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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 05:07:17 -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/t1355738862tjdgjdj8wemy9i4.htm/, Retrieved Fri, 26 Apr 2024 00:14:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200738, Retrieved Fri, 26 Apr 2024 00:14:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2012-12-17 10:07:17] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
2.07
2.08
2.08
2.08
2.09
2.09
2.09
2.1
2.1
2.1
2.11
2.11
2.11
2.13
2.18
2.2
2.21
2.21
2.22
2.22
2.23
2.23
2.23
2.23
2.24
2.25
2.26
2.27
2.28
2.29
2.3
2.3
2.3
2.32
2.32
2.32
2.33
2.34
2.34
2.34
2.35
2.35
2.36
2.37
2.37
2.37
2.38
2.38
2.38
2.39
2.4
2.41
2.42
2.43
2.43
2.43
2.43
2.44
2.44
2.45
2.45
2.48
2.49
2.49
2.5
2.51
2.52
2.53
2.54
2.54
2.56
2.56




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200738&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]2 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=200738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200738&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 time2 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0335395346302571
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0335395346302571 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200738&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]0.0335395346302571[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200738&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
beta0.0335395346302571
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
32.082.09-0.0100000000000002
42.082.0896646046537-0.00966460465369767
52.092.089340458311230.000659541688772691
62.092.09936257903254-0.00936257903253779
72.092.09904856248885-0.00904856248884744
82.12.09874507791390.00125492208610156
92.12.10878716741666-0.00878716741666397
102.12.10849244991079-0.00849244991079079
112.112.108207617092910.00179238290708783
122.112.11826773278149-0.00826773278149506
132.112.11799043687156-0.00799043687155621
142.132.117722441337390.0122775586626078
152.182.138134224941330.0418657750586688
162.22.189538383553730.0104616164462659
172.212.209889261300820.000110738699177659
182.212.21989297542526-0.00989297542525813
192.222.219561169633390.00043883036661363
202.222.22957588779966-0.00957588779966434
212.232.229254716979190.000745283020807896
222.232.23927971342488-0.00927971342487766
232.232.23896847615511-0.00896847615510543
242.232.23866767763852-0.00866767763852039
252.242.23837696776420.00162303223580063
262.252.248431403510080.00156859648992169
272.262.258484013506370.00151598649362716
282.272.268534858987870.00146514101212558
292.282.278583999135590.00141600086441063
302.292.288631491145620.00136850885438289
312.32.298677390295730.0013226097042689
322.32.30872175000971-0.00872175000970943
332.32.30842922657322-0.00842922657322243
342.322.308146514236660.0118534857633366
352.322.32854407463291-0.0085440746329124
362.322.32825751034588-0.00825751034587796
372.332.327980557291670.00201944270832755
382.342.338048288460320.00195171153967699
