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Author's title

Opgave10: Exponential Smoothing Gemiddelede Prijs Zakje Frieten - Dave Flor...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 May 2008 11:55:28 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/24/t1211651891ejanves0wlxq7u2.htm/, Retrieved Tue, 14 May 2024 19:56:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13096, Retrieved Tue, 14 May 2024 19:56:23 +0000
QR Codes:

Original text written by user:Exponential Smoothing Gemiddelede Prijs Zakje Frieten
IsPrivate?No (this computation is public)
User-defined keywordsExponential Smoothing, Gemiddelede Prijs, Zakje Frieten
Estimated Impact192
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave10: Exponen...] [2008-05-24 17:55:28] [dffb8b44dc5a91f197edbc7a955d0e55] [Current]
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Dataseries X:
1,72
1,73
1,73
1,73
1,73
1,73
1,74
1,74
1,74
1,74
1,75
1,75
1,75
1,75
1,75
1,76
1,77
1,77
1,78
1,78
1,78
1,79
1,8
1,8
1,82
1,83
1,85
1,86
1,86
1,87
1,88
1,88
1,89
1,9
1,9
1,9
1,9
1,92
1,92
1,93
1,93
1,93
1,94
1,94
1,95
1,96
1,96
1,96
1,96
1,97
1,97
1,98
1,99
1,99
1,99
2
2
2,01
2,01
2,01
2,02
2,02
2,02
2,02
2,03
2,03
2,03
2,04
2,04
2,05
2,06
2,06




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' @ 193.190.124.24

\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' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13096&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' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13096&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13096&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' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.823465303952612
beta0.208609164233188
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.823465303952612 \tabularnewline
beta & 0.208609164233188 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13096&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]0.823465303952612[/C][/ROW]
[ROW][C]beta[/C][C]0.208609164233188[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13096&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13096&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
alpha0.823465303952612
beta0.208609164233188
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31.731.74-0.01
41.731.74004752287215-0.0100475228721482
51.731.73832992462616-0.00832992462615989
61.731.73659577442420-0.00659577442419734
71.741.735156598726690.00484340127331162
81.741.74396919845957-0.00396919845956822
91.741.74484308960228-0.00484308960228019
101.741.74416540411147-0.0041654041114656
111.751.74333022595730.00666977404269975
121.751.75256319092666-0.00256319092665946
131.751.75375281847946-0.00375281847946218
141.751.75331816081959-0.00331816081959224
151.751.75267142700324-0.00267142700323908
161.761.752098351879910.00790164812009131
171.771.761589201424540.00841079857545779
181.771.77294414594316-0.00294414594315939
191.781.774442935140320.0055570648596821
201.781.78389678246284-0.00389678246283864
211.781.78489631584824-0.00489631584823513
221.791.78423166723980.00576833276019961
231.81.793339884835750.0066601151642467
241.81.80432654492613-0.00432654492613116
