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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 16 Jan 2010 04:41:42 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/16/t1263642161tio2ubsnjuw65bw.htm/, Retrieved Fri, 03 May 2024 12:11:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72226, Retrieved Fri, 03 May 2024 12:11:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact166
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2009-12-21 15:37:35] [e5e09c53da17fb7444fa9ceb236a5291]
-    D  [Standard Deviation-Mean Plot] [] [2009-12-21 15:51:38] [e5e09c53da17fb7444fa9ceb236a5291]
- RMPD    [Classical Decomposition] [] [2010-01-12 09:15:15] [e5e09c53da17fb7444fa9ceb236a5291]
- RMPD      [Exponential Smoothing] [] [2010-01-16 11:07:46] [74be16979710d4c4e7c6647856088456]
-   PD          [Exponential Smoothing] [] [2010-01-16 11:41:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
2,14
2,45
2,52
2,3
2,25
2,06
1,99
2,25
2,26
2,36
2,3
2,19
2,31
2,21
2,21
2,26
2,18
2,21
2,33
2,12
2,08
1,97
2,09
2,11
2,24
2,45
2,68
2,73
2,76
2,83
3,16
3,22
3,22
3,34
3,35
3,42
3,58
3,71
3,68
3,83
3,94
3,88
4,03
4,15
4,32
4,4
4,37
4,14
4,11
4,16
3,98
4,13
3,76
3,66
3,85
4,03
4,31
4,58
4,46
4,41
3,84
2,84
2,66
2,17
1,43
1,47
1,29
1,23
1,09
0,94
0,76
0,67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72226&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72226&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999926825388514
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999926825388514 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72226&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]0.999926825388514[/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=72226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72226&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
alpha0.999926825388514
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
22.452.140.31
32.522.449977315870440.0700226841295604
42.32.51999487611729-0.219994876117294
52.252.30001609803959-0.0500160980395887
62.062.25000365990854-0.190003659908542
71.992.06001390344399-0.0700139034439948
82.251.990005123240180.259994876759817
92.262.249980974975900.0100190250240950
102.362.259999266861740.100000733138264
112.32.35999268248520-0.0599926824852042
122.192.30000438994123-0.110004389941233
132.312.190008049528500.119991950471504
142.212.30999121963564-0.0999912196356432
152.212.21000731681865-7.31681864918343e-06
162.262.210000000535410.0499999994645943
172.182.25999634126946-0.0799963412694646
182.212.180005853701190.0299941462988071
192.332.209997805190.120002194810002
202.122.32999121888602-0.209991218886017
212.082.12001536602586-0.0400153660258575
221.972.08000292810886-0.110002928108863
232.091.970008049421530.119991950578473
242.112.089991219635630.0200087803643649
252.242.109998535865270.130001464134730
262.452.239990487193370.210009512806631
272.682.449984632635490.230015367364508
282.732.679983168714860.0500168312851423
292.762.729996340037800.0300036599621967
302.832.759997804493840.0700021955061612
313.162.829994877616540.330005122383459
323.223.159975852003380.0600241479966188