392.342.3481137479571-0.00811374795709607
402.342.34784161662651-0.00784161662650762
412.352.347578612454110.00242138754589449
422.352.35765982466555-0.00765982466555437
432.362.357402917710920.00259708228907751
442.372.367490022642290.00250997735770575
452.372.3775742061148-0.00757420611480475
462.372.37732017076652-0.00732017076652047
472.382.37707465564560.00292534435440261
482.382.38717277033388-0.00717277033387731
492.382.38693219895487-0.00693219895486941
502.392.386699696227960.0033003037720416
512.42.396810386880610.00318961311938848
522.412.406917365020290.00308263497971417
532.422.417020755162940.00297924483705891
542.432.427120677648330.00287932235167476
552.432.43721724878005-0.00721724878005103
562.432.43697518561466-0.00697518561465715
572.432.43674124113518-0.00674124113518193
582.442.436515143044680.00348485695532208
592.442.44663202352521-0.00663202352521219
602.452.446409588542520.00359041145748051
612.452.45653000927193-0.00653000927193448
622.482.456310995799820.0236890042001772
632.492.487105513976550.00289448602344944
642.492.49720259369077-0.00720259369077114
652.52.496961022050250.00303897794974795
662.512.507062947956440.00293705204356165
672.522.517161455315160.00283854468483646
682.532.527256658782920.0027433412170792
692.542.537348669170670.00265133082932678
702.542.54743759357284-0.00743759357283968
712.562.547188140145640.0128118598543621
722.562.5676178439629-0.00761784396290111

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2.08 & 2.09 & -0.0100000000000002 \tabularnewline
4 & 2.08 & 2.0896646046537 & -0.00966460465369767 \tabularnewline
5 & 2.09 & 2.08934045831123 & 0.000659541688772691 \tabularnewline
6 & 2.09 & 2.09936257903254 & -0.00936257903253779 \tabularnewline
7 & 2.09 & 2.09904856248885 & -0.00904856248884744 \tabularnewline
8 & 2.1 & 2.0987450779139 & 0.00125492208610156 \tabularnewline
9 & 2.1 & 2.10878716741666 & -0.00878716741666397 \tabularnewline
10 & 2.1 & 2.10849244991079 & -0.00849244991079079 \tabularnewline
11 & 2.11 & 2.10820761709291 & 0.00179238290708783 \tabularnewline
12 & 2.11 & 2.11826773278149 & -0.00826773278149506 \tabularnewline
13 & 2.11 & 2.11799043687156 & -0.00799043687155621 \tabularnewline
14 & 2.13 & 2.11772244133739 & 0.0122775586626078 \tabularnewline
15 & 2.18 & 2.13813422494133 & 0.0418657750586688 \tabularnewline
16 & 2.2 & 2.18953838355373 & 0.0104616164462659 \tabularnewline
17 & 2.21 & 2.20988926130082 & 0.000110738699177659 \tabularnewline
18 & 2.21 & 2.21989297542526 & -0.00989297542525813 \tabularnewline
19 & 2.22 & 2.21956116963339 & 0.00043883036661363 \tabularnewline
20 & 2.22 & 2.22957588779966 & -0.00957588779966434 \tabularnewline
21 & 2.23 & 2.22925471697919 & 0.000745283020807896 \tabularnewline
22 & 2.23 & 2.23927971342488 & -0.00927971342487766 \tabularnewline
23 & 2.23 & 2.23896847615511 & -0.00896847615510543 \tabularnewline
24 & 2.23 & 2.23866767763852 & -0.00866767763852039 \tabularnewline
25 & 2.24 & 2.2383769677642 & 0.00162303223580063 \tabularnewline
26 & 2.25 & 2.24843140351008 & 0.00156859648992169 \tabularnewline
