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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 27 Nov 2014 12:20:01 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/27/t1417090821kqdbwo1b2a3ksub.htm/, Retrieved Wed, 29 May 2024 14:22:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=259908, Retrieved Wed, 29 May 2024 14:22:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-27 12:20:01] [7686dea5cfa8a11058319f854e13a03d] [Current]
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Dataseries X:
3,59
3,59
3,59
3,59
3,59
3,59
3,59
3,61
3,71
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,83
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,92
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
3,98
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,09
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,21
4,23
4,23
4,23
4,23




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259908&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]1 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=259908&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259908&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 time1 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0250894996494445
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0250894996494445 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259908&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]0.0250894996494445[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259908&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259908&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
beta0.0250894996494445
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.593.590
43.593.590
53.593.590
63.593.590
73.593.590
83.613.590.02
93.713.610501789992990.099498210007011
103.833.712998150298080.11700184970192
113.833.83593366816516-0.00593366816516072
123.833.83578479539981-0.00578479539981114
133.833.83563965777766-0.0056396577776554
143.833.83549816158582-0.00549816158582006
153.833.83536021546264-0.00536021546263976
163.833.83522573033867-0.00522573033866891
173.833.83509461937917-0.005094619379169
183.833.83496679792804-0.00496679792804144
193.833.83484218345317-0.00484218345316689
203.833.83472069549312-0.00472069549311582
213.923.83460225560520.0853977443948035
223.923.92674484228325-0.00674484228325323
233.923.92657561756515-0.00657561756515213
243.923.92641063861056-0.00641063861055624
253.923.92624979889538-0.00624979889538402
263.923.92609299456819-0.0060929945681889
273.923.92594012438311-0.00594012438310632
283.923.92579108963448-0.00579108963447883
293.923.92564579409312-0.00564579409312449
303.923.9255041439442-0.00550414394420429
313.923.92536604772665-0.00536604772664573
323.923.92523141627409-0.00523141627408918
333.983.925100162657310.0548998373426857
343.983.98647757210708-0.006477572107078
353.983.98631505306397-0.00631505306396818
363.983.98615661154233-0.00615661154233393
373.983.9860021452392-0.00600214523920073
383.983.98585155441833-0.00585155441832574
393.983.9857047418458-0.00570474184579828
403.983.98556161272726-0.00556161272725797
413.983.98542207464669-0.00542207464668731
423.983.98528603750674-0.00528603750673984
433.983.98515341347057-0.00515341347056752
443.983.9850241169051-0.0050241169051044
454.093.984898064325770.105101935674225
464.094.09753501930403-0.00753501930402933
474.094.09734596943984-0.00734596943984211
484.094.09716166274216-0.00716166274215624
494.094.0969819802073-0.00698198020729812
504.094.09680680581733-0.00680680581733473
