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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 24 Dec 2010 12:23:32 +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/2010/Dec/24/t1293193383fprtd92tj5mkwv2.htm/, Retrieved Tue, 30 Apr 2024 07:40:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114838, Retrieved Tue, 30 Apr 2024 07:40:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Aantal bezoekers ...] [2010-12-24 12:23:32] [e842a08483892f7b463fc61c717af4b4] [Current]
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Dataseries X:
 6.715 
 7.703 
 9.856 
 8.326 
 9.269 
 7.035 
 10.342 
 11.682 
 10.304 
 11.385 
 9.777 
 8.882 
 7.897 
 6.930 
 9.545 
 9.110 
 7.459 
 7.320 
 10.017 
 12.307 
 11.072 
 10.749 
 9.589 
 9.080 
 7.384 
 8.062 
 8.511 
 8.684 
 8.306 
 7.643 
 10.577 
 13.747 
 11.783 
 11.611 
 9.946 
 8.693 
 7.303 
 7.609 
 9.423 
 8.584 
 7.586 
 6.843 
 11.811 
 13.414 
 12.103 
 11.501 
 8.213 
 7.982 
 7.687 
 7.180 
 7.862 
 8.043 
 8.340 
 6.692 
 10.065 
 12.684 
 11.587 
 9.843 
 8.110 
 7.940 
 6.475 
 6.121 
 9.669 
 7.778 
 7.826 
 7.403 
 10.741 
 14.023 
 11.519 
 10.236 
 8.075 
 8.157 




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=114838&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=114838&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114838&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
alpha0.172101349199545
beta1.00695276769591e-17
gamma0.56714601229616

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.172101349199545 \tabularnewline
beta & 1.00695276769591e-17 \tabularnewline
gamma & 0.56714601229616 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114838&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]0.172101349199545[/C][/ROW]
[ROW][C]beta[/C][C]1.00695276769591e-17[/C][/ROW]
[ROW][C]gamma[/C][C]0.56714601229616[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114838&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114838&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
alpha0.172101349199545
beta1.00695276769591e-17
gamma0.56714601229616







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137.8978.04931704059829-0.152317040598291
146.937.03634972158939-0.106349721589392
159.5459.56775177353435-0.0227517735343454
169.119.11608281179655-0.00608281179655101
177.4597.49111593419692-0.0321159341969199
187.327.3389187211083-0.0189187211083066
1910.01710.2761594328646-0.259159432864589
2012.30711.54726272732830.759737272671716
2111.07210.33792785284310.734072147156912
2210.74911.5183009756294-0.769300975629413
239.5899.81339988896721-0.224399888967211
249.088.936068681166540.143931318833458
257.3847.89873391652774-0.514733916527737
268.0626.844977632430941.21702236756906
278.5119.64338633832118-1.13238633832118
288.6849.0085745054646-0.3245745054646
298.3067.316571200525190.989428799474812
307.6437.346379826127120.296620173872875
3110.57710.22512272336370.351877276636287
3213.74712.07979842645681.66720157354325
3311.78311.01458859439490.768411405605077
3411.61111.49497860819920.116021391800825
359.94610.1982952347580-0.252295234757987
368.6939.48910922139479-0.79610922139479
377.3037.9807229199573-0.677722919957302
387.6097.71204384688817-0.103043846888166
399.4239.180127378920880.242872621079121
408.5849.16129896664135-0.577298966641346