27 & 2.26 & 2.25848401350637 & 0.00151598649362716 \tabularnewline
28 & 2.27 & 2.26853485898787 & 0.00146514101212558 \tabularnewline
29 & 2.28 & 2.27858399913559 & 0.00141600086441063 \tabularnewline
30 & 2.29 & 2.28863149114562 & 0.00136850885438289 \tabularnewline
31 & 2.3 & 2.29867739029573 & 0.0013226097042689 \tabularnewline
32 & 2.3 & 2.30872175000971 & -0.00872175000970943 \tabularnewline
33 & 2.3 & 2.30842922657322 & -0.00842922657322243 \tabularnewline
34 & 2.32 & 2.30814651423666 & 0.0118534857633366 \tabularnewline
35 & 2.32 & 2.32854407463291 & -0.0085440746329124 \tabularnewline
36 & 2.32 & 2.32825751034588 & -0.00825751034587796 \tabularnewline
37 & 2.33 & 2.32798055729167 & 0.00201944270832755 \tabularnewline
38 & 2.34 & 2.33804828846032 & 0.00195171153967699 \tabularnewline
39 & 2.34 & 2.3481137479571 & -0.00811374795709607 \tabularnewline
40 & 2.34 & 2.34784161662651 & -0.00784161662650762 \tabularnewline
41 & 2.35 & 2.34757861245411 & 0.00242138754589449 \tabularnewline
42 & 2.35 & 2.35765982466555 & -0.00765982466555437 \tabularnewline
43 & 2.36 & 2.35740291771092 & 0.00259708228907751 \tabularnewline
44 & 2.37 & 2.36749002264229 & 0.00250997735770575 \tabularnewline
45 & 2.37 & 2.3775742061148 & -0.00757420611480475 \tabularnewline
46 & 2.37 & 2.37732017076652 & -0.00732017076652047 \tabularnewline
47 & 2.38 & 2.3770746556456 & 0.00292534435440261 \tabularnewline
48 & 2.38 & 2.38717277033388 & -0.00717277033387731 \tabularnewline
49 & 2.38 & 2.38693219895487 & -0.00693219895486941 \tabularnewline
50 & 2.39 & 2.38669969622796 & 0.0033003037720416 \tabularnewline
51 & 2.4 & 2.39681038688061 & 0.00318961311938848 \tabularnewline
52 & 2.41 & 2.40691736502029 & 0.00308263497971417 \tabularnewline
53 & 2.42 & 2.41702075516294 & 0.00297924483705891 \tabularnewline
54 & 2.43 & 2.42712067764833 & 0.00287932235167476 \tabularnewline
55 & 2.43 & 2.43721724878005 & -0.00721724878005103 \tabularnewline
56 & 2.43 & 2.43697518561466 & -0.00697518561465715 \tabularnewline
57 & 2.43 & 2.43674124113518 & -0.00674124113518193 \tabularnewline
58 & 2.44 & 2.43651514304468 & 0.00348485695532208 \tabularnewline
59 & 2.44 & 2.44663202352521 & -0.00663202352521219 \tabularnewline
60 & 2.45 & 2.44640958854252 & 0.00359041145748051 \tabularnewline
61 & 2.45 & 2.45653000927193 & -0.00653000927193448 \tabularnewline
62 & 2.48 & 2.45631099579982 & 0.0236890042001772 \tabularnewline
63 & 2.49 & 2.48710551397655 & 0.00289448602344944 \tabularnewline
64 & 2.49 & 2.49720259369077 & -0.00720259369077114 \tabularnewline
65 & 2.5 & 2.49696102205025 & 0.00303897794974795 \tabularnewline
66 & 2.51 & 2.50706294795644 & 0.00293705204356165 \tabularnewline
67 & 2.52 & 2.51716145531516 & 0.00283854468483646 \tabularnewline
68 & 2.53 & 2.52725665878292 & 0.0027433412170792 \tabularnewline
69 & 2.54 & 2.53734866917067 & 0.00265133082932678 \tabularnewline
70 & 2.54 & 2.54743759357284 & -0.00743759357283968 \tabularnewline
71 & 2.56 & 2.54718814014564 & 0.0128118598543621 \tabularnewline
