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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 21 May 2013 10:05:09 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/21/t1369145261ec0luh9k7jsecqk.htm/, Retrieved Thu, 02 May 2024 02:54:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=209215, Retrieved Thu, 02 May 2024 02:54:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [cons prijzen van ...] [2013-05-21 14:05:09] [2ad6cfb061f4abd47c32d0a7b72d8383] [Current]
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Dataseries X:
4,69
4,69
4,69
4,69
4,69
4,69
4,69
4,73
4,78
4,79
4,79
4,8
4,8
4,81
5,16
5,26
5,29
5,29
5,29
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,3
5,35
5,44
5,47
5,47
5,48
5,48
5,48
5,48
5,48
5,48
5,48
5,5
5,55
5,57
5,58
5,58
5,58
5,59
5,59
5,59
5,55
5,61
5,61
5,61
5,63
5,69
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,7
5,71
5,74
5,77
5,79
5,79
5,8
5,8
5,8
5,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 6 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209215&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209215&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209215&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 time6 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.586892430925192
beta0.0611759905828995
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.586892430925192 \tabularnewline
beta & 0.0611759905828995 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209215&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]0.586892430925192[/C][/ROW]
[ROW][C]beta[/C][C]0.0611759905828995[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209215&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209215&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
alpha0.586892430925192
beta0.0611759905828995
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134.84.55185770732030.248142292679695
144.814.712347587313710.097652412686287
155.165.128572146864220.031427853135785
165.265.26218163652571-0.00218163652570702
175.295.30651462785455-0.0165146278545478
185.295.31209319761571-0.0220931976157148
195.295.198690155408870.0913098445911338
205.35.3458499172712-0.0458499172711981
215.35.40558426662543-0.105584266625427
225.35.36052140157731-0.0605214015773088
235.35.32284569929771-0.0228456992977106
245.35.31636966289758-0.0163696628975813
255.35.41791452232925-0.117914522329252
265.35.283100587460740.0168994125392636
275.35.64204749277152-0.342047492771518
285.355.52130789359185-0.171307893591855
295.445.430340175061150.0096598249388542
305.475.419379102692740.0506208973072582
315.475.366620299360540.103379700639464
325.485.438858373243320.0411416267566791
335.485.50301848742882-0.0230184874288231
345.485.50564009447451-0.0256400944745145
355.485.48541743876542-0.00541743876541911
365.485.473995442909140.00600455709085601
375.485.53102646246438-0.0510264624643755
385.485.475866296780150.00413370321985251
395.55.66478420184505-0.16478420184505
405.555.71487878921021-0.164878789210212
415.575.69707030631351-0.127070306313514
425.585.60873156025362-0.0287315602536182
435.585.513131813556090.0668681864439051
445.585.520701497016630.059298502983367
455.595.552674954216970.0373250457830343
