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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 06:23:00 -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/t1243945617c3shpjb71jj8wyq.htm/, Retrieved Fri, 10 May 2024 13:04:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41207, Retrieved Fri, 10 May 2024 13:04:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact125
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] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   PD    [Exponential Smoothing] [Opgave 10 Oefenin...] [2009-06-02 19:12:36] [74be16979710d4c4e7c6647856088456]
-   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 time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41207&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41207&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41207&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.892317039957039
beta0.637835382133787
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.892317039957039 \tabularnewline
beta & 0.637835382133787 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41207&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]0.892317039957039[/C][/ROW]
[ROW][C]beta[/C][C]0.637835382133787[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41207&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41207&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
alpha0.892317039957039
beta0.637835382133787
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133855.83849.530093874086.26990612591726
143860.43864.82369864823-4.42369864822604
153855.13858.91748719337-3.81748719336747
163839.53841.8247905871-2.32479058710305
1738333834.19969985771-1.19969985770558
183833.63833.433643147850.166356852148510
193826.83840.93065989168-14.1306598916790
203818.23811.003264130817.19673586919407
213811.43807.420245370093.97975462991508
223806.83807.36773811876-0.567738118757461
233810.33803.582276883316.71772311669474
243818.23802.7181819395715.4818180604279
253858.93824.8922684274334.0077315725721
263867.83887.21966999135-19.4196699913455
273872.33882.88471468827-10.5847146882652
283873.33870.867095599542.4329044004603
293876.73881.29822741484-4.59822741484231
303882.63889.48576212567-6.88576212567432
313883.53897.06539473905-13.5653947390542
323882.23877.996791390124.20320860987795
333888.13877.7511786362710.3488213637256
343893.73892.947572239020.752427760975479
353901.93901.98838317014-0.0883831701371491
363914.33902.8022242026211.4977757973820
373930.33928.115218635622.18478136437625
383948.33942.793507388775.5064926112309
393971.53962.314364045759.18563595424848
403990.13980.989048348679.11095165133156
4139934012.23183109414-19.2318310941419
4239984014.61995026851-16.6199502685085
434015.84014.904390351630.895609648369827
444041.24020.6751481352120.5248518647863
454060.74054.920281507155.77971849284768
464076.74081.77150743348-5.07150743348393
4741034099.12638643333.87361356669680
484125.34120.267194726265.03280527374227
494139.74150.96422013967-11.2642201396657
504146.74158.38153890182-11.6815389018202
5141584157.497209183010.502790816988636
524155.14157.58286774021-2.48286774021199
534144.84158.25524055099-13.4552405509930
544148.24152.60315481844-4.40315481843663
554142.54159.38170602198-16.8817060219781
564142.14134.579999455947.52000054405744
574145.44131.3165853596514.0834146403540