72 & 2.56 & 2.5676178439629 & -0.00761784396290111 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200738&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]2.08[/C][C]2.09[/C][C]-0.0100000000000002[/C][/ROW]
[ROW][C]4[/C][C]2.08[/C][C]2.0896646046537[/C][C]-0.00966460465369767[/C][/ROW]
[ROW][C]5[/C][C]2.09[/C][C]2.08934045831123[/C][C]0.000659541688772691[/C][/ROW]
[ROW][C]6[/C][C]2.09[/C][C]2.09936257903254[/C][C]-0.00936257903253779[/C][/ROW]
[ROW][C]7[/C][C]2.09[/C][C]2.09904856248885[/C][C]-0.00904856248884744[/C][/ROW]
[ROW][C]8[/C][C]2.1[/C][C]2.0987450779139[/C][C]0.00125492208610156[/C][/ROW]
[ROW][C]9[/C][C]2.1[/C][C]2.10878716741666[/C][C]-0.00878716741666397[/C][/ROW]
[ROW][C]10[/C][C]2.1[/C][C]2.10849244991079[/C][C]-0.00849244991079079[/C][/ROW]
[ROW][C]11[/C][C]2.11[/C][C]2.10820761709291[/C][C]0.00179238290708783[/C][/ROW]
[ROW][C]12[/C][C]2.11[/C][C]2.11826773278149[/C][C]-0.00826773278149506[/C][/ROW]
[ROW][C]13[/C][C]2.11[/C][C]2.11799043687156[/C][C]-0.00799043687155621[/C][/ROW]
[ROW][C]14[/C][C]2.13[/C][C]2.11772244133739[/C][C]0.0122775586626078[/C][/ROW]
[ROW][C]15[/C][C]2.18[/C][C]2.13813422494133[/C][C]0.0418657750586688[/C][/ROW]
[ROW][C]16[/C][C]2.2[/C][C]2.18953838355373[/C][C]0.0104616164462659[/C][/ROW]
[ROW][C]17[/C][C]2.21[/C][C]2.20988926130082[/C][C]0.000110738699177659[/C][/ROW]
[ROW][C]18[/C][C]2.21[/C][C]2.21989297542526[/C][C]-0.00989297542525813[/C][/ROW]
[ROW][C]19[/C][C]2.22[/C][C]2.21956116963339[/C][C]0.00043883036661363[/C][/ROW]
[ROW][C]20[/C][C]2.22[/C][C]2.22957588779966[/C][C]-0.00957588779966434[/C][/ROW]
[ROW][C]21[/C][C]2.23[/C][C]2.22925471697919[/C][C]0.000745283020807896[/C][/ROW]
[ROW][C]22[/C][C]2.23[/C][C]2.23927971342488[/C][C]-0.00927971342487766[/C][/ROW]
[ROW][C]23[/C][C]2.23[/C][C]2.23896847615511[/C][C]-0.00896847615510543[/C][/ROW]
[ROW][C]24[/C][C]2.23[/C][C]2.23866767763852[/C][C]-0.00866767763852039[/C][/ROW]
[ROW][C]25[/C][C]2.24[/C][C]2.2383769677642[/C][C]0.00162303223580063[/C][/ROW]
[ROW][C]26[/C][C]2.25[/C][C]2.24843140351008[/C][C]0.00156859648992169[/C][/ROW]
[ROW][C]27[/C][C]2.26[/C][C]2.25848401350637[/C][C]0.00151598649362716[/C][/ROW]
[ROW][C]28[/C][C]2.27[/C][C]2.26853485898787[/C][C]0.00146514101212558[/C][/ROW]
[ROW][C]29[/C][C]2.28[/C][C]2.27858399913559[/C][C]0.00141600086441063[/C][/ROW]
[ROW][C]30[/C][C]2.29[/C][C]2.28863149114562[/C][C]0.00136850885438289[/C][/ROW]
[ROW][C]31[/C][C]2.3[/C][C]2.29867739029573[/C][C]0.0013226097042689[/C][/ROW]
[ROW][C]32[/C][C]2.3[/C][C]2.30872175000971[/C][C]-0.00872175000970943[/C][/ROW]
[ROW][C]33[/C][C]2.3[/C][C]2.30842922657322[/C][C]-0.00842922657322243[/C][/ROW]
[ROW][C]34[/C][C]2.32[/C][C]2.30814651423666[/C][C]0.0118534857633366[/C][/ROW]
[ROW][C]35[/C][C]2.32[/C][C]2.32854407463291[/C][C]-0.0085440746329124[/C][/ROW]
[ROW][C]36[/C][C]2.32[/C][C]2.32825751034588[/C][C]-0.00825751034587796[/C][/ROW]
[ROW][C]37[/C][C]2.33[/C][C]2.32798055729167[/C][C]0.00201944270832755[/C][/ROW]
[ROW][C]38[/C][C]2.34[/C][C]2.33804828846032[/C][C]0.00195171153967699[/C][/ROW]
[ROW][C]39[/C][C]2.34[/C][C]2.3481137479571[/C][C]-0.00811374795709607[/C][/ROW]
[ROW][C]40[/C][C]2.34[/C][C]2.34784161662651[/C][C]-0.00784161662650762[/C][/ROW]