514.094.09663602646517-0.00663602646516637
524.094.0964695318815-0.00646953188149535
534.094.09630721456362-0.00630721456362249
544.094.09614896970604-0.00614896970603951
554.094.09599469513276-0.00599469513275519
564.094.09584429123132-0.00584429123132324
574.214.095697660888520.114302339111476
584.214.21856544938559-0.00856544938559178
594.214.21835054654623-0.00835054654623502
604.214.21814103551159-0.00814103551159029
614.214.21793678100398-0.0079367810039761
624.214.21773765113976-0.00773765113975955
634.214.2175435173442-0.00754351734420045
644.214.21735425426844-0.00735425426843772
654.214.21716973970855-0.00716973970854795
664.214.21698985452664-0.00698985452664402
674.214.21681448257395-0.00681448257394734
684.214.2166435106158-0.00664351061579715
694.234.216476828258530.0135231717414692
704.234.2368161178712-0.00681611787119873
714.234.23664510488426-0.0066451048842584
724.234.23647838252759-0.00647838252759403

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.59 & 3.59 & 0 \tabularnewline
4 & 3.59 & 3.59 & 0 \tabularnewline
5 & 3.59 & 3.59 & 0 \tabularnewline
6 & 3.59 & 3.59 & 0 \tabularnewline
7 & 3.59 & 3.59 & 0 \tabularnewline
8 & 3.61 & 3.59 & 0.02 \tabularnewline
9 & 3.71 & 3.61050178999299 & 0.099498210007011 \tabularnewline
10 & 3.83 & 3.71299815029808 & 0.11700184970192 \tabularnewline
11 & 3.83 & 3.83593366816516 & -0.00593366816516072 \tabularnewline
12 & 3.83 & 3.83578479539981 & -0.00578479539981114 \tabularnewline
13 & 3.83 & 3.83563965777766 & -0.0056396577776554 \tabularnewline
14 & 3.83 & 3.83549816158582 & -0.00549816158582006 \tabularnewline
15 & 3.83 & 3.83536021546264 & -0.00536021546263976 \tabularnewline
16 & 3.83 & 3.83522573033867 & -0.00522573033866891 \tabularnewline
17 & 3.83 & 3.83509461937917 & -0.005094619379169 \tabularnewline
18 & 3.83 & 3.83496679792804 & -0.00496679792804144 \tabularnewline
19 & 3.83 & 3.83484218345317 & -0.00484218345316689 \tabularnewline
20 & 3.83 & 3.83472069549312 & -0.00472069549311582 \tabularnewline
21 & 3.92 & 3.8346022556052 & 0.0853977443948035 \tabularnewline
22 & 3.92 & 3.92674484228325 & -0.00674484228325323 \tabularnewline
23 & 3.92 & 3.92657561756515 & -0.00657561756515213 \tabularnewline
24 & 3.92 & 3.92641063861056 & -0.00641063861055624 \tabularnewline
25 & 3.92 & 3.92624979889538 & -0.00624979889538402 \tabularnewline
26 & 3.92 & 3.92609299456819 & -0.0060929945681889 \tabularnewline
27 & 3.92 & 3.92594012438311 & -0.00594012438310632 \tabularnewline
28 & 3.92 & 3.92579108963448 & -0.00579108963447883 \tabularnewline
29 & 3.92 & 3.92564579409312 & -0.00564579409312449 \tabularnewline
30 & 3.92 & 3.9255041439442 & -0.00550414394420429 \tabularnewline
31 & 3.92 & 3.92536604772665 & -0.00536604772664573 \tabularnewline
32 & 3.92 & 3.92523141627409 & -0.00523141627408918 \tabularnewline
33 & 3.98 & 3.92510016265731 & 0.0548998373426857 \tabularnewline
34 & 3.98 & 3.98647757210708 & -0.006477572107078 \tabularnewline
35 & 3.98 & 3.98631505306397 & -0.00631505306396818 \tabularnewline
36 & 3.98 & 3.98615661154233 & -0.00615661154233393 \tabularnewline
37 & 3.98 & 3.9860021452392 & -0.00600214523920073 \tabularnewline
38 & 3.98 & 3.98585155441833 & -0.00585155441832574 \tabularnewline
39 & 3.98 & 3.9857047418458 & -0.00570474184579828 \tabularnewline
40 & 3.98 & 3.98556161272726 & -0.00556161272725797 \tabularnewline
41 & 3.98 & 3.98542207464669 & -0.00542207464668731 \tabularnewline
42 & 3.98 & 3.98528603750674 & -0.00528603750673984 \tabularnewline
43 & 3.98 & 3.98515341347057 & -0.00515341347056752 \tabularnewline
