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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 13:17:22 -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/21/t1356113877qvp6vkx8nkkjg2e.htm/, Retrieved Wed, 24 Apr 2024 19:16:09 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204063, Retrieved Wed, 24 Apr 2024 19:16:09 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact65
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [oefening 10.2doub...] [2012-12-21 18:17:22] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
101,81
101,72
101,78
102,04
102,36
102,56
102,69
102,77
102,85
102,9
102,72
102,79
102,9
102,91
103,29
103,35
102,97
103,05
103,18
103,21
103,32
103,31
103,6
103,68
103,77
103,82
103,86
103,9
103,63
103,65
103,7
103,77
103,94
104,03
104,03
104,29
104,35
104,67
104,73
104,86
104,05
104,15
104,27
104,33
104,41
104,4
104,41
104,6
104,61
104,65
104,55
104,51
104,74
104,89
104,91
104,93
104,95
104,97
105,16
105,29
105,35
105,36
105,45
105,3
105,73
105,86
105,85
105,95
105,97
106,15
105,37
105,39




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204063&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204063&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204063&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0721091693624068
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0721091693624068 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204063&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]0.0721091693624068[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204063&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204063&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
beta0.0721091693624068
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3101.78101.630.150000000000006
4102.04101.7008163754040.339183624595648
5102.36101.9852746248350.374725375164715
6102.56102.3322957603770.227704239622582
7102.69102.5487153239570.141284676043085
8102.77102.688903244590.0810967554099875
9102.85102.7747510642610.0752489357393813
10102.9102.8601772025120.0398227974878296
11102.72102.913048791361-0.193048791360724
12102.79102.7191282033690.0708717966307262
13102.9102.7942387097560.105761290244459
14102.91102.911865068546-0.00186506854578283
15103.29102.9217305800020.368269419997887
16103.35103.328286181980.0217138180202312
17102.97103.389851947361-0.419851947360868
18103.05102.9795767721810.0704232278185088
19103.18103.0646549326430.115345067356699
20103.21103.202972369640.0070276303595449
21103.32103.2334791262280.0865208737717325
22103.31103.349718074568-0.0397180745684409
23103.6103.3368540372030.263145962797353
24103.68103.6458292740010.0341707259989761
25103.77103.7282932966690.0417067033306608
26103.82103.821300732403-0.00130073240335093
27103.86103.87120693767-0.0112069376701811
28103.9103.910398814704-0.0103988147036773
29103.63103.949648964813-0.319648964813055
30103.65103.656599343473-0.00659934347281421
31103.7103.6761234702970.0238765297033297
32103.77103.7278451870210.0421548129791631
33103.94103.8008849355690.139115064430612
34104.03103.9809164073110.0490835926887314
35104.03104.074455784409-0.0444557844093794
