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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 02 Jun 2009 13:12:36 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/02/t124397063275a4fh7l00hi0pe.htm/, Retrieved Fri, 10 May 2024 05:01:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41382, Retrieved Fri, 10 May 2024 05:01:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Opgave 10 Oefenin...] [2009-06-02 12:23:00] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [Opgave 10 Oefenin...] [2009-06-02 19:12:36] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   P       [Exponential Smoothing] [Opgave 10 Oefenin...] [2009-06-07 17:38:07] [74be16979710d4c4e7c6647856088456]
-   P       [Exponential Smoothing] [Opgave 10 Oefenin...] [2009-06-07 17:49:36] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
3779.7
3795.5
3813.1
3826.9
3833.3
3844.8
3851.3
3851.8
3854.1
3858.4
3861.6
3856.3
3855.8
3860.4
3855.1
3839.5
3833
3833.6
3826.8
3818.2
3811.4
3806.8
3810.3
3818.2
3858.9
3867.8
3872.3
3873.3
3876.7
3882.6
3883.5
3882.2
3888.1
3893.7
3901.9
3914.3
3930.3
3948.3
3971.5
3990.1
3993
3998
4015.8
4041.2
4060.7
4076.7
4103
4125.3
4139.7
4146.7
4158
4155.1
4144.8
4148.2
4142.5
4142.1
4145.4
4146.3
4143.5
4149.2
4158.9
4166.1
4179.1
4194.4
4211.7
4226.3
4235.8
4243.6
4258.7
4278.2
4298
4315.1
4334.3
4356
4374
4395.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41382&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' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41382&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41382&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' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.953329031569823
beta0.626323202133583
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.953329031569823 \tabularnewline
beta & 0.626323202133583 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41382&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]0.953329031569823[/C][/ROW]
[ROW][C]beta[/C][C]0.626323202133583[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41382&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41382&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
alpha0.953329031569823
beta0.626323202133583
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
53833.33808.7635871323524.5364128676538
63844.83861.02704115044-16.2270411504383
73851.33861.14357370245-9.84357370245107
83851.83862.39634606019-10.5963460601874
93854.13852.251562824801.84843717520471
103858.43860.20611213384-1.80611213384418
113861.63862.19267532288-0.592675322885043
123856.33865.57620559282-9.2762055928174
133855.83851.404466157494.39553384251258
143860.43857.273698273213.12630172678837
153855.13862.62068956048-7.52068956048197
163839.53853.45652546211-13.9565254621148
1738333827.143547274105.85645272589545
183833.63826.880152704646.71984729535689
193826.83829.84500527164-3.04500527163873
203818.23822.00413013856-3.80413013855605
213811.43809.720872721781.67912727821704
223806.83806.432065448890.367934551109556
233810.33800.0229112285510.2770887714491
243818.23809.933939290748.26606070926118
253858.93821.7050545191337.1949454808714
263867.83885.74113334937-17.9411333493663
273872.33884.91421961965-12.6142196196479
283873.33881.81730666609-8.517306666085
293876.73877.81418623354-1.11418623353939
303882.63878.75665534183.84334465820257
313883.53887.95911392597-4.45911392597145
323882.23886.70995606965-4.50995606964534
