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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 12 Jan 2014 18:36:21 -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/2014/Jan/12/t1389569949n3agdvvy0zoyiqw.htm/, Retrieved Sun, 19 May 2024 08:01:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=233090, Retrieved Sun, 19 May 2024 08:01:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Notched Boxplots] [] [2013-10-03 17:28:47] [a34010c147419b4d17f3a47c5d12dd10]
- RMPD    [Exponential Smoothing] [] [2014-01-12 23:36:21] [f243590dc1e514197869e3522ad9f6bb] [Current]
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Dataseries X:
2.58
2.59
2.6
2.6
2.61
2.62
2.64
2.65
2.66
2.67
2.68
2.69
2.69
2.71
2.72
2.73
2.73
2.74
2.74
2.74
2.74
2.74
2.75
2.75
2.75
2.75
2.77
2.78
2.79
2.8
2.82
2.83
2.84
2.87
2.89
2.9
2.9
2.91
2.92
2.92
2.92
2.92
2.94
2.95
2.95
2.97
2.99
3
3
3.01
3.03
3.03
3.04
3.04
3.05
3.05
3.09
3.09
3.09
3.1
3.1
3.11
3.12
3.12
3.12
3.13
3.15
3.16
3.16
3.18
3.19
3.19
3.2
3.21
3.26
3.27
3.28
3.29
3.29
3.3
3.3
3.31
3.31
3.31




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 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 & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233090&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]5 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=233090&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233090&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 time5 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.89772622335835
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.89772622335835 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233090&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]0.89772622335835[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233090&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233090&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
alpha0.89772622335835
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132.692.629783653846150.060216346153847
142.712.704486843133680.00551315686631915
152.722.72091487822979-0.000914878229793192
162.732.73240563098879-0.00240563098879143
172.732.73297476257016-0.00297476257015949
182.742.74344963647306-0.00344963647305851
192.742.74099820362054-0.00099820362053693
202.742.74908081965786-0.0090808196578589
212.742.74949079265847-0.00949079265847441
222.742.7491160554789-0.00911605547890115
232.752.74907772969230.000922270307702089
242.752.75846773886961-0.00846773886960994
252.752.75641997704092-0.00641997704092212
262.752.76570728980554-0.0157072898055448
272.772.762427754027280.00757224597271655
282.782.78138515582907-0.00138515582907228
292.792.782812187485370.0071878125146263
302.82.80236170439126-0.0023617043912556
312.822.801137653993810.0188623460061876
322.832.826222966574070.00377703342592639
332.842.8381338419770.0018661580230015
342.872.847992863028180.0220071369718235
352.892.876921300748570.0130786992514276
362.92.89626410326980.00373589673020369
372.92.90538129747525-0.00538129747525318
382.912.91465121157235-0.00465121157235293
392.922.92367789319404-0.00367789319403711
402.922.93161964273823-0.0116196427382342
412.922.9247356969631-0.00473569696310294
422.922.9326045015773-0.0126045015772975
