0.482051513000499
26107.83106.5736272945731.25637270542713
27108.06107.7423570533040.317642946696139
28108.49108.0378416359050.452158364094842
29107.9108.458458013111-0.558458013110751
30108.02107.9389573139110.0810426860885514
31108.46108.0143465662810.445653433719386
32108.31108.428911788701-0.118911788701141
33107.69108.318295133692-0.628295133692149
34107.71107.733829061769-0.0238290617694616
35107.74107.7116622847520.0283377152484547
36108.15107.7380231973710.411976802628942
37107.39108.121261027244-0.731261027243846
38109.16107.4410118302911.71898816970882
39109.65109.0400855925330.609914407467073
40110.4109.607453154090.792546845909598
41110.26110.344712949692-0.0847129496922321
42110.5110.2659094665960.234090533404384
43110.31110.483670144972-0.173670144971624
44109.85110.322115006314-0.472115006313587
45109.4109.882934136625-0.482934136625246
46109.75109.4336888652640.316311134736395
47109.79109.7279345413970.0620654586026461
48110.27109.7856703933020.4843296066975
49109.19110.236213788536-1.04621378853601
50111.78109.2629825305072.51701746949345
51111.58111.604416093283-0.0244160932825537
52111.71111.5817032353160.128296764683867
53111.59111.701050182434-0.111050182433985
54112.14111.5977467181340.542253281866422
55111.73112.102173107333-0.3721731073326
56111.32111.755962318082-0.435962318081891
57111.29111.350412171516-0.0604121715157504
58112.45111.2942142755131.15578572448678
59112.61112.3693738719360.240626128063582
60114.3112.593214230281.70678576971981
61113.32114.180936816288-0.86093681628779
62114.85113.3800578468261.4699421531742
63115.35114.7474587228610.602541277138982
64114.9115.307967494195-0.407967494194679
65115.49114.9284592885480.561540711452082
66115.55115.4508276410110.0991723589894349
67115.44115.543081863578-0.103081863578311
68114.81115.447190858442-0.637190858441841
69113.83114.854449616106-1.02444961610551
70113.64113.901464289784-0.261464289783888
71113.26113.658239413124-0.398239413124372
72114.68113.2877806701041.39221932989631

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 104.76 & 104.31 & 0.450000000000003 \tabularnewline
3 & 105.68 & 104.728608577819 & 0.951391422181416 \tabularnewline
4 & 106.22 & 105.613632156015 & 0.606367843985467 \tabularnewline
5 & 106.69 & 106.177700557805 & 0.512299442195058 \tabularnewline
6 & 107.17 & 106.654262648726 & 0.515737351273884 \tabularnewline
7 & 107.46 & 107.134022824603 & 0.325977175396787 \tabularnewline
8 & 107.16 & 107.437260250812 & -0.277260250812475 \tabularnewline
9 & 107.35 & 107.179341319083 & 0.170658680916944 \tabularnewline
10 & 107.65 & 107.338095069552 & 0.31190493044798 \tabularnewline
11 & 107.75 & 107.628241912551 & 0.121758087449237 \tabularnewline
12 & 108.22 & 107.741506312162 & 0.478493687838039 \tabularnewline
13 & 108.68 & 108.186620894742 & 0.493379105257929 \tabularnewline
14 & 109.35 & 108.645582507136 & 0.704417492863627 \tabularnewline
15 & 109.54 & 109.300860740199 & 0.239139259801007 \tabularnewline
16 & 109.46 & 109.523317952301 & -0.0633179523009773 \tabularnewline
17 & 108.86 & 109.46441697905 & -0.604416979049645 \tabularnewline
18 & 108.63 & 108.902163352362 & -0.272163352362142 \tabularnewline
19 & 107.55 & 108.648985765992 & -1.09898576599178 \tabularnewline