36104.29104.0712501147220.218749885277731
37104.35104.3470239872480.00297601275222803
38104.67104.4072385850550.262761414944663
39104.73104.746186092427-0.016186092427489
40104.86104.8050189267470.0549810732526765
41104.05104.93898356627-0.888983566270227
42104.15104.064879699730.0851203002703613
43104.27104.1710176538780.0989823461219714
44104.33104.2981551886380.0318448113615801
45104.41104.3604514915340.0495485084657901
46104.4104.444024393323-0.0440243933228146
47104.41104.430849830889-0.0208498308886362
48104.6104.4393463669020.160653633098093
49104.61104.64093096694-0.0309309669396498
50104.65104.6487005606060.0012994393939465
51104.55104.688794262101-0.138794262101413
52104.51104.578785923149-0.0687859231489938
53104.74104.5338258273670.206174172633098
54104.89104.7786928756990.111307124300552
55104.91104.936719139977-0.0267191399768905
56104.93104.954792444987-0.0247924449870567
57104.95104.973004682373-0.0230046823726013
58104.97104.991345833835-0.0213458338352552
59105.16105.0098066034880.150193396511952
60105.29105.2106369245540.0793630754457695
61105.35105.3463597300030.00364026999730527
62105.36105.406622226848-0.0466222268484415
63105.45105.4132603367970.03673966320342
64105.3105.505909603393-0.20590960339284
65105.73105.3410616329280.388938367071574
66105.86105.7991076555110.0608923444888632
67105.85105.933498551893-0.0834985518927596
68105.95105.9174775406730.0325224593272111
69105.97106.019822708201-0.0498227082005087
70106.15106.0362300340970.113769965903217
71105.37106.224433891836-0.854433891836464
72105.39105.3828213736210.00717862637895905

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 101.78 & 101.63 & 0.150000000000006 \tabularnewline
4 & 102.04 & 101.700816375404 & 0.339183624595648 \tabularnewline
5 & 102.36 & 101.985274624835 & 0.374725375164715 \tabularnewline
6 & 102.56 & 102.332295760377 & 0.227704239622582 \tabularnewline
7 & 102.69 & 102.548715323957 & 0.141284676043085 \tabularnewline
8 & 102.77 & 102.68890324459 & 0.0810967554099875 \tabularnewline
9 & 102.85 & 102.774751064261 & 0.0752489357393813 \tabularnewline
10 & 102.9 & 102.860177202512 & 0.0398227974878296 \tabularnewline
11 & 102.72 & 102.913048791361 & -0.193048791360724 \tabularnewline
12 & 102.79 & 102.719128203369 & 0.0708717966307262 \tabularnewline
13 & 102.9 & 102.794238709756 & 0.105761290244459 \tabularnewline
14 & 102.91 & 102.911865068546 & -0.00186506854578283 \tabularnewline
15 & 103.29 & 102.921730580002 & 0.368269419997887 \tabularnewline
16 & 103.35 & 103.32828618198 & 0.0217138180202312 \tabularnewline
17 & 102.97 & 103.389851947361 & -0.419851947360868 \tabularnewline
18 & 103.05 & 102.979576772181 & 0.0704232278185088 \tabularnewline
19 & 103.18 & 103.064654932643 & 0.115345067356699 \tabularnewline
20 & 103.21 & 103.20297236964 & 0.0070276303595449 \tabularnewline
21 & 103.32 & 103.233479126228 & 0.0865208737717325 \tabularnewline
22 & 103.31 & 103.349718074568 & -0.0397180745684409 \tabularnewline
23 & 103.6 & 103.336854037203 & 0.263145962797353 \tabularnewline
24 & 103.68 & 103.645829274001 & 0.0341707259989761 \tabularnewline
25 & 103.77 & 103.728293296669 & 0.0417067033306608 \tabularnewline