432.942.924355887335180.0156441126648175
442.952.945009275562610.00499072443739346
452.952.95781428076943-0.00781428076943103
462.972.961042812045380.00895718795461686
472.992.977342823274370.0126571767256318
4832.995351690272190.0046483097278136
4933.00435553166836-0.004355531668363
503.013.01462097127189-0.00462097127189498
513.033.023774345350730.00622565464927272
523.033.03979453677912-0.00979453677912057
533.043.035253083616510.00474691638348812
543.043.05082990653236-0.01082990653236
553.053.047063485261360.00293651473863843
563.053.05521936734651-0.00521936734651218
573.093.057548889173610.032451110826389
583.093.09863999982516-0.00863999982515962
593.093.09952096595202-0.00952096595202168
603.13.096800835608240.0031991643917606
613.13.10358288437091-0.00358288437091447
623.113.11451480220405-0.00451480220404976
633.123.12487281243597-0.00487281243597293
643.123.12929117344296-0.00929117344295749
653.123.1266888120799-0.00668881207989758
663.133.13040638116328-0.000406381163277292
673.153.137405375850170.0125946241498296
683.163.153397463159120.00660253684088152
693.163.17019252045591-0.0101925204559099
703.183.168798781973380.0112012180266197
713.193.187401629936260.00259837006373687
723.193.19686228111315-0.00686228111315135
733.23.193918280660850.00608171933915092
743.213.21343105592656-0.00343105592656201
753.263.224725358552760.0352746414472418
763.273.264733259245020.00526674075497624
773.283.275466072539640.00453392746036352
783.293.289901117142569.88828574381984e-05
793.293.29868336250408-0.00868336250408053
803.33.294960809814490.0050391901855078
813.33.3086347158839-0.00863471588389952
823.313.31082747784762-0.000827477847623381
833.313.31775200434036-0.00775200434035783
843.313.31695327646776-0.00695327646776356

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2.69 & 2.62978365384615 & 0.060216346153847 \tabularnewline
14 & 2.71 & 2.70448684313368 & 0.00551315686631915 \tabularnewline
15 & 2.72 & 2.72091487822979 & -0.000914878229793192 \tabularnewline
16 & 2.73 & 2.73240563098879 & -0.00240563098879143 \tabularnewline
17 & 2.73 & 2.73297476257016 & -0.00297476257015949 \tabularnewline
18 & 2.74 & 2.74344963647306 & -0.00344963647305851 \tabularnewline
19 & 2.74 & 2.74099820362054 & -0.00099820362053693 \tabularnewline
20 & 2.74 & 2.74908081965786 & -0.0090808196578589 \tabularnewline
21 & 2.74 & 2.74949079265847 & -0.00949079265847441 \tabularnewline
22 & 2.74 & 2.7491160554789 & -0.00911605547890115 \tabularnewline
23 & 2.75 & 2.7490777296923 & 0.000922270307702089 \tabularnewline
24 & 2.75 & 2.75846773886961 & -0.00846773886960994 \tabularnewline
25 & 2.75 & 2.75641997704092 & -0.00641997704092212 \tabularnewline
26 & 2.75 & 2.76570728980554 & -0.0157072898055448 \tabularnewline
27 & 2.77 & 2.76242775402728 & 0.00757224597271655 \tabularnewline
28 & 2.78 & 2.78138515582907 & -0.00138515582907228 \tabularnewline
29 & 2.79 & 2.78281218748537 & 0.0071878125146263 \tabularnewline
30 & 2.8 & 2.80236170439126 & -0.0023617043912556 \tabularnewline
31 & 2.82 & 2.80113765399381 & 0.0188623460061876 \tabularnewline
32 & 2.83 & 2.82622296657407 & 0.00377703342592639 \tabularnewline
33 & 2.84 & 2.838133841977 & 0.0018661580230015 \tabularnewline