333888.13883.147975985954.95202401404731
343893.73889.998028116313.70197188368684
353901.93898.488584164843.41141583516492
363914.33909.252096586045.04790341396347
373930.33925.473062106114.82693789389123
383948.33942.278507219136.02149278086654
393971.53964.490163567727.0098364322821
403990.13992.44306525081-2.34306525080865
4139934010.8955595138-17.8955595138009
4239984001.77961145368-3.77961145368454
434015.84004.5381792024011.2618207976047
444041.24028.4935694447712.7064305552340
454060.74061.94174084626-1.24174084625793
464076.74080.67032043543-3.97032043543049
4741034095.15772375567.84227624440018
484125.34125.076107947880.223892052119481
494139.74147.67231163608-7.97231163608012
504146.74157.53459980018-10.8345998001769
5141584159.63123052326-1.63123052326318
524155.14168.0864119263-12.9864119262975
534144.84157.74536911135-12.9453691113495
544148.24139.808485461468.39151453854356
554142.54149.21609995201-6.71609995201106
564142.14137.814742048534.28525795147380
574145.44139.773002858375.62699714162864
584146.34147.45750214121-1.15750214120726
594143.54148.27467061052-4.77467061052266
604149.24141.614747506717.58525249329159
614158.94151.127552754967.7724472450418
624166.14166.16942031988-0.0694203198809191
634179.14174.136448422694.96355157731523
644194.44189.431577898364.9684221016405
654211.74206.98130085374.71869914629769
664226.34227.4485221859-1.14852218590022
674235.84242.69597429281-6.89597429281184
684243.64247.66840880222-4.06840880221898
694258.74252.170288404766.52971159523986
704278.24270.752109549467.44789045054404
7142984295.733488009462.26651199053958
724315.14316.84840386786-1.74840386786036
734334.34332.711340315611.58865968439295
7443564352.322304172293.67769582770507
7543744376.92782063219-2.92782063219056
764395.54393.257990345352.24200965465388

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 3833.3 & 3808.76358713235 & 24.5364128676538 \tabularnewline
6 & 3844.8 & 3861.02704115044 & -16.2270411504383 \tabularnewline
7 & 3851.3 & 3861.14357370245 & -9.84357370245107 \tabularnewline
8 & 3851.8 & 3862.39634606019 & -10.5963460601874 \tabularnewline
9 & 3854.1 & 3852.25156282480 & 1.84843717520471 \tabularnewline
10 & 3858.4 & 3860.20611213384 & -1.80611213384418 \tabularnewline
11 & 3861.6 & 3862.19267532288 & -0.592675322885043 \tabularnewline
12 & 3856.3 & 3865.57620559282 & -9.2762055928174 \tabularnewline
13 & 3855.8 & 3851.40446615749 & 4.39553384251258 \tabularnewline
14 & 3860.4 & 3857.27369827321 & 3.12630172678837 \tabularnewline
15 & 3855.1 & 3862.62068956048 & -7.52068956048197 \tabularnewline
16 & 3839.5 & 3853.45652546211 & -13.9565254621148 \tabularnewline
17 & 3833 & 3827.14354727410 & 5.85645272589545 \tabularnewline
18 & 3833.6 & 3826.88015270464 & 6.71984729535689 \tabularnewline
19 & 3826.8 & 3829.84500527164 & -3.04500527163873 \tabularnewline
20 & 3818.2 & 3822.00413013856 & -3.80413013855605 \tabularnewline
21 & 3811.4 & 3809.72087272178 & 1.67912727821704 \tabularnewline
22 & 3806.8 & 3806.43206544889 & 0.367934551109556 \tabularnewline
23 & 3810.3 & 3800.02291122855 & 10.2770887714491 \tabularnewline
24 & 3818.2 & 3809.93393929074 & 8.26606070926118 \tabularnewline
25 & 3858.9 & 3821.70505451913 & 37.1949454808714 \tabularnewline
26 & 3867.8 & 3885.74113334937 & -17.9411333493663 \tabularnewline
27 & 3872.3 & 3884.91421961965 & -12.6142196196479 \tabularnewline
28 & 3873.3 & 3881.81730666609 & -8.517306666085 \tabularnewline