20 & 106.8 & 107.626663835892 & -0.826663835892461 \tabularnewline
21 & 106.07 & 106.857667007721 & -0.787667007721339 \tabularnewline
22 & 106.44 & 106.124946639062 & 0.315053360938336 \tabularnewline
23 & 106.38 & 106.418022282082 & -0.0380222820824798 \tabularnewline
24 & 107.07 & 106.382652385576 & 0.687347614424112 \tabularnewline
25 & 106.54 & 107.022051513001 & -0.482051513000499 \tabularnewline
26 & 107.83 & 106.573627294573 & 1.25637270542713 \tabularnewline
27 & 108.06 & 107.742357053304 & 0.317642946696139 \tabularnewline
28 & 108.49 & 108.037841635905 & 0.452158364094842 \tabularnewline
29 & 107.9 & 108.458458013111 & -0.558458013110751 \tabularnewline
30 & 108.02 & 107.938957313911 & 0.0810426860885514 \tabularnewline
31 & 108.46 & 108.014346566281 & 0.445653433719386 \tabularnewline
32 & 108.31 & 108.428911788701 & -0.118911788701141 \tabularnewline
33 & 107.69 & 108.318295133692 & -0.628295133692149 \tabularnewline
34 & 107.71 & 107.733829061769 & -0.0238290617694616 \tabularnewline
35 & 107.74 & 107.711662284752 & 0.0283377152484547 \tabularnewline
36 & 108.15 & 107.738023197371 & 0.411976802628942 \tabularnewline
37 & 107.39 & 108.121261027244 & -0.731261027243846 \tabularnewline
38 & 109.16 & 107.441011830291 & 1.71898816970882 \tabularnewline
39 & 109.65 & 109.040085592533 & 0.609914407467073 \tabularnewline
40 & 110.4 & 109.60745315409 & 0.792546845909598 \tabularnewline
41 & 110.26 & 110.344712949692 & -0.0847129496922321 \tabularnewline
42 & 110.5 & 110.265909466596 & 0.234090533404384 \tabularnewline
43 & 110.31 & 110.483670144972 & -0.173670144971624 \tabularnewline
44 & 109.85 & 110.322115006314 & -0.472115006313587 \tabularnewline
45 & 109.4 & 109.882934136625 & -0.482934136625246 \tabularnewline
46 & 109.75 & 109.433688865264 & 0.316311134736395 \tabularnewline
47 & 109.79 & 109.727934541397 & 0.0620654586026461 \tabularnewline
48 & 110.27 & 109.785670393302 & 0.4843296066975 \tabularnewline
49 & 109.19 & 110.236213788536 & -1.04621378853601 \tabularnewline
50 & 111.78 & 109.262982530507 & 2.51701746949345 \tabularnewline
51 & 111.58 & 111.604416093283 & -0.0244160932825537 \tabularnewline
52 & 111.71 & 111.581703235316 & 0.128296764683867 \tabularnewline
53 & 111.59 & 111.701050182434 & -0.111050182433985 \tabularnewline
54 & 112.14 & 111.597746718134 & 0.542253281866422 \tabularnewline
55 & 111.73 & 112.102173107333 & -0.3721731073326 \tabularnewline
56 & 111.32 & 111.755962318082 & -0.435962318081891 \tabularnewline
57 & 111.29 & 111.350412171516 & -0.0604121715157504 \tabularnewline
58 & 112.45 & 111.294214275513 & 1.15578572448678 \tabularnewline
59 & 112.61 & 112.369373871936 & 0.240626128063582 \tabularnewline
60 & 114.3 & 112.59321423028 & 1.70678576971981 \tabularnewline
61 & 113.32 & 114.180936816288 & -0.86093681628779 \tabularnewline
62 & 114.85 & 113.380057846826 & 1.4699421531742 \tabularnewline
63 & 115.35 & 114.747458722861 & 0.602541277138982 \tabularnewline
64 & 114.9 & 115.307967494195 & -0.407967494194679 \tabularnewline
65 & 115.49 & 114.928459288548 & 0.561540711452082 \tabularnewline
66 & 115.55 & 115.450827641011 & 0.0991723589894349 \tabularnewline
67 & 115.44 & 115.543081863578 & -0.103081863578311 \tabularnewline
