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Author's title

datareeks - exponential Smoothing gemiddelde gokuitgaven - Frederik Verbrak...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 14:51:38 +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/2011/May/20/t13059028983eiwupje4vfa84r.htm/, Retrieved Mon, 13 May 2024 13:12:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122464, Retrieved Mon, 13 May 2024 13:12:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact76
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Datareeks-tijdree...] [2011-05-20 09:52:47] [84d07acf15b5851f5f3dc97fb3479c7e]
- RMPD  [(Partial) Autocorrelation Function] [ datareeks - gemi...] [2011-05-20 10:50:15] [1a2529c7ddde8b9806f7cce4d00981a3]
- RM D      [Exponential Smoothing] [datareeks - expon...] [2011-05-20 14:51:38] [31886bd2f92a612f059dd2285dd41f3c] [Current]
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Dataseries X:
5.81    
5.76    
5.99    
6.12    
6.03    
6.25    
5.80    
5.67    
5.89    
5.91    
5.86    
6.07    
6.27    
6.68    
6.77    
6.71    
6.62
6.50
5.89
6.05
6.43
6.47
6.62
6.77
6.70
6.95
6.73
7.07
7.28
7.32
6.76
6.93
6.99
7.16
7.28
7.08
7.34
7.87
6.28
6.30
6.36
6.28
5.89
6.04
5.96
6.10
6.26
6.02
6.25
6.41
6.22
6.57
6.18
6.26
6.10
6.02
6.06
6.35
6.21
6.48
6.74
6.53
6.80
6.75
6.56
6.66
6.18
6.40
6.43
6.54
6.44
6.64
6.82
6.97
7.00
6.91
6.74
6.98
6.37
6.56
6.63
6.87
6.68
6.75
6.84
7.15
7.09
6.97
7.15




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122464&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122464&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122464&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.790049205367589
beta0.00443492636579578
gamma0.910460748484263

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.790049205367589 \tabularnewline
beta & 0.00443492636579578 \tabularnewline
gamma & 0.910460748484263 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122464&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]0.790049205367589[/C][/ROW]
[ROW][C]beta[/C][C]0.00443492636579578[/C][/ROW]
[ROW][C]gamma[/C][C]0.910460748484263[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122464&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122464&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
alpha0.790049205367589
beta0.00443492636579578
gamma0.910460748484263







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136.276.005134714719070.264865285280932
146.686.645047572770730.0349524272292676
156.776.766836252561940.00316374743805969
166.716.705575762316130.00442423768386568
176.626.605924432614310.0140755673856905
186.56.478490964555690.0215090354443106
195.896.32768873003534-0.437688730035343
206.055.830384491645580.219615508354418
216.436.204522939793470.225477060206529
226.476.385652571456080.084347428543924
236.626.38736971614250.232630283857501
246.776.81092562846281-0.0409256284628086
256.77.0870432851245-0.387043285124504
266.957.19609101986052-0.246091019860518
276.737.09083234591805-0.36083234591805
287.076.739436620890720.330563379109281
297.286.891942951380710.388057048619291
307.327.045903022941040.274096977058964
316.766.96777018469932-0.207770184699319
326.936.768267730510680.161732269489317
336.997.12075248225123-0.130752482251235
347.166.987714007976360.172285992023641
357.287.078754333403910.201245666596092
367.087.43942399108796-0.359423991087963