29 & 3876.7 & 3877.81418623354 & -1.11418623353939 \tabularnewline
30 & 3882.6 & 3878.7566553418 & 3.84334465820257 \tabularnewline
31 & 3883.5 & 3887.95911392597 & -4.45911392597145 \tabularnewline
32 & 3882.2 & 3886.70995606965 & -4.50995606964534 \tabularnewline
33 & 3888.1 & 3883.14797598595 & 4.95202401404731 \tabularnewline
34 & 3893.7 & 3889.99802811631 & 3.70197188368684 \tabularnewline
35 & 3901.9 & 3898.48858416484 & 3.41141583516492 \tabularnewline
36 & 3914.3 & 3909.25209658604 & 5.04790341396347 \tabularnewline
37 & 3930.3 & 3925.47306210611 & 4.82693789389123 \tabularnewline
38 & 3948.3 & 3942.27850721913 & 6.02149278086654 \tabularnewline
39 & 3971.5 & 3964.49016356772 & 7.0098364322821 \tabularnewline
40 & 3990.1 & 3992.44306525081 & -2.34306525080865 \tabularnewline
41 & 3993 & 4010.8955595138 & -17.8955595138009 \tabularnewline
42 & 3998 & 4001.77961145368 & -3.77961145368454 \tabularnewline
43 & 4015.8 & 4004.53817920240 & 11.2618207976047 \tabularnewline
44 & 4041.2 & 4028.49356944477 & 12.7064305552340 \tabularnewline
45 & 4060.7 & 4061.94174084626 & -1.24174084625793 \tabularnewline
46 & 4076.7 & 4080.67032043543 & -3.97032043543049 \tabularnewline
47 & 4103 & 4095.1577237556 & 7.84227624440018 \tabularnewline
48 & 4125.3 & 4125.07610794788 & 0.223892052119481 \tabularnewline
49 & 4139.7 & 4147.67231163608 & -7.97231163608012 \tabularnewline
50 & 4146.7 & 4157.53459980018 & -10.8345998001769 \tabularnewline
51 & 4158 & 4159.63123052326 & -1.63123052326318 \tabularnewline
52 & 4155.1 & 4168.0864119263 & -12.9864119262975 \tabularnewline
53 & 4144.8 & 4157.74536911135 & -12.9453691113495 \tabularnewline
54 & 4148.2 & 4139.80848546146 & 8.39151453854356 \tabularnewline
55 & 4142.5 & 4149.21609995201 & -6.71609995201106 \tabularnewline
56 & 4142.1 & 4137.81474204853 & 4.28525795147380 \tabularnewline
57 & 4145.4 & 4139.77300285837 & 5.62699714162864 \tabularnewline
58 & 4146.3 & 4147.45750214121 & -1.15750214120726 \tabularnewline
59 & 4143.5 & 4148.27467061052 & -4.77467061052266 \tabularnewline
60 & 4149.2 & 4141.61474750671 & 7.58525249329159 \tabularnewline
61 & 4158.9 & 4151.12755275496 & 7.7724472450418 \tabularnewline
62 & 4166.1 & 4166.16942031988 & -0.0694203198809191 \tabularnewline
63 & 4179.1 & 4174.13644842269 & 4.96355157731523 \tabularnewline
64 & 4194.4 & 4189.43157789836 & 4.9684221016405 \tabularnewline
65 & 4211.7 & 4206.9813008537 & 4.71869914629769 \tabularnewline
66 & 4226.3 & 4227.4485221859 & -1.14852218590022 \tabularnewline
67 & 4235.8 & 4242.69597429281 & -6.89597429281184 \tabularnewline
68 & 4243.6 & 4247.66840880222 & -4.06840880221898 \tabularnewline
69 & 4258.7 & 4252.17028840476 & 6.52971159523986 \tabularnewline
70 & 4278.2 & 4270.75210954946 & 7.44789045054404 \tabularnewline
71 & 4298 & 4295.73348800946 & 2.26651199053958 \tabularnewline
72 & 4315.1 & 4316.84840386786 & -1.74840386786036 \tabularnewline
73 & 4334.3 & 4332.71134031561 & 1.58865968439295 \tabularnewline
74 & 4356 & 4352.32230417229 & 3.67769582770507 \tabularnewline
75 & 4374 & 4376.92782063219 & -2.92782063219056 \tabularnewline
76 & 4395.5 & 4393.25799034535 & 2.24200965465388 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41382&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]5[/C][C]3833.3[/C][C]3808.76358713235[/C][C]24.5364128676538[/C][/ROW]
[ROW][C]6[/C][C]3844.8[/C][C]3861.02704115044[/C][C]-16.2270411504383[/C][/ROW]