68 & 114.81 & 115.447190858442 & -0.637190858441841 \tabularnewline
69 & 113.83 & 114.854449616106 & -1.02444961610551 \tabularnewline
70 & 113.64 & 113.901464289784 & -0.261464289783888 \tabularnewline
71 & 113.26 & 113.658239413124 & -0.398239413124372 \tabularnewline
72 & 114.68 & 113.287780670104 & 1.39221932989631 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261302&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]2[/C][C]104.76[/C][C]104.31[/C][C]0.450000000000003[/C][/ROW]
[ROW][C]3[/C][C]105.68[/C][C]104.728608577819[/C][C]0.951391422181416[/C][/ROW]
[ROW][C]4[/C][C]106.22[/C][C]105.613632156015[/C][C]0.606367843985467[/C][/ROW]
[ROW][C]5[/C][C]106.69[/C][C]106.177700557805[/C][C]0.512299442195058[/C][/ROW]
[ROW][C]6[/C][C]107.17[/C][C]106.654262648726[/C][C]0.515737351273884[/C][/ROW]
[ROW][C]7[/C][C]107.46[/C][C]107.134022824603[/C][C]0.325977175396787[/C][/ROW]
[ROW][C]8[/C][C]107.16[/C][C]107.437260250812[/C][C]-0.277260250812475[/C][/ROW]
[ROW][C]9[/C][C]107.35[/C][C]107.179341319083[/C][C]0.170658680916944[/C][/ROW]
[ROW][C]10[/C][C]107.65[/C][C]107.338095069552[/C][C]0.31190493044798[/C][/ROW]
[ROW][C]11[/C][C]107.75[/C][C]107.628241912551[/C][C]0.121758087449237[/C][/ROW]
[ROW][C]12[/C][C]108.22[/C][C]107.741506312162[/C][C]0.478493687838039[/C][/ROW]
[ROW][C]13[/C][C]108.68[/C][C]108.186620894742[/C][C]0.493379105257929[/C][/ROW]
[ROW][C]14[/C][C]109.35[/C][C]108.645582507136[/C][C]0.704417492863627[/C][/ROW]
[ROW][C]15[/C][C]109.54[/C][C]109.300860740199[/C][C]0.239139259801007[/C][/ROW]
[ROW][C]16[/C][C]109.46[/C][C]109.523317952301[/C][C]-0.0633179523009773[/C][/ROW]
[ROW][C]17[/C][C]108.86[/C][C]109.46441697905[/C][C]-0.604416979049645[/C][/ROW]
[ROW][C]18[/C][C]108.63[/C][C]108.902163352362[/C][C]-0.272163352362142[/C][/ROW]
[ROW][C]19[/C][C]107.55[/C][C]108.648985765992[/C][C]-1.09898576599178[/C][/ROW]
[ROW][C]20[/C][C]106.8[/C][C]107.626663835892[/C][C]-0.826663835892461[/C][/ROW]
[ROW][C]21[/C][C]106.07[/C][C]106.857667007721[/C][C]-0.787667007721339[/C][/ROW]
[ROW][C]22[/C][C]106.44[/C][C]106.124946639062[/C][C]0.315053360938336[/C][/ROW]
[ROW][C]23[/C][C]106.38[/C][C]106.418022282082[/C][C]-0.0380222820824798[/C][/ROW]
[ROW][C]24[/C][C]107.07[/C][C]106.382652385576[/C][C]0.687347614424112[/C][/ROW]
[ROW][C]25[/C][C]106.54[/C][C]107.022051513001[/C][C]-0.482051513000499[/C][/ROW]
[ROW][C]26[/C][C]107.83[/C][C]106.573627294573[/C][C]1.25637270542713[/C][/ROW]
[ROW][C]27[/C][C]108.06[/C][C]107.742357053304[/C][C]0.317642946696139[/C][/ROW]
[ROW][C]28[/C][C]108.49[/C][C]108.037841635905[/C][C]0.452158364094842[/C][/ROW]
[ROW][C]29[/C][C]107.9[/C][C]108.458458013111[/C][C]-0.558458013110751[/C][/ROW]
[ROW][C]30[/C][C]108.02[/C][C]107.938957313911[/C][C]0.0810426860885514[/C][/ROW]
[ROW][C]31[/C][C]108.46[/C][C]108.014346566281[/C][C]0.445653433719386[/C][/ROW]
[ROW][C]32[/C][C]108.31[/C][C]108.428911788701[/C][C]-0.118911788701141[/C][/ROW]
[ROW][C]33[/C][C]107.69[/C][C]108.318295133692[/C][C]-0.628295133692149[/C][/ROW]
[ROW][C]34[/C][C]107.71[/C][C]107.733829061769[/C][C]-0.0238290617694616[/C][/ROW]
[ROW][C]35[/C][C]107.74[/C][C]107.711662284752[/C][C]0.0283377152484547[/C][/ROW]