417.5868.04277778851734-0.456777788517337
426.8437.49839134998603-0.655391349986029
4311.81110.23923716740631.57176283259374
4413.41412.92145342590840.4925465740916
4512.10311.23206647089140.870933529108557
4611.50111.42377785283040.0772221471695875
478.2139.94747790242363-1.73447790242363
487.9828.72786414919892-0.745864149198918
497.6877.28371212759890.403287872401103
507.187.47091094812189-0.290910948121889
517.8629.06908371574186-1.20708371574186
528.0438.41561297133932-0.372612971339322
538.347.388907973048690.951092026951311
546.6926.9935609331211-0.301560933121097
5510.06510.8410381222180-0.776038122217965
5612.68412.61246009441430.0715399055856949
5711.58711.02828491450930.55871508549069
589.84310.7935843004140-0.950584300414015
598.118.28973288608468-0.179732886084679
607.947.801885974531540.13811402546846
616.4757.04943996131487-0.574439961314871
626.1216.74241679207219-0.621416792072193
639.6697.853529829579831.81547017042017
647.7788.11206159500171-0.334061595001715
657.8267.713523015605430.112476984394566
667.4036.585679253081830.81732074691817
6710.74110.40293174550170.338068254498262
6814.02312.76406422249521.25893577750484
6911.51911.6129894248065-0.0939894248065176
7010.23610.5572819280311-0.321281928031121
718.0758.52367942579023-0.448679425790234
728.1578.138788105877940.0182118941220626

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7.897 & 8.04931704059829 & -0.152317040598291 \tabularnewline
14 & 6.93 & 7.03634972158939 & -0.106349721589392 \tabularnewline
15 & 9.545 & 9.56775177353435 & -0.0227517735343454 \tabularnewline
16 & 9.11 & 9.11608281179655 & -0.00608281179655101 \tabularnewline
17 & 7.459 & 7.49111593419692 & -0.0321159341969199 \tabularnewline
18 & 7.32 & 7.3389187211083 & -0.0189187211083066 \tabularnewline
19 & 10.017 & 10.2761594328646 & -0.259159432864589 \tabularnewline
20 & 12.307 & 11.5472627273283 & 0.759737272671716 \tabularnewline
21 & 11.072 & 10.3379278528431 & 0.734072147156912 \tabularnewline
22 & 10.749 & 11.5183009756294 & -0.769300975629413 \tabularnewline
23 & 9.589 & 9.81339988896721 & -0.224399888967211 \tabularnewline
24 & 9.08 & 8.93606868116654 & 0.143931318833458 \tabularnewline
25 & 7.384 & 7.89873391652774 & -0.514733916527737 \tabularnewline
26 & 8.062 & 6.84497763243094 & 1.21702236756906 \tabularnewline
27 & 8.511 & 9.64338633832118 & -1.13238633832118 \tabularnewline
28 & 8.684 & 9.0085745054646 & -0.3245745054646 \tabularnewline
29 & 8.306 & 7.31657120052519 & 0.989428799474812 \tabularnewline
30 & 7.643 & 7.34637982612712 & 0.296620173872875 \tabularnewline
31 & 10.577 & 10.2251227233637 & 0.351877276636287 \tabularnewline
32 & 13.747 & 12.0797984264568 & 1.66720157354325 \tabularnewline
33 & 11.783 & 11.0145885943949 & 0.768411405605077 \tabularnewline
34 & 11.611 & 11.4949786081992 & 0.116021391800825 \tabularnewline
35 & 9.946 & 10.1982952347580 & -0.252295234757987 \tabularnewline
36 & 8.693 & 9.48910922139479 & -0.79610922139479 \tabularnewline
37 & 7.303 & 7.9807229199573 & -0.677722919957302 \tabularnewline
38 & 7.609 & 7.71204384688817 & -0.103043846888166 \tabularnewline
39 & 9.423 & 9.18012737892088 & 0.242872621079121 \tabularnewline
40 & 8.584 & 9.16129896664135 & -0.577298966641346 \tabularnewline
41 & 7.586 & 8.04277778851734 & -0.456777788517337 \tabularnewline