34 & 2.87 & 2.84799286302818 & 0.0220071369718235 \tabularnewline
35 & 2.89 & 2.87692130074857 & 0.0130786992514276 \tabularnewline
36 & 2.9 & 2.8962641032698 & 0.00373589673020369 \tabularnewline
37 & 2.9 & 2.90538129747525 & -0.00538129747525318 \tabularnewline
38 & 2.91 & 2.91465121157235 & -0.00465121157235293 \tabularnewline
39 & 2.92 & 2.92367789319404 & -0.00367789319403711 \tabularnewline
40 & 2.92 & 2.93161964273823 & -0.0116196427382342 \tabularnewline
41 & 2.92 & 2.9247356969631 & -0.00473569696310294 \tabularnewline
42 & 2.92 & 2.9326045015773 & -0.0126045015772975 \tabularnewline
43 & 2.94 & 2.92435588733518 & 0.0156441126648175 \tabularnewline
44 & 2.95 & 2.94500927556261 & 0.00499072443739346 \tabularnewline
45 & 2.95 & 2.95781428076943 & -0.00781428076943103 \tabularnewline
46 & 2.97 & 2.96104281204538 & 0.00895718795461686 \tabularnewline
47 & 2.99 & 2.97734282327437 & 0.0126571767256318 \tabularnewline
48 & 3 & 2.99535169027219 & 0.0046483097278136 \tabularnewline
49 & 3 & 3.00435553166836 & -0.004355531668363 \tabularnewline
50 & 3.01 & 3.01462097127189 & -0.00462097127189498 \tabularnewline
51 & 3.03 & 3.02377434535073 & 0.00622565464927272 \tabularnewline
52 & 3.03 & 3.03979453677912 & -0.00979453677912057 \tabularnewline
53 & 3.04 & 3.03525308361651 & 0.00474691638348812 \tabularnewline
54 & 3.04 & 3.05082990653236 & -0.01082990653236 \tabularnewline
55 & 3.05 & 3.04706348526136 & 0.00293651473863843 \tabularnewline
56 & 3.05 & 3.05521936734651 & -0.00521936734651218 \tabularnewline
57 & 3.09 & 3.05754888917361 & 0.032451110826389 \tabularnewline
58 & 3.09 & 3.09863999982516 & -0.00863999982515962 \tabularnewline
59 & 3.09 & 3.09952096595202 & -0.00952096595202168 \tabularnewline
60 & 3.1 & 3.09680083560824 & 0.0031991643917606 \tabularnewline
61 & 3.1 & 3.10358288437091 & -0.00358288437091447 \tabularnewline
62 & 3.11 & 3.11451480220405 & -0.00451480220404976 \tabularnewline
63 & 3.12 & 3.12487281243597 & -0.00487281243597293 \tabularnewline
64 & 3.12 & 3.12929117344296 & -0.00929117344295749 \tabularnewline
65 & 3.12 & 3.1266888120799 & -0.00668881207989758 \tabularnewline
66 & 3.13 & 3.13040638116328 & -0.000406381163277292 \tabularnewline
67 & 3.15 & 3.13740537585017 & 0.0125946241498296 \tabularnewline
68 & 3.16 & 3.15339746315912 & 0.00660253684088152 \tabularnewline
69 & 3.16 & 3.17019252045591 & -0.0101925204559099 \tabularnewline
70 & 3.18 & 3.16879878197338 & 0.0112012180266197 \tabularnewline
71 & 3.19 & 3.18740162993626 & 0.00259837006373687 \tabularnewline
72 & 3.19 & 3.19686228111315 & -0.00686228111315135 \tabularnewline
73 & 3.2 & 3.19391828066085 & 0.00608171933915092 \tabularnewline
74 & 3.21 & 3.21343105592656 & -0.00343105592656201 \tabularnewline
75 & 3.26 & 3.22472535855276 & 0.0352746414472418 \tabularnewline
76 & 3.27 & 3.26473325924502 & 0.00526674075497624 \tabularnewline
77 & 3.28 & 3.27546607253964 & 0.00453392746036352 \tabularnewline
78 & 3.29 & 3.28990111714256 & 9.88828574381984e-05 \tabularnewline
79 & 3.29 & 3.29868336250408 & -0.00868336250408053 \tabularnewline
80 & 3.3 & 3.29496080981449 & 0.0050391901855078 \tabularnewline
81 & 3.3 & 3.3086347158839 & -0.00863471588389952 \tabularnewline