377.347.40499384141914-0.0649938414191356
387.877.832875243836430.0371247561635712
396.287.93081818628042-1.65081818628042
406.36.68681723664301-0.386817236643013
416.366.288970843958730.0710291560412735
426.286.190810939038680.089189060961318
435.895.92885085405116-0.0388508540511632
446.045.927726346556130.112273653443869
455.966.16205467894051-0.202054678940506
466.16.025526694197460.0744733058025417
476.266.049574053084520.210425946915479
486.026.2937208608802-0.273720860880203
496.256.33910124086385-0.0891012408638492
506.416.69402583507748-0.284025835077483
516.226.209522124144860.0104778758551411
526.576.509798607907810.0602013920921882
536.186.54989686954732-0.369896869547321
546.266.107254186606030.152745813393966
556.15.8721009318750.227899068125004
566.026.10981784742629-0.0898178474262883
576.066.12154748840332-0.0615474884033178
586.356.148136579463590.20186342053641
596.216.29529171874476-0.0852917187447568
606.486.209708176224990.270291823775011
616.746.737166030787340.00283396921266199
626.537.15305644915515-0.623056449155147
636.86.446979051041650.353020948958346
646.757.0491669649905-0.2991669649905
656.566.71413617678361-0.154136176783609
666.666.535526259824740.124473740175263
676.186.26824163141441-0.0882416314144132
686.46.193300802791410.206699197208589
696.436.44732049495923-0.0173204949592334
706.546.56364382298656-0.0236438229865579
716.446.4734637417974-0.0334637417973935
726.646.494866937386370.14513306261363
736.826.87579663362076-0.0557966336207567
746.977.11880632914136-0.148806329141363
7576.966747985930130.0332520140698707
766.917.19331361652164-0.283313616521643
776.746.89363504515358-0.15363504515358
786.986.76613178210460.213868217895395
796.376.50970866641909-0.139708666419086
806.566.449297024433970.110702975566025
816.636.583832317030290.0461676829697142
826.876.750973955527860.119026044472145
836.686.76622330712744-0.0862233071274359
846.756.78091928977597-0.0309192897759702
856.846.98648794517266-0.146487945172659
867.157.139657601339860.0103423986601392
877.097.14616507889787-0.0561650788978687
886.977.23992776665109-0.269927766651091
897.156.972354839200580.177645160799422

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 6.27 & 6.00513471471907 & 0.264865285280932 \tabularnewline
14 & 6.68 & 6.64504757277073 & 0.0349524272292676 \tabularnewline
15 & 6.77 & 6.76683625256194 & 0.00316374743805969 \tabularnewline
16 & 6.71 & 6.70557576231613 & 0.00442423768386568 \tabularnewline
17 & 6.62 & 6.60592443261431 & 0.0140755673856905 \tabularnewline
18 & 6.5 & 6.47849096455569 & 0.0215090354443106 \tabularnewline
19 & 5.89 & 6.32768873003534 & -0.437688730035343 \tabularnewline
20 & 6.05 & 5.83038449164558 & 0.219615508354418 \tabularnewline
21 & 6.43 & 6.20452293979347 & 0.225477060206529 \tabularnewline
22 & 6.47 & 6.38565257145608 & 0.084347428543924 \tabularnewline
23 & 6.62 & 6.3873697161425 & 0.232630283857501 \tabularnewline
24 & 6.77 & 6.81092562846281 & -0.0409256284628086 \tabularnewline
25 & 6.7 & 7.0870432851245 & -0.387043285124504 \tabularnewline
26 & 6.95 & 7.19609101986052 & -0.246091019860518 \tabularnewline
27 & 6.73 & 7.09083234591805 & -0.36083234591805 \tabularnewline
28 & 7.07 & 6.73943662089072 & 0.330563379109281 \tabularnewline
29 & 7.28 & 6.89194295138071 & 0.388057048619291 \tabularnewline
30 & 7.32 & 7.04590302294104 & 0.274096977058964 \tabularnewline