42 & 6.843 & 7.49839134998603 & -0.655391349986029 \tabularnewline
43 & 11.811 & 10.2392371674063 & 1.57176283259374 \tabularnewline
44 & 13.414 & 12.9214534259084 & 0.4925465740916 \tabularnewline
45 & 12.103 & 11.2320664708914 & 0.870933529108557 \tabularnewline
46 & 11.501 & 11.4237778528304 & 0.0772221471695875 \tabularnewline
47 & 8.213 & 9.94747790242363 & -1.73447790242363 \tabularnewline
48 & 7.982 & 8.72786414919892 & -0.745864149198918 \tabularnewline
49 & 7.687 & 7.2837121275989 & 0.403287872401103 \tabularnewline
50 & 7.18 & 7.47091094812189 & -0.290910948121889 \tabularnewline
51 & 7.862 & 9.06908371574186 & -1.20708371574186 \tabularnewline
52 & 8.043 & 8.41561297133932 & -0.372612971339322 \tabularnewline
53 & 8.34 & 7.38890797304869 & 0.951092026951311 \tabularnewline
54 & 6.692 & 6.9935609331211 & -0.301560933121097 \tabularnewline
55 & 10.065 & 10.8410381222180 & -0.776038122217965 \tabularnewline
56 & 12.684 & 12.6124600944143 & 0.0715399055856949 \tabularnewline
57 & 11.587 & 11.0282849145093 & 0.55871508549069 \tabularnewline
58 & 9.843 & 10.7935843004140 & -0.950584300414015 \tabularnewline
59 & 8.11 & 8.28973288608468 & -0.179732886084679 \tabularnewline
60 & 7.94 & 7.80188597453154 & 0.13811402546846 \tabularnewline
61 & 6.475 & 7.04943996131487 & -0.574439961314871 \tabularnewline
62 & 6.121 & 6.74241679207219 & -0.621416792072193 \tabularnewline
63 & 9.669 & 7.85352982957983 & 1.81547017042017 \tabularnewline
64 & 7.778 & 8.11206159500171 & -0.334061595001715 \tabularnewline
65 & 7.826 & 7.71352301560543 & 0.112476984394566 \tabularnewline
66 & 7.403 & 6.58567925308183 & 0.81732074691817 \tabularnewline
67 & 10.741 & 10.4029317455017 & 0.338068254498262 \tabularnewline
68 & 14.023 & 12.7640642224952 & 1.25893577750484 \tabularnewline
69 & 11.519 & 11.6129894248065 & -0.0939894248065176 \tabularnewline
70 & 10.236 & 10.5572819280311 & -0.321281928031121 \tabularnewline
71 & 8.075 & 8.52367942579023 & -0.448679425790234 \tabularnewline
72 & 8.157 & 8.13878810587794 & 0.0182118941220626 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114838&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]7.897[/C][C]8.04931704059829[/C][C]-0.152317040598291[/C][/ROW]
[ROW][C]14[/C][C]6.93[/C][C]7.03634972158939[/C][C]-0.106349721589392[/C][/ROW]
[ROW][C]15[/C][C]9.545[/C][C]9.56775177353435[/C][C]-0.0227517735343454[/C][/ROW]
[ROW][C]16[/C][C]9.11[/C][C]9.11608281179655[/C][C]-0.00608281179655101[/C][/ROW]
[ROW][C]17[/C][C]7.459[/C][C]7.49111593419692[/C][C]-0.0321159341969199[/C][/ROW]
[ROW][C]18[/C][C]7.32[/C][C]7.3389187211083[/C][C]-0.0189187211083066[/C][/ROW]
[ROW][C]19[/C][C]10.017[/C][C]10.2761594328646[/C][C]-0.259159432864589[/C][/ROW]
[ROW][C]20[/C][C]12.307[/C][C]11.5472627273283[/C][C]0.759737272671716[/C][/ROW]
[ROW][C]21[/C][C]11.072[/C][C]10.3379278528431[/C][C]0.734072147156912[/C][/ROW]
[ROW][C]22[/C][C]10.749[/C][C]11.5183009756294[/C][C]-0.769300975629413[/C][/ROW]
[ROW][C]23[/C][C]9.589[/C][C]9.81339988896721[/C][C]-0.224399888967211[/C][/ROW]
[ROW][C]24[/C][C]9.08[/C][C]8.93606868116654[/C][C]0.143931318833458[/C][/ROW]
[ROW][C]25[/C][C]7.384[/C][C]7.89873391652774[/C][C]-0.514733916527737[/C][/ROW]
[ROW][C]26[/C][C]8.062[/C][C]6.84497763243094[/C][C]1.21702236756906[/C][/ROW]