[ROW][C]7[/C][C]3851.3[/C][C]3861.14357370245[/C][C]-9.84357370245107[/C][/ROW]
[ROW][C]8[/C][C]3851.8[/C][C]3862.39634606019[/C][C]-10.5963460601874[/C][/ROW]
[ROW][C]9[/C][C]3854.1[/C][C]3852.25156282480[/C][C]1.84843717520471[/C][/ROW]
[ROW][C]10[/C][C]3858.4[/C][C]3860.20611213384[/C][C]-1.80611213384418[/C][/ROW]
[ROW][C]11[/C][C]3861.6[/C][C]3862.19267532288[/C][C]-0.592675322885043[/C][/ROW]
[ROW][C]12[/C][C]3856.3[/C][C]3865.57620559282[/C][C]-9.2762055928174[/C][/ROW]
[ROW][C]13[/C][C]3855.8[/C][C]3851.40446615749[/C][C]4.39553384251258[/C][/ROW]
[ROW][C]14[/C][C]3860.4[/C][C]3857.27369827321[/C][C]3.12630172678837[/C][/ROW]
[ROW][C]15[/C][C]3855.1[/C][C]3862.62068956048[/C][C]-7.52068956048197[/C][/ROW]
[ROW][C]16[/C][C]3839.5[/C][C]3853.45652546211[/C][C]-13.9565254621148[/C][/ROW]
[ROW][C]17[/C][C]3833[/C][C]3827.14354727410[/C][C]5.85645272589545[/C][/ROW]
[ROW][C]18[/C][C]3833.6[/C][C]3826.88015270464[/C][C]6.71984729535689[/C][/ROW]
[ROW][C]19[/C][C]3826.8[/C][C]3829.84500527164[/C][C]-3.04500527163873[/C][/ROW]
[ROW][C]20[/C][C]3818.2[/C][C]3822.00413013856[/C][C]-3.80413013855605[/C][/ROW]
[ROW][C]21[/C][C]3811.4[/C][C]3809.72087272178[/C][C]1.67912727821704[/C][/ROW]
[ROW][C]22[/C][C]3806.8[/C][C]3806.43206544889[/C][C]0.367934551109556[/C][/ROW]
[ROW][C]23[/C][C]3810.3[/C][C]3800.02291122855[/C][C]10.2770887714491[/C][/ROW]
[ROW][C]24[/C][C]3818.2[/C][C]3809.93393929074[/C][C]8.26606070926118[/C][/ROW]
[ROW][C]25[/C][C]3858.9[/C][C]3821.70505451913[/C][C]37.1949454808714[/C][/ROW]
[ROW][C]26[/C][C]3867.8[/C][C]3885.74113334937[/C][C]-17.9411333493663[/C][/ROW]
[ROW][C]27[/C][C]3872.3[/C][C]3884.91421961965[/C][C]-12.6142196196479[/C][/ROW]
[ROW][C]28[/C][C]3873.3[/C][C]3881.81730666609[/C][C]-8.517306666085[/C][/ROW]
[ROW][C]29[/C][C]3876.7[/C][C]3877.81418623354[/C][C]-1.11418623353939[/C][/ROW]
[ROW][C]30[/C][C]3882.6[/C][C]3878.7566553418[/C][C]3.84334465820257[/C][/ROW]
[ROW][C]31[/C][C]3883.5[/C][C]3887.95911392597[/C][C]-4.45911392597145[/C][/ROW]
[ROW][C]32[/C][C]3882.2[/C][C]3886.70995606965[/C][C]-4.50995606964534[/C][/ROW]
[ROW][C]33[/C][C]3888.1[/C][C]3883.14797598595[/C][C]4.95202401404731[/C][/ROW]
[ROW][C]34[/C][C]3893.7[/C][C]3889.99802811631[/C][C]3.70197188368684[/C][/ROW]
[ROW][C]35[/C][C]3901.9[/C][C]3898.48858416484[/C][C]3.41141583516492[/C][/ROW]
[ROW][C]36[/C][C]3914.3[/C][C]3909.25209658604[/C][C]5.04790341396347[/C][/ROW]
[ROW][C]37[/C][C]3930.3[/C][C]3925.47306210611[/C][C]4.82693789389123[/C][/ROW]
[ROW][C]38[/C][C]3948.3[/C][C]3942.27850721913[/C][C]6.02149278086654[/C][/ROW]
[ROW][C]39[/C][C]3971.5[/C][C]3964.49016356772[/C][C]7.0098364322821[/C][/ROW]
[ROW][C]40[/C][C]3990.1[/C][C]3992.44306525081[/C][C]-2.34306525080865[/C][/ROW]
[ROW][C]41[/C][C]3993[/C][C]4010.8955595138[/C][C]-17.8955595138009[/C][/ROW]
[ROW][C]42[/C][C]3998[/C][C]4001.77961145368[/C][C]-3.77961145368454[/C][/ROW]
[ROW][C]43[/C][C]4015.8[/C][C]4004.53817920240[/C][C]11.2618207976047[/C][/ROW]
[ROW][C]44[/C][C]4041.2[/C][C]4028.49356944477[/C][C]12.7064305552340[/C][/ROW]
[ROW][C]45[/C][C]4060.7[/C][C]4061.94174084626[/C][C]-1.24174084625793[/C][/ROW]
[ROW][C]46[/C][C]4076.7[/C][C]4080.67032043543[/C][C]-3.97032043543049[/C][/ROW]
[ROW][C]47[/C][C]4103[/C][C]4095.1577237556[/C][C]7.84227624440018[/C][/ROW]
[ROW][C]48[/C][C]4125.3[/C][C]4125.07610794788[/C][C]0.223892052119481[/C][/ROW]
[ROW][C]49[/C][C]4139.7[/C][C]4147.67231163608[/C][C]-7.97231163608012[/C][/ROW]