[ROW][C]36[/C][C]108.15[/C][C]107.738023197371[/C][C]0.411976802628942[/C][/ROW]
[ROW][C]37[/C][C]107.39[/C][C]108.121261027244[/C][C]-0.731261027243846[/C][/ROW]
[ROW][C]38[/C][C]109.16[/C][C]107.441011830291[/C][C]1.71898816970882[/C][/ROW]
[ROW][C]39[/C][C]109.65[/C][C]109.040085592533[/C][C]0.609914407467073[/C][/ROW]
[ROW][C]40[/C][C]110.4[/C][C]109.60745315409[/C][C]0.792546845909598[/C][/ROW]
[ROW][C]41[/C][C]110.26[/C][C]110.344712949692[/C][C]-0.0847129496922321[/C][/ROW]
[ROW][C]42[/C][C]110.5[/C][C]110.265909466596[/C][C]0.234090533404384[/C][/ROW]
[ROW][C]43[/C][C]110.31[/C][C]110.483670144972[/C][C]-0.173670144971624[/C][/ROW]
[ROW][C]44[/C][C]109.85[/C][C]110.322115006314[/C][C]-0.472115006313587[/C][/ROW]
[ROW][C]45[/C][C]109.4[/C][C]109.882934136625[/C][C]-0.482934136625246[/C][/ROW]
[ROW][C]46[/C][C]109.75[/C][C]109.433688865264[/C][C]0.316311134736395[/C][/ROW]
[ROW][C]47[/C][C]109.79[/C][C]109.727934541397[/C][C]0.0620654586026461[/C][/ROW]
[ROW][C]48[/C][C]110.27[/C][C]109.785670393302[/C][C]0.4843296066975[/C][/ROW]
[ROW][C]49[/C][C]109.19[/C][C]110.236213788536[/C][C]-1.04621378853601[/C][/ROW]
[ROW][C]50[/C][C]111.78[/C][C]109.262982530507[/C][C]2.51701746949345[/C][/ROW]
[ROW][C]51[/C][C]111.58[/C][C]111.604416093283[/C][C]-0.0244160932825537[/C][/ROW]
[ROW][C]52[/C][C]111.71[/C][C]111.581703235316[/C][C]0.128296764683867[/C][/ROW]
[ROW][C]53[/C][C]111.59[/C][C]111.701050182434[/C][C]-0.111050182433985[/C][/ROW]
[ROW][C]54[/C][C]112.14[/C][C]111.597746718134[/C][C]0.542253281866422[/C][/ROW]
[ROW][C]55[/C][C]111.73[/C][C]112.102173107333[/C][C]-0.3721731073326[/C][/ROW]
[ROW][C]56[/C][C]111.32[/C][C]111.755962318082[/C][C]-0.435962318081891[/C][/ROW]
[ROW][C]57[/C][C]111.29[/C][C]111.350412171516[/C][C]-0.0604121715157504[/C][/ROW]
[ROW][C]58[/C][C]112.45[/C][C]111.294214275513[/C][C]1.15578572448678[/C][/ROW]
[ROW][C]59[/C][C]112.61[/C][C]112.369373871936[/C][C]0.240626128063582[/C][/ROW]
[ROW][C]60[/C][C]114.3[/C][C]112.59321423028[/C][C]1.70678576971981[/C][/ROW]
[ROW][C]61[/C][C]113.32[/C][C]114.180936816288[/C][C]-0.86093681628779[/C][/ROW]
[ROW][C]62[/C][C]114.85[/C][C]113.380057846826[/C][C]1.4699421531742[/C][/ROW]
[ROW][C]63[/C][C]115.35[/C][C]114.747458722861[/C][C]0.602541277138982[/C][/ROW]
[ROW][C]64[/C][C]114.9[/C][C]115.307967494195[/C][C]-0.407967494194679[/C][/ROW]
[ROW][C]65[/C][C]115.49[/C][C]114.928459288548[/C][C]0.561540711452082[/C][/ROW]
[ROW][C]66[/C][C]115.55[/C][C]115.450827641011[/C][C]0.0991723589894349[/C][/ROW]
[ROW][C]67[/C][C]115.44[/C][C]115.543081863578[/C][C]-0.103081863578311[/C][/ROW]
[ROW][C]68[/C][C]114.81[/C][C]115.447190858442[/C][C]-0.637190858441841[/C][/ROW]
[ROW][C]69[/C][C]113.83[/C][C]114.854449616106[/C][C]-1.02444961610551[/C][/ROW]
[ROW][C]70[/C][C]113.64[/C][C]113.901464289784[/C][C]-0.261464289783888[/C][/ROW]
[ROW][C]71[/C][C]113.26[/C][C]113.658239413124[/C][C]-0.398239413124372[/C][/ROW]
[ROW][C]72[/C][C]114.68[/C][C]113.287780670104[/C][C]1.39221932989631[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261302&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
2104.76104.310.450000000000003
3105.68104.7286085778190.951391422181416
4106.22105.6136321560150.606367843985467
5106.69106.1777005578050.512299442195058