44 & 3.98 & 3.9850241169051 & -0.0050241169051044 \tabularnewline
45 & 4.09 & 3.98489806432577 & 0.105101935674225 \tabularnewline
46 & 4.09 & 4.09753501930403 & -0.00753501930402933 \tabularnewline
47 & 4.09 & 4.09734596943984 & -0.00734596943984211 \tabularnewline
48 & 4.09 & 4.09716166274216 & -0.00716166274215624 \tabularnewline
49 & 4.09 & 4.0969819802073 & -0.00698198020729812 \tabularnewline
50 & 4.09 & 4.09680680581733 & -0.00680680581733473 \tabularnewline
51 & 4.09 & 4.09663602646517 & -0.00663602646516637 \tabularnewline
52 & 4.09 & 4.0964695318815 & -0.00646953188149535 \tabularnewline
53 & 4.09 & 4.09630721456362 & -0.00630721456362249 \tabularnewline
54 & 4.09 & 4.09614896970604 & -0.00614896970603951 \tabularnewline
55 & 4.09 & 4.09599469513276 & -0.00599469513275519 \tabularnewline
56 & 4.09 & 4.09584429123132 & -0.00584429123132324 \tabularnewline
57 & 4.21 & 4.09569766088852 & 0.114302339111476 \tabularnewline
58 & 4.21 & 4.21856544938559 & -0.00856544938559178 \tabularnewline
59 & 4.21 & 4.21835054654623 & -0.00835054654623502 \tabularnewline
60 & 4.21 & 4.21814103551159 & -0.00814103551159029 \tabularnewline
61 & 4.21 & 4.21793678100398 & -0.0079367810039761 \tabularnewline
62 & 4.21 & 4.21773765113976 & -0.00773765113975955 \tabularnewline
63 & 4.21 & 4.2175435173442 & -0.00754351734420045 \tabularnewline
64 & 4.21 & 4.21735425426844 & -0.00735425426843772 \tabularnewline
65 & 4.21 & 4.21716973970855 & -0.00716973970854795 \tabularnewline
66 & 4.21 & 4.21698985452664 & -0.00698985452664402 \tabularnewline
67 & 4.21 & 4.21681448257395 & -0.00681448257394734 \tabularnewline
68 & 4.21 & 4.2166435106158 & -0.00664351061579715 \tabularnewline
69 & 4.23 & 4.21647682825853 & 0.0135231717414692 \tabularnewline
70 & 4.23 & 4.2368161178712 & -0.00681611787119873 \tabularnewline
71 & 4.23 & 4.23664510488426 & -0.0066451048842584 \tabularnewline
72 & 4.23 & 4.23647838252759 & -0.00647838252759403 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259908&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]3.59[/C][C]3.59[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]3.59[/C][C]3.59[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]3.59[/C][C]3.59[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]3.59[/C][C]3.59[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]3.59[/C][C]3.59[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]3.61[/C][C]3.59[/C][C]0.02[/C][/ROW]
[ROW][C]9[/C][C]3.71[/C][C]3.61050178999299[/C][C]0.099498210007011[/C][/ROW]
[ROW][C]10[/C][C]3.83[/C][C]3.71299815029808[/C][C]0.11700184970192[/C][/ROW]
[ROW][C]11[/C][C]3.83[/C][C]3.83593366816516[/C][C]-0.00593366816516072[/C][/ROW]
[ROW][C]12[/C][C]3.83[/C][C]3.83578479539981[/C][C]-0.00578479539981114[/C][/ROW]
[ROW][C]13[/C][C]3.83[/C][C]3.83563965777766[/C][C]-0.0056396577776554[/C][/ROW]
[ROW][C]14[/C][C]3.83[/C][C]3.83549816158582[/C][C]-0.00549816158582006[/C][/ROW]
[ROW][C]15[/C][C]3.83[/C][C]3.83536021546264[/C][C]-0.00536021546263976[/C][/ROW]
[ROW][C]16[/C][C]3.83[/C][C]3.83522573033867[/C][C]-0.00522573033866891[/C][/ROW]
[ROW][C]17[/C][C]3.83[/C][C]3.83509461937917[/C][C]-0.005094619379169[/C][/ROW]
[ROW][C]18[/C][C]3.83[/C][C]3.83496679792804[/C][C]-0.00496679792804144[/C][/ROW]
[ROW][C]19[/C][C]3.83[/C][C]3.83484218345317[/C][C]-0.00484218345316689[/C][/ROW]
[ROW][C]20[/C][C]3.83[/C][C]3.83472069549312[/C][C]-0.00472069549311582[/C][/ROW]
[ROW][C]21[/C][C]3.92[/C][C]3.8346022556052[/C][C]0.0853977443948035[/C][/ROW]
[ROW][C]22[/C][C]3.92[/C][C]3.92674484228325[/C][C]-0.00674484228325323[/C][/ROW]