584146.34144.89582931941.40417068059924
594143.54153.23768022431-9.73768022430613
604149.24138.7665828693310.4334171306718
614158.94152.035400781096.86459921891128
624166.14165.402959220010.697040779987219
634179.14173.741277220545.35872277946328
644194.44177.4100184224816.9899815775198
654211.74204.896546883036.80345311696783
664226.34240.63916135374-14.3391613537424
674235.84254.0367061512-18.2367061512032
684243.64246.60749624002-3.0074962400231
694258.74244.455250007114.2447499928994
704278.24266.7173205261211.4826794738838
7142984298.66598326539-0.665983265386785
724315.14315.30603415217-0.206034152173743
734334.34333.536283599730.763716400270823
7443564352.126273234573.87372676542873
7543744376.9981395221-2.99813952209843
764395.54382.358716474613.1412835254023

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3855.8 & 3849.53009387408 & 6.26990612591726 \tabularnewline
14 & 3860.4 & 3864.82369864823 & -4.42369864822604 \tabularnewline
15 & 3855.1 & 3858.91748719337 & -3.81748719336747 \tabularnewline
16 & 3839.5 & 3841.8247905871 & -2.32479058710305 \tabularnewline
17 & 3833 & 3834.19969985771 & -1.19969985770558 \tabularnewline
18 & 3833.6 & 3833.43364314785 & 0.166356852148510 \tabularnewline
19 & 3826.8 & 3840.93065989168 & -14.1306598916790 \tabularnewline
20 & 3818.2 & 3811.00326413081 & 7.19673586919407 \tabularnewline
21 & 3811.4 & 3807.42024537009 & 3.97975462991508 \tabularnewline
22 & 3806.8 & 3807.36773811876 & -0.567738118757461 \tabularnewline
23 & 3810.3 & 3803.58227688331 & 6.71772311669474 \tabularnewline
24 & 3818.2 & 3802.71818193957 & 15.4818180604279 \tabularnewline
25 & 3858.9 & 3824.89226842743 & 34.0077315725721 \tabularnewline
26 & 3867.8 & 3887.21966999135 & -19.4196699913455 \tabularnewline
27 & 3872.3 & 3882.88471468827 & -10.5847146882652 \tabularnewline
28 & 3873.3 & 3870.86709559954 & 2.4329044004603 \tabularnewline
29 & 3876.7 & 3881.29822741484 & -4.59822741484231 \tabularnewline
30 & 3882.6 & 3889.48576212567 & -6.88576212567432 \tabularnewline
31 & 3883.5 & 3897.06539473905 & -13.5653947390542 \tabularnewline
32 & 3882.2 & 3877.99679139012 & 4.20320860987795 \tabularnewline
33 & 3888.1 & 3877.75117863627 & 10.3488213637256 \tabularnewline
34 & 3893.7 & 3892.94757223902 & 0.752427760975479 \tabularnewline
35 & 3901.9 & 3901.98838317014 & -0.0883831701371491 \tabularnewline
36 & 3914.3 & 3902.80222420262 & 11.4977757973820 \tabularnewline
37 & 3930.3 & 3928.11521863562 & 2.18478136437625 \tabularnewline
38 & 3948.3 & 3942.79350738877 & 5.5064926112309 \tabularnewline
39 & 3971.5 & 3962.31436404575 & 9.18563595424848 \tabularnewline
40 & 3990.1 & 3980.98904834867 & 9.11095165133156 \tabularnewline
41 & 3993 & 4012.23183109414 & -19.2318310941419 \tabularnewline
42 & 3998 & 4014.61995026851 & -16.6199502685085 \tabularnewline
43 & 4015.8 & 4014.90439035163 & 0.895609648369827 \tabularnewline
44 & 4041.2 & 4020.67514813521 & 20.5248518647863 \tabularnewline
45 & 4060.7 & 4054.92028150715 & 5.77971849284768 \tabularnewline
46 & 4076.7 & 4081.77150743348 & -5.07150743348393 \tabularnewline
47 & 4103 & 4099.1263864333 & 3.87361356669680 \tabularnewline
48 & 4125.3 & 4120.26719472626 & 5.03280527374227 \tabularnewline
49 & 4139.7 & 4150.96422013967 & -11.2642201396657 \tabularnewline
50 & 4146.7 & 4158.38153890182 & -11.6815389018202 \tabularnewline