251.821.805522847316430.0144771526835714
261.831.824690262435350.00530973756464626
271.851.837220748786040.0127792512139626
281.861.858097371020940.00190262897905535
291.861.87034431041034-0.0103443104103431
301.871.87072934957296-0.000729349572960558
311.881.87890668595750.00109331404249802
321.881.88877273470998-0.00877273470998063
331.891.889007433127160.000992566872841438
341.91.897454024108770.00254597589123184
351.91.90761714739129-0.00761714739129471
361.91.90810279934356-0.00810279934355829
371.91.90679661537381-0.0067966153738126
381.921.905398489622910.0146015103770907
391.921.92412926062266-0.00412926062266039
401.931.926726557251380.0032734427486234
411.931.93598204314233-0.00598204314233208
421.931.93658834775013-0.0065883477501325
431.941.935563619303040.00443638069696162
441.941.94437946438025-0.00437946438024794
451.951.945183451970720.00481654802928144
461.961.954387434937880.00561256506211794
471.961.96521105025904-0.00521105025904189
481.961.96622662713385-0.00622662713385091
491.961.96533628668080-0.00533628668080288
501.971.964262430519300.00573756948070425
511.971.97329312419399-0.00329312419399108
521.981.974321654150320.00567834584967808
531.991.983713318341310.00628668165869328
541.991.99468586728306-0.00468586728306164
551.991.99581795330601-0.00581795330600521
5621.995018383734580.00498161626541593
5722.00396763904480-0.00396763904480357
582.012.004865922518350.00513407748165084
592.012.01414109795477-0.00414109795477291
602.012.01506712044935-0.00506712044934599
612.022.014360153392320.00563984660767547
622.022.02343882865304-0.00343882865303691
632.022.02445079956112-0.00445079956111849
642.022.02386487846795-0.00386487846794559
652.032.023097524932790.0069024750672142
662.032.03238243724317-0.00238243724317400
672.032.03361228560719-0.00361228560719029
682.042.033208869391320.00679113060867831
692.042.04253890224645-0.00253890224645481
702.052.043749838016960.00625016198303863
712.062.053271931115710.00672806888429323
722.062.06434332784589-0.00434332784588998

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1.73 & 1.74 & -0.01 \tabularnewline
4 & 1.73 & 1.74004752287215 & -0.0100475228721482 \tabularnewline
5 & 1.73 & 1.73832992462616 & -0.00832992462615989 \tabularnewline
6 & 1.73 & 1.73659577442420 & -0.00659577442419734 \tabularnewline
7 & 1.74 & 1.73515659872669 & 0.00484340127331162 \tabularnewline
8 & 1.74 & 1.74396919845957 & -0.00396919845956822 \tabularnewline
9 & 1.74 & 1.74484308960228 & -0.00484308960228019 \tabularnewline
10 & 1.74 & 1.74416540411147 & -0.0041654041114656 \tabularnewline
11 & 1.75 & 1.7433302259573 & 0.00666977404269975 \tabularnewline
12 & 1.75 & 1.75256319092666 & -0.00256319092665946 \tabularnewline
13 & 1.75 & 1.75375281847946 & -0.00375281847946218 \tabularnewline
14 & 1.75 & 1.75331816081959 & -0.00331816081959224 \tabularnewline
15 & 1.75 & 1.75267142700324 & -0.00267142700323908 \tabularnewline
16 & 1.76 & 1.75209835187991 & 0.00790164812009131 \tabularnewline
17 & 1.77 & 1.76158920142454 & 0.00841079857545779 \tabularnewline
18 & 1.77 & 1.77294414594316 & -0.00294414594315939 \tabularnewline
19 & 1.78 & 1.77444293514032 & 0.0055570648596821 \tabularnewline