[ROW][C]50[/C][C]4146.7[/C][C]4157.53459980018[/C][C]-10.8345998001769[/C][/ROW]
[ROW][C]51[/C][C]4158[/C][C]4159.63123052326[/C][C]-1.63123052326318[/C][/ROW]
[ROW][C]52[/C][C]4155.1[/C][C]4168.0864119263[/C][C]-12.9864119262975[/C][/ROW]
[ROW][C]53[/C][C]4144.8[/C][C]4157.74536911135[/C][C]-12.9453691113495[/C][/ROW]
[ROW][C]54[/C][C]4148.2[/C][C]4139.80848546146[/C][C]8.39151453854356[/C][/ROW]
[ROW][C]55[/C][C]4142.5[/C][C]4149.21609995201[/C][C]-6.71609995201106[/C][/ROW]
[ROW][C]56[/C][C]4142.1[/C][C]4137.81474204853[/C][C]4.28525795147380[/C][/ROW]
[ROW][C]57[/C][C]4145.4[/C][C]4139.77300285837[/C][C]5.62699714162864[/C][/ROW]
[ROW][C]58[/C][C]4146.3[/C][C]4147.45750214121[/C][C]-1.15750214120726[/C][/ROW]
[ROW][C]59[/C][C]4143.5[/C][C]4148.27467061052[/C][C]-4.77467061052266[/C][/ROW]
[ROW][C]60[/C][C]4149.2[/C][C]4141.61474750671[/C][C]7.58525249329159[/C][/ROW]
[ROW][C]61[/C][C]4158.9[/C][C]4151.12755275496[/C][C]7.7724472450418[/C][/ROW]
[ROW][C]62[/C][C]4166.1[/C][C]4166.16942031988[/C][C]-0.0694203198809191[/C][/ROW]
[ROW][C]63[/C][C]4179.1[/C][C]4174.13644842269[/C][C]4.96355157731523[/C][/ROW]
[ROW][C]64[/C][C]4194.4[/C][C]4189.43157789836[/C][C]4.9684221016405[/C][/ROW]
[ROW][C]65[/C][C]4211.7[/C][C]4206.9813008537[/C][C]4.71869914629769[/C][/ROW]
[ROW][C]66[/C][C]4226.3[/C][C]4227.4485221859[/C][C]-1.14852218590022[/C][/ROW]
[ROW][C]67[/C][C]4235.8[/C][C]4242.69597429281[/C][C]-6.89597429281184[/C][/ROW]
[ROW][C]68[/C][C]4243.6[/C][C]4247.66840880222[/C][C]-4.06840880221898[/C][/ROW]
[ROW][C]69[/C][C]4258.7[/C][C]4252.17028840476[/C][C]6.52971159523986[/C][/ROW]
[ROW][C]70[/C][C]4278.2[/C][C]4270.75210954946[/C][C]7.44789045054404[/C][/ROW]
[ROW][C]71[/C][C]4298[/C][C]4295.73348800946[/C][C]2.26651199053958[/C][/ROW]
[ROW][C]72[/C][C]4315.1[/C][C]4316.84840386786[/C][C]-1.74840386786036[/C][/ROW]
[ROW][C]73[/C][C]4334.3[/C][C]4332.71134031561[/C][C]1.58865968439295[/C][/ROW]
[ROW][C]74[/C][C]4356[/C][C]4352.32230417229[/C][C]3.67769582770507[/C][/ROW]
[ROW][C]75[/C][C]4374[/C][C]4376.92782063219[/C][C]-2.92782063219056[/C][/ROW]
[ROW][C]76[/C][C]4395.5[/C][C]4393.25799034535[/C][C]2.24200965465388[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41382&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41382&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
53833.33808.7635871323524.5364128676538
63844.83861.02704115044-16.2270411504383
73851.33861.14357370245-9.84357370245107
83851.83862.39634606019-10.5963460601874
93854.13852.251562824801.84843717520471
103858.43860.20611213384-1.80611213384418
113861.63862.19267532288-0.592675322885043
123856.33865.57620559282-9.2762055928174
133855.83851.404466157494.39553384251258
143860.43857.273698273213.12630172678837
153855.13862.62068956048-7.52068956048197
163839.53853.45652546211-13.9565254621148
1738333827.143547274105.85645272589545
183833.63826.880152704646.71984729535689
193826.83829.84500527164-3.04500527163873
203818.23822.00413013856-3.80413013855605
213811.43809.720872721781.67912727821704
223806.83806.432065448890.367934551109556
233810.33800.0229112285510.2770887714491
243818.23809.933939290748.26606070926118
253858.93821.7050545191337.1949454808714
263867.83885.74113334937-17.9411333493663
273872.33884.91421961965-12.6142196196479
283873.33881.81730666609-8.517306666085
293876.73877.81418623354-1.11418623353939
303882.63878.75665534183.84334465820257
313883.53887.95911392597-4.45911392597145