333.223.219995607756294.39224370918367e-06
343.343.21999999967860.120000000321400
353.353.33999121904660.0100087809534024
363.423.349999267611340.0700007323886576
373.583.419994877723600.160005122276397
383.713.579988291687340.130011708312658
393.683.70999048644376-0.0299904864437552
403.833.680002194542190.149997805457806
413.943.829989023968860.110010976031138
423.883.93999194998957-0.0599919499895698
434.033.880004389887630.149995610112368
444.154.029989024129510.120010975870495
454.324.149991218243470.170008781756533
464.44.319987559673450.0800124403265547
474.374.39999414512077-0.0299941451207655
484.144.37000219480992-0.230002194809916
494.114.14001683032125-0.0300168303212454
504.164.11000219646990.0499978035301032
513.984.15999634143015-0.179996341430151
524.133.980013171162350.149986828837647
533.764.12998902477207-0.369989024772072
543.663.76002707380314-0.100027073803142
553.853.660007319442260.189992680557736
564.033.849986097359420.180013902640585
574.314.029986827552610.280013172447387
584.584.30997951014490.270020489855106
594.464.57998024135556-0.119980241355562
604.414.46000877950755-0.0500087795075466
613.844.41000365937301-0.570003659373011
622.843.84004170979632-1.00004170979632
632.662.84007317766358-0.180073177663584
642.172.66001317678481-0.490013176784815
651.432.17003585652383-0.740035856523834
661.471.430054151836290.0399458481637129
671.291.46999707697808-0.17999707697808
681.231.29001317121618-0.0600131712161767
691.091.23000439144049-0.140004391440488
700.941.09001024476695-0.150010244766950
710.760.94001097694138-0.180010976941380
720.670.760013172233301-0.090013172233301

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2.45 & 2.14 & 0.31 \tabularnewline
3 & 2.52 & 2.44997731587044 & 0.0700226841295604 \tabularnewline
4 & 2.3 & 2.51999487611729 & -0.219994876117294 \tabularnewline
5 & 2.25 & 2.30001609803959 & -0.0500160980395887 \tabularnewline
6 & 2.06 & 2.25000365990854 & -0.190003659908542 \tabularnewline
7 & 1.99 & 2.06001390344399 & -0.0700139034439948 \tabularnewline
8 & 2.25 & 1.99000512324018 & 0.259994876759817 \tabularnewline
9 & 2.26 & 2.24998097497590 & 0.0100190250240950 \tabularnewline
10 & 2.36 & 2.25999926686174 & 0.100000733138264 \tabularnewline
11 & 2.3 & 2.35999268248520 & -0.0599926824852042 \tabularnewline
12 & 2.19 & 2.30000438994123 & -0.110004389941233 \tabularnewline
13 & 2.31 & 2.19000804952850 & 0.119991950471504 \tabularnewline
14 & 2.21 & 2.30999121963564 & -0.0999912196356432 \tabularnewline
15 & 2.21 & 2.21000731681865 & -7.31681864918343e-06 \tabularnewline
16 & 2.26 & 2.21000000053541 & 0.0499999994645943 \tabularnewline
17 & 2.18 & 2.25999634126946 & -0.0799963412694646 \tabularnewline
18 & 2.21 & 2.18000585370119 & 0.0299941462988071 \tabularnewline
19 & 2.33 & 2.20999780519 & 0.120002194810002 \tabularnewline
20 & 2.12 & 2.32999121888602 & -0.209991218886017 \tabularnewline
21 & 2.08 & 2.12001536602586 & -0.0400153660258575 \tabularnewline
22 & 1.97 & 2.08000292810886 & -0.110002928108863 \tabularnewline
23 & 2.09 & 1.97000804942153 & 0.119991950578473 \tabularnewline