465.595.575465530095430.0145344699045724
475.595.574311629655360.015688370344642
485.555.56785085391406-0.0178508539140561
495.615.574861489478150.0351385105218514
505.615.583191663929830.0268083360701699
515.615.70780022644842-0.097800226448415
525.635.79297807387139-0.162978073871388
535.695.78678605844674-0.0967860584467415
545.75.75178379700558-0.0517837970055766
555.75.674475555261640.0255244447383554
565.75.645959354188710.0540406458112903
575.75.657493062742010.0425069372579863
585.75.665974405787330.0340255942126735
595.75.669498641565240.0305013584347602
605.75.650855011913910.0491449880860886
615.75.71572285766731-0.0157228576673099
625.75.684563626125920.0154363738740848
635.75.74515484384821-0.0451548438482092
645.715.83083825222981-0.120838252229805
655.745.87590422123124-0.135904221231243
665.775.83274456761358-0.0627445676135769
675.795.77590487111270.014095128887301
685.795.746744227835140.0432557721648612
695.85.741307219698820.058692780301179
705.85.750563579376720.0494364206232785
715.85.757030302895640.0429696971043647
725.85.748982678802210.0510173211977936

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4.8 & 4.5518577073203 & 0.248142292679695 \tabularnewline
14 & 4.81 & 4.71234758731371 & 0.097652412686287 \tabularnewline
15 & 5.16 & 5.12857214686422 & 0.031427853135785 \tabularnewline
16 & 5.26 & 5.26218163652571 & -0.00218163652570702 \tabularnewline
17 & 5.29 & 5.30651462785455 & -0.0165146278545478 \tabularnewline
18 & 5.29 & 5.31209319761571 & -0.0220931976157148 \tabularnewline
19 & 5.29 & 5.19869015540887 & 0.0913098445911338 \tabularnewline
20 & 5.3 & 5.3458499172712 & -0.0458499172711981 \tabularnewline
21 & 5.3 & 5.40558426662543 & -0.105584266625427 \tabularnewline
22 & 5.3 & 5.36052140157731 & -0.0605214015773088 \tabularnewline
23 & 5.3 & 5.32284569929771 & -0.0228456992977106 \tabularnewline
24 & 5.3 & 5.31636966289758 & -0.0163696628975813 \tabularnewline
25 & 5.3 & 5.41791452232925 & -0.117914522329252 \tabularnewline
26 & 5.3 & 5.28310058746074 & 0.0168994125392636 \tabularnewline
27 & 5.3 & 5.64204749277152 & -0.342047492771518 \tabularnewline
28 & 5.35 & 5.52130789359185 & -0.171307893591855 \tabularnewline
29 & 5.44 & 5.43034017506115 & 0.0096598249388542 \tabularnewline
30 & 5.47 & 5.41937910269274 & 0.0506208973072582 \tabularnewline
31 & 5.47 & 5.36662029936054 & 0.103379700639464 \tabularnewline
32 & 5.48 & 5.43885837324332 & 0.0411416267566791 \tabularnewline
33 & 5.48 & 5.50301848742882 & -0.0230184874288231 \tabularnewline
34 & 5.48 & 5.50564009447451 & -0.0256400944745145 \tabularnewline
35 & 5.48 & 5.48541743876542 & -0.00541743876541911 \tabularnewline
36 & 5.48 & 5.47399544290914 & 0.00600455709085601 \tabularnewline
37 & 5.48 & 5.53102646246438 & -0.0510264624643755 \tabularnewline
38 & 5.48 & 5.47586629678015 & 0.00413370321985251 \tabularnewline
39 & 5.5 & 5.66478420184505 & -0.16478420184505 \tabularnewline
40 & 5.55 & 5.71487878921021 & -0.164878789210212 \tabularnewline
41 & 5.57 & 5.69707030631351 & -0.127070306313514 \tabularnewline
42 & 5.58 & 5.60873156025362 & -0.0287315602536182 \tabularnewline
43 & 5.58 & 5.51313181355609 & 0.0668681864439051 \tabularnewline
44 & 5.58 & 5.52070149701663 & 0.059298502983367 \tabularnewline