51 & 4158 & 4157.49720918301 & 0.502790816988636 \tabularnewline
52 & 4155.1 & 4157.58286774021 & -2.48286774021199 \tabularnewline
53 & 4144.8 & 4158.25524055099 & -13.4552405509930 \tabularnewline
54 & 4148.2 & 4152.60315481844 & -4.40315481843663 \tabularnewline
55 & 4142.5 & 4159.38170602198 & -16.8817060219781 \tabularnewline
56 & 4142.1 & 4134.57999945594 & 7.52000054405744 \tabularnewline
57 & 4145.4 & 4131.31658535965 & 14.0834146403540 \tabularnewline
58 & 4146.3 & 4144.8958293194 & 1.40417068059924 \tabularnewline
59 & 4143.5 & 4153.23768022431 & -9.73768022430613 \tabularnewline
60 & 4149.2 & 4138.76658286933 & 10.4334171306718 \tabularnewline
61 & 4158.9 & 4152.03540078109 & 6.86459921891128 \tabularnewline
62 & 4166.1 & 4165.40295922001 & 0.697040779987219 \tabularnewline
63 & 4179.1 & 4173.74127722054 & 5.35872277946328 \tabularnewline
64 & 4194.4 & 4177.41001842248 & 16.9899815775198 \tabularnewline
65 & 4211.7 & 4204.89654688303 & 6.80345311696783 \tabularnewline
66 & 4226.3 & 4240.63916135374 & -14.3391613537424 \tabularnewline
67 & 4235.8 & 4254.0367061512 & -18.2367061512032 \tabularnewline
68 & 4243.6 & 4246.60749624002 & -3.0074962400231 \tabularnewline
69 & 4258.7 & 4244.4552500071 & 14.2447499928994 \tabularnewline
70 & 4278.2 & 4266.71732052612 & 11.4826794738838 \tabularnewline
71 & 4298 & 4298.66598326539 & -0.665983265386785 \tabularnewline
72 & 4315.1 & 4315.30603415217 & -0.206034152173743 \tabularnewline
73 & 4334.3 & 4333.53628359973 & 0.763716400270823 \tabularnewline
74 & 4356 & 4352.12627323457 & 3.87372676542873 \tabularnewline
75 & 4374 & 4376.9981395221 & -2.99813952209843 \tabularnewline
76 & 4395.5 & 4382.3587164746 & 13.1412835254023 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41207&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]3855.8[/C][C]3849.53009387408[/C][C]6.26990612591726[/C][/ROW]
[ROW][C]14[/C][C]3860.4[/C][C]3864.82369864823[/C][C]-4.42369864822604[/C][/ROW]
[ROW][C]15[/C][C]3855.1[/C][C]3858.91748719337[/C][C]-3.81748719336747[/C][/ROW]
[ROW][C]16[/C][C]3839.5[/C][C]3841.8247905871[/C][C]-2.32479058710305[/C][/ROW]
[ROW][C]17[/C][C]3833[/C][C]3834.19969985771[/C][C]-1.19969985770558[/C][/ROW]
[ROW][C]18[/C][C]3833.6[/C][C]3833.43364314785[/C][C]0.166356852148510[/C][/ROW]
[ROW][C]19[/C][C]3826.8[/C][C]3840.93065989168[/C][C]-14.1306598916790[/C][/ROW]
[ROW][C]20[/C][C]3818.2[/C][C]3811.00326413081[/C][C]7.19673586919407[/C][/ROW]
[ROW][C]21[/C][C]3811.4[/C][C]3807.42024537009[/C][C]3.97975462991508[/C][/ROW]
[ROW][C]22[/C][C]3806.8[/C][C]3807.36773811876[/C][C]-0.567738118757461[/C][/ROW]
[ROW][C]23[/C][C]3810.3[/C][C]3803.58227688331[/C][C]6.71772311669474[/C][/ROW]
[ROW][C]24[/C][C]3818.2[/C][C]3802.71818193957[/C][C]15.4818180604279[/C][/ROW]
[ROW][C]25[/C][C]3858.9[/C][C]3824.89226842743[/C][C]34.0077315725721[/C][/ROW]
[ROW][C]26[/C][C]3867.8[/C][C]3887.21966999135[/C][C]-19.4196699913455[/C][/ROW]
[ROW][C]27[/C][C]3872.3[/C][C]3882.88471468827[/C][C]-10.5847146882652[/C][/ROW]
[ROW][C]28[/C][C]3873.3[/C][C]3870.86709559954[/C][C]2.4329044004603[/C][/ROW]
[ROW][C]29[/C][C]3876.7[/C][C]3881.29822741484[/C][C]-4.59822741484231[/C][/ROW]
[ROW][C]30[/C][C]3882.6[/C][C]3889.48576212567[/C][C]-6.88576212567432[/C][/ROW]
[ROW][C]31[/C][C]3883.5[/C][C]3897.06539473905[/C][C]-13.5653947390542[/C][/ROW]
[ROW][C]32[/C][C]3882.2[/C][C]3877.99679139012[/C][C]4.20320860987795[/C][/ROW]