20 & 1.78 & 1.78389678246284 & -0.00389678246283864 \tabularnewline
21 & 1.78 & 1.78489631584824 & -0.00489631584823513 \tabularnewline
22 & 1.79 & 1.7842316672398 & 0.00576833276019961 \tabularnewline
23 & 1.8 & 1.79333988483575 & 0.0066601151642467 \tabularnewline
24 & 1.8 & 1.80432654492613 & -0.00432654492613116 \tabularnewline
25 & 1.82 & 1.80552284731643 & 0.0144771526835714 \tabularnewline
26 & 1.83 & 1.82469026243535 & 0.00530973756464626 \tabularnewline
27 & 1.85 & 1.83722074878604 & 0.0127792512139626 \tabularnewline
28 & 1.86 & 1.85809737102094 & 0.00190262897905535 \tabularnewline
29 & 1.86 & 1.87034431041034 & -0.0103443104103431 \tabularnewline
30 & 1.87 & 1.87072934957296 & -0.000729349572960558 \tabularnewline
31 & 1.88 & 1.8789066859575 & 0.00109331404249802 \tabularnewline
32 & 1.88 & 1.88877273470998 & -0.00877273470998063 \tabularnewline
33 & 1.89 & 1.88900743312716 & 0.000992566872841438 \tabularnewline
34 & 1.9 & 1.89745402410877 & 0.00254597589123184 \tabularnewline
35 & 1.9 & 1.90761714739129 & -0.00761714739129471 \tabularnewline
36 & 1.9 & 1.90810279934356 & -0.00810279934355829 \tabularnewline
37 & 1.9 & 1.90679661537381 & -0.0067966153738126 \tabularnewline
38 & 1.92 & 1.90539848962291 & 0.0146015103770907 \tabularnewline
39 & 1.92 & 1.92412926062266 & -0.00412926062266039 \tabularnewline
40 & 1.93 & 1.92672655725138 & 0.0032734427486234 \tabularnewline
41 & 1.93 & 1.93598204314233 & -0.00598204314233208 \tabularnewline
42 & 1.93 & 1.93658834775013 & -0.0065883477501325 \tabularnewline
43 & 1.94 & 1.93556361930304 & 0.00443638069696162 \tabularnewline
44 & 1.94 & 1.94437946438025 & -0.00437946438024794 \tabularnewline
45 & 1.95 & 1.94518345197072 & 0.00481654802928144 \tabularnewline
46 & 1.96 & 1.95438743493788 & 0.00561256506211794 \tabularnewline
47 & 1.96 & 1.96521105025904 & -0.00521105025904189 \tabularnewline
48 & 1.96 & 1.96622662713385 & -0.00622662713385091 \tabularnewline
49 & 1.96 & 1.96533628668080 & -0.00533628668080288 \tabularnewline
50 & 1.97 & 1.96426243051930 & 0.00573756948070425 \tabularnewline
51 & 1.97 & 1.97329312419399 & -0.00329312419399108 \tabularnewline
52 & 1.98 & 1.97432165415032 & 0.00567834584967808 \tabularnewline
53 & 1.99 & 1.98371331834131 & 0.00628668165869328 \tabularnewline
54 & 1.99 & 1.99468586728306 & -0.00468586728306164 \tabularnewline
55 & 1.99 & 1.99581795330601 & -0.00581795330600521 \tabularnewline
56 & 2 & 1.99501838373458 & 0.00498161626541593 \tabularnewline
57 & 2 & 2.00396763904480 & -0.00396763904480357 \tabularnewline
58 & 2.01 & 2.00486592251835 & 0.00513407748165084 \tabularnewline
59 & 2.01 & 2.01414109795477 & -0.00414109795477291 \tabularnewline
60 & 2.01 & 2.01506712044935 & -0.00506712044934599 \tabularnewline
61 & 2.02 & 2.01436015339232 & 0.00563984660767547 \tabularnewline
62 & 2.02 & 2.02343882865304 & -0.00343882865303691 \tabularnewline
63 & 2.02 & 2.02445079956112 & -0.00445079956111849 \tabularnewline
64 & 2.02 & 2.02386487846795 & -0.00386487846794559 \tabularnewline
65 & 2.03 & 2.02309752493279 & 0.0069024750672142 \tabularnewline
66 & 2.03 & 2.03238243724317 & -0.00238243724317400 \tabularnewline
67 & 2.03 & 2.03361228560719 & -0.00361228560719029 \tabularnewline