[ROW][C]23[/C][C]3.92[/C][C]3.92657561756515[/C][C]-0.00657561756515213[/C][/ROW]
[ROW][C]24[/C][C]3.92[/C][C]3.92641063861056[/C][C]-0.00641063861055624[/C][/ROW]
[ROW][C]25[/C][C]3.92[/C][C]3.92624979889538[/C][C]-0.00624979889538402[/C][/ROW]
[ROW][C]26[/C][C]3.92[/C][C]3.92609299456819[/C][C]-0.0060929945681889[/C][/ROW]
[ROW][C]27[/C][C]3.92[/C][C]3.92594012438311[/C][C]-0.00594012438310632[/C][/ROW]
[ROW][C]28[/C][C]3.92[/C][C]3.92579108963448[/C][C]-0.00579108963447883[/C][/ROW]
[ROW][C]29[/C][C]3.92[/C][C]3.92564579409312[/C][C]-0.00564579409312449[/C][/ROW]
[ROW][C]30[/C][C]3.92[/C][C]3.9255041439442[/C][C]-0.00550414394420429[/C][/ROW]
[ROW][C]31[/C][C]3.92[/C][C]3.92536604772665[/C][C]-0.00536604772664573[/C][/ROW]
[ROW][C]32[/C][C]3.92[/C][C]3.92523141627409[/C][C]-0.00523141627408918[/C][/ROW]
[ROW][C]33[/C][C]3.98[/C][C]3.92510016265731[/C][C]0.0548998373426857[/C][/ROW]
[ROW][C]34[/C][C]3.98[/C][C]3.98647757210708[/C][C]-0.006477572107078[/C][/ROW]
[ROW][C]35[/C][C]3.98[/C][C]3.98631505306397[/C][C]-0.00631505306396818[/C][/ROW]
[ROW][C]36[/C][C]3.98[/C][C]3.98615661154233[/C][C]-0.00615661154233393[/C][/ROW]
[ROW][C]37[/C][C]3.98[/C][C]3.9860021452392[/C][C]-0.00600214523920073[/C][/ROW]
[ROW][C]38[/C][C]3.98[/C][C]3.98585155441833[/C][C]-0.00585155441832574[/C][/ROW]
[ROW][C]39[/C][C]3.98[/C][C]3.9857047418458[/C][C]-0.00570474184579828[/C][/ROW]
[ROW][C]40[/C][C]3.98[/C][C]3.98556161272726[/C][C]-0.00556161272725797[/C][/ROW]
[ROW][C]41[/C][C]3.98[/C][C]3.98542207464669[/C][C]-0.00542207464668731[/C][/ROW]
[ROW][C]42[/C][C]3.98[/C][C]3.98528603750674[/C][C]-0.00528603750673984[/C][/ROW]
[ROW][C]43[/C][C]3.98[/C][C]3.98515341347057[/C][C]-0.00515341347056752[/C][/ROW]
[ROW][C]44[/C][C]3.98[/C][C]3.9850241169051[/C][C]-0.0050241169051044[/C][/ROW]
[ROW][C]45[/C][C]4.09[/C][C]3.98489806432577[/C][C]0.105101935674225[/C][/ROW]
[ROW][C]46[/C][C]4.09[/C][C]4.09753501930403[/C][C]-0.00753501930402933[/C][/ROW]
[ROW][C]47[/C][C]4.09[/C][C]4.09734596943984[/C][C]-0.00734596943984211[/C][/ROW]
[ROW][C]48[/C][C]4.09[/C][C]4.09716166274216[/C][C]-0.00716166274215624[/C][/ROW]
[ROW][C]49[/C][C]4.09[/C][C]4.0969819802073[/C][C]-0.00698198020729812[/C][/ROW]
[ROW][C]50[/C][C]4.09[/C][C]4.09680680581733[/C][C]-0.00680680581733473[/C][/ROW]
[ROW][C]51[/C][C]4.09[/C][C]4.09663602646517[/C][C]-0.00663602646516637[/C][/ROW]
[ROW][C]52[/C][C]4.09[/C][C]4.0964695318815[/C][C]-0.00646953188149535[/C][/ROW]
[ROW][C]53[/C][C]4.09[/C][C]4.09630721456362[/C][C]-0.00630721456362249[/C][/ROW]
[ROW][C]54[/C][C]4.09[/C][C]4.09614896970604[/C][C]-0.00614896970603951[/C][/ROW]
[ROW][C]55[/C][C]4.09[/C][C]4.09599469513276[/C][C]-0.00599469513275519[/C][/ROW]
[ROW][C]56[/C][C]4.09[/C][C]4.09584429123132[/C][C]-0.00584429123132324[/C][/ROW]
[ROW][C]57[/C][C]4.21[/C][C]4.09569766088852[/C][C]0.114302339111476[/C][/ROW]
[ROW][C]58[/C][C]4.21[/C][C]4.21856544938559[/C][C]-0.00856544938559178[/C][/ROW]
[ROW][C]59[/C][C]4.21[/C][C]4.21835054654623[/C][C]-0.00835054654623502[/C][/ROW]
[ROW][C]60[/C][C]4.21[/C][C]4.21814103551159[/C][C]-0.00814103551159029[/C][/ROW]
[ROW][C]61[/C][C]4.21[/C][C]4.21793678100398[/C][C]-0.0079367810039761[/C][/ROW]
[ROW][C]62[/C][C]4.21[/C][C]4.21773765113976[/C][C]-0.00773765113975955[/C][/ROW]
[ROW][C]63[/C][C]4.21[/C][C]4.2175435173442[/C][C]-0.00754351734420045[/C][/ROW]
[ROW][C]64[/C][C]4.21[/C][C]4.21735425426844[/C][C]-0.00735425426843772[/C][/ROW]
[ROW][C]65[/C][C]4.21[/C][C]4.21716973970855[/C][C]-0.00716973970854795[/C][/ROW]