45 & 5.59 & 5.55267495421697 & 0.0373250457830343 \tabularnewline
46 & 5.59 & 5.57546553009543 & 0.0145344699045724 \tabularnewline
47 & 5.59 & 5.57431162965536 & 0.015688370344642 \tabularnewline
48 & 5.55 & 5.56785085391406 & -0.0178508539140561 \tabularnewline
49 & 5.61 & 5.57486148947815 & 0.0351385105218514 \tabularnewline
50 & 5.61 & 5.58319166392983 & 0.0268083360701699 \tabularnewline
51 & 5.61 & 5.70780022644842 & -0.097800226448415 \tabularnewline
52 & 5.63 & 5.79297807387139 & -0.162978073871388 \tabularnewline
53 & 5.69 & 5.78678605844674 & -0.0967860584467415 \tabularnewline
54 & 5.7 & 5.75178379700558 & -0.0517837970055766 \tabularnewline
55 & 5.7 & 5.67447555526164 & 0.0255244447383554 \tabularnewline
56 & 5.7 & 5.64595935418871 & 0.0540406458112903 \tabularnewline
57 & 5.7 & 5.65749306274201 & 0.0425069372579863 \tabularnewline
58 & 5.7 & 5.66597440578733 & 0.0340255942126735 \tabularnewline
59 & 5.7 & 5.66949864156524 & 0.0305013584347602 \tabularnewline
60 & 5.7 & 5.65085501191391 & 0.0491449880860886 \tabularnewline
61 & 5.7 & 5.71572285766731 & -0.0157228576673099 \tabularnewline
62 & 5.7 & 5.68456362612592 & 0.0154363738740848 \tabularnewline
63 & 5.7 & 5.74515484384821 & -0.0451548438482092 \tabularnewline
64 & 5.71 & 5.83083825222981 & -0.120838252229805 \tabularnewline
65 & 5.74 & 5.87590422123124 & -0.135904221231243 \tabularnewline
66 & 5.77 & 5.83274456761358 & -0.0627445676135769 \tabularnewline
67 & 5.79 & 5.7759048711127 & 0.014095128887301 \tabularnewline
68 & 5.79 & 5.74674422783514 & 0.0432557721648612 \tabularnewline
69 & 5.8 & 5.74130721969882 & 0.058692780301179 \tabularnewline
70 & 5.8 & 5.75056357937672 & 0.0494364206232785 \tabularnewline
71 & 5.8 & 5.75703030289564 & 0.0429696971043647 \tabularnewline
72 & 5.8 & 5.74898267880221 & 0.0510173211977936 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209215&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]13[/C][C]4.8[/C][C]4.5518577073203[/C][C]0.248142292679695[/C][/ROW]
[ROW][C]14[/C][C]4.81[/C][C]4.71234758731371[/C][C]0.097652412686287[/C][/ROW]
[ROW][C]15[/C][C]5.16[/C][C]5.12857214686422[/C][C]0.031427853135785[/C][/ROW]
[ROW][C]16[/C][C]5.26[/C][C]5.26218163652571[/C][C]-0.00218163652570702[/C][/ROW]
[ROW][C]17[/C][C]5.29[/C][C]5.30651462785455[/C][C]-0.0165146278545478[/C][/ROW]
[ROW][C]18[/C][C]5.29[/C][C]5.31209319761571[/C][C]-0.0220931976157148[/C][/ROW]
[ROW][C]19[/C][C]5.29[/C][C]5.19869015540887[/C][C]0.0913098445911338[/C][/ROW]
[ROW][C]20[/C][C]5.3[/C][C]5.3458499172712[/C][C]-0.0458499172711981[/C][/ROW]
[ROW][C]21[/C][C]5.3[/C][C]5.40558426662543[/C][C]-0.105584266625427[/C][/ROW]
[ROW][C]22[/C][C]5.3[/C][C]5.36052140157731[/C][C]-0.0605214015773088[/C][/ROW]
[ROW][C]23[/C][C]5.3[/C][C]5.32284569929771[/C][C]-0.0228456992977106[/C][/ROW]
[ROW][C]24[/C][C]5.3[/C][C]5.31636966289758[/C][C]-0.0163696628975813[/C][/ROW]
[ROW][C]25[/C][C]5.3[/C][C]5.41791452232925[/C][C]-0.117914522329252[/C][/ROW]
[ROW][C]26[/C][C]5.3[/C][C]5.28310058746074[/C][C]0.0168994125392636[/C][/ROW]
[ROW][C]27[/C][C]5.3[/C][C]5.64204749277152[/C][C]-0.342047492771518[/C][/ROW]
[ROW][C]28[/C][C]5.35[/C][C]5.52130789359185[/C][C]-0.171307893591855[/C][/ROW]