68 & 2.04 & 2.03320886939132 & 0.00679113060867831 \tabularnewline
69 & 2.04 & 2.04253890224645 & -0.00253890224645481 \tabularnewline
70 & 2.05 & 2.04374983801696 & 0.00625016198303863 \tabularnewline
71 & 2.06 & 2.05327193111571 & 0.00672806888429323 \tabularnewline
72 & 2.06 & 2.06434332784589 & -0.00434332784588998 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13096&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]1.73[/C][C]1.74[/C][C]-0.01[/C][/ROW]
[ROW][C]4[/C][C]1.73[/C][C]1.74004752287215[/C][C]-0.0100475228721482[/C][/ROW]
[ROW][C]5[/C][C]1.73[/C][C]1.73832992462616[/C][C]-0.00832992462615989[/C][/ROW]
[ROW][C]6[/C][C]1.73[/C][C]1.73659577442420[/C][C]-0.00659577442419734[/C][/ROW]
[ROW][C]7[/C][C]1.74[/C][C]1.73515659872669[/C][C]0.00484340127331162[/C][/ROW]
[ROW][C]8[/C][C]1.74[/C][C]1.74396919845957[/C][C]-0.00396919845956822[/C][/ROW]
[ROW][C]9[/C][C]1.74[/C][C]1.74484308960228[/C][C]-0.00484308960228019[/C][/ROW]
[ROW][C]10[/C][C]1.74[/C][C]1.74416540411147[/C][C]-0.0041654041114656[/C][/ROW]
[ROW][C]11[/C][C]1.75[/C][C]1.7433302259573[/C][C]0.00666977404269975[/C][/ROW]
[ROW][C]12[/C][C]1.75[/C][C]1.75256319092666[/C][C]-0.00256319092665946[/C][/ROW]
[ROW][C]13[/C][C]1.75[/C][C]1.75375281847946[/C][C]-0.00375281847946218[/C][/ROW]
[ROW][C]14[/C][C]1.75[/C][C]1.75331816081959[/C][C]-0.00331816081959224[/C][/ROW]
[ROW][C]15[/C][C]1.75[/C][C]1.75267142700324[/C][C]-0.00267142700323908[/C][/ROW]
[ROW][C]16[/C][C]1.76[/C][C]1.75209835187991[/C][C]0.00790164812009131[/C][/ROW]
[ROW][C]17[/C][C]1.77[/C][C]1.76158920142454[/C][C]0.00841079857545779[/C][/ROW]
[ROW][C]18[/C][C]1.77[/C][C]1.77294414594316[/C][C]-0.00294414594315939[/C][/ROW]
[ROW][C]19[/C][C]1.78[/C][C]1.77444293514032[/C][C]0.0055570648596821[/C][/ROW]
[ROW][C]20[/C][C]1.78[/C][C]1.78389678246284[/C][C]-0.00389678246283864[/C][/ROW]
[ROW][C]21[/C][C]1.78[/C][C]1.78489631584824[/C][C]-0.00489631584823513[/C][/ROW]
[ROW][C]22[/C][C]1.79[/C][C]1.7842316672398[/C][C]0.00576833276019961[/C][/ROW]
[ROW][C]23[/C][C]1.8[/C][C]1.79333988483575[/C][C]0.0066601151642467[/C][/ROW]
[ROW][C]24[/C][C]1.8[/C][C]1.80432654492613[/C][C]-0.00432654492613116[/C][/ROW]
[ROW][C]25[/C][C]1.82[/C][C]1.80552284731643[/C][C]0.0144771526835714[/C][/ROW]
[ROW][C]26[/C][C]1.83[/C][C]1.82469026243535[/C][C]0.00530973756464626[/C][/ROW]
[ROW][C]27[/C][C]1.85[/C][C]1.83722074878604[/C][C]0.0127792512139626[/C][/ROW]
[ROW][C]28[/C][C]1.86[/C][C]1.85809737102094[/C][C]0.00190262897905535[/C][/ROW]
[ROW][C]29[/C][C]1.86[/C][C]1.87034431041034[/C][C]-0.0103443104103431[/C][/ROW]
[ROW][C]30[/C][C]1.87[/C][C]1.87072934957296[/C][C]-0.000729349572960558[/C][/ROW]
[ROW][C]31[/C][C]1.88[/C][C]1.8789066859575[/C][C]0.00109331404249802[/C][/ROW]
[ROW][C]32[/C][C]1.88[/C][C]1.88877273470998[/C][C]-0.00877273470998063[/C][/ROW]
[ROW][C]33[/C][C]1.89[/C][C]1.88900743312716[/C][C]0.000992566872841438[/C][/ROW]
[ROW][C]34[/C][C]1.9[/C][C]1.89745402410877[/C][C]0.00254597589123184[/C][/ROW]
[ROW][C]35[/C][C]1.9[/C][C]1.90761714739129[/C][C]-0.00761714739129471[/C][/ROW]
[ROW][C]36[/C][C]1.9[/C][C]1.90810279934356[/C][C]-0.00810279934355829[/C][/ROW]