82 & 3.31 & 3.31082747784762 & -0.000827477847623381 \tabularnewline
83 & 3.31 & 3.31775200434036 & -0.00775200434035783 \tabularnewline
84 & 3.31 & 3.31695327646776 & -0.00695327646776356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233090&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]2.69[/C][C]2.62978365384615[/C][C]0.060216346153847[/C][/ROW]
[ROW][C]14[/C][C]2.71[/C][C]2.70448684313368[/C][C]0.00551315686631915[/C][/ROW]
[ROW][C]15[/C][C]2.72[/C][C]2.72091487822979[/C][C]-0.000914878229793192[/C][/ROW]
[ROW][C]16[/C][C]2.73[/C][C]2.73240563098879[/C][C]-0.00240563098879143[/C][/ROW]
[ROW][C]17[/C][C]2.73[/C][C]2.73297476257016[/C][C]-0.00297476257015949[/C][/ROW]
[ROW][C]18[/C][C]2.74[/C][C]2.74344963647306[/C][C]-0.00344963647305851[/C][/ROW]
[ROW][C]19[/C][C]2.74[/C][C]2.74099820362054[/C][C]-0.00099820362053693[/C][/ROW]
[ROW][C]20[/C][C]2.74[/C][C]2.74908081965786[/C][C]-0.0090808196578589[/C][/ROW]
[ROW][C]21[/C][C]2.74[/C][C]2.74949079265847[/C][C]-0.00949079265847441[/C][/ROW]
[ROW][C]22[/C][C]2.74[/C][C]2.7491160554789[/C][C]-0.00911605547890115[/C][/ROW]
[ROW][C]23[/C][C]2.75[/C][C]2.7490777296923[/C][C]0.000922270307702089[/C][/ROW]
[ROW][C]24[/C][C]2.75[/C][C]2.75846773886961[/C][C]-0.00846773886960994[/C][/ROW]
[ROW][C]25[/C][C]2.75[/C][C]2.75641997704092[/C][C]-0.00641997704092212[/C][/ROW]
[ROW][C]26[/C][C]2.75[/C][C]2.76570728980554[/C][C]-0.0157072898055448[/C][/ROW]
[ROW][C]27[/C][C]2.77[/C][C]2.76242775402728[/C][C]0.00757224597271655[/C][/ROW]
[ROW][C]28[/C][C]2.78[/C][C]2.78138515582907[/C][C]-0.00138515582907228[/C][/ROW]
[ROW][C]29[/C][C]2.79[/C][C]2.78281218748537[/C][C]0.0071878125146263[/C][/ROW]
[ROW][C]30[/C][C]2.8[/C][C]2.80236170439126[/C][C]-0.0023617043912556[/C][/ROW]
[ROW][C]31[/C][C]2.82[/C][C]2.80113765399381[/C][C]0.0188623460061876[/C][/ROW]
[ROW][C]32[/C][C]2.83[/C][C]2.82622296657407[/C][C]0.00377703342592639[/C][/ROW]
[ROW][C]33[/C][C]2.84[/C][C]2.838133841977[/C][C]0.0018661580230015[/C][/ROW]
[ROW][C]34[/C][C]2.87[/C][C]2.84799286302818[/C][C]0.0220071369718235[/C][/ROW]
[ROW][C]35[/C][C]2.89[/C][C]2.87692130074857[/C][C]0.0130786992514276[/C][/ROW]
[ROW][C]36[/C][C]2.9[/C][C]2.8962641032698[/C][C]0.00373589673020369[/C][/ROW]
[ROW][C]37[/C][C]2.9[/C][C]2.90538129747525[/C][C]-0.00538129747525318[/C][/ROW]
[ROW][C]38[/C][C]2.91[/C][C]2.91465121157235[/C][C]-0.00465121157235293[/C][/ROW]
[ROW][C]39[/C][C]2.92[/C][C]2.92367789319404[/C][C]-0.00367789319403711[/C][/ROW]
[ROW][C]40[/C][C]2.92[/C][C]2.93161964273823[/C][C]-0.0116196427382342[/C][/ROW]
[ROW][C]41[/C][C]2.92[/C][C]2.9247356969631[/C][C]-0.00473569696310294[/C][/ROW]
[ROW][C]42[/C][C]2.92[/C][C]2.9326045015773[/C][C]-0.0126045015772975[/C][/ROW]
[ROW][C]43[/C][C]2.94[/C][C]2.92435588733518[/C][C]0.0156441126648175[/C][/ROW]
[ROW][C]44[/C][C]2.95[/C][C]2.94500927556261[/C][C]0.00499072443739346[/C][/ROW]
[ROW][C]45[/C][C]2.95[/C][C]2.95781428076943[/C][C]-0.00781428076943103[/C][/ROW]
[ROW][C]46[/C][C]2.97[/C][C]2.96104281204538[/C][C]0.00895718795461686[/C][/ROW]
[ROW][C]47[/C][C]2.99[/C][C]2.97734282327437[/C][C]0.0126571767256318[/C][/ROW]
[ROW][C]48[/C][C]3[/C][C]2.99535169027219[/C][C]0.0046483097278136[/C][/ROW]
[ROW][C]49[/C][C]3[/C][C]3.00435553166836[/C][C]-0.004355531668363[/C][/ROW]