[ROW][C]33[/C][C]3888.1[/C][C]3877.75117863627[/C][C]10.3488213637256[/C][/ROW]
[ROW][C]34[/C][C]3893.7[/C][C]3892.94757223902[/C][C]0.752427760975479[/C][/ROW]
[ROW][C]35[/C][C]3901.9[/C][C]3901.98838317014[/C][C]-0.0883831701371491[/C][/ROW]
[ROW][C]36[/C][C]3914.3[/C][C]3902.80222420262[/C][C]11.4977757973820[/C][/ROW]
[ROW][C]37[/C][C]3930.3[/C][C]3928.11521863562[/C][C]2.18478136437625[/C][/ROW]
[ROW][C]38[/C][C]3948.3[/C][C]3942.79350738877[/C][C]5.5064926112309[/C][/ROW]
[ROW][C]39[/C][C]3971.5[/C][C]3962.31436404575[/C][C]9.18563595424848[/C][/ROW]
[ROW][C]40[/C][C]3990.1[/C][C]3980.98904834867[/C][C]9.11095165133156[/C][/ROW]
[ROW][C]41[/C][C]3993[/C][C]4012.23183109414[/C][C]-19.2318310941419[/C][/ROW]
[ROW][C]42[/C][C]3998[/C][C]4014.61995026851[/C][C]-16.6199502685085[/C][/ROW]
[ROW][C]43[/C][C]4015.8[/C][C]4014.90439035163[/C][C]0.895609648369827[/C][/ROW]
[ROW][C]44[/C][C]4041.2[/C][C]4020.67514813521[/C][C]20.5248518647863[/C][/ROW]
[ROW][C]45[/C][C]4060.7[/C][C]4054.92028150715[/C][C]5.77971849284768[/C][/ROW]
[ROW][C]46[/C][C]4076.7[/C][C]4081.77150743348[/C][C]-5.07150743348393[/C][/ROW]
[ROW][C]47[/C][C]4103[/C][C]4099.1263864333[/C][C]3.87361356669680[/C][/ROW]
[ROW][C]48[/C][C]4125.3[/C][C]4120.26719472626[/C][C]5.03280527374227[/C][/ROW]
[ROW][C]49[/C][C]4139.7[/C][C]4150.96422013967[/C][C]-11.2642201396657[/C][/ROW]
[ROW][C]50[/C][C]4146.7[/C][C]4158.38153890182[/C][C]-11.6815389018202[/C][/ROW]
[ROW][C]51[/C][C]4158[/C][C]4157.49720918301[/C][C]0.502790816988636[/C][/ROW]
[ROW][C]52[/C][C]4155.1[/C][C]4157.58286774021[/C][C]-2.48286774021199[/C][/ROW]
[ROW][C]53[/C][C]4144.8[/C][C]4158.25524055099[/C][C]-13.4552405509930[/C][/ROW]
[ROW][C]54[/C][C]4148.2[/C][C]4152.60315481844[/C][C]-4.40315481843663[/C][/ROW]
[ROW][C]55[/C][C]4142.5[/C][C]4159.38170602198[/C][C]-16.8817060219781[/C][/ROW]
[ROW][C]56[/C][C]4142.1[/C][C]4134.57999945594[/C][C]7.52000054405744[/C][/ROW]
[ROW][C]57[/C][C]4145.4[/C][C]4131.31658535965[/C][C]14.0834146403540[/C][/ROW]
[ROW][C]58[/C][C]4146.3[/C][C]4144.8958293194[/C][C]1.40417068059924[/C][/ROW]
[ROW][C]59[/C][C]4143.5[/C][C]4153.23768022431[/C][C]-9.73768022430613[/C][/ROW]
[ROW][C]60[/C][C]4149.2[/C][C]4138.76658286933[/C][C]10.4334171306718[/C][/ROW]
[ROW][C]61[/C][C]4158.9[/C][C]4152.03540078109[/C][C]6.86459921891128[/C][/ROW]
[ROW][C]62[/C][C]4166.1[/C][C]4165.40295922001[/C][C]0.697040779987219[/C][/ROW]
[ROW][C]63[/C][C]4179.1[/C][C]4173.74127722054[/C][C]5.35872277946328[/C][/ROW]
[ROW][C]64[/C][C]4194.4[/C][C]4177.41001842248[/C][C]16.9899815775198[/C][/ROW]
[ROW][C]65[/C][C]4211.7[/C][C]4204.89654688303[/C][C]6.80345311696783[/C][/ROW]
[ROW][C]66[/C][C]4226.3[/C][C]4240.63916135374[/C][C]-14.3391613537424[/C][/ROW]
[ROW][C]67[/C][C]4235.8[/C][C]4254.0367061512[/C][C]-18.2367061512032[/C][/ROW]
[ROW][C]68[/C][C]4243.6[/C][C]4246.60749624002[/C][C]-3.0074962400231[/C][/ROW]
[ROW][C]69[/C][C]4258.7[/C][C]4244.4552500071[/C][C]14.2447499928994[/C][/ROW]
[ROW][C]70[/C][C]4278.2[/C][C]4266.71732052612[/C][C]11.4826794738838[/C][/ROW]
[ROW][C]71[/C][C]4298[/C][C]4298.66598326539[/C][C]-0.665983265386785[/C][/ROW]
[ROW][C]72[/C][C]4315.1[/C][C]4315.30603415217[/C][C]-0.206034152173743[/C][/ROW]
[ROW][C]73[/C][C]4334.3[/C][C]4333.53628359973[/C][C]0.763716400270823[/C][/ROW]