6107.17106.6542626487260.515737351273884
7107.46107.1340228246030.325977175396787
8107.16107.437260250812-0.277260250812475
9107.35107.1793413190830.170658680916944
10107.65107.3380950695520.31190493044798
11107.75107.6282419125510.121758087449237
12108.22107.7415063121620.478493687838039
13108.68108.1866208947420.493379105257929
14109.35108.6455825071360.704417492863627
15109.54109.3008607401990.239139259801007
16109.46109.523317952301-0.0633179523009773
17108.86109.46441697905-0.604416979049645
18108.63108.902163352362-0.272163352362142
19107.55108.648985765992-1.09898576599178
20106.8107.626663835892-0.826663835892461
21106.07106.857667007721-0.787667007721339
22106.44106.1249466390620.315053360938336
23106.38106.418022282082-0.0380222820824798
24107.07106.3826523855760.687347614424112
25106.54107.022051513001-0.482051513000499
26107.83106.5736272945731.25637270542713
27108.06107.7423570533040.317642946696139
28108.49108.0378416359050.452158364094842
29107.9108.458458013111-0.558458013110751
30108.02107.9389573139110.0810426860885514
31108.46108.0143465662810.445653433719386
32108.31108.428911788701-0.118911788701141
33107.69108.318295133692-0.628295133692149
34107.71107.733829061769-0.0238290617694616
35107.74107.7116622847520.0283377152484547
36108.15107.7380231973710.411976802628942
37107.39108.121261027244-0.731261027243846
38109.16107.4410118302911.71898816970882
39109.65109.0400855925330.609914407467073
40110.4109.607453154090.792546845909598
41110.26110.344712949692-0.0847129496922321
42110.5110.2659094665960.234090533404384
43110.31110.483670144972-0.173670144971624
44109.85110.322115006314-0.472115006313587
45109.4109.882934136625-0.482934136625246
46109.75109.4336888652640.316311134736395
47109.79109.7279345413970.0620654586026461
48110.27109.7856703933020.4843296066975
49109.19110.236213788536-1.04621378853601
50111.78109.2629825305072.51701746949345
51111.58111.604416093283-0.0244160932825537
52111.71111.5817032353160.128296764683867
53111.59111.701050182434-0.111050182433985
54112.14111.5977467181340.542253281866422
55111.73112.102173107333-0.3721731073326
56111.32111.755962318082-0.435962318081891
57111.29111.350412171516-0.0604121715157504
58112.45111.2942142755131.15578572448678
59112.61112.3693738719360.240626128063582
60114.3112.593214230281.70678576971981
61113.32114.180936816288-0.86093681628779
62114.85113.3800578468261.4699421531742
63115.35114.7474587228610.602541277138982
64114.9115.307967494195-0.407967494194679
65115.49114.9284592885480.561540711452082
66115.55115.4508276410110.0991723589894349
67115.44115.543081863578-0.103081863578311
68114.81115.447190858442-0.637190858441841
69113.83114.854449616106-1.02444961610551
70113.64113.901464289784-0.261464289783888
71113.26113.658239413124-0.398239413124372
72114.68113.2877806701041.39221932989631







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73114.582880567214113.226301083203115.939460051225
74114.582880567214112.730094499722116.435666634706
75114.582880567214112.341157005455116.824604128973
76114.582880567214112.010365680415117.155395454012
77114.582880567214111.717511278928117.448249855499
78114.582880567214111.451930316299117.713830818128
79114.582880567214111.207179486081117.958581648346