[ROW][C]27[/C][C]8.511[/C][C]9.64338633832118[/C][C]-1.13238633832118[/C][/ROW]
[ROW][C]28[/C][C]8.684[/C][C]9.0085745054646[/C][C]-0.3245745054646[/C][/ROW]
[ROW][C]29[/C][C]8.306[/C][C]7.31657120052519[/C][C]0.989428799474812[/C][/ROW]
[ROW][C]30[/C][C]7.643[/C][C]7.34637982612712[/C][C]0.296620173872875[/C][/ROW]
[ROW][C]31[/C][C]10.577[/C][C]10.2251227233637[/C][C]0.351877276636287[/C][/ROW]
[ROW][C]32[/C][C]13.747[/C][C]12.0797984264568[/C][C]1.66720157354325[/C][/ROW]
[ROW][C]33[/C][C]11.783[/C][C]11.0145885943949[/C][C]0.768411405605077[/C][/ROW]
[ROW][C]34[/C][C]11.611[/C][C]11.4949786081992[/C][C]0.116021391800825[/C][/ROW]
[ROW][C]35[/C][C]9.946[/C][C]10.1982952347580[/C][C]-0.252295234757987[/C][/ROW]
[ROW][C]36[/C][C]8.693[/C][C]9.48910922139479[/C][C]-0.79610922139479[/C][/ROW]
[ROW][C]37[/C][C]7.303[/C][C]7.9807229199573[/C][C]-0.677722919957302[/C][/ROW]
[ROW][C]38[/C][C]7.609[/C][C]7.71204384688817[/C][C]-0.103043846888166[/C][/ROW]
[ROW][C]39[/C][C]9.423[/C][C]9.18012737892088[/C][C]0.242872621079121[/C][/ROW]
[ROW][C]40[/C][C]8.584[/C][C]9.16129896664135[/C][C]-0.577298966641346[/C][/ROW]
[ROW][C]41[/C][C]7.586[/C][C]8.04277778851734[/C][C]-0.456777788517337[/C][/ROW]
[ROW][C]42[/C][C]6.843[/C][C]7.49839134998603[/C][C]-0.655391349986029[/C][/ROW]
[ROW][C]43[/C][C]11.811[/C][C]10.2392371674063[/C][C]1.57176283259374[/C][/ROW]
[ROW][C]44[/C][C]13.414[/C][C]12.9214534259084[/C][C]0.4925465740916[/C][/ROW]
[ROW][C]45[/C][C]12.103[/C][C]11.2320664708914[/C][C]0.870933529108557[/C][/ROW]
[ROW][C]46[/C][C]11.501[/C][C]11.4237778528304[/C][C]0.0772221471695875[/C][/ROW]
[ROW][C]47[/C][C]8.213[/C][C]9.94747790242363[/C][C]-1.73447790242363[/C][/ROW]
[ROW][C]48[/C][C]7.982[/C][C]8.72786414919892[/C][C]-0.745864149198918[/C][/ROW]
[ROW][C]49[/C][C]7.687[/C][C]7.2837121275989[/C][C]0.403287872401103[/C][/ROW]
[ROW][C]50[/C][C]7.18[/C][C]7.47091094812189[/C][C]-0.290910948121889[/C][/ROW]
[ROW][C]51[/C][C]7.862[/C][C]9.06908371574186[/C][C]-1.20708371574186[/C][/ROW]
[ROW][C]52[/C][C]8.043[/C][C]8.41561297133932[/C][C]-0.372612971339322[/C][/ROW]
[ROW][C]53[/C][C]8.34[/C][C]7.38890797304869[/C][C]0.951092026951311[/C][/ROW]
[ROW][C]54[/C][C]6.692[/C][C]6.9935609331211[/C][C]-0.301560933121097[/C][/ROW]
[ROW][C]55[/C][C]10.065[/C][C]10.8410381222180[/C][C]-0.776038122217965[/C][/ROW]
[ROW][C]56[/C][C]12.684[/C][C]12.6124600944143[/C][C]0.0715399055856949[/C][/ROW]
[ROW][C]57[/C][C]11.587[/C][C]11.0282849145093[/C][C]0.55871508549069[/C][/ROW]
[ROW][C]58[/C][C]9.843[/C][C]10.7935843004140[/C][C]-0.950584300414015[/C][/ROW]
[ROW][C]59[/C][C]8.11[/C][C]8.28973288608468[/C][C]-0.179732886084679[/C][/ROW]
[ROW][C]60[/C][C]7.94[/C][C]7.80188597453154[/C][C]0.13811402546846[/C][/ROW]
[ROW][C]61[/C][C]6.475[/C][C]7.04943996131487[/C][C]-0.574439961314871[/C][/ROW]
[ROW][C]62[/C][C]6.121[/C][C]6.74241679207219[/C][C]-0.621416792072193[/C][/ROW]
[ROW][C]63[/C][C]9.669[/C][C]7.85352982957983[/C][C]1.81547017042017[/C][/ROW]
[ROW][C]64[/C][C]7.778[/C][C]8.11206159500171[/C][C]-0.334061595001715[/C][/ROW]
[ROW][C]65[/C][C]7.826[/C][C]7.71352301560543[/C][C]0.112476984394566[/C][/ROW]
[ROW][C]66[/C][C]7.403[/C][C]6.58567925308183[/C][C]0.81732074691817[/C][/ROW]
[ROW][C]67[/C][C]10.741[/C][C]10.4029317455017[/C][C]0.338068254498262[/C][/ROW]
[ROW][C]68[/C][C]14.023[/C][C]12.7640642224952[/C][C]1.25893577750484[/C][/ROW]