[ROW][C]41[/C][C]2.35[/C][C]2.34757861245411[/C][C]0.00242138754589449[/C][/ROW]
[ROW][C]42[/C][C]2.35[/C][C]2.35765982466555[/C][C]-0.00765982466555437[/C][/ROW]
[ROW][C]43[/C][C]2.36[/C][C]2.35740291771092[/C][C]0.00259708228907751[/C][/ROW]
[ROW][C]44[/C][C]2.37[/C][C]2.36749002264229[/C][C]0.00250997735770575[/C][/ROW]
[ROW][C]45[/C][C]2.37[/C][C]2.3775742061148[/C][C]-0.00757420611480475[/C][/ROW]
[ROW][C]46[/C][C]2.37[/C][C]2.37732017076652[/C][C]-0.00732017076652047[/C][/ROW]
[ROW][C]47[/C][C]2.38[/C][C]2.3770746556456[/C][C]0.00292534435440261[/C][/ROW]
[ROW][C]48[/C][C]2.38[/C][C]2.38717277033388[/C][C]-0.00717277033387731[/C][/ROW]
[ROW][C]49[/C][C]2.38[/C][C]2.38693219895487[/C][C]-0.00693219895486941[/C][/ROW]
[ROW][C]50[/C][C]2.39[/C][C]2.38669969622796[/C][C]0.0033003037720416[/C][/ROW]
[ROW][C]51[/C][C]2.4[/C][C]2.39681038688061[/C][C]0.00318961311938848[/C][/ROW]
[ROW][C]52[/C][C]2.41[/C][C]2.40691736502029[/C][C]0.00308263497971417[/C][/ROW]
[ROW][C]53[/C][C]2.42[/C][C]2.41702075516294[/C][C]0.00297924483705891[/C][/ROW]
[ROW][C]54[/C][C]2.43[/C][C]2.42712067764833[/C][C]0.00287932235167476[/C][/ROW]
[ROW][C]55[/C][C]2.43[/C][C]2.43721724878005[/C][C]-0.00721724878005103[/C][/ROW]
[ROW][C]56[/C][C]2.43[/C][C]2.43697518561466[/C][C]-0.00697518561465715[/C][/ROW]
[ROW][C]57[/C][C]2.43[/C][C]2.43674124113518[/C][C]-0.00674124113518193[/C][/ROW]
[ROW][C]58[/C][C]2.44[/C][C]2.43651514304468[/C][C]0.00348485695532208[/C][/ROW]
[ROW][C]59[/C][C]2.44[/C][C]2.44663202352521[/C][C]-0.00663202352521219[/C][/ROW]
[ROW][C]60[/C][C]2.45[/C][C]2.44640958854252[/C][C]0.00359041145748051[/C][/ROW]
[ROW][C]61[/C][C]2.45[/C][C]2.45653000927193[/C][C]-0.00653000927193448[/C][/ROW]
[ROW][C]62[/C][C]2.48[/C][C]2.45631099579982[/C][C]0.0236890042001772[/C][/ROW]
[ROW][C]63[/C][C]2.49[/C][C]2.48710551397655[/C][C]0.00289448602344944[/C][/ROW]
[ROW][C]64[/C][C]2.49[/C][C]2.49720259369077[/C][C]-0.00720259369077114[/C][/ROW]
[ROW][C]65[/C][C]2.5[/C][C]2.49696102205025[/C][C]0.00303897794974795[/C][/ROW]
[ROW][C]66[/C][C]2.51[/C][C]2.50706294795644[/C][C]0.00293705204356165[/C][/ROW]
[ROW][C]67[/C][C]2.52[/C][C]2.51716145531516[/C][C]0.00283854468483646[/C][/ROW]
[ROW][C]68[/C][C]2.53[/C][C]2.52725665878292[/C][C]0.0027433412170792[/C][/ROW]
[ROW][C]69[/C][C]2.54[/C][C]2.53734866917067[/C][C]0.00265133082932678[/C][/ROW]
[ROW][C]70[/C][C]2.54[/C][C]2.54743759357284[/C][C]-0.00743759357283968[/C][/ROW]
[ROW][C]71[/C][C]2.56[/C][C]2.54718814014564[/C][C]0.0128118598543621[/C][/ROW]
[ROW][C]72[/C][C]2.56[/C][C]2.5676178439629[/C][C]-0.00761784396290111[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200738&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200738&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
32.082.09-0.0100000000000002
42.082.0896646046537-0.00966460465369767
52.092.089340458311230.000659541688772691
62.092.09936257903254-0.00936257903253779
72.092.09904856248885-0.00904856248884744
82.12.09874507791390.00125492208610156
92.12.10878716741666-0.00878716741666397