31 & 6.76 & 6.96777018469932 & -0.207770184699319 \tabularnewline
32 & 6.93 & 6.76826773051068 & 0.161732269489317 \tabularnewline
33 & 6.99 & 7.12075248225123 & -0.130752482251235 \tabularnewline
34 & 7.16 & 6.98771400797636 & 0.172285992023641 \tabularnewline
35 & 7.28 & 7.07875433340391 & 0.201245666596092 \tabularnewline
36 & 7.08 & 7.43942399108796 & -0.359423991087963 \tabularnewline
37 & 7.34 & 7.40499384141914 & -0.0649938414191356 \tabularnewline
38 & 7.87 & 7.83287524383643 & 0.0371247561635712 \tabularnewline
39 & 6.28 & 7.93081818628042 & -1.65081818628042 \tabularnewline
40 & 6.3 & 6.68681723664301 & -0.386817236643013 \tabularnewline
41 & 6.36 & 6.28897084395873 & 0.0710291560412735 \tabularnewline
42 & 6.28 & 6.19081093903868 & 0.089189060961318 \tabularnewline
43 & 5.89 & 5.92885085405116 & -0.0388508540511632 \tabularnewline
44 & 6.04 & 5.92772634655613 & 0.112273653443869 \tabularnewline
45 & 5.96 & 6.16205467894051 & -0.202054678940506 \tabularnewline
46 & 6.1 & 6.02552669419746 & 0.0744733058025417 \tabularnewline
47 & 6.26 & 6.04957405308452 & 0.210425946915479 \tabularnewline
48 & 6.02 & 6.2937208608802 & -0.273720860880203 \tabularnewline
49 & 6.25 & 6.33910124086385 & -0.0891012408638492 \tabularnewline
50 & 6.41 & 6.69402583507748 & -0.284025835077483 \tabularnewline
51 & 6.22 & 6.20952212414486 & 0.0104778758551411 \tabularnewline
52 & 6.57 & 6.50979860790781 & 0.0602013920921882 \tabularnewline
53 & 6.18 & 6.54989686954732 & -0.369896869547321 \tabularnewline
54 & 6.26 & 6.10725418660603 & 0.152745813393966 \tabularnewline
55 & 6.1 & 5.872100931875 & 0.227899068125004 \tabularnewline
56 & 6.02 & 6.10981784742629 & -0.0898178474262883 \tabularnewline
57 & 6.06 & 6.12154748840332 & -0.0615474884033178 \tabularnewline
58 & 6.35 & 6.14813657946359 & 0.20186342053641 \tabularnewline
59 & 6.21 & 6.29529171874476 & -0.0852917187447568 \tabularnewline
60 & 6.48 & 6.20970817622499 & 0.270291823775011 \tabularnewline
61 & 6.74 & 6.73716603078734 & 0.00283396921266199 \tabularnewline
62 & 6.53 & 7.15305644915515 & -0.623056449155147 \tabularnewline
63 & 6.8 & 6.44697905104165 & 0.353020948958346 \tabularnewline
64 & 6.75 & 7.0491669649905 & -0.2991669649905 \tabularnewline
65 & 6.56 & 6.71413617678361 & -0.154136176783609 \tabularnewline
66 & 6.66 & 6.53552625982474 & 0.124473740175263 \tabularnewline
67 & 6.18 & 6.26824163141441 & -0.0882416314144132 \tabularnewline
68 & 6.4 & 6.19330080279141 & 0.206699197208589 \tabularnewline
69 & 6.43 & 6.44732049495923 & -0.0173204949592334 \tabularnewline
70 & 6.54 & 6.56364382298656 & -0.0236438229865579 \tabularnewline
71 & 6.44 & 6.4734637417974 & -0.0334637417973935 \tabularnewline
72 & 6.64 & 6.49486693738637 & 0.14513306261363 \tabularnewline
73 & 6.82 & 6.87579663362076 & -0.0557966336207567 \tabularnewline
74 & 6.97 & 7.11880632914136 & -0.148806329141363 \tabularnewline
75 & 7 & 6.96674798593013 & 0.0332520140698707 \tabularnewline
76 & 6.91 & 7.19331361652164 & -0.283313616521643 \tabularnewline
77 & 6.74 & 6.89363504515358 & -0.15363504515358 \tabularnewline
78 & 6.98 & 6.7661317821046 & 0.213868217895395 \tabularnewline
79 & 6.37 & 6.50970866641909 & -0.139708666419086 \tabularnewline
80 & 6.56 & 6.44929702443397 & 0.110702975566025 \tabularnewline
81 & 6.63 & 6.58383231703029 & 0.0461676829697142 \tabularnewline
82 & 6.87 & 6.75097395552786 & 0.119026044472145 \tabularnewline