80114.582880567214110.979012353112118.186748781315
81114.582880567214110.764454920424118.401306214003
82114.582880567214110.561328287867118.60443284656
83114.582880567214110.367979494713118.797781639714
84114.582880567214110.18311928205118.982641852377

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 114.582880567214 & 113.226301083203 & 115.939460051225 \tabularnewline
74 & 114.582880567214 & 112.730094499722 & 116.435666634706 \tabularnewline
75 & 114.582880567214 & 112.341157005455 & 116.824604128973 \tabularnewline
76 & 114.582880567214 & 112.010365680415 & 117.155395454012 \tabularnewline
77 & 114.582880567214 & 111.717511278928 & 117.448249855499 \tabularnewline
78 & 114.582880567214 & 111.451930316299 & 117.713830818128 \tabularnewline
79 & 114.582880567214 & 111.207179486081 & 117.958581648346 \tabularnewline
80 & 114.582880567214 & 110.979012353112 & 118.186748781315 \tabularnewline
81 & 114.582880567214 & 110.764454920424 & 118.401306214003 \tabularnewline
82 & 114.582880567214 & 110.561328287867 & 118.60443284656 \tabularnewline
83 & 114.582880567214 & 110.367979494713 & 118.797781639714 \tabularnewline
84 & 114.582880567214 & 110.18311928205 & 118.982641852377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261302&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]114.582880567214[/C][C]113.226301083203[/C][C]115.939460051225[/C][/ROW]
[ROW][C]74[/C][C]114.582880567214[/C][C]112.730094499722[/C][C]116.435666634706[/C][/ROW]
[ROW][C]75[/C][C]114.582880567214[/C][C]112.341157005455[/C][C]116.824604128973[/C][/ROW]
[ROW][C]76[/C][C]114.582880567214[/C][C]112.010365680415[/C][C]117.155395454012[/C][/ROW]
[ROW][C]77[/C][C]114.582880567214[/C][C]111.717511278928[/C][C]117.448249855499[/C][/ROW]
[ROW][C]78[/C][C]114.582880567214[/C][C]111.451930316299[/C][C]117.713830818128[/C][/ROW]
[ROW][C]79[/C][C]114.582880567214[/C][C]111.207179486081[/C][C]117.958581648346[/C][/ROW]
[ROW][C]80[/C][C]114.582880567214[/C][C]110.979012353112[/C][C]118.186748781315[/C][/ROW]
[ROW][C]81[/C][C]114.582880567214[/C][C]110.764454920424[/C][C]118.401306214003[/C][/ROW]
[ROW][C]82[/C][C]114.582880567214[/C][C]110.561328287867[/C][C]118.60443284656[/C][/ROW]
[ROW][C]83[/C][C]114.582880567214[/C][C]110.367979494713[/C][C]118.797781639714[/C][/ROW]
[ROW][C]84[/C][C]114.582880567214[/C][C]110.18311928205[/C][C]118.982641852377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261302&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261302&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
73114.582880567214113.226301083203115.939460051225
74114.582880567214112.730094499722116.435666634706
75114.582880567214112.341157005455116.824604128973
76114.582880567214112.010365680415117.155395454012
77114.582880567214111.717511278928117.448249855499
78114.582880567214111.451930316299117.713830818128
79114.582880567214111.207179486081117.958581648346
80114.582880567214110.979012353112118.186748781315
81114.582880567214110.764454920424118.401306214003
82114.582880567214110.561328287867118.60443284656
83114.582880567214110.367979494713118.797781639714
84114.582880567214110.18311928205118.982641852377



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')