[ROW][C]69[/C][C]11.519[/C][C]11.6129894248065[/C][C]-0.0939894248065176[/C][/ROW]
[ROW][C]70[/C][C]10.236[/C][C]10.5572819280311[/C][C]-0.321281928031121[/C][/ROW]
[ROW][C]71[/C][C]8.075[/C][C]8.52367942579023[/C][C]-0.448679425790234[/C][/ROW]
[ROW][C]72[/C][C]8.157[/C][C]8.13878810587794[/C][C]0.0182118941220626[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114838&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114838&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
137.8978.04931704059829-0.152317040598291
146.937.03634972158939-0.106349721589392
159.5459.56775177353435-0.0227517735343454
169.119.11608281179655-0.00608281179655101
177.4597.49111593419692-0.0321159341969199
187.327.3389187211083-0.0189187211083066
1910.01710.2761594328646-0.259159432864589
2012.30711.54726272732830.759737272671716
2111.07210.33792785284310.734072147156912
2210.74911.5183009756294-0.769300975629413
239.5899.81339988896721-0.224399888967211
249.088.936068681166540.143931318833458
257.3847.89873391652774-0.514733916527737
268.0626.844977632430941.21702236756906
278.5119.64338633832118-1.13238633832118
288.6849.0085745054646-0.3245745054646
298.3067.316571200525190.989428799474812
307.6437.346379826127120.296620173872875
3110.57710.22512272336370.351877276636287
3213.74712.07979842645681.66720157354325
3311.78311.01458859439490.768411405605077
3411.61111.49497860819920.116021391800825
359.94610.1982952347580-0.252295234757987
368.6939.48910922139479-0.79610922139479
377.3037.9807229199573-0.677722919957302
387.6097.71204384688817-0.103043846888166
399.4239.180127378920880.242872621079121
408.5849.16129896664135-0.577298966641346
417.5868.04277778851734-0.456777788517337
426.8437.49839134998603-0.655391349986029
4311.81110.23923716740631.57176283259374
4413.41412.92145342590840.4925465740916
4512.10311.23206647089140.870933529108557
4611.50111.42377785283040.0772221471695875
478.2139.94747790242363-1.73447790242363
487.9828.72786414919892-0.745864149198918
497.6877.28371212759890.403287872401103
507.187.47091094812189-0.290910948121889
517.8629.06908371574186-1.20708371574186
528.0438.41561297133932-0.372612971339322
538.347.388907973048690.951092026951311
546.6926.9935609331211-0.301560933121097
5510.06510.8410381222180-0.776038122217965
5612.68412.61246009441430.0715399055856949
5711.58711.02828491450930.55871508549069
589.84310.7935843004140-0.950584300414015
598.118.28973288608468-0.179732886084679
607.947.801885974531540.13811402546846
616.4757.04943996131487-0.574439961314871
626.1216.74241679207219-0.621416792072193
639.6697.853529829579831.81547017042017
647.7788.11206159500171-0.334061595001715
657.8267.713523015605430.112476984394566
667.4036.585679253081830.81732074691817
6710.74110.40293174550170.338068254498262
6814.02312.76406422249521.25893577750484
6911.51911.6129894248065-0.0939894248065176
7010.23610.5572819280311-0.321281928031121
718.0758.52367942579023-0.448679425790234
728.1578.138788105877940.0182118941220626







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
737.031134589561185.625366134962718.43690304415965
746.800915838903475.374480659268178.22735101853877
759.163190031785157.7163833081837510.6099967553866
768.099987036505946.633091651955559.56688242105633
777.968608373182236.481895743595649.45532100276882