26 & 103.82 & 103.821300732403 & -0.00130073240335093 \tabularnewline
27 & 103.86 & 103.87120693767 & -0.0112069376701811 \tabularnewline
28 & 103.9 & 103.910398814704 & -0.0103988147036773 \tabularnewline
29 & 103.63 & 103.949648964813 & -0.319648964813055 \tabularnewline
30 & 103.65 & 103.656599343473 & -0.00659934347281421 \tabularnewline
31 & 103.7 & 103.676123470297 & 0.0238765297033297 \tabularnewline
32 & 103.77 & 103.727845187021 & 0.0421548129791631 \tabularnewline
33 & 103.94 & 103.800884935569 & 0.139115064430612 \tabularnewline
34 & 104.03 & 103.980916407311 & 0.0490835926887314 \tabularnewline
35 & 104.03 & 104.074455784409 & -0.0444557844093794 \tabularnewline
36 & 104.29 & 104.071250114722 & 0.218749885277731 \tabularnewline
37 & 104.35 & 104.347023987248 & 0.00297601275222803 \tabularnewline
38 & 104.67 & 104.407238585055 & 0.262761414944663 \tabularnewline
39 & 104.73 & 104.746186092427 & -0.016186092427489 \tabularnewline
40 & 104.86 & 104.805018926747 & 0.0549810732526765 \tabularnewline
41 & 104.05 & 104.93898356627 & -0.888983566270227 \tabularnewline
42 & 104.15 & 104.06487969973 & 0.0851203002703613 \tabularnewline
43 & 104.27 & 104.171017653878 & 0.0989823461219714 \tabularnewline
44 & 104.33 & 104.298155188638 & 0.0318448113615801 \tabularnewline
45 & 104.41 & 104.360451491534 & 0.0495485084657901 \tabularnewline
46 & 104.4 & 104.444024393323 & -0.0440243933228146 \tabularnewline
47 & 104.41 & 104.430849830889 & -0.0208498308886362 \tabularnewline
48 & 104.6 & 104.439346366902 & 0.160653633098093 \tabularnewline
49 & 104.61 & 104.64093096694 & -0.0309309669396498 \tabularnewline
50 & 104.65 & 104.648700560606 & 0.0012994393939465 \tabularnewline
51 & 104.55 & 104.688794262101 & -0.138794262101413 \tabularnewline
52 & 104.51 & 104.578785923149 & -0.0687859231489938 \tabularnewline
53 & 104.74 & 104.533825827367 & 0.206174172633098 \tabularnewline
54 & 104.89 & 104.778692875699 & 0.111307124300552 \tabularnewline
55 & 104.91 & 104.936719139977 & -0.0267191399768905 \tabularnewline
56 & 104.93 & 104.954792444987 & -0.0247924449870567 \tabularnewline
57 & 104.95 & 104.973004682373 & -0.0230046823726013 \tabularnewline
58 & 104.97 & 104.991345833835 & -0.0213458338352552 \tabularnewline
59 & 105.16 & 105.009806603488 & 0.150193396511952 \tabularnewline
60 & 105.29 & 105.210636924554 & 0.0793630754457695 \tabularnewline
61 & 105.35 & 105.346359730003 & 0.00364026999730527 \tabularnewline
62 & 105.36 & 105.406622226848 & -0.0466222268484415 \tabularnewline
63 & 105.45 & 105.413260336797 & 0.03673966320342 \tabularnewline
64 & 105.3 & 105.505909603393 & -0.20590960339284 \tabularnewline
65 & 105.73 & 105.341061632928 & 0.388938367071574 \tabularnewline
66 & 105.86 & 105.799107655511 & 0.0608923444888632 \tabularnewline
67 & 105.85 & 105.933498551893 & -0.0834985518927596 \tabularnewline
68 & 105.95 & 105.917477540673 & 0.0325224593272111 \tabularnewline
69 & 105.97 & 106.019822708201 & -0.0498227082005087 \tabularnewline
70 & 106.15 & 106.036230034097 & 0.113769965903217 \tabularnewline
71 & 105.37 & 106.224433891836 & -0.854433891836464 \tabularnewline