[ROW][C]50[/C][C]3.01[/C][C]3.01462097127189[/C][C]-0.00462097127189498[/C][/ROW]
[ROW][C]51[/C][C]3.03[/C][C]3.02377434535073[/C][C]0.00622565464927272[/C][/ROW]
[ROW][C]52[/C][C]3.03[/C][C]3.03979453677912[/C][C]-0.00979453677912057[/C][/ROW]
[ROW][C]53[/C][C]3.04[/C][C]3.03525308361651[/C][C]0.00474691638348812[/C][/ROW]
[ROW][C]54[/C][C]3.04[/C][C]3.05082990653236[/C][C]-0.01082990653236[/C][/ROW]
[ROW][C]55[/C][C]3.05[/C][C]3.04706348526136[/C][C]0.00293651473863843[/C][/ROW]
[ROW][C]56[/C][C]3.05[/C][C]3.05521936734651[/C][C]-0.00521936734651218[/C][/ROW]
[ROW][C]57[/C][C]3.09[/C][C]3.05754888917361[/C][C]0.032451110826389[/C][/ROW]
[ROW][C]58[/C][C]3.09[/C][C]3.09863999982516[/C][C]-0.00863999982515962[/C][/ROW]
[ROW][C]59[/C][C]3.09[/C][C]3.09952096595202[/C][C]-0.00952096595202168[/C][/ROW]
[ROW][C]60[/C][C]3.1[/C][C]3.09680083560824[/C][C]0.0031991643917606[/C][/ROW]
[ROW][C]61[/C][C]3.1[/C][C]3.10358288437091[/C][C]-0.00358288437091447[/C][/ROW]
[ROW][C]62[/C][C]3.11[/C][C]3.11451480220405[/C][C]-0.00451480220404976[/C][/ROW]
[ROW][C]63[/C][C]3.12[/C][C]3.12487281243597[/C][C]-0.00487281243597293[/C][/ROW]
[ROW][C]64[/C][C]3.12[/C][C]3.12929117344296[/C][C]-0.00929117344295749[/C][/ROW]
[ROW][C]65[/C][C]3.12[/C][C]3.1266888120799[/C][C]-0.00668881207989758[/C][/ROW]
[ROW][C]66[/C][C]3.13[/C][C]3.13040638116328[/C][C]-0.000406381163277292[/C][/ROW]
[ROW][C]67[/C][C]3.15[/C][C]3.13740537585017[/C][C]0.0125946241498296[/C][/ROW]
[ROW][C]68[/C][C]3.16[/C][C]3.15339746315912[/C][C]0.00660253684088152[/C][/ROW]
[ROW][C]69[/C][C]3.16[/C][C]3.17019252045591[/C][C]-0.0101925204559099[/C][/ROW]
[ROW][C]70[/C][C]3.18[/C][C]3.16879878197338[/C][C]0.0112012180266197[/C][/ROW]
[ROW][C]71[/C][C]3.19[/C][C]3.18740162993626[/C][C]0.00259837006373687[/C][/ROW]
[ROW][C]72[/C][C]3.19[/C][C]3.19686228111315[/C][C]-0.00686228111315135[/C][/ROW]
[ROW][C]73[/C][C]3.2[/C][C]3.19391828066085[/C][C]0.00608171933915092[/C][/ROW]
[ROW][C]74[/C][C]3.21[/C][C]3.21343105592656[/C][C]-0.00343105592656201[/C][/ROW]
[ROW][C]75[/C][C]3.26[/C][C]3.22472535855276[/C][C]0.0352746414472418[/C][/ROW]
[ROW][C]76[/C][C]3.27[/C][C]3.26473325924502[/C][C]0.00526674075497624[/C][/ROW]
[ROW][C]77[/C][C]3.28[/C][C]3.27546607253964[/C][C]0.00453392746036352[/C][/ROW]
[ROW][C]78[/C][C]3.29[/C][C]3.28990111714256[/C][C]9.88828574381984e-05[/C][/ROW]
[ROW][C]79[/C][C]3.29[/C][C]3.29868336250408[/C][C]-0.00868336250408053[/C][/ROW]
[ROW][C]80[/C][C]3.3[/C][C]3.29496080981449[/C][C]0.0050391901855078[/C][/ROW]
[ROW][C]81[/C][C]3.3[/C][C]3.3086347158839[/C][C]-0.00863471588389952[/C][/ROW]
[ROW][C]82[/C][C]3.31[/C][C]3.31082747784762[/C][C]-0.000827477847623381[/C][/ROW]
[ROW][C]83[/C][C]3.31[/C][C]3.31775200434036[/C][C]-0.00775200434035783[/C][/ROW]
[ROW][C]84[/C][C]3.31[/C][C]3.31695327646776[/C][C]-0.00695327646776356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233090&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233090&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
132.692.629783653846150.060216346153847
142.712.704486843133680.00551315686631915
152.722.72091487822979-0.000914878229793192
162.732.73240563098879-0.00240563098879143
172.732.73297476257016-0.00297476257015949