787.152359100199365.646089928792978.65862827160575
7910.60392165279469.0783466167880512.1294966888011
8013.339255728231211.794616105457214.8838953510051
8111.33626467206429.772792914084412.8997364300439
8210.19001009234078.6079303498000811.7720898348813
838.151882496385646.551411101603969.75235389116732
848.063433389811416.444779300985939.68208747863689

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 7.03113458956118 & 5.62536613496271 & 8.43690304415965 \tabularnewline
74 & 6.80091583890347 & 5.37448065926817 & 8.22735101853877 \tabularnewline
75 & 9.16319003178515 & 7.71638330818375 & 10.6099967553866 \tabularnewline
76 & 8.09998703650594 & 6.63309165195555 & 9.56688242105633 \tabularnewline
77 & 7.96860837318223 & 6.48189574359564 & 9.45532100276882 \tabularnewline
78 & 7.15235910019936 & 5.64608992879297 & 8.65862827160575 \tabularnewline
79 & 10.6039216527946 & 9.07834661678805 & 12.1294966888011 \tabularnewline
80 & 13.3392557282312 & 11.7946161054572 & 14.8838953510051 \tabularnewline
81 & 11.3362646720642 & 9.7727929140844 & 12.8997364300439 \tabularnewline
82 & 10.1900100923407 & 8.60793034980008 & 11.7720898348813 \tabularnewline
83 & 8.15188249638564 & 6.55141110160396 & 9.75235389116732 \tabularnewline
84 & 8.06343338981141 & 6.44477930098593 & 9.68208747863689 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114838&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]7.03113458956118[/C][C]5.62536613496271[/C][C]8.43690304415965[/C][/ROW]
[ROW][C]74[/C][C]6.80091583890347[/C][C]5.37448065926817[/C][C]8.22735101853877[/C][/ROW]
[ROW][C]75[/C][C]9.16319003178515[/C][C]7.71638330818375[/C][C]10.6099967553866[/C][/ROW]
[ROW][C]76[/C][C]8.09998703650594[/C][C]6.63309165195555[/C][C]9.56688242105633[/C][/ROW]
[ROW][C]77[/C][C]7.96860837318223[/C][C]6.48189574359564[/C][C]9.45532100276882[/C][/ROW]
[ROW][C]78[/C][C]7.15235910019936[/C][C]5.64608992879297[/C][C]8.65862827160575[/C][/ROW]
[ROW][C]79[/C][C]10.6039216527946[/C][C]9.07834661678805[/C][C]12.1294966888011[/C][/ROW]
[ROW][C]80[/C][C]13.3392557282312[/C][C]11.7946161054572[/C][C]14.8838953510051[/C][/ROW]
[ROW][C]81[/C][C]11.3362646720642[/C][C]9.7727929140844[/C][C]12.8997364300439[/C][/ROW]
[ROW][C]82[/C][C]10.1900100923407[/C][C]8.60793034980008[/C][C]11.7720898348813[/C][/ROW]
[ROW][C]83[/C][C]8.15188249638564[/C][C]6.55141110160396[/C][C]9.75235389116732[/C][/ROW]
[ROW][C]84[/C][C]8.06343338981141[/C][C]6.44477930098593[/C][C]9.68208747863689[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114838&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114838&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
737.031134589561185.625366134962718.43690304415965
746.800915838903475.374480659268178.22735101853877
759.163190031785157.7163833081837510.6099967553866
768.099987036505946.633091651955559.56688242105633
777.968608373182236.481895743595649.45532100276882
787.152359100199365.646089928792978.65862827160575
7910.60392165279469.0783466167880512.1294966888011
8013.339255728231211.794616105457214.8838953510051
8111.33626467206429.772792914084412.8997364300439
8210.19001009234078.6079303498000811.7720898348813
838.151882496385646.551411101603969.75235389116732
848.063433389811416.444779300985939.68208747863689



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')