[ROW][C]37[/C][C]1.9[/C][C]1.90679661537381[/C][C]-0.0067966153738126[/C][/ROW]
[ROW][C]38[/C][C]1.92[/C][C]1.90539848962291[/C][C]0.0146015103770907[/C][/ROW]
[ROW][C]39[/C][C]1.92[/C][C]1.92412926062266[/C][C]-0.00412926062266039[/C][/ROW]
[ROW][C]40[/C][C]1.93[/C][C]1.92672655725138[/C][C]0.0032734427486234[/C][/ROW]
[ROW][C]41[/C][C]1.93[/C][C]1.93598204314233[/C][C]-0.00598204314233208[/C][/ROW]
[ROW][C]42[/C][C]1.93[/C][C]1.93658834775013[/C][C]-0.0065883477501325[/C][/ROW]
[ROW][C]43[/C][C]1.94[/C][C]1.93556361930304[/C][C]0.00443638069696162[/C][/ROW]
[ROW][C]44[/C][C]1.94[/C][C]1.94437946438025[/C][C]-0.00437946438024794[/C][/ROW]
[ROW][C]45[/C][C]1.95[/C][C]1.94518345197072[/C][C]0.00481654802928144[/C][/ROW]
[ROW][C]46[/C][C]1.96[/C][C]1.95438743493788[/C][C]0.00561256506211794[/C][/ROW]
[ROW][C]47[/C][C]1.96[/C][C]1.96521105025904[/C][C]-0.00521105025904189[/C][/ROW]
[ROW][C]48[/C][C]1.96[/C][C]1.96622662713385[/C][C]-0.00622662713385091[/C][/ROW]
[ROW][C]49[/C][C]1.96[/C][C]1.96533628668080[/C][C]-0.00533628668080288[/C][/ROW]
[ROW][C]50[/C][C]1.97[/C][C]1.96426243051930[/C][C]0.00573756948070425[/C][/ROW]
[ROW][C]51[/C][C]1.97[/C][C]1.97329312419399[/C][C]-0.00329312419399108[/C][/ROW]
[ROW][C]52[/C][C]1.98[/C][C]1.97432165415032[/C][C]0.00567834584967808[/C][/ROW]
[ROW][C]53[/C][C]1.99[/C][C]1.98371331834131[/C][C]0.00628668165869328[/C][/ROW]
[ROW][C]54[/C][C]1.99[/C][C]1.99468586728306[/C][C]-0.00468586728306164[/C][/ROW]
[ROW][C]55[/C][C]1.99[/C][C]1.99581795330601[/C][C]-0.00581795330600521[/C][/ROW]
[ROW][C]56[/C][C]2[/C][C]1.99501838373458[/C][C]0.00498161626541593[/C][/ROW]
[ROW][C]57[/C][C]2[/C][C]2.00396763904480[/C][C]-0.00396763904480357[/C][/ROW]
[ROW][C]58[/C][C]2.01[/C][C]2.00486592251835[/C][C]0.00513407748165084[/C][/ROW]
[ROW][C]59[/C][C]2.01[/C][C]2.01414109795477[/C][C]-0.00414109795477291[/C][/ROW]
[ROW][C]60[/C][C]2.01[/C][C]2.01506712044935[/C][C]-0.00506712044934599[/C][/ROW]
[ROW][C]61[/C][C]2.02[/C][C]2.01436015339232[/C][C]0.00563984660767547[/C][/ROW]
[ROW][C]62[/C][C]2.02[/C][C]2.02343882865304[/C][C]-0.00343882865303691[/C][/ROW]
[ROW][C]63[/C][C]2.02[/C][C]2.02445079956112[/C][C]-0.00445079956111849[/C][/ROW]
[ROW][C]64[/C][C]2.02[/C][C]2.02386487846795[/C][C]-0.00386487846794559[/C][/ROW]
[ROW][C]65[/C][C]2.03[/C][C]2.02309752493279[/C][C]0.0069024750672142[/C][/ROW]
[ROW][C]66[/C][C]2.03[/C][C]2.03238243724317[/C][C]-0.00238243724317400[/C][/ROW]
[ROW][C]67[/C][C]2.03[/C][C]2.03361228560719[/C][C]-0.00361228560719029[/C][/ROW]
[ROW][C]68[/C][C]2.04[/C][C]2.03320886939132[/C][C]0.00679113060867831[/C][/ROW]
[ROW][C]69[/C][C]2.04[/C][C]2.04253890224645[/C][C]-0.00253890224645481[/C][/ROW]
[ROW][C]70[/C][C]2.05[/C][C]2.04374983801696[/C][C]0.00625016198303863[/C][/ROW]
[ROW][C]71[/C][C]2.06[/C][C]2.05327193111571[/C][C]0.00672806888429323[/C][/ROW]
[ROW][C]72[/C][C]2.06[/C][C]2.06434332784589[/C][C]-0.00434332784588998[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13096&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13096&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
31.731.74-0.01
41.731.74004752287215-0.0100475228721482
51.731.73832992462616-0.00832992462615989
61.731.73659577442420-0.00659577442419734