24 & 2.11 & 2.08999121963563 & 0.0200087803643649 \tabularnewline
25 & 2.24 & 2.10999853586527 & 0.130001464134730 \tabularnewline
26 & 2.45 & 2.23999048719337 & 0.210009512806631 \tabularnewline
27 & 2.68 & 2.44998463263549 & 0.230015367364508 \tabularnewline
28 & 2.73 & 2.67998316871486 & 0.0500168312851423 \tabularnewline
29 & 2.76 & 2.72999634003780 & 0.0300036599621967 \tabularnewline
30 & 2.83 & 2.75999780449384 & 0.0700021955061612 \tabularnewline
31 & 3.16 & 2.82999487761654 & 0.330005122383459 \tabularnewline
32 & 3.22 & 3.15997585200338 & 0.0600241479966188 \tabularnewline
33 & 3.22 & 3.21999560775629 & 4.39224370918367e-06 \tabularnewline
34 & 3.34 & 3.2199999996786 & 0.120000000321400 \tabularnewline
35 & 3.35 & 3.3399912190466 & 0.0100087809534024 \tabularnewline
36 & 3.42 & 3.34999926761134 & 0.0700007323886576 \tabularnewline
37 & 3.58 & 3.41999487772360 & 0.160005122276397 \tabularnewline
38 & 3.71 & 3.57998829168734 & 0.130011708312658 \tabularnewline
39 & 3.68 & 3.70999048644376 & -0.0299904864437552 \tabularnewline
40 & 3.83 & 3.68000219454219 & 0.149997805457806 \tabularnewline
41 & 3.94 & 3.82998902396886 & 0.110010976031138 \tabularnewline
42 & 3.88 & 3.93999194998957 & -0.0599919499895698 \tabularnewline
43 & 4.03 & 3.88000438988763 & 0.149995610112368 \tabularnewline
44 & 4.15 & 4.02998902412951 & 0.120010975870495 \tabularnewline
45 & 4.32 & 4.14999121824347 & 0.170008781756533 \tabularnewline
46 & 4.4 & 4.31998755967345 & 0.0800124403265547 \tabularnewline
47 & 4.37 & 4.39999414512077 & -0.0299941451207655 \tabularnewline
48 & 4.14 & 4.37000219480992 & -0.230002194809916 \tabularnewline
49 & 4.11 & 4.14001683032125 & -0.0300168303212454 \tabularnewline
50 & 4.16 & 4.1100021964699 & 0.0499978035301032 \tabularnewline
51 & 3.98 & 4.15999634143015 & -0.179996341430151 \tabularnewline
52 & 4.13 & 3.98001317116235 & 0.149986828837647 \tabularnewline
53 & 3.76 & 4.12998902477207 & -0.369989024772072 \tabularnewline
54 & 3.66 & 3.76002707380314 & -0.100027073803142 \tabularnewline
55 & 3.85 & 3.66000731944226 & 0.189992680557736 \tabularnewline
56 & 4.03 & 3.84998609735942 & 0.180013902640585 \tabularnewline
57 & 4.31 & 4.02998682755261 & 0.280013172447387 \tabularnewline
58 & 4.58 & 4.3099795101449 & 0.270020489855106 \tabularnewline
59 & 4.46 & 4.57998024135556 & -0.119980241355562 \tabularnewline
60 & 4.41 & 4.46000877950755 & -0.0500087795075466 \tabularnewline
61 & 3.84 & 4.41000365937301 & -0.570003659373011 \tabularnewline
62 & 2.84 & 3.84004170979632 & -1.00004170979632 \tabularnewline
63 & 2.66 & 2.84007317766358 & -0.180073177663584 \tabularnewline
64 & 2.17 & 2.66001317678481 & -0.490013176784815 \tabularnewline
65 & 1.43 & 2.17003585652383 & -0.740035856523834 \tabularnewline
66 & 1.47 & 1.43005415183629 & 0.0399458481637129 \tabularnewline
67 & 1.29 & 1.46999707697808 & -0.17999707697808 \tabularnewline
68 & 1.23 & 1.29001317121618 & -0.0600131712161767 \tabularnewline
69 & 1.09 & 1.23000439144049 & -0.140004391440488 \tabularnewline
70 & 0.94 & 1.09001024476695 & -0.150010244766950 \tabularnewline
71 & 0.76 & 0.94001097694138 & -0.180010976941380 \tabularnewline