[ROW][C]29[/C][C]5.44[/C][C]5.43034017506115[/C][C]0.0096598249388542[/C][/ROW]
[ROW][C]30[/C][C]5.47[/C][C]5.41937910269274[/C][C]0.0506208973072582[/C][/ROW]
[ROW][C]31[/C][C]5.47[/C][C]5.36662029936054[/C][C]0.103379700639464[/C][/ROW]
[ROW][C]32[/C][C]5.48[/C][C]5.43885837324332[/C][C]0.0411416267566791[/C][/ROW]
[ROW][C]33[/C][C]5.48[/C][C]5.50301848742882[/C][C]-0.0230184874288231[/C][/ROW]
[ROW][C]34[/C][C]5.48[/C][C]5.50564009447451[/C][C]-0.0256400944745145[/C][/ROW]
[ROW][C]35[/C][C]5.48[/C][C]5.48541743876542[/C][C]-0.00541743876541911[/C][/ROW]
[ROW][C]36[/C][C]5.48[/C][C]5.47399544290914[/C][C]0.00600455709085601[/C][/ROW]
[ROW][C]37[/C][C]5.48[/C][C]5.53102646246438[/C][C]-0.0510264624643755[/C][/ROW]
[ROW][C]38[/C][C]5.48[/C][C]5.47586629678015[/C][C]0.00413370321985251[/C][/ROW]
[ROW][C]39[/C][C]5.5[/C][C]5.66478420184505[/C][C]-0.16478420184505[/C][/ROW]
[ROW][C]40[/C][C]5.55[/C][C]5.71487878921021[/C][C]-0.164878789210212[/C][/ROW]
[ROW][C]41[/C][C]5.57[/C][C]5.69707030631351[/C][C]-0.127070306313514[/C][/ROW]
[ROW][C]42[/C][C]5.58[/C][C]5.60873156025362[/C][C]-0.0287315602536182[/C][/ROW]
[ROW][C]43[/C][C]5.58[/C][C]5.51313181355609[/C][C]0.0668681864439051[/C][/ROW]
[ROW][C]44[/C][C]5.58[/C][C]5.52070149701663[/C][C]0.059298502983367[/C][/ROW]
[ROW][C]45[/C][C]5.59[/C][C]5.55267495421697[/C][C]0.0373250457830343[/C][/ROW]
[ROW][C]46[/C][C]5.59[/C][C]5.57546553009543[/C][C]0.0145344699045724[/C][/ROW]
[ROW][C]47[/C][C]5.59[/C][C]5.57431162965536[/C][C]0.015688370344642[/C][/ROW]
[ROW][C]48[/C][C]5.55[/C][C]5.56785085391406[/C][C]-0.0178508539140561[/C][/ROW]
[ROW][C]49[/C][C]5.61[/C][C]5.57486148947815[/C][C]0.0351385105218514[/C][/ROW]
[ROW][C]50[/C][C]5.61[/C][C]5.58319166392983[/C][C]0.0268083360701699[/C][/ROW]
[ROW][C]51[/C][C]5.61[/C][C]5.70780022644842[/C][C]-0.097800226448415[/C][/ROW]
[ROW][C]52[/C][C]5.63[/C][C]5.79297807387139[/C][C]-0.162978073871388[/C][/ROW]
[ROW][C]53[/C][C]5.69[/C][C]5.78678605844674[/C][C]-0.0967860584467415[/C][/ROW]
[ROW][C]54[/C][C]5.7[/C][C]5.75178379700558[/C][C]-0.0517837970055766[/C][/ROW]
[ROW][C]55[/C][C]5.7[/C][C]5.67447555526164[/C][C]0.0255244447383554[/C][/ROW]
[ROW][C]56[/C][C]5.7[/C][C]5.64595935418871[/C][C]0.0540406458112903[/C][/ROW]
[ROW][C]57[/C][C]5.7[/C][C]5.65749306274201[/C][C]0.0425069372579863[/C][/ROW]
[ROW][C]58[/C][C]5.7[/C][C]5.66597440578733[/C][C]0.0340255942126735[/C][/ROW]
[ROW][C]59[/C][C]5.7[/C][C]5.66949864156524[/C][C]0.0305013584347602[/C][/ROW]
[ROW][C]60[/C][C]5.7[/C][C]5.65085501191391[/C][C]0.0491449880860886[/C][/ROW]
[ROW][C]61[/C][C]5.7[/C][C]5.71572285766731[/C][C]-0.0157228576673099[/C][/ROW]
[ROW][C]62[/C][C]5.7[/C][C]5.68456362612592[/C][C]0.0154363738740848[/C][/ROW]
[ROW][C]63[/C][C]5.7[/C][C]5.74515484384821[/C][C]-0.0451548438482092[/C][/ROW]
[ROW][C]64[/C][C]5.71[/C][C]5.83083825222981[/C][C]-0.120838252229805[/C][/ROW]
[ROW][C]65[/C][C]5.74[/C][C]5.87590422123124[/C][C]-0.135904221231243[/C][/ROW]
[ROW][C]66[/C][C]5.77[/C][C]5.83274456761358[/C][C]-0.0627445676135769[/C][/ROW]
[ROW][C]67[/C][C]5.79[/C][C]5.7759048711127[/C][C]0.014095128887301[/C][/ROW]
[ROW][C]68[/C][C]5.79[/C][C]5.74674422783514[/C][C]0.0432557721648612[/C][/ROW]
[ROW][C]69[/C][C]5.8[/C][C]5.74130721969882[/C][C]0.058692780301179[/C][/ROW]