83 & 6.68 & 6.76622330712744 & -0.0862233071274359 \tabularnewline
84 & 6.75 & 6.78091928977597 & -0.0309192897759702 \tabularnewline
85 & 6.84 & 6.98648794517266 & -0.146487945172659 \tabularnewline
86 & 7.15 & 7.13965760133986 & 0.0103423986601392 \tabularnewline
87 & 7.09 & 7.14616507889787 & -0.0561650788978687 \tabularnewline
88 & 6.97 & 7.23992776665109 & -0.269927766651091 \tabularnewline
89 & 7.15 & 6.97235483920058 & 0.177645160799422 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122464&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]6.27[/C][C]6.00513471471907[/C][C]0.264865285280932[/C][/ROW]
[ROW][C]14[/C][C]6.68[/C][C]6.64504757277073[/C][C]0.0349524272292676[/C][/ROW]
[ROW][C]15[/C][C]6.77[/C][C]6.76683625256194[/C][C]0.00316374743805969[/C][/ROW]
[ROW][C]16[/C][C]6.71[/C][C]6.70557576231613[/C][C]0.00442423768386568[/C][/ROW]
[ROW][C]17[/C][C]6.62[/C][C]6.60592443261431[/C][C]0.0140755673856905[/C][/ROW]
[ROW][C]18[/C][C]6.5[/C][C]6.47849096455569[/C][C]0.0215090354443106[/C][/ROW]
[ROW][C]19[/C][C]5.89[/C][C]6.32768873003534[/C][C]-0.437688730035343[/C][/ROW]
[ROW][C]20[/C][C]6.05[/C][C]5.83038449164558[/C][C]0.219615508354418[/C][/ROW]
[ROW][C]21[/C][C]6.43[/C][C]6.20452293979347[/C][C]0.225477060206529[/C][/ROW]
[ROW][C]22[/C][C]6.47[/C][C]6.38565257145608[/C][C]0.084347428543924[/C][/ROW]
[ROW][C]23[/C][C]6.62[/C][C]6.3873697161425[/C][C]0.232630283857501[/C][/ROW]
[ROW][C]24[/C][C]6.77[/C][C]6.81092562846281[/C][C]-0.0409256284628086[/C][/ROW]
[ROW][C]25[/C][C]6.7[/C][C]7.0870432851245[/C][C]-0.387043285124504[/C][/ROW]
[ROW][C]26[/C][C]6.95[/C][C]7.19609101986052[/C][C]-0.246091019860518[/C][/ROW]
[ROW][C]27[/C][C]6.73[/C][C]7.09083234591805[/C][C]-0.36083234591805[/C][/ROW]
[ROW][C]28[/C][C]7.07[/C][C]6.73943662089072[/C][C]0.330563379109281[/C][/ROW]
[ROW][C]29[/C][C]7.28[/C][C]6.89194295138071[/C][C]0.388057048619291[/C][/ROW]
[ROW][C]30[/C][C]7.32[/C][C]7.04590302294104[/C][C]0.274096977058964[/C][/ROW]
[ROW][C]31[/C][C]6.76[/C][C]6.96777018469932[/C][C]-0.207770184699319[/C][/ROW]
[ROW][C]32[/C][C]6.93[/C][C]6.76826773051068[/C][C]0.161732269489317[/C][/ROW]
[ROW][C]33[/C][C]6.99[/C][C]7.12075248225123[/C][C]-0.130752482251235[/C][/ROW]
[ROW][C]34[/C][C]7.16[/C][C]6.98771400797636[/C][C]0.172285992023641[/C][/ROW]
[ROW][C]35[/C][C]7.28[/C][C]7.07875433340391[/C][C]0.201245666596092[/C][/ROW]
[ROW][C]36[/C][C]7.08[/C][C]7.43942399108796[/C][C]-0.359423991087963[/C][/ROW]
[ROW][C]37[/C][C]7.34[/C][C]7.40499384141914[/C][C]-0.0649938414191356[/C][/ROW]
[ROW][C]38[/C][C]7.87[/C][C]7.83287524383643[/C][C]0.0371247561635712[/C][/ROW]
[ROW][C]39[/C][C]6.28[/C][C]7.93081818628042[/C][C]-1.65081818628042[/C][/ROW]
[ROW][C]40[/C][C]6.3[/C][C]6.68681723664301[/C][C]-0.386817236643013[/C][/ROW]
[ROW][C]41[/C][C]6.36[/C][C]6.28897084395873[/C][C]0.0710291560412735[/C][/ROW]
[ROW][C]42[/C][C]6.28[/C][C]6.19081093903868[/C][C]0.089189060961318[/C][/ROW]
[ROW][C]43[/C][C]5.89[/C][C]5.92885085405116[/C][C]-0.0388508540511632[/C][/ROW]
[ROW][C]44[/C][C]6.04[/C][C]5.92772634655613[/C][C]0.112273653443869[/C][/ROW]
[ROW][C]45[/C][C]5.96[/C][C]6.16205467894051[/C][C]-0.202054678940506[/C][/ROW]
[ROW][C]46[/C][C]6.1[/C][C]6.02552669419746[/C][C]0.0744733058025417[/C][/ROW]
[ROW][C]47[/C][C]6.26[/C][C]6.04957405308452[/C][C]0.210425946915479[/C][/ROW]
[ROW][C]48[/C][C]6.02[/C][C]6.2937208608802[/C][C]-0.273720860880203[/C][/ROW]