[ROW][C]74[/C][C]4356[/C][C]4352.12627323457[/C][C]3.87372676542873[/C][/ROW]
[ROW][C]75[/C][C]4374[/C][C]4376.9981395221[/C][C]-2.99813952209843[/C][/ROW]
[ROW][C]76[/C][C]4395.5[/C][C]4382.3587164746[/C][C]13.1412835254023[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41207&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41207&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
133855.83849.530093874086.26990612591726
143860.43864.82369864823-4.42369864822604
153855.13858.91748719337-3.81748719336747
163839.53841.8247905871-2.32479058710305
1738333834.19969985771-1.19969985770558
183833.63833.433643147850.166356852148510
193826.83840.93065989168-14.1306598916790
203818.23811.003264130817.19673586919407
213811.43807.420245370093.97975462991508
223806.83807.36773811876-0.567738118757461
233810.33803.582276883316.71772311669474
243818.23802.7181819395715.4818180604279
253858.93824.8922684274334.0077315725721
263867.83887.21966999135-19.4196699913455
273872.33882.88471468827-10.5847146882652
283873.33870.867095599542.4329044004603
293876.73881.29822741484-4.59822741484231
303882.63889.48576212567-6.88576212567432
313883.53897.06539473905-13.5653947390542
323882.23877.996791390124.20320860987795
333888.13877.7511786362710.3488213637256
343893.73892.947572239020.752427760975479
353901.93901.98838317014-0.0883831701371491
363914.33902.8022242026211.4977757973820
373930.33928.115218635622.18478136437625
383948.33942.793507388775.5064926112309
393971.53962.314364045759.18563595424848
403990.13980.989048348679.11095165133156
4139934012.23183109414-19.2318310941419
4239984014.61995026851-16.6199502685085
434015.84014.904390351630.895609648369827
444041.24020.6751481352120.5248518647863
454060.74054.920281507155.77971849284768
464076.74081.77150743348-5.07150743348393
4741034099.12638643333.87361356669680
484125.34120.267194726265.03280527374227
494139.74150.96422013967-11.2642201396657
504146.74158.38153890182-11.6815389018202
5141584157.497209183010.502790816988636
524155.14157.58286774021-2.48286774021199
534144.84158.25524055099-13.4552405509930
544148.24152.60315481844-4.40315481843663
554142.54159.38170602198-16.8817060219781
564142.14134.579999455947.52000054405744
574145.44131.3165853596514.0834146403540
584146.34144.89582931941.40417068059924
594143.54153.23768022431-9.73768022430613
604149.24138.7665828693310.4334171306718
614158.94152.035400781096.86459921891128
624166.14165.402959220010.697040779987219
634179.14173.741277220545.35872277946328
644194.44177.4100184224816.9899815775198
654211.74204.896546883036.80345311696783
664226.34240.63916135374-14.3391613537424
674235.84254.0367061512-18.2367061512032
684243.64246.60749624002-3.0074962400231
694258.74244.455250007114.2447499928994
704278.24266.7173205261211.4826794738838
7142984298.66598326539-0.665983265386785
724315.14315.30603415217-0.206034152173743
734334.34333.536283599730.763716400270823
7443564352.126273234573.87372676542873
7543744376.9981395221-2.99813952209843
764395.54382.358716474613.1412835254023







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
774411.069167595034390.65248805974431.48584713037
784440.927948296454404.751746308544477.10415028436
794477.687528592774422.537319758644532.83773742690
804509.34927027154432.644540739594586.0539998034
814534.246720712744433.813401196114634.68004022937
824557.809576420294431.638863473404683.98028936718