[ROW][C]70[/C][C]5.8[/C][C]5.75056357937672[/C][C]0.0494364206232785[/C][/ROW]
[ROW][C]71[/C][C]5.8[/C][C]5.75703030289564[/C][C]0.0429696971043647[/C][/ROW]
[ROW][C]72[/C][C]5.8[/C][C]5.74898267880221[/C][C]0.0510173211977936[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209215&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209215&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
134.84.55185770732030.248142292679695
144.814.712347587313710.097652412686287
155.165.128572146864220.031427853135785
165.265.26218163652571-0.00218163652570702
175.295.30651462785455-0.0165146278545478
185.295.31209319761571-0.0220931976157148
195.295.198690155408870.0913098445911338
205.35.3458499172712-0.0458499172711981
215.35.40558426662543-0.105584266625427
225.35.36052140157731-0.0605214015773088
235.35.32284569929771-0.0228456992977106
245.35.31636966289758-0.0163696628975813
255.35.41791452232925-0.117914522329252
265.35.283100587460740.0168994125392636
275.35.64204749277152-0.342047492771518
285.355.52130789359185-0.171307893591855
295.445.430340175061150.0096598249388542
305.475.419379102692740.0506208973072582
315.475.366620299360540.103379700639464
325.485.438858373243320.0411416267566791
335.485.50301848742882-0.0230184874288231
345.485.50564009447451-0.0256400944745145
355.485.48541743876542-0.00541743876541911
365.485.473995442909140.00600455709085601
375.485.53102646246438-0.0510264624643755
385.485.475866296780150.00413370321985251
395.55.66478420184505-0.16478420184505
405.555.71487878921021-0.164878789210212
415.575.69707030631351-0.127070306313514
425.585.60873156025362-0.0287315602536182
435.585.513131813556090.0668681864439051
445.585.520701497016630.059298502983367
455.595.552674954216970.0373250457830343
465.595.575465530095430.0145344699045724
475.595.574311629655360.015688370344642
485.555.56785085391406-0.0178508539140561
495.615.574861489478150.0351385105218514
505.615.583191663929830.0268083360701699
515.615.70780022644842-0.097800226448415
525.635.79297807387139-0.162978073871388
535.695.78678605844674-0.0967860584467415
545.75.75178379700558-0.0517837970055766
555.75.674475555261640.0255244447383554
565.75.645959354188710.0540406458112903
575.75.657493062742010.0425069372579863
585.75.665974405787330.0340255942126735
595.75.669498641565240.0305013584347602
605.75.650855011913910.0491449880860886
615.75.71572285766731-0.0157228576673099
625.75.684563626125920.0154363738740848
635.75.74515484384821-0.0451548438482092
645.715.83083825222981-0.120838252229805
655.745.87590422123124-0.135904221231243
665.775.83274456761358-0.0627445676135769
675.795.77590487111270.014095128887301
685.795.746744227835140.0432557721648612
695.85.741307219698820.058692780301179
705.85.750563579376720.0494364206232785
715.85.757030302895640.0429696971043647
725.85.748982678802210.0510173211977936







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
735.784418035928075.61143318407925.95740288777694
745.771933240661925.568404483744225.97546199757961
755.794870232080365.561483156164726.028257307996
765.874246665961075.610082454763156.13841087715898
775.988366247245735.692128411273096.28460408321836
786.064841501355365.737411773849736.392271228861