[ROW][C]49[/C][C]6.25[/C][C]6.33910124086385[/C][C]-0.0891012408638492[/C][/ROW]
[ROW][C]50[/C][C]6.41[/C][C]6.69402583507748[/C][C]-0.284025835077483[/C][/ROW]
[ROW][C]51[/C][C]6.22[/C][C]6.20952212414486[/C][C]0.0104778758551411[/C][/ROW]
[ROW][C]52[/C][C]6.57[/C][C]6.50979860790781[/C][C]0.0602013920921882[/C][/ROW]
[ROW][C]53[/C][C]6.18[/C][C]6.54989686954732[/C][C]-0.369896869547321[/C][/ROW]
[ROW][C]54[/C][C]6.26[/C][C]6.10725418660603[/C][C]0.152745813393966[/C][/ROW]
[ROW][C]55[/C][C]6.1[/C][C]5.872100931875[/C][C]0.227899068125004[/C][/ROW]
[ROW][C]56[/C][C]6.02[/C][C]6.10981784742629[/C][C]-0.0898178474262883[/C][/ROW]
[ROW][C]57[/C][C]6.06[/C][C]6.12154748840332[/C][C]-0.0615474884033178[/C][/ROW]
[ROW][C]58[/C][C]6.35[/C][C]6.14813657946359[/C][C]0.20186342053641[/C][/ROW]
[ROW][C]59[/C][C]6.21[/C][C]6.29529171874476[/C][C]-0.0852917187447568[/C][/ROW]
[ROW][C]60[/C][C]6.48[/C][C]6.20970817622499[/C][C]0.270291823775011[/C][/ROW]
[ROW][C]61[/C][C]6.74[/C][C]6.73716603078734[/C][C]0.00283396921266199[/C][/ROW]
[ROW][C]62[/C][C]6.53[/C][C]7.15305644915515[/C][C]-0.623056449155147[/C][/ROW]
[ROW][C]63[/C][C]6.8[/C][C]6.44697905104165[/C][C]0.353020948958346[/C][/ROW]
[ROW][C]64[/C][C]6.75[/C][C]7.0491669649905[/C][C]-0.2991669649905[/C][/ROW]
[ROW][C]65[/C][C]6.56[/C][C]6.71413617678361[/C][C]-0.154136176783609[/C][/ROW]
[ROW][C]66[/C][C]6.66[/C][C]6.53552625982474[/C][C]0.124473740175263[/C][/ROW]
[ROW][C]67[/C][C]6.18[/C][C]6.26824163141441[/C][C]-0.0882416314144132[/C][/ROW]
[ROW][C]68[/C][C]6.4[/C][C]6.19330080279141[/C][C]0.206699197208589[/C][/ROW]
[ROW][C]69[/C][C]6.43[/C][C]6.44732049495923[/C][C]-0.0173204949592334[/C][/ROW]
[ROW][C]70[/C][C]6.54[/C][C]6.56364382298656[/C][C]-0.0236438229865579[/C][/ROW]
[ROW][C]71[/C][C]6.44[/C][C]6.4734637417974[/C][C]-0.0334637417973935[/C][/ROW]
[ROW][C]72[/C][C]6.64[/C][C]6.49486693738637[/C][C]0.14513306261363[/C][/ROW]
[ROW][C]73[/C][C]6.82[/C][C]6.87579663362076[/C][C]-0.0557966336207567[/C][/ROW]
[ROW][C]74[/C][C]6.97[/C][C]7.11880632914136[/C][C]-0.148806329141363[/C][/ROW]
[ROW][C]75[/C][C]7[/C][C]6.96674798593013[/C][C]0.0332520140698707[/C][/ROW]
[ROW][C]76[/C][C]6.91[/C][C]7.19331361652164[/C][C]-0.283313616521643[/C][/ROW]
[ROW][C]77[/C][C]6.74[/C][C]6.89363504515358[/C][C]-0.15363504515358[/C][/ROW]
[ROW][C]78[/C][C]6.98[/C][C]6.7661317821046[/C][C]0.213868217895395[/C][/ROW]
[ROW][C]79[/C][C]6.37[/C][C]6.50970866641909[/C][C]-0.139708666419086[/C][/ROW]
[ROW][C]80[/C][C]6.56[/C][C]6.44929702443397[/C][C]0.110702975566025[/C][/ROW]
[ROW][C]81[/C][C]6.63[/C][C]6.58383231703029[/C][C]0.0461676829697142[/C][/ROW]
[ROW][C]82[/C][C]6.87[/C][C]6.75097395552786[/C][C]0.119026044472145[/C][/ROW]
[ROW][C]83[/C][C]6.68[/C][C]6.76622330712744[/C][C]-0.0862233071274359[/C][/ROW]
[ROW][C]84[/C][C]6.75[/C][C]6.78091928977597[/C][C]-0.0309192897759702[/C][/ROW]
[ROW][C]85[/C][C]6.84[/C][C]6.98648794517266[/C][C]-0.146487945172659[/C][/ROW]
[ROW][C]86[/C][C]7.15[/C][C]7.13965760133986[/C][C]0.0103423986601392[/C][/ROW]
[ROW][C]87[/C][C]7.09[/C][C]7.14616507889787[/C][C]-0.0561650788978687[/C][/ROW]
[ROW][C]88[/C][C]6.97[/C][C]7.23992776665109[/C][C]-0.269927766651091[/C][/ROW]
[ROW][C]89[/C][C]7.15[/C][C]6.97235483920058[/C][C]0.177645160799422[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122464&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122464&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