834586.28155767484432.339155288694740.2239600609
844611.841934618194428.439030750324795.24483848606
854638.847751150044424.251858225334853.44364407474
864665.095018198834417.747703285214912.44233311245
874691.58591079274409.958031145624973.21379043979
884708.198321442784392.155772222945024.24087066262

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 4411.06916759503 & 4390.6524880597 & 4431.48584713037 \tabularnewline
78 & 4440.92794829645 & 4404.75174630854 & 4477.10415028436 \tabularnewline
79 & 4477.68752859277 & 4422.53731975864 & 4532.83773742690 \tabularnewline
80 & 4509.3492702715 & 4432.64454073959 & 4586.0539998034 \tabularnewline
81 & 4534.24672071274 & 4433.81340119611 & 4634.68004022937 \tabularnewline
82 & 4557.80957642029 & 4431.63886347340 & 4683.98028936718 \tabularnewline
83 & 4586.2815576748 & 4432.33915528869 & 4740.2239600609 \tabularnewline
84 & 4611.84193461819 & 4428.43903075032 & 4795.24483848606 \tabularnewline
85 & 4638.84775115004 & 4424.25185822533 & 4853.44364407474 \tabularnewline
86 & 4665.09501819883 & 4417.74770328521 & 4912.44233311245 \tabularnewline
87 & 4691.5859107927 & 4409.95803114562 & 4973.21379043979 \tabularnewline
88 & 4708.19832144278 & 4392.15577222294 & 5024.24087066262 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41207&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]4411.06916759503[/C][C]4390.6524880597[/C][C]4431.48584713037[/C][/ROW]
[ROW][C]78[/C][C]4440.92794829645[/C][C]4404.75174630854[/C][C]4477.10415028436[/C][/ROW]
[ROW][C]79[/C][C]4477.68752859277[/C][C]4422.53731975864[/C][C]4532.83773742690[/C][/ROW]
[ROW][C]80[/C][C]4509.3492702715[/C][C]4432.64454073959[/C][C]4586.0539998034[/C][/ROW]
[ROW][C]81[/C][C]4534.24672071274[/C][C]4433.81340119611[/C][C]4634.68004022937[/C][/ROW]
[ROW][C]82[/C][C]4557.80957642029[/C][C]4431.63886347340[/C][C]4683.98028936718[/C][/ROW]
[ROW][C]83[/C][C]4586.2815576748[/C][C]4432.33915528869[/C][C]4740.2239600609[/C][/ROW]
[ROW][C]84[/C][C]4611.84193461819[/C][C]4428.43903075032[/C][C]4795.24483848606[/C][/ROW]
[ROW][C]85[/C][C]4638.84775115004[/C][C]4424.25185822533[/C][C]4853.44364407474[/C][/ROW]
[ROW][C]86[/C][C]4665.09501819883[/C][C]4417.74770328521[/C][C]4912.44233311245[/C][/ROW]
[ROW][C]87[/C][C]4691.5859107927[/C][C]4409.95803114562[/C][C]4973.21379043979[/C][/ROW]
[ROW][C]88[/C][C]4708.19832144278[/C][C]4392.15577222294[/C][C]5024.24087066262[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41207&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41207&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
774411.069167595034390.65248805974431.48584713037
784440.927948296454404.751746308544477.10415028436
794477.687528592774422.537319758644532.83773742690
804509.34927027154432.644540739594586.0539998034
814534.246720712744433.813401196114634.68004022937
824557.809576420294431.638863473404683.98028936718
834586.28155767484432.339155288694740.2239600609
844611.841934618194428.439030750324795.24483848606
854638.847751150044424.251858225334853.44364407474
864665.095018198834417.747703285214912.44233311245
874691.58591079274409.958031145624973.21379043979
884708.198321442784392.155772222945024.24087066262



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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=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')