72 & 105.39 & 105.382821373621 & 0.00717862637895905 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204063&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]101.78[/C][C]101.63[/C][C]0.150000000000006[/C][/ROW]
[ROW][C]4[/C][C]102.04[/C][C]101.700816375404[/C][C]0.339183624595648[/C][/ROW]
[ROW][C]5[/C][C]102.36[/C][C]101.985274624835[/C][C]0.374725375164715[/C][/ROW]
[ROW][C]6[/C][C]102.56[/C][C]102.332295760377[/C][C]0.227704239622582[/C][/ROW]
[ROW][C]7[/C][C]102.69[/C][C]102.548715323957[/C][C]0.141284676043085[/C][/ROW]
[ROW][C]8[/C][C]102.77[/C][C]102.68890324459[/C][C]0.0810967554099875[/C][/ROW]
[ROW][C]9[/C][C]102.85[/C][C]102.774751064261[/C][C]0.0752489357393813[/C][/ROW]
[ROW][C]10[/C][C]102.9[/C][C]102.860177202512[/C][C]0.0398227974878296[/C][/ROW]
[ROW][C]11[/C][C]102.72[/C][C]102.913048791361[/C][C]-0.193048791360724[/C][/ROW]
[ROW][C]12[/C][C]102.79[/C][C]102.719128203369[/C][C]0.0708717966307262[/C][/ROW]
[ROW][C]13[/C][C]102.9[/C][C]102.794238709756[/C][C]0.105761290244459[/C][/ROW]
[ROW][C]14[/C][C]102.91[/C][C]102.911865068546[/C][C]-0.00186506854578283[/C][/ROW]
[ROW][C]15[/C][C]103.29[/C][C]102.921730580002[/C][C]0.368269419997887[/C][/ROW]
[ROW][C]16[/C][C]103.35[/C][C]103.32828618198[/C][C]0.0217138180202312[/C][/ROW]
[ROW][C]17[/C][C]102.97[/C][C]103.389851947361[/C][C]-0.419851947360868[/C][/ROW]
[ROW][C]18[/C][C]103.05[/C][C]102.979576772181[/C][C]0.0704232278185088[/C][/ROW]
[ROW][C]19[/C][C]103.18[/C][C]103.064654932643[/C][C]0.115345067356699[/C][/ROW]
[ROW][C]20[/C][C]103.21[/C][C]103.20297236964[/C][C]0.0070276303595449[/C][/ROW]
[ROW][C]21[/C][C]103.32[/C][C]103.233479126228[/C][C]0.0865208737717325[/C][/ROW]
[ROW][C]22[/C][C]103.31[/C][C]103.349718074568[/C][C]-0.0397180745684409[/C][/ROW]
[ROW][C]23[/C][C]103.6[/C][C]103.336854037203[/C][C]0.263145962797353[/C][/ROW]
[ROW][C]24[/C][C]103.68[/C][C]103.645829274001[/C][C]0.0341707259989761[/C][/ROW]
[ROW][C]25[/C][C]103.77[/C][C]103.728293296669[/C][C]0.0417067033306608[/C][/ROW]
[ROW][C]26[/C][C]103.82[/C][C]103.821300732403[/C][C]-0.00130073240335093[/C][/ROW]
[ROW][C]27[/C][C]103.86[/C][C]103.87120693767[/C][C]-0.0112069376701811[/C][/ROW]
[ROW][C]28[/C][C]103.9[/C][C]103.910398814704[/C][C]-0.0103988147036773[/C][/ROW]
[ROW][C]29[/C][C]103.63[/C][C]103.949648964813[/C][C]-0.319648964813055[/C][/ROW]
[ROW][C]30[/C][C]103.65[/C][C]103.656599343473[/C][C]-0.00659934347281421[/C][/ROW]
[ROW][C]31[/C][C]103.7[/C][C]103.676123470297[/C][C]0.0238765297033297[/C][/ROW]
[ROW][C]32[/C][C]103.77[/C][C]103.727845187021[/C][C]0.0421548129791631[/C][/ROW]
[ROW][C]33[/C][C]103.94[/C][C]103.800884935569[/C][C]0.139115064430612[/C][/ROW]
[ROW][C]34[/C][C]104.03[/C][C]103.980916407311[/C][C]0.0490835926887314[/C][/ROW]
[ROW][C]35[/C][C]104.03[/C][C]104.074455784409[/C][C]-0.0444557844093794[/C][/ROW]
[ROW][C]36[/C][C]104.29[/C][C]104.071250114722[/C][C]0.218749885277731[/C][/ROW]
[ROW][C]37[/C][C]104.35[/C][C]104.347023987248[/C][C]0.00297601275222803[/C][/ROW]
[ROW][C]38[/C][C]104.67[/C][C]104.407238585055[/C][C]0.262761414944663[/C][/ROW]
[ROW][C]39[/C][C]104.73[/C][C]104.746186092427[/C][C]-0.016186092427489[/C][/ROW]