136.276.005134714719070.264865285280932
146.686.645047572770730.0349524272292676
156.776.766836252561940.00316374743805969
166.716.705575762316130.00442423768386568
176.626.605924432614310.0140755673856905
186.56.478490964555690.0215090354443106
195.896.32768873003534-0.437688730035343
206.055.830384491645580.219615508354418
216.436.204522939793470.225477060206529
226.476.385652571456080.084347428543924
236.626.38736971614250.232630283857501
246.776.81092562846281-0.0409256284628086
256.77.0870432851245-0.387043285124504
266.957.19609101986052-0.246091019860518
276.737.09083234591805-0.36083234591805
287.076.739436620890720.330563379109281
297.286.891942951380710.388057048619291
307.327.045903022941040.274096977058964
316.766.96777018469932-0.207770184699319
326.936.768267730510680.161732269489317
336.997.12075248225123-0.130752482251235
347.166.987714007976360.172285992023641
357.287.078754333403910.201245666596092
367.087.43942399108796-0.359423991087963
377.347.40499384141914-0.0649938414191356
387.877.832875243836430.0371247561635712
396.287.93081818628042-1.65081818628042
406.36.68681723664301-0.386817236643013
416.366.288970843958730.0710291560412735
426.286.190810939038680.089189060961318
435.895.92885085405116-0.0388508540511632
446.045.927726346556130.112273653443869
455.966.16205467894051-0.202054678940506
466.16.025526694197460.0744733058025417
476.266.049574053084520.210425946915479
486.026.2937208608802-0.273720860880203
496.256.33910124086385-0.0891012408638492
506.416.69402583507748-0.284025835077483
516.226.209522124144860.0104778758551411
526.576.509798607907810.0602013920921882
536.186.54989686954732-0.369896869547321
546.266.107254186606030.152745813393966
556.15.8721009318750.227899068125004
566.026.10981784742629-0.0898178474262883
576.066.12154748840332-0.0615474884033178
586.356.148136579463590.20186342053641
596.216.29529171874476-0.0852917187447568
606.486.209708176224990.270291823775011
616.746.737166030787340.00283396921266199
626.537.15305644915515-0.623056449155147
636.86.446979051041650.353020948958346
646.757.0491669649905-0.2991669649905
656.566.71413617678361-0.154136176783609
666.666.535526259824740.124473740175263
676.186.26824163141441-0.0882416314144132
686.46.193300802791410.206699197208589
696.436.44732049495923-0.0173204949592334
706.546.56364382298656-0.0236438229865579
716.446.4734637417974-0.0334637417973935
726.646.494866937386370.14513306261363
736.826.87579663362076-0.0557966336207567
746.977.11880632914136-0.148806329141363
7576.966747985930130.0332520140698707
766.917.19331361652164-0.283313616521643
776.746.89363504515358-0.15363504515358
786.986.76613178210460.213868217895395
796.376.50970866641909-0.139708666419086
806.566.449297024433970.110702975566025
816.636.583832317030290.0461676829697142
826.876.750973955527860.119026044472145
836.686.76622330712744-0.0862233071274359
846.756.78091928977597-0.0309192897759702
856.846.98648794517266-0.146487945172659
867.157.139657601339860.0103423986601392
877.097.14616507889787-0.0561650788978687
886.977.23992776665109-0.269927766651091
897.156.972354839200580.177645160799422







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
907.177237725718196.642288936202057.71218651523433
916.667764598043955.999778048624657.33575114746325
926.767959639068425.966705057209567.56921422092729