102.12.10849244991079-0.00849244991079079
112.112.108207617092910.00179238290708783
122.112.11826773278149-0.00826773278149506
132.112.11799043687156-0.00799043687155621
142.132.117722441337390.0122775586626078
152.182.138134224941330.0418657750586688
162.22.189538383553730.0104616164462659
172.212.209889261300820.000110738699177659
182.212.21989297542526-0.00989297542525813
192.222.219561169633390.00043883036661363
202.222.22957588779966-0.00957588779966434
212.232.229254716979190.000745283020807896
222.232.23927971342488-0.00927971342487766
232.232.23896847615511-0.00896847615510543
242.232.23866767763852-0.00866767763852039
252.242.23837696776420.00162303223580063
262.252.248431403510080.00156859648992169
272.262.258484013506370.00151598649362716
282.272.268534858987870.00146514101212558
292.282.278583999135590.00141600086441063
302.292.288631491145620.00136850885438289
312.32.298677390295730.0013226097042689
322.32.30872175000971-0.00872175000970943
332.32.30842922657322-0.00842922657322243
342.322.308146514236660.0118534857633366
352.322.32854407463291-0.0085440746329124
362.322.32825751034588-0.00825751034587796
372.332.327980557291670.00201944270832755
382.342.338048288460320.00195171153967699
392.342.3481137479571-0.00811374795709607
402.342.34784161662651-0.00784161662650762
412.352.347578612454110.00242138754589449
422.352.35765982466555-0.00765982466555437
432.362.357402917710920.00259708228907751
442.372.367490022642290.00250997735770575
452.372.3775742061148-0.00757420611480475
462.372.37732017076652-0.00732017076652047
472.382.37707465564560.00292534435440261
482.382.38717277033388-0.00717277033387731
492.382.38693219895487-0.00693219895486941
502.392.386699696227960.0033003037720416
512.42.396810386880610.00318961311938848
522.412.406917365020290.00308263497971417
532.422.417020755162940.00297924483705891
542.432.427120677648330.00287932235167476
552.432.43721724878005-0.00721724878005103
562.432.43697518561466-0.00697518561465715
572.432.43674124113518-0.00674124113518193
582.442.436515143044680.00348485695532208
592.442.44663202352521-0.00663202352521219
602.452.446409588542520.00359041145748051
612.452.45653000927193-0.00653000927193448
622.482.456310995799820.0236890042001772
632.492.487105513976550.00289448602344944
642.492.49720259369077-0.00720259369077114
652.52.496961022050250.00303897794974795
662.512.507062947956440.00293705204356165
672.522.517161455315160.00283854468483646
682.532.527256658782920.0027433412170792
692.542.537348669170670.00265133082932678
702.542.54743759357284-0.00743759357283968
712.562.547188140145640.0128118598543621
722.562.5676178439629-0.00761784396290111







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.56736234502152.55046739894032.5842572911027
742.5747246900432.55042764304312.5990217370429
752.58208703506452.551832051163912.61234201896509
762.5894493800862.553936930745632.62496182942637
772.59681172510752.556459541817922.63716390839708
782.6041740701292.559257479136212.64909066112178
792.61153641515052.562247668057242.66082516224375
802.6188987601722.565376968269992.672420552074