182.742.74344963647306-0.00344963647305851
192.742.74099820362054-0.00099820362053693
202.742.74908081965786-0.0090808196578589
212.742.74949079265847-0.00949079265847441
222.742.7491160554789-0.00911605547890115
232.752.74907772969230.000922270307702089
242.752.75846773886961-0.00846773886960994
252.752.75641997704092-0.00641997704092212
262.752.76570728980554-0.0157072898055448
272.772.762427754027280.00757224597271655
282.782.78138515582907-0.00138515582907228
292.792.782812187485370.0071878125146263
302.82.80236170439126-0.0023617043912556
312.822.801137653993810.0188623460061876
322.832.826222966574070.00377703342592639
332.842.8381338419770.0018661580230015
342.872.847992863028180.0220071369718235
352.892.876921300748570.0130786992514276
362.92.89626410326980.00373589673020369
372.92.90538129747525-0.00538129747525318
382.912.91465121157235-0.00465121157235293
392.922.92367789319404-0.00367789319403711
402.922.93161964273823-0.0116196427382342
412.922.9247356969631-0.00473569696310294
422.922.9326045015773-0.0126045015772975
432.942.924355887335180.0156441126648175
442.952.945009275562610.00499072443739346
452.952.95781428076943-0.00781428076943103
462.972.961042812045380.00895718795461686
472.992.977342823274370.0126571767256318
4832.995351690272190.0046483097278136
4933.00435553166836-0.004355531668363
503.013.01462097127189-0.00462097127189498
513.033.023774345350730.00622565464927272
523.033.03979453677912-0.00979453677912057
533.043.035253083616510.00474691638348812
543.043.05082990653236-0.01082990653236
553.053.047063485261360.00293651473863843
563.053.05521936734651-0.00521936734651218
573.093.057548889173610.032451110826389
583.093.09863999982516-0.00863999982515962
593.093.09952096595202-0.00952096595202168
603.13.096800835608240.0031991643917606
613.13.10358288437091-0.00358288437091447
623.113.11451480220405-0.00451480220404976
633.123.12487281243597-0.00487281243597293
643.123.12929117344296-0.00929117344295749
653.123.1266888120799-0.00668881207989758
663.133.13040638116328-0.000406381163277292
673.153.137405375850170.0125946241498296
683.163.153397463159120.00660253684088152
693.163.17019252045591-0.0101925204559099
703.183.168798781973380.0112012180266197
713.193.187401629936260.00259837006373687
723.193.19686228111315-0.00686228111315135
733.23.193918280660850.00608171933915092
743.213.21343105592656-0.00343105592656201
753.263.224725358552760.0352746414472418
763.273.264733259245020.00526674075497624
773.283.275466072539640.00453392746036352
783.293.289901117142569.88828574381984e-05
793.293.29868336250408-0.00868336250408053
803.33.294960809814490.0050391901855078
813.33.3086347158839-0.00863471588389952
823.313.31082747784762-0.000827477847623381
833.313.31775200434036-0.00775200434035783
843.313.31695327646776-0.00695327646776356







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853.315251418910533.291712196569683.33879064125138
863.328331567789613.296698562954553.35996457262468
873.346664597142863.308622528306143.38470666597958
883.351936505855493.308419256311653.39545375539933
893.357866280279523.30948960186583.40624295869323
903.367777510545353.314986838823673.42056818226704
913.375572792772193.31870973774253.43243584780188