[ROW][C]40[/C][C]104.86[/C][C]104.805018926747[/C][C]0.0549810732526765[/C][/ROW]
[ROW][C]41[/C][C]104.05[/C][C]104.93898356627[/C][C]-0.888983566270227[/C][/ROW]
[ROW][C]42[/C][C]104.15[/C][C]104.06487969973[/C][C]0.0851203002703613[/C][/ROW]
[ROW][C]43[/C][C]104.27[/C][C]104.171017653878[/C][C]0.0989823461219714[/C][/ROW]
[ROW][C]44[/C][C]104.33[/C][C]104.298155188638[/C][C]0.0318448113615801[/C][/ROW]
[ROW][C]45[/C][C]104.41[/C][C]104.360451491534[/C][C]0.0495485084657901[/C][/ROW]
[ROW][C]46[/C][C]104.4[/C][C]104.444024393323[/C][C]-0.0440243933228146[/C][/ROW]
[ROW][C]47[/C][C]104.41[/C][C]104.430849830889[/C][C]-0.0208498308886362[/C][/ROW]
[ROW][C]48[/C][C]104.6[/C][C]104.439346366902[/C][C]0.160653633098093[/C][/ROW]
[ROW][C]49[/C][C]104.61[/C][C]104.64093096694[/C][C]-0.0309309669396498[/C][/ROW]
[ROW][C]50[/C][C]104.65[/C][C]104.648700560606[/C][C]0.0012994393939465[/C][/ROW]
[ROW][C]51[/C][C]104.55[/C][C]104.688794262101[/C][C]-0.138794262101413[/C][/ROW]
[ROW][C]52[/C][C]104.51[/C][C]104.578785923149[/C][C]-0.0687859231489938[/C][/ROW]
[ROW][C]53[/C][C]104.74[/C][C]104.533825827367[/C][C]0.206174172633098[/C][/ROW]
[ROW][C]54[/C][C]104.89[/C][C]104.778692875699[/C][C]0.111307124300552[/C][/ROW]
[ROW][C]55[/C][C]104.91[/C][C]104.936719139977[/C][C]-0.0267191399768905[/C][/ROW]
[ROW][C]56[/C][C]104.93[/C][C]104.954792444987[/C][C]-0.0247924449870567[/C][/ROW]
[ROW][C]57[/C][C]104.95[/C][C]104.973004682373[/C][C]-0.0230046823726013[/C][/ROW]
[ROW][C]58[/C][C]104.97[/C][C]104.991345833835[/C][C]-0.0213458338352552[/C][/ROW]
[ROW][C]59[/C][C]105.16[/C][C]105.009806603488[/C][C]0.150193396511952[/C][/ROW]
[ROW][C]60[/C][C]105.29[/C][C]105.210636924554[/C][C]0.0793630754457695[/C][/ROW]
[ROW][C]61[/C][C]105.35[/C][C]105.346359730003[/C][C]0.00364026999730527[/C][/ROW]
[ROW][C]62[/C][C]105.36[/C][C]105.406622226848[/C][C]-0.0466222268484415[/C][/ROW]
[ROW][C]63[/C][C]105.45[/C][C]105.413260336797[/C][C]0.03673966320342[/C][/ROW]
[ROW][C]64[/C][C]105.3[/C][C]105.505909603393[/C][C]-0.20590960339284[/C][/ROW]
[ROW][C]65[/C][C]105.73[/C][C]105.341061632928[/C][C]0.388938367071574[/C][/ROW]
[ROW][C]66[/C][C]105.86[/C][C]105.799107655511[/C][C]0.0608923444888632[/C][/ROW]
[ROW][C]67[/C][C]105.85[/C][C]105.933498551893[/C][C]-0.0834985518927596[/C][/ROW]
[ROW][C]68[/C][C]105.95[/C][C]105.917477540673[/C][C]0.0325224593272111[/C][/ROW]
[ROW][C]69[/C][C]105.97[/C][C]106.019822708201[/C][C]-0.0498227082005087[/C][/ROW]
[ROW][C]70[/C][C]106.15[/C][C]106.036230034097[/C][C]0.113769965903217[/C][/ROW]
[ROW][C]71[/C][C]105.37[/C][C]106.224433891836[/C][C]-0.854433891836464[/C][/ROW]
[ROW][C]72[/C][C]105.39[/C][C]105.382821373621[/C][C]0.00717862637895905[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204063&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204063&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
3101.78101.630.150000000000006
4102.04101.7008163754040.339183624595648
5102.36101.9852746248350.374725375164715
6102.56102.3322957603770.227704239622582
7102.69102.5487153239570.141284676043085
8102.77102.688903244590.0810967554099875
9102.85102.7747510642610.0752489357393813