71.741.735156598726690.00484340127331162
81.741.74396919845957-0.00396919845956822
91.741.74484308960228-0.00484308960228019
101.741.74416540411147-0.0041654041114656
111.751.74333022595730.00666977404269975
121.751.75256319092666-0.00256319092665946
131.751.75375281847946-0.00375281847946218
141.751.75331816081959-0.00331816081959224
151.751.75267142700324-0.00267142700323908
161.761.752098351879910.00790164812009131
171.771.761589201424540.00841079857545779
181.771.77294414594316-0.00294414594315939
191.781.774442935140320.0055570648596821
201.781.78389678246284-0.00389678246283864
211.781.78489631584824-0.00489631584823513
221.791.78423166723980.00576833276019961
231.81.793339884835750.0066601151642467
241.81.80432654492613-0.00432654492613116
251.821.805522847316430.0144771526835714
261.831.824690262435350.00530973756464626
271.851.837220748786040.0127792512139626
281.861.858097371020940.00190262897905535
291.861.87034431041034-0.0103443104103431
301.871.87072934957296-0.000729349572960558
311.881.87890668595750.00109331404249802
321.881.88877273470998-0.00877273470998063
331.891.889007433127160.000992566872841438
341.91.897454024108770.00254597589123184
351.91.90761714739129-0.00761714739129471
361.91.90810279934356-0.00810279934355829
371.91.90679661537381-0.0067966153738126
381.921.905398489622910.0146015103770907
391.921.92412926062266-0.00412926062266039
401.931.926726557251380.0032734427486234
411.931.93598204314233-0.00598204314233208
421.931.93658834775013-0.0065883477501325
431.941.935563619303040.00443638069696162
441.941.94437946438025-0.00437946438024794
451.951.945183451970720.00481654802928144
461.961.954387434937880.00561256506211794
471.961.96521105025904-0.00521105025904189
481.961.96622662713385-0.00622662713385091
491.961.96533628668080-0.00533628668080288
501.971.964262430519300.00573756948070425
511.971.97329312419399-0.00329312419399108
521.981.974321654150320.00567834584967808
531.991.983713318341310.00628668165869328
541.991.99468586728306-0.00468586728306164
551.991.99581795330601-0.00581795330600521
5621.995018383734580.00498161626541593
5722.00396763904480-0.00396763904480357
582.012.004865922518350.00513407748165084
592.012.01414109795477-0.00414109795477291
602.012.01506712044935-0.00506712044934599
612.022.014360153392320.00563984660767547
622.022.02343882865304-0.00343882865303691
632.022.02445079956112-0.00445079956111849
642.022.02386487846795-0.00386487846794559
652.032.023097524932790.0069024750672142
662.032.03238243724317-0.00238243724317400
672.032.03361228560719-0.00361228560719029
682.042.033208869391320.00679113060867831
692.042.04253890224645-0.00253890224645481
702.052.043749838016960.00625016198303863
712.062.053271931115710.00672806888429323
722.062.06434332784589-0.00434332784588998







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732.065551706182762.053452011270482.07765140109504
742.070336664304402.053265722743912.08740760586490
752.075121622426052.052967357550282.09727588730183
762.07990658054772.052461612278882.10735154881653
772.084691538669352.051717276189842.11766580114886
782.089476496791002.050724993496392.12822800008560
792.094261454912652.049484253181372.13903865664392