936.801944376578325.889415281905217.71447347125144
946.94816784029625.923629262534067.97270641805833
956.826867852621075.730539822304247.9231958829379
966.92049938582775.729961638788068.11103713286734
977.131342257195295.83373766358588.42894685080478
987.440904667067916.023495838220468.85831349591536
997.42397719761135.945739750527168.90221464469544
1007.522260195232225.964855812341789.07966457812267
1017.55324235889449-9.2871591520991524.3936438698881

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
90 & 7.17723772571819 & 6.64228893620205 & 7.71218651523433 \tabularnewline
91 & 6.66776459804395 & 5.99977804862465 & 7.33575114746325 \tabularnewline
92 & 6.76795963906842 & 5.96670505720956 & 7.56921422092729 \tabularnewline
93 & 6.80194437657832 & 5.88941528190521 & 7.71447347125144 \tabularnewline
94 & 6.9481678402962 & 5.92362926253406 & 7.97270641805833 \tabularnewline
95 & 6.82686785262107 & 5.73053982230424 & 7.9231958829379 \tabularnewline
96 & 6.9204993858277 & 5.72996163878806 & 8.11103713286734 \tabularnewline
97 & 7.13134225719529 & 5.8337376635858 & 8.42894685080478 \tabularnewline
98 & 7.44090466706791 & 6.02349583822046 & 8.85831349591536 \tabularnewline
99 & 7.4239771976113 & 5.94573975052716 & 8.90221464469544 \tabularnewline
100 & 7.52226019523222 & 5.96485581234178 & 9.07966457812267 \tabularnewline
101 & 7.55324235889449 & -9.28715915209915 & 24.3936438698881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122464&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]90[/C][C]7.17723772571819[/C][C]6.64228893620205[/C][C]7.71218651523433[/C][/ROW]
[ROW][C]91[/C][C]6.66776459804395[/C][C]5.99977804862465[/C][C]7.33575114746325[/C][/ROW]
[ROW][C]92[/C][C]6.76795963906842[/C][C]5.96670505720956[/C][C]7.56921422092729[/C][/ROW]
[ROW][C]93[/C][C]6.80194437657832[/C][C]5.88941528190521[/C][C]7.71447347125144[/C][/ROW]
[ROW][C]94[/C][C]6.9481678402962[/C][C]5.92362926253406[/C][C]7.97270641805833[/C][/ROW]
[ROW][C]95[/C][C]6.82686785262107[/C][C]5.73053982230424[/C][C]7.9231958829379[/C][/ROW]
[ROW][C]96[/C][C]6.9204993858277[/C][C]5.72996163878806[/C][C]8.11103713286734[/C][/ROW]
[ROW][C]97[/C][C]7.13134225719529[/C][C]5.8337376635858[/C][C]8.42894685080478[/C][/ROW]
[ROW][C]98[/C][C]7.44090466706791[/C][C]6.02349583822046[/C][C]8.85831349591536[/C][/ROW]
[ROW][C]99[/C][C]7.4239771976113[/C][C]5.94573975052716[/C][C]8.90221464469544[/C][/ROW]
[ROW][C]100[/C][C]7.52226019523222[/C][C]5.96485581234178[/C][C]9.07966457812267[/C][/ROW]
[ROW][C]101[/C][C]7.55324235889449[/C][C]-9.28715915209915[/C][C]24.3936438698881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122464&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122464&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
907.177237725718196.642288936202057.71218651523433
916.667764598043955.999778048624657.33575114746325
926.767959639068425.966705057209567.56921422092729
936.801944376578325.889415281905217.71447347125144
946.94816784029625.923629262534067.97270641805833
956.826867852621075.730539822304247.9231958829379
966.92049938582775.729961638788068.11103713286734
977.131342257195295.83373766358588.42894685080478
987.440904667067916.023495838220468.85831349591536
997.42397719761135.945739750527168.90221464469544
1007.522260195232225.964855812341789.07966457812267
1017.55324235889449-9.2871591520991524.3936438698881



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')