72 & 0.67 & 0.760013172233301 & -0.090013172233301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72226&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]2.45[/C][C]2.14[/C][C]0.31[/C][/ROW]
[ROW][C]3[/C][C]2.52[/C][C]2.44997731587044[/C][C]0.0700226841295604[/C][/ROW]
[ROW][C]4[/C][C]2.3[/C][C]2.51999487611729[/C][C]-0.219994876117294[/C][/ROW]
[ROW][C]5[/C][C]2.25[/C][C]2.30001609803959[/C][C]-0.0500160980395887[/C][/ROW]
[ROW][C]6[/C][C]2.06[/C][C]2.25000365990854[/C][C]-0.190003659908542[/C][/ROW]
[ROW][C]7[/C][C]1.99[/C][C]2.06001390344399[/C][C]-0.0700139034439948[/C][/ROW]
[ROW][C]8[/C][C]2.25[/C][C]1.99000512324018[/C][C]0.259994876759817[/C][/ROW]
[ROW][C]9[/C][C]2.26[/C][C]2.24998097497590[/C][C]0.0100190250240950[/C][/ROW]
[ROW][C]10[/C][C]2.36[/C][C]2.25999926686174[/C][C]0.100000733138264[/C][/ROW]
[ROW][C]11[/C][C]2.3[/C][C]2.35999268248520[/C][C]-0.0599926824852042[/C][/ROW]
[ROW][C]12[/C][C]2.19[/C][C]2.30000438994123[/C][C]-0.110004389941233[/C][/ROW]
[ROW][C]13[/C][C]2.31[/C][C]2.19000804952850[/C][C]0.119991950471504[/C][/ROW]
[ROW][C]14[/C][C]2.21[/C][C]2.30999121963564[/C][C]-0.0999912196356432[/C][/ROW]
[ROW][C]15[/C][C]2.21[/C][C]2.21000731681865[/C][C]-7.31681864918343e-06[/C][/ROW]
[ROW][C]16[/C][C]2.26[/C][C]2.21000000053541[/C][C]0.0499999994645943[/C][/ROW]
[ROW][C]17[/C][C]2.18[/C][C]2.25999634126946[/C][C]-0.0799963412694646[/C][/ROW]
[ROW][C]18[/C][C]2.21[/C][C]2.18000585370119[/C][C]0.0299941462988071[/C][/ROW]
[ROW][C]19[/C][C]2.33[/C][C]2.20999780519[/C][C]0.120002194810002[/C][/ROW]
[ROW][C]20[/C][C]2.12[/C][C]2.32999121888602[/C][C]-0.209991218886017[/C][/ROW]
[ROW][C]21[/C][C]2.08[/C][C]2.12001536602586[/C][C]-0.0400153660258575[/C][/ROW]
[ROW][C]22[/C][C]1.97[/C][C]2.08000292810886[/C][C]-0.110002928108863[/C][/ROW]
[ROW][C]23[/C][C]2.09[/C][C]1.97000804942153[/C][C]0.119991950578473[/C][/ROW]
[ROW][C]24[/C][C]2.11[/C][C]2.08999121963563[/C][C]0.0200087803643649[/C][/ROW]
[ROW][C]25[/C][C]2.24[/C][C]2.10999853586527[/C][C]0.130001464134730[/C][/ROW]
[ROW][C]26[/C][C]2.45[/C][C]2.23999048719337[/C][C]0.210009512806631[/C][/ROW]
[ROW][C]27[/C][C]2.68[/C][C]2.44998463263549[/C][C]0.230015367364508[/C][/ROW]
[ROW][C]28[/C][C]2.73[/C][C]2.67998316871486[/C][C]0.0500168312851423[/C][/ROW]
[ROW][C]29[/C][C]2.76[/C][C]2.72999634003780[/C][C]0.0300036599621967[/C][/ROW]
[ROW][C]30[/C][C]2.83[/C][C]2.75999780449384[/C][C]0.0700021955061612[/C][/ROW]
[ROW][C]31[/C][C]3.16[/C][C]2.82999487761654[/C][C]0.330005122383459[/C][/ROW]
[ROW][C]32[/C][C]3.22[/C][C]3.15997585200338[/C][C]0.0600241479966188[/C][/ROW]
[ROW][C]33[/C][C]3.22[/C][C]3.21999560775629[/C][C]4.39224370918367e-06[/C][/ROW]
[ROW][C]34[/C][C]3.34[/C][C]3.2199999996786[/C][C]0.120000000321400[/C][/ROW]
[ROW][C]35[/C][C]3.35[/C][C]3.3399912190466[/C][C]0.0100087809534024[/C][/ROW]
[ROW][C]36[/C][C]3.42[/C][C]3.34999926761134[/C][C]0.0700007323886576[/C][/ROW]
[ROW][C]37[/C][C]3.58[/C][C]3.41999487772360[/C][C]0.160005122276397[/C][/ROW]
[ROW][C]38[/C][C]3.71[/C][C]3.57998829168734[/C][C]0.130011708312658[/C][/ROW]
[ROW][C]39[/C][C]3.68[/C][C]3.70999048644376[/C][C]-0.0299904864437552[/C][/ROW]