802.099046413034292.047998408225332.15009441784325
812.103831371155942.046272510370642.16139023194125
822.108616329277592.044312291910592.17292036664459
832.113401287399242.042123664386172.18467891041230
842.118186245520892.039712467327002.19666002371478

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2.06555170618276 & 2.05345201127048 & 2.07765140109504 \tabularnewline
74 & 2.07033666430440 & 2.05326572274391 & 2.08740760586490 \tabularnewline
75 & 2.07512162242605 & 2.05296735755028 & 2.09727588730183 \tabularnewline
76 & 2.0799065805477 & 2.05246161227888 & 2.10735154881653 \tabularnewline
77 & 2.08469153866935 & 2.05171727618984 & 2.11766580114886 \tabularnewline
78 & 2.08947649679100 & 2.05072499349639 & 2.12822800008560 \tabularnewline
79 & 2.09426145491265 & 2.04948425318137 & 2.13903865664392 \tabularnewline
80 & 2.09904641303429 & 2.04799840822533 & 2.15009441784325 \tabularnewline
81 & 2.10383137115594 & 2.04627251037064 & 2.16139023194125 \tabularnewline
82 & 2.10861632927759 & 2.04431229191059 & 2.17292036664459 \tabularnewline
83 & 2.11340128739924 & 2.04212366438617 & 2.18467891041230 \tabularnewline
84 & 2.11818624552089 & 2.03971246732700 & 2.19666002371478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13096&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]2.06555170618276[/C][C]2.05345201127048[/C][C]2.07765140109504[/C][/ROW]
[ROW][C]74[/C][C]2.07033666430440[/C][C]2.05326572274391[/C][C]2.08740760586490[/C][/ROW]
[ROW][C]75[/C][C]2.07512162242605[/C][C]2.05296735755028[/C][C]2.09727588730183[/C][/ROW]
[ROW][C]76[/C][C]2.0799065805477[/C][C]2.05246161227888[/C][C]2.10735154881653[/C][/ROW]
[ROW][C]77[/C][C]2.08469153866935[/C][C]2.05171727618984[/C][C]2.11766580114886[/C][/ROW]
[ROW][C]78[/C][C]2.08947649679100[/C][C]2.05072499349639[/C][C]2.12822800008560[/C][/ROW]
[ROW][C]79[/C][C]2.09426145491265[/C][C]2.04948425318137[/C][C]2.13903865664392[/C][/ROW]
[ROW][C]80[/C][C]2.09904641303429[/C][C]2.04799840822533[/C][C]2.15009441784325[/C][/ROW]
[ROW][C]81[/C][C]2.10383137115594[/C][C]2.04627251037064[/C][C]2.16139023194125[/C][/ROW]
[ROW][C]82[/C][C]2.10861632927759[/C][C]2.04431229191059[/C][C]2.17292036664459[/C][/ROW]
[ROW][C]83[/C][C]2.11340128739924[/C][C]2.04212366438617[/C][C]2.18467891041230[/C][/ROW]
[ROW][C]84[/C][C]2.11818624552089[/C][C]2.03971246732700[/C][C]2.19666002371478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13096&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13096&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
732.065551706182762.053452011270482.07765140109504
742.070336664304402.053265722743912.08740760586490
752.075121622426052.052967357550282.09727588730183
762.07990658054772.052461612278882.10735154881653
772.084691538669352.051717276189842.11766580114886
782.089476496791002.050724993496392.12822800008560
792.094261454912652.049484253181372.13903865664392
802.099046413034292.047998408225332.15009441784325
812.103831371155942.046272510370642.16139023194125
822.108616329277592.044312291910592.17292036664459
832.113401287399242.042123664386172.18467891041230
842.118186245520892.039712467327002.19666002371478



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')