10102.9102.8601772025120.0398227974878296
11102.72102.913048791361-0.193048791360724
12102.79102.7191282033690.0708717966307262
13102.9102.7942387097560.105761290244459
14102.91102.911865068546-0.00186506854578283
15103.29102.9217305800020.368269419997887
16103.35103.328286181980.0217138180202312
17102.97103.389851947361-0.419851947360868
18103.05102.9795767721810.0704232278185088
19103.18103.0646549326430.115345067356699
20103.21103.202972369640.0070276303595449
21103.32103.2334791262280.0865208737717325
22103.31103.349718074568-0.0397180745684409
23103.6103.3368540372030.263145962797353
24103.68103.6458292740010.0341707259989761
25103.77103.7282932966690.0417067033306608
26103.82103.821300732403-0.00130073240335093
27103.86103.87120693767-0.0112069376701811
28103.9103.910398814704-0.0103988147036773
29103.63103.949648964813-0.319648964813055
30103.65103.656599343473-0.00659934347281421
31103.7103.6761234702970.0238765297033297
32103.77103.7278451870210.0421548129791631
33103.94103.8008849355690.139115064430612
34104.03103.9809164073110.0490835926887314
35104.03104.074455784409-0.0444557844093794
36104.29104.0712501147220.218749885277731
37104.35104.3470239872480.00297601275222803
38104.67104.4072385850550.262761414944663
39104.73104.746186092427-0.016186092427489
40104.86104.8050189267470.0549810732526765
41104.05104.93898356627-0.888983566270227
42104.15104.064879699730.0851203002703613
43104.27104.1710176538780.0989823461219714
44104.33104.2981551886380.0318448113615801
45104.41104.3604514915340.0495485084657901
46104.4104.444024393323-0.0440243933228146
47104.41104.430849830889-0.0208498308886362
48104.6104.4393463669020.160653633098093
49104.61104.64093096694-0.0309309669396498
50104.65104.6487005606060.0012994393939465
51104.55104.688794262101-0.138794262101413
52104.51104.578785923149-0.0687859231489938
53104.74104.5338258273670.206174172633098
54104.89104.7786928756990.111307124300552
55104.91104.936719139977-0.0267191399768905
56104.93104.954792444987-0.0247924449870567
57104.95104.973004682373-0.0230046823726013
58104.97104.991345833835-0.0213458338352552
59105.16105.0098066034880.150193396511952
60105.29105.2106369245540.0793630754457695
61105.35105.3463597300030.00364026999730527
62105.36105.406622226848-0.0466222268484415
63105.45105.4132603367970.03673966320342
64105.3105.505909603393-0.20590960339284
65105.73105.3410616329280.388938367071574
66105.86105.7991076555110.0608923444888632
67105.85105.933498551893-0.0834985518927596
68105.95105.9174775406730.0325224593272111
69105.97106.019822708201-0.0498227082005087
70106.15106.0362300340970.113769965903217
71105.37106.224433891836-0.854433891836464
72105.39105.3828213736210.00717862637895905







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73105.403339018406104.997882103699105.808795933114
74105.416678036813104.822241959991106.011114113635
75105.430017055219104.675970344176106.184063766263
76105.443356073626104.542355789544106.344356357707
77105.456695092032104.415201414149106.498188769915
78105.470034110438104.291467704543106.648600516334
79105.483373128845104.169432410536106.797313847153
80105.496712147251104.048028945635106.945395348867