[ROW][C]66[/C][C]4.21[/C][C]4.21698985452664[/C][C]-0.00698985452664402[/C][/ROW]
[ROW][C]67[/C][C]4.21[/C][C]4.21681448257395[/C][C]-0.00681448257394734[/C][/ROW]
[ROW][C]68[/C][C]4.21[/C][C]4.2166435106158[/C][C]-0.00664351061579715[/C][/ROW]
[ROW][C]69[/C][C]4.23[/C][C]4.21647682825853[/C][C]0.0135231717414692[/C][/ROW]
[ROW][C]70[/C][C]4.23[/C][C]4.2368161178712[/C][C]-0.00681611787119873[/C][/ROW]
[ROW][C]71[/C][C]4.23[/C][C]4.23664510488426[/C][C]-0.0066451048842584[/C][/ROW]
[ROW][C]72[/C][C]4.23[/C][C]4.23647838252759[/C][C]-0.00647838252759403[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259908&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259908&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
33.593.590
43.593.590
53.593.590
63.593.590
73.593.590
83.613.590.02
93.713.610501789992990.099498210007011
103.833.712998150298080.11700184970192
113.833.83593366816516-0.00593366816516072
123.833.83578479539981-0.00578479539981114
133.833.83563965777766-0.0056396577776554
143.833.83549816158582-0.00549816158582006
153.833.83536021546264-0.00536021546263976
163.833.83522573033867-0.00522573033866891
173.833.83509461937917-0.005094619379169
183.833.83496679792804-0.00496679792804144
193.833.83484218345317-0.00484218345316689
203.833.83472069549312-0.00472069549311582
213.923.83460225560520.0853977443948035
223.923.92674484228325-0.00674484228325323
233.923.92657561756515-0.00657561756515213
243.923.92641063861056-0.00641063861055624
253.923.92624979889538-0.00624979889538402
263.923.92609299456819-0.0060929945681889
273.923.92594012438311-0.00594012438310632
283.923.92579108963448-0.00579108963447883
293.923.92564579409312-0.00564579409312449
303.923.9255041439442-0.00550414394420429
313.923.92536604772665-0.00536604772664573
323.923.92523141627409-0.00523141627408918
333.983.925100162657310.0548998373426857
343.983.98647757210708-0.006477572107078
353.983.98631505306397-0.00631505306396818
363.983.98615661154233-0.00615661154233393
373.983.9860021452392-0.00600214523920073
383.983.98585155441833-0.00585155441832574
393.983.9857047418458-0.00570474184579828
403.983.98556161272726-0.00556161272725797
413.983.98542207464669-0.00542207464668731
423.983.98528603750674-0.00528603750673984
433.983.98515341347057-0.00515341347056752
443.983.9850241169051-0.0050241169051044
454.093.984898064325770.105101935674225
464.094.09753501930403-0.00753501930402933
474.094.09734596943984-0.00734596943984211
484.094.09716166274216-0.00716166274215624
494.094.0969819802073-0.00698198020729812
504.094.09680680581733-0.00680680581733473
514.094.09663602646517-0.00663602646516637
524.094.0964695318815-0.00646953188149535
534.094.09630721456362-0.00630721456362249
544.094.09614896970604-0.00614896970603951
554.094.09599469513276-0.00599469513275519
564.094.09584429123132-0.00584429123132324
574.214.095697660888520.114302339111476
584.214.21856544938559-0.00856544938559178
594.214.21835054654623-0.00835054654623502
604.214.21814103551159-0.00814103551159029
614.214.21793678100398-0.0079367810039761
624.214.21773765113976-0.00773765113975955
634.214.2175435173442-0.00754351734420045
644.214.21735425426844-0.00735425426843772
654.214.21716973970855-0.00716973970854795
664.214.21698985452664-0.00698985452664402
674.214.21681448257395-0.00681448257394734
684.214.2166435106158-0.00664351061579715
694.234.216476828258530.0135231717414692
704.234.2368161178712-0.00681611787119873
714.234.23664510488426-0.0066451048842584
724.234.23647838252759-0.00647838252759403







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