796.086400554968585.729778681120136.44302242881703
806.068292917560485.684283574057126.45230226106384
816.049527386390695.638166328154246.46088844462713
826.023962810551215.585631773767226.4622938473352
836.000666477558185.535195782241046.46613717287533
845.97098493370622-5.7969506945282217.7389205619407

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 5.78441803592807 & 5.6114331840792 & 5.95740288777694 \tabularnewline
74 & 5.77193324066192 & 5.56840448374422 & 5.97546199757961 \tabularnewline
75 & 5.79487023208036 & 5.56148315616472 & 6.028257307996 \tabularnewline
76 & 5.87424666596107 & 5.61008245476315 & 6.13841087715898 \tabularnewline
77 & 5.98836624724573 & 5.69212841127309 & 6.28460408321836 \tabularnewline
78 & 6.06484150135536 & 5.73741177384973 & 6.392271228861 \tabularnewline
79 & 6.08640055496858 & 5.72977868112013 & 6.44302242881703 \tabularnewline
80 & 6.06829291756048 & 5.68428357405712 & 6.45230226106384 \tabularnewline
81 & 6.04952738639069 & 5.63816632815424 & 6.46088844462713 \tabularnewline
82 & 6.02396281055121 & 5.58563177376722 & 6.4622938473352 \tabularnewline
83 & 6.00066647755818 & 5.53519578224104 & 6.46613717287533 \tabularnewline
84 & 5.97098493370622 & -5.79695069452822 & 17.7389205619407 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=209215&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]5.78441803592807[/C][C]5.6114331840792[/C][C]5.95740288777694[/C][/ROW]
[ROW][C]74[/C][C]5.77193324066192[/C][C]5.56840448374422[/C][C]5.97546199757961[/C][/ROW]
[ROW][C]75[/C][C]5.79487023208036[/C][C]5.56148315616472[/C][C]6.028257307996[/C][/ROW]
[ROW][C]76[/C][C]5.87424666596107[/C][C]5.61008245476315[/C][C]6.13841087715898[/C][/ROW]
[ROW][C]77[/C][C]5.98836624724573[/C][C]5.69212841127309[/C][C]6.28460408321836[/C][/ROW]
[ROW][C]78[/C][C]6.06484150135536[/C][C]5.73741177384973[/C][C]6.392271228861[/C][/ROW]
[ROW][C]79[/C][C]6.08640055496858[/C][C]5.72977868112013[/C][C]6.44302242881703[/C][/ROW]
[ROW][C]80[/C][C]6.06829291756048[/C][C]5.68428357405712[/C][C]6.45230226106384[/C][/ROW]
[ROW][C]81[/C][C]6.04952738639069[/C][C]5.63816632815424[/C][C]6.46088844462713[/C][/ROW]
[ROW][C]82[/C][C]6.02396281055121[/C][C]5.58563177376722[/C][C]6.4622938473352[/C][/ROW]
[ROW][C]83[/C][C]6.00066647755818[/C][C]5.53519578224104[/C][C]6.46613717287533[/C][/ROW]
[ROW][C]84[/C][C]5.97098493370622[/C][C]-5.79695069452822[/C][C]17.7389205619407[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=209215&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=209215&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
735.784418035928075.61143318407925.95740288777694
745.771933240661925.568404483744225.97546199757961
755.794870232080365.561483156164726.028257307996
765.874246665961075.610082454763156.13841087715898
775.988366247245735.692128411273096.28460408321836
786.064841501355365.737411773849736.392271228861
796.086400554968585.729778681120136.44302242881703
806.068292917560485.684283574057126.45230226106384
816.049527386390695.638166328154246.46088844462713
826.023962810551215.585631773767226.4622938473352
836.000666477558185.535195782241046.46613717287533
845.97098493370622-5.7969506945282217.7389205619407



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')