[ROW][C]40[/C][C]3.83[/C][C]3.68000219454219[/C][C]0.149997805457806[/C][/ROW]
[ROW][C]41[/C][C]3.94[/C][C]3.82998902396886[/C][C]0.110010976031138[/C][/ROW]
[ROW][C]42[/C][C]3.88[/C][C]3.93999194998957[/C][C]-0.0599919499895698[/C][/ROW]
[ROW][C]43[/C][C]4.03[/C][C]3.88000438988763[/C][C]0.149995610112368[/C][/ROW]
[ROW][C]44[/C][C]4.15[/C][C]4.02998902412951[/C][C]0.120010975870495[/C][/ROW]
[ROW][C]45[/C][C]4.32[/C][C]4.14999121824347[/C][C]0.170008781756533[/C][/ROW]
[ROW][C]46[/C][C]4.4[/C][C]4.31998755967345[/C][C]0.0800124403265547[/C][/ROW]
[ROW][C]47[/C][C]4.37[/C][C]4.39999414512077[/C][C]-0.0299941451207655[/C][/ROW]
[ROW][C]48[/C][C]4.14[/C][C]4.37000219480992[/C][C]-0.230002194809916[/C][/ROW]
[ROW][C]49[/C][C]4.11[/C][C]4.14001683032125[/C][C]-0.0300168303212454[/C][/ROW]
[ROW][C]50[/C][C]4.16[/C][C]4.1100021964699[/C][C]0.0499978035301032[/C][/ROW]
[ROW][C]51[/C][C]3.98[/C][C]4.15999634143015[/C][C]-0.179996341430151[/C][/ROW]
[ROW][C]52[/C][C]4.13[/C][C]3.98001317116235[/C][C]0.149986828837647[/C][/ROW]
[ROW][C]53[/C][C]3.76[/C][C]4.12998902477207[/C][C]-0.369989024772072[/C][/ROW]
[ROW][C]54[/C][C]3.66[/C][C]3.76002707380314[/C][C]-0.100027073803142[/C][/ROW]
[ROW][C]55[/C][C]3.85[/C][C]3.66000731944226[/C][C]0.189992680557736[/C][/ROW]
[ROW][C]56[/C][C]4.03[/C][C]3.84998609735942[/C][C]0.180013902640585[/C][/ROW]
[ROW][C]57[/C][C]4.31[/C][C]4.02998682755261[/C][C]0.280013172447387[/C][/ROW]
[ROW][C]58[/C][C]4.58[/C][C]4.3099795101449[/C][C]0.270020489855106[/C][/ROW]
[ROW][C]59[/C][C]4.46[/C][C]4.57998024135556[/C][C]-0.119980241355562[/C][/ROW]
[ROW][C]60[/C][C]4.41[/C][C]4.46000877950755[/C][C]-0.0500087795075466[/C][/ROW]
[ROW][C]61[/C][C]3.84[/C][C]4.41000365937301[/C][C]-0.570003659373011[/C][/ROW]
[ROW][C]62[/C][C]2.84[/C][C]3.84004170979632[/C][C]-1.00004170979632[/C][/ROW]
[ROW][C]63[/C][C]2.66[/C][C]2.84007317766358[/C][C]-0.180073177663584[/C][/ROW]
[ROW][C]64[/C][C]2.17[/C][C]2.66001317678481[/C][C]-0.490013176784815[/C][/ROW]
[ROW][C]65[/C][C]1.43[/C][C]2.17003585652383[/C][C]-0.740035856523834[/C][/ROW]
[ROW][C]66[/C][C]1.47[/C][C]1.43005415183629[/C][C]0.0399458481637129[/C][/ROW]
[ROW][C]67[/C][C]1.29[/C][C]1.46999707697808[/C][C]-0.17999707697808[/C][/ROW]
[ROW][C]68[/C][C]1.23[/C][C]1.29001317121618[/C][C]-0.0600131712161767[/C][/ROW]
[ROW][C]69[/C][C]1.09[/C][C]1.23000439144049[/C][C]-0.140004391440488[/C][/ROW]
[ROW][C]70[/C][C]0.94[/C][C]1.09001024476695[/C][C]-0.150010244766950[/C][/ROW]
[ROW][C]71[/C][C]0.76[/C][C]0.94001097694138[/C][C]-0.180010976941380[/C][/ROW]
[ROW][C]72[/C][C]0.67[/C][C]0.760013172233301[/C][C]-0.090013172233301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72226&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
22.452.140.31
32.522.449977315870440.0700226841295604
42.32.51999487611729-0.219994876117294
52.252.30001609803959-0.0500160980395887
62.062.25000365990854-0.190003659908542
71.992.06001390344399-0.0700139034439948
82.251.990005123240180.259994876759817
92.262.249980974975900.0100190250240950
102.362.259999266861740.100000733138264
112.32.35999268248520-0.0599926824852042