81105.510051165658103.926556038239107.093546293076
82105.523390184064103.804532646577107.242247721551
83105.53672920247103.681618454105107.391839950836
84105.550068220877103.557567178132107.542569263622

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 105.403339018406 & 104.997882103699 & 105.808795933114 \tabularnewline
74 & 105.416678036813 & 104.822241959991 & 106.011114113635 \tabularnewline
75 & 105.430017055219 & 104.675970344176 & 106.184063766263 \tabularnewline
76 & 105.443356073626 & 104.542355789544 & 106.344356357707 \tabularnewline
77 & 105.456695092032 & 104.415201414149 & 106.498188769915 \tabularnewline
78 & 105.470034110438 & 104.291467704543 & 106.648600516334 \tabularnewline
79 & 105.483373128845 & 104.169432410536 & 106.797313847153 \tabularnewline
80 & 105.496712147251 & 104.048028945635 & 106.945395348867 \tabularnewline
81 & 105.510051165658 & 103.926556038239 & 107.093546293076 \tabularnewline
82 & 105.523390184064 & 103.804532646577 & 107.242247721551 \tabularnewline
83 & 105.53672920247 & 103.681618454105 & 107.391839950836 \tabularnewline
84 & 105.550068220877 & 103.557567178132 & 107.542569263622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204063&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]105.403339018406[/C][C]104.997882103699[/C][C]105.808795933114[/C][/ROW]
[ROW][C]74[/C][C]105.416678036813[/C][C]104.822241959991[/C][C]106.011114113635[/C][/ROW]
[ROW][C]75[/C][C]105.430017055219[/C][C]104.675970344176[/C][C]106.184063766263[/C][/ROW]
[ROW][C]76[/C][C]105.443356073626[/C][C]104.542355789544[/C][C]106.344356357707[/C][/ROW]
[ROW][C]77[/C][C]105.456695092032[/C][C]104.415201414149[/C][C]106.498188769915[/C][/ROW]
[ROW][C]78[/C][C]105.470034110438[/C][C]104.291467704543[/C][C]106.648600516334[/C][/ROW]
[ROW][C]79[/C][C]105.483373128845[/C][C]104.169432410536[/C][C]106.797313847153[/C][/ROW]
[ROW][C]80[/C][C]105.496712147251[/C][C]104.048028945635[/C][C]106.945395348867[/C][/ROW]
[ROW][C]81[/C][C]105.510051165658[/C][C]103.926556038239[/C][C]107.093546293076[/C][/ROW]
[ROW][C]82[/C][C]105.523390184064[/C][C]103.804532646577[/C][C]107.242247721551[/C][/ROW]
[ROW][C]83[/C][C]105.53672920247[/C][C]103.681618454105[/C][C]107.391839950836[/C][/ROW]
[ROW][C]84[/C][C]105.550068220877[/C][C]103.557567178132[/C][C]107.542569263622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204063&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204063&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
73105.403339018406104.997882103699105.808795933114
74105.416678036813104.822241959991106.011114113635
75105.430017055219104.675970344176106.184063766263
76105.443356073626104.542355789544106.344356357707
77105.456695092032104.415201414149106.498188769915
78105.470034110438104.291467704543106.648600516334
79105.483373128845104.169432410536106.797313847153
80105.496712147251104.048028945635106.945395348867
81105.510051165658103.926556038239107.093546293076
82105.523390184064103.804532646577107.242247721551
83105.53672920247103.681618454105107.391839950836
84105.550068220877103.557567178132107.542569263622



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')