734.236315843151444.178528632814414.29410305348847
744.242631686302884.159876678866584.32538669373918
754.248947529454324.146325441800144.3515696171085
764.255263372605764.135295582439144.37523116277238
774.26157921575724.12580171833064.3973567131838
784.267895058908644.11734516217284.41844495564447
794.274210902060074.109633556658434.43878824746171
804.280526745211514.102478924143594.45857456627944
814.286842588362954.095752433062664.47793274366324
824.293158431514394.089361548910214.49695531411857
834.299474274665834.0832373757584.51571117357366
844.305790117817274.077327138615524.53425309701902

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 4.23631584315144 & 4.17852863281441 & 4.29410305348847 \tabularnewline
74 & 4.24263168630288 & 4.15987667886658 & 4.32538669373918 \tabularnewline
75 & 4.24894752945432 & 4.14632544180014 & 4.3515696171085 \tabularnewline
76 & 4.25526337260576 & 4.13529558243914 & 4.37523116277238 \tabularnewline
77 & 4.2615792157572 & 4.1258017183306 & 4.3973567131838 \tabularnewline
78 & 4.26789505890864 & 4.1173451621728 & 4.41844495564447 \tabularnewline
79 & 4.27421090206007 & 4.10963355665843 & 4.43878824746171 \tabularnewline
80 & 4.28052674521151 & 4.10247892414359 & 4.45857456627944 \tabularnewline
81 & 4.28684258836295 & 4.09575243306266 & 4.47793274366324 \tabularnewline
82 & 4.29315843151439 & 4.08936154891021 & 4.49695531411857 \tabularnewline
83 & 4.29947427466583 & 4.083237375758 & 4.51571117357366 \tabularnewline
84 & 4.30579011781727 & 4.07732713861552 & 4.53425309701902 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=259908&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]4.23631584315144[/C][C]4.17852863281441[/C][C]4.29410305348847[/C][/ROW]
[ROW][C]74[/C][C]4.24263168630288[/C][C]4.15987667886658[/C][C]4.32538669373918[/C][/ROW]
[ROW][C]75[/C][C]4.24894752945432[/C][C]4.14632544180014[/C][C]4.3515696171085[/C][/ROW]
[ROW][C]76[/C][C]4.25526337260576[/C][C]4.13529558243914[/C][C]4.37523116277238[/C][/ROW]
[ROW][C]77[/C][C]4.2615792157572[/C][C]4.1258017183306[/C][C]4.3973567131838[/C][/ROW]
[ROW][C]78[/C][C]4.26789505890864[/C][C]4.1173451621728[/C][C]4.41844495564447[/C][/ROW]
[ROW][C]79[/C][C]4.27421090206007[/C][C]4.10963355665843[/C][C]4.43878824746171[/C][/ROW]
[ROW][C]80[/C][C]4.28052674521151[/C][C]4.10247892414359[/C][C]4.45857456627944[/C][/ROW]
[ROW][C]81[/C][C]4.28684258836295[/C][C]4.09575243306266[/C][C]4.47793274366324[/C][/ROW]
[ROW][C]82[/C][C]4.29315843151439[/C][C]4.08936154891021[/C][C]4.49695531411857[/C][/ROW]
[ROW][C]83[/C][C]4.29947427466583[/C][C]4.083237375758[/C][C]4.51571117357366[/C][/ROW]
[ROW][C]84[/C][C]4.30579011781727[/C][C]4.07732713861552[/C][C]4.53425309701902[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=259908&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=259908&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
734.236315843151444.178528632814414.29410305348847
744.242631686302884.159876678866584.32538669373918
754.248947529454324.146325441800144.3515696171085
764.255263372605764.135295582439144.37523116277238
774.26157921575724.12580171833064.3973567131838
784.267895058908644.11734516217284.41844495564447
794.274210902060074.109633556658434.43878824746171
804.280526745211514.102478924143594.45857456627944
814.286842588362954.095752433062664.47793274366324
824.293158431514394.089361548910214.49695531411857
834.299474274665834.0832373757584.51571117357366
844.305790117817274.077327138615524.53425309701902



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')