122.192.30000438994123-0.110004389941233
132.312.190008049528500.119991950471504
142.212.30999121963564-0.0999912196356432
152.212.21000731681865-7.31681864918343e-06
162.262.210000000535410.0499999994645943
172.182.25999634126946-0.0799963412694646
182.212.180005853701190.0299941462988071
192.332.209997805190.120002194810002
202.122.32999121888602-0.209991218886017
212.082.12001536602586-0.0400153660258575
221.972.08000292810886-0.110002928108863
232.091.970008049421530.119991950578473
242.112.089991219635630.0200087803643649
252.242.109998535865270.130001464134730
262.452.239990487193370.210009512806631
272.682.449984632635490.230015367364508
282.732.679983168714860.0500168312851423
292.762.729996340037800.0300036599621967
302.832.759997804493840.0700021955061612
313.162.829994877616540.330005122383459
323.223.159975852003380.0600241479966188
333.223.219995607756294.39224370918367e-06
343.343.21999999967860.120000000321400
353.353.33999121904660.0100087809534024
363.423.349999267611340.0700007323886576
373.583.419994877723600.160005122276397
383.713.579988291687340.130011708312658
393.683.70999048644376-0.0299904864437552
403.833.680002194542190.149997805457806
413.943.829989023968860.110010976031138
423.883.93999194998957-0.0599919499895698
434.033.880004389887630.149995610112368
444.154.029989024129510.120010975870495
454.324.149991218243470.170008781756533
464.44.319987559673450.0800124403265547
474.374.39999414512077-0.0299941451207655
484.144.37000219480992-0.230002194809916
494.114.14001683032125-0.0300168303212454
504.164.11000219646990.0499978035301032
513.984.15999634143015-0.179996341430151
524.133.980013171162350.149986828837647
533.764.12998902477207-0.369989024772072
543.663.76002707380314-0.100027073803142
553.853.660007319442260.189992680557736
564.033.849986097359420.180013902640585
574.314.029986827552610.280013172447387
584.584.30997951014490.270020489855106
594.464.57998024135556-0.119980241355562
604.414.46000877950755-0.0500087795075466
613.844.41000365937301-0.570003659373011
622.843.84004170979632-1.00004170979632
632.662.84007317766358-0.180073177663584
642.172.66001317678481-0.490013176784815
651.432.17003585652383-0.740035856523834
661.471.430054151836290.0399458481637129
671.291.46999707697808-0.17999707697808
681.231.29001317121618-0.0600131712161767
691.091.23000439144049-0.140004391440488
700.941.09001024476695-0.150010244766950
710.760.94001097694138-0.180010976941380
720.670.760013172233301-0.090013172233301







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
730.6700065866789070.2288694047373541.11114376862046
740.6700065866789070.04616722612906411.29384594722875
750.670006586678907-0.09402815222446171.43404132558228
760.670006586678907-0.2122193575842621.55223253094208
770.670006586678907-0.3163483956732591.65636156903107
780.670006586678907-0.4104885246894161.75050169804723
790.670006586678907-0.4970594869307861.8370726602886
800.670006586678907-0.5776378957962281.91765106915404
810.670006586678907-0.6533188793839771.99333205274179
820.670006586678907-0.7248997985708172.06491297192863
830.670006586678907-0.7929825992313492.13299577258916