323882.23886.70995606965-4.50995606964534
333888.13883.147975985954.95202401404731
343893.73889.998028116313.70197188368684
353901.93898.488584164843.41141583516492
363914.33909.252096586045.04790341396347
373930.33925.473062106114.82693789389123
383948.33942.278507219136.02149278086654
393971.53964.490163567727.0098364322821
403990.13992.44306525081-2.34306525080865
4139934010.8955595138-17.8955595138009
4239984001.77961145368-3.77961145368454
434015.84004.5381792024011.2618207976047
444041.24028.4935694447712.7064305552340
454060.74061.94174084626-1.24174084625793
464076.74080.67032043543-3.97032043543049
4741034095.15772375567.84227624440018
484125.34125.076107947880.223892052119481
494139.74147.67231163608-7.97231163608012
504146.74157.53459980018-10.8345998001769
5141584159.63123052326-1.63123052326318
524155.14168.0864119263-12.9864119262975
534144.84157.74536911135-12.9453691113495
544148.24139.808485461468.39151453854356
554142.54149.21609995201-6.71609995201106
564142.14137.814742048534.28525795147380
574145.44139.773002858375.62699714162864
584146.34147.45750214121-1.15750214120726
594143.54148.27467061052-4.77467061052266
604149.24141.614747506717.58525249329159
614158.94151.127552754967.7724472450418
624166.14166.16942031988-0.0694203198809191
634179.14174.136448422694.96355157731523
644194.44189.431577898364.9684221016405
654211.74206.98130085374.71869914629769
664226.34227.4485221859-1.14852218590022
674235.84242.69597429281-6.89597429281184
684243.64247.66840880222-4.06840880221898
694258.74252.170288404766.52971159523986
704278.24270.752109549467.44789045054404
7142984295.733488009462.26651199053958
724315.14316.84840386786-1.74840386786036
734334.34332.711340315611.58865968439295
7443564352.322304172293.67769582770507
7543744376.92782063219-2.92782063219056
764395.54393.257990345352.24200965465388







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
774415.817467838394398.241746280244433.39318939654
784435.790943752914403.366700913254468.21518659257
794456.173212994874406.41508174724505.93134424254
804476.881195318764409.83445694874543.92793368881

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 4415.81746783839 & 4398.24174628024 & 4433.39318939654 \tabularnewline
78 & 4435.79094375291 & 4403.36670091325 & 4468.21518659257 \tabularnewline
79 & 4456.17321299487 & 4406.4150817472 & 4505.93134424254 \tabularnewline
80 & 4476.88119531876 & 4409.8344569487 & 4543.92793368881 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41382&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]77[/C][C]4415.81746783839[/C][C]4398.24174628024[/C][C]4433.39318939654[/C][/ROW]
[ROW][C]78[/C][C]4435.79094375291[/C][C]4403.36670091325[/C][C]4468.21518659257[/C][/ROW]
[ROW][C]79[/C][C]4456.17321299487[/C][C]4406.4150817472[/C][C]4505.93134424254[/C][/ROW]
[ROW][C]80[/C][C]4476.88119531876[/C][C]4409.8344569487[/C][C]4543.92793368881[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41382&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41382&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
774415.817467838394398.241746280244433.39318939654
784435.790943752914403.366700913254468.21518659257
794456.173212994874406.41508174724505.93134424254
804476.881195318764409.83445694874543.92793368881



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 4 ; 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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')