923.381048979598173.320386313700673.44171164549568
933.38880059047843.324562665229563.45303851572723
943.399543439041463.331919012635333.46716786544759
953.406502616621383.335653374894743.47735185834803
963.412744755244763.33881122388233.48667828660721

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3.31525141891053 & 3.29171219656968 & 3.33879064125138 \tabularnewline
86 & 3.32833156778961 & 3.29669856295455 & 3.35996457262468 \tabularnewline
87 & 3.34666459714286 & 3.30862252830614 & 3.38470666597958 \tabularnewline
88 & 3.35193650585549 & 3.30841925631165 & 3.39545375539933 \tabularnewline
89 & 3.35786628027952 & 3.3094896018658 & 3.40624295869323 \tabularnewline
90 & 3.36777751054535 & 3.31498683882367 & 3.42056818226704 \tabularnewline
91 & 3.37557279277219 & 3.3187097377425 & 3.43243584780188 \tabularnewline
92 & 3.38104897959817 & 3.32038631370067 & 3.44171164549568 \tabularnewline
93 & 3.3888005904784 & 3.32456266522956 & 3.45303851572723 \tabularnewline
94 & 3.39954343904146 & 3.33191901263533 & 3.46716786544759 \tabularnewline
95 & 3.40650261662138 & 3.33565337489474 & 3.47735185834803 \tabularnewline
96 & 3.41274475524476 & 3.3388112238823 & 3.48667828660721 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=233090&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]85[/C][C]3.31525141891053[/C][C]3.29171219656968[/C][C]3.33879064125138[/C][/ROW]
[ROW][C]86[/C][C]3.32833156778961[/C][C]3.29669856295455[/C][C]3.35996457262468[/C][/ROW]
[ROW][C]87[/C][C]3.34666459714286[/C][C]3.30862252830614[/C][C]3.38470666597958[/C][/ROW]
[ROW][C]88[/C][C]3.35193650585549[/C][C]3.30841925631165[/C][C]3.39545375539933[/C][/ROW]
[ROW][C]89[/C][C]3.35786628027952[/C][C]3.3094896018658[/C][C]3.40624295869323[/C][/ROW]
[ROW][C]90[/C][C]3.36777751054535[/C][C]3.31498683882367[/C][C]3.42056818226704[/C][/ROW]
[ROW][C]91[/C][C]3.37557279277219[/C][C]3.3187097377425[/C][C]3.43243584780188[/C][/ROW]
[ROW][C]92[/C][C]3.38104897959817[/C][C]3.32038631370067[/C][C]3.44171164549568[/C][/ROW]
[ROW][C]93[/C][C]3.3888005904784[/C][C]3.32456266522956[/C][C]3.45303851572723[/C][/ROW]
[ROW][C]94[/C][C]3.39954343904146[/C][C]3.33191901263533[/C][C]3.46716786544759[/C][/ROW]
[ROW][C]95[/C][C]3.40650261662138[/C][C]3.33565337489474[/C][C]3.47735185834803[/C][/ROW]
[ROW][C]96[/C][C]3.41274475524476[/C][C]3.3388112238823[/C][C]3.48667828660721[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=233090&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=233090&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
853.315251418910533.291712196569683.33879064125138
863.328331567789613.296698562954553.35996457262468
873.346664597142863.308622528306143.38470666597958
883.351936505855493.308419256311653.39545375539933
893.357866280279523.30948960186583.40624295869323
903.367777510545353.314986838823673.42056818226704
913.375572792772193.31870973774253.43243584780188
923.381048979598173.320386313700673.44171164549568
933.38880059047843.324562665229563.45303851572723
943.399543439041463.331919012635333.46716786544759
953.406502616621383.335653374894743.47735185834803
963.412744755244763.33881122388233.48667828660721



Parameters (Session):
par1 = 750 ; par2 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')