840.670006586678907-0.8580349351948462.19804810855266

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 0.670006586678907 & 0.228869404737354 & 1.11114376862046 \tabularnewline
74 & 0.670006586678907 & 0.0461672261290641 & 1.29384594722875 \tabularnewline
75 & 0.670006586678907 & -0.0940281522244617 & 1.43404132558228 \tabularnewline
76 & 0.670006586678907 & -0.212219357584262 & 1.55223253094208 \tabularnewline
77 & 0.670006586678907 & -0.316348395673259 & 1.65636156903107 \tabularnewline
78 & 0.670006586678907 & -0.410488524689416 & 1.75050169804723 \tabularnewline
79 & 0.670006586678907 & -0.497059486930786 & 1.8370726602886 \tabularnewline
80 & 0.670006586678907 & -0.577637895796228 & 1.91765106915404 \tabularnewline
81 & 0.670006586678907 & -0.653318879383977 & 1.99333205274179 \tabularnewline
82 & 0.670006586678907 & -0.724899798570817 & 2.06491297192863 \tabularnewline
83 & 0.670006586678907 & -0.792982599231349 & 2.13299577258916 \tabularnewline
84 & 0.670006586678907 & -0.858034935194846 & 2.19804810855266 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72226&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]0.670006586678907[/C][C]0.228869404737354[/C][C]1.11114376862046[/C][/ROW]
[ROW][C]74[/C][C]0.670006586678907[/C][C]0.0461672261290641[/C][C]1.29384594722875[/C][/ROW]
[ROW][C]75[/C][C]0.670006586678907[/C][C]-0.0940281522244617[/C][C]1.43404132558228[/C][/ROW]
[ROW][C]76[/C][C]0.670006586678907[/C][C]-0.212219357584262[/C][C]1.55223253094208[/C][/ROW]
[ROW][C]77[/C][C]0.670006586678907[/C][C]-0.316348395673259[/C][C]1.65636156903107[/C][/ROW]
[ROW][C]78[/C][C]0.670006586678907[/C][C]-0.410488524689416[/C][C]1.75050169804723[/C][/ROW]
[ROW][C]79[/C][C]0.670006586678907[/C][C]-0.497059486930786[/C][C]1.8370726602886[/C][/ROW]
[ROW][C]80[/C][C]0.670006586678907[/C][C]-0.577637895796228[/C][C]1.91765106915404[/C][/ROW]
[ROW][C]81[/C][C]0.670006586678907[/C][C]-0.653318879383977[/C][C]1.99333205274179[/C][/ROW]
[ROW][C]82[/C][C]0.670006586678907[/C][C]-0.724899798570817[/C][C]2.06491297192863[/C][/ROW]
[ROW][C]83[/C][C]0.670006586678907[/C][C]-0.792982599231349[/C][C]2.13299577258916[/C][/ROW]
[ROW][C]84[/C][C]0.670006586678907[/C][C]-0.858034935194846[/C][C]2.19804810855266[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72226&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72226&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
730.6700065866789070.2288694047373541.11114376862046
740.6700065866789070.04616722612906411.29384594722875
750.670006586678907-0.09402815222446171.43404132558228
760.670006586678907-0.2122193575842621.55223253094208
770.670006586678907-0.3163483956732591.65636156903107
780.670006586678907-0.4104885246894161.75050169804723
790.670006586678907-0.4970594869307861.8370726602886
800.670006586678907-0.5776378957962281.91765106915404
810.670006586678907-0.6533188793839771.99333205274179
820.670006586678907-0.7248997985708172.06491297192863
830.670006586678907-0.7929825992313492.13299577258916
840.670006586678907-0.8580349351948462.19804810855266



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')