812.62626110519352.56860915654572.68391305384129
822.6336234502152.571918363756752.69532853667325
832.64098579523652.575285445728022.70668614474497
842.648348140257992.578695831923152.71800044859284

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.5673623450215 & 2.5504673989403 & 2.5842572911027 \tabularnewline
74 & 2.574724690043 & 2.5504276430431 & 2.5990217370429 \tabularnewline
75 & 2.5820870350645 & 2.55183205116391 & 2.61234201896509 \tabularnewline
76 & 2.589449380086 & 2.55393693074563 & 2.62496182942637 \tabularnewline
77 & 2.5968117251075 & 2.55645954181792 & 2.63716390839708 \tabularnewline
78 & 2.604174070129 & 2.55925747913621 & 2.64909066112178 \tabularnewline
79 & 2.6115364151505 & 2.56224766805724 & 2.66082516224375 \tabularnewline
80 & 2.618898760172 & 2.56537696826999 & 2.672420552074 \tabularnewline
81 & 2.6262611051935 & 2.5686091565457 & 2.68391305384129 \tabularnewline
82 & 2.633623450215 & 2.57191836375675 & 2.69532853667325 \tabularnewline
83 & 2.6409857952365 & 2.57528544572802 & 2.70668614474497 \tabularnewline
84 & 2.64834814025799 & 2.57869583192315 & 2.71800044859284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200738&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]2.5673623450215[/C][C]2.5504673989403[/C][C]2.5842572911027[/C][/ROW]
[ROW][C]74[/C][C]2.574724690043[/C][C]2.5504276430431[/C][C]2.5990217370429[/C][/ROW]
[ROW][C]75[/C][C]2.5820870350645[/C][C]2.55183205116391[/C][C]2.61234201896509[/C][/ROW]
[ROW][C]76[/C][C]2.589449380086[/C][C]2.55393693074563[/C][C]2.62496182942637[/C][/ROW]
[ROW][C]77[/C][C]2.5968117251075[/C][C]2.55645954181792[/C][C]2.63716390839708[/C][/ROW]
[ROW][C]78[/C][C]2.604174070129[/C][C]2.55925747913621[/C][C]2.64909066112178[/C][/ROW]
[ROW][C]79[/C][C]2.6115364151505[/C][C]2.56224766805724[/C][C]2.66082516224375[/C][/ROW]
[ROW][C]80[/C][C]2.618898760172[/C][C]2.56537696826999[/C][C]2.672420552074[/C][/ROW]
[ROW][C]81[/C][C]2.6262611051935[/C][C]2.5686091565457[/C][C]2.68391305384129[/C][/ROW]
[ROW][C]82[/C][C]2.633623450215[/C][C]2.57191836375675[/C][C]2.69532853667325[/C][/ROW]
[ROW][C]83[/C][C]2.6409857952365[/C][C]2.57528544572802[/C][C]2.70668614474497[/C][/ROW]
[ROW][C]84[/C][C]2.64834814025799[/C][C]2.57869583192315[/C][C]2.71800044859284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200738&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200738&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
732.56736234502152.55046739894032.5842572911027
742.5747246900432.55042764304312.5990217370429
752.58208703506452.551832051163912.61234201896509
762.5894493800862.553936930745632.62496182942637
772.59681172510752.556459541817922.63716390839708
782.6041740701292.559257479136212.64909066112178
792.61153641515052.562247668057242.66082516224375
802.6188987601722.565376968269992.672420552074
812.62626110519352.56860915654572.68391305384129
822.6336234502152.571918363756752.69532853667325
832.64098579523652.575285445728022.70668614474497
842.648348140257992.578695831923152.71800044859284



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')