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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 24 Nov 2012 17:27:08 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/24/t1353796040gqih3k61nw7d5zj.htm/, Retrieved Mon, 29 Apr 2024 01:58:02 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=192529, Retrieved Mon, 29 Apr 2024 01:58:02 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact80

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [...] [2012-11-24 22:27:08] [0ce3a3cc7b36ec2616d0d876d7c7ef2d] [Current]
- R PD      [Exponential Smoothing] [...] [2012-11-24 22:32:33] [0883bf8f4217d775edf6393676d58a73]
-   P         [Exponential Smoothing] [...] [2012-11-24 22:35:06] [0883bf8f4217d775edf6393676d58a73]
-    D      [Exponential Smoothing] [Single] [2012-12-21 11:31:18] [0604709baf8ca89a71bc0fcadc3cdffd]
- R PD        [Exponential Smoothing] [double] [2012-12-21 11:32:59] [0604709baf8ca89a71bc0fcadc3cdffd]
-   P           [Exponential Smoothing] [triple] [2012-12-21 11:34:02] [0604709baf8ca89a71bc0fcadc3cdffd]
- RMPD          [Histogram] [] [2012-12-21 13:41:38] [0604709baf8ca89a71bc0fcadc3cdffd]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1,2999
1,3074
1,3242
1,3516
1,3511
1,3419
1,3716
1,3622
1,3896
1,4227
1,4684
1,457
1,4718
1,4748
1,5527
1,5751
1,5557
1,5553
1,577
1,4975
1,437
1,3322
1,2732
1,3449
1,3239
1,2785
1,305
1,319
1,365
1,4016
1,4088
1,4268
1,4562
1,4816
1,4914
1,4614
1,4272
1,3686
1,3569
1,3406
1,2565
1,2209
1,277
1,2894
1,3067
1,3898
1,3661
1,322
1,336
1,3649
1,3999
1,4442
1,4349
1,4388
1,4264
1,4343
1,377
1,3706
1,3556
1,3179

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192529&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192529&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192529&T=0

As an alternative you can also use a QR Code:  
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'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999955974511879
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999955974511879 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192529&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]0.999955974511879[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192529&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192529&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999955974511879
betaFALSE
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21.30741.29990.00749999999999984
31.32421.307399669808840.016800330191161
41.35161.324199260357260.0274007396427371
51.35111.35159879366906-0.000498793669062358
61.34191.35110002195963-0.00920002195963465
71.37161.341900405035460.0296995949645424
81.36221.37159869246083-0.00939869246083447
91.38961.362200413782020.0273995862179766
101.42271.389598793719840.0331012062801577
111.46841.422698542703240.0457014572967638
121.4571.46839798797103-0.0113979879710344
131.47181.457000501801980.014799498198016
141.47481.471799348444870.00300065155513218
151.55271.474799867894850.0779001321051493
161.57511.552696570408660.0224034295913407
171.55571.57509901367808-0.0193990136780766
181.55531.55570085405105-0.000400854051046506
191.5771.55530001764780.0216999823522048
201.49751.57699904464768-0.0794990446476846
211.4371.49750349998425-0.0605034999842458
221.33221.43700266369612-0.10480266369612
231.27321.33220461398843-0.0590046139884255
241.34491.273202597706930.0716974022930676
251.32391.34489684348687-0.020996843486867
261.27851.32390092439628-0.0454009243962836
271.3051.278501998797860.0264980012021423
281.3191.304998833412560.0140011665874371
291.3651.318999383591810.0460006164081934
301.40161.364997974800410.0366020251995911
311.40881.401598388577970.00720161142202569
321.42681.408799682945540.018000317054458
331.45621.426799207527260.0294007924727446
341.48161.456198705615760.0254012943842399
351.49141.481598881695620.00980111830438424
361.46141.49139956850098-0.0299995685009826
371.42721.46140132074565-0.0342013207456466
381.36861.42720150572984-0.0586015057298401
391.35691.36860257995989-0.0117025799598944
401.34061.35690051521179-0.016300515211795
411.25651.34060071763814-0.084100717638139
421.22091.25650370257515-0.0356037025751452
431.2771.220901567470380.056098432529615
441.28941.276997530239120.0124024697608751
451.30671.289399453975210.017300546024785
461.38981.306699238335020.0831007616649835
471.36611.3897963414484-0.0236963414484044
481.3221.366101043243-0.0441010432429989
491.3361.322001941569960.0139980584300445
501.36491.335999383728650.028900616271355
511.39991.364898727636260.0350012723637383
521.44421.39989845905190.0443015409481007
531.43491.44419804960304-0.00929804960303504
541.43881.434900409351170.00389959064882772
551.42641.43879982831862-0.0123998283186184
561.43431.426400545908490.00789945409150561
571.3771.43429965222268-0.0572996522226776
581.37061.37700252264516-0.00640252264515828
591.35561.37060028187418-0.0150002818741848
601.31791.35560066039473-0.0377006603947314

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.3074 & 1.2999 & 0.00749999999999984 \tabularnewline
3 & 1.3242 & 1.30739966980884 & 0.016800330191161 \tabularnewline
4 & 1.3516 & 1.32419926035726 & 0.0274007396427371 \tabularnewline
5 & 1.3511 & 1.35159879366906 & -0.000498793669062358 \tabularnewline
6 & 1.3419 & 1.35110002195963 & -0.00920002195963465 \tabularnewline
7 & 1.3716 & 1.34190040503546 & 0.0296995949645424 \tabularnewline
8 & 1.3622 & 1.37159869246083 & -0.00939869246083447 \tabularnewline
9 & 1.3896 & 1.36220041378202 & 0.0273995862179766 \tabularnewline
10 & 1.4227 & 1.38959879371984 & 0.0331012062801577 \tabularnewline
11 & 1.4684 & 1.42269854270324 & 0.0457014572967638 \tabularnewline
12 & 1.457 & 1.46839798797103 & -0.0113979879710344 \tabularnewline
13 & 1.4718 & 1.45700050180198 & 0.014799498198016 \tabularnewline
14 & 1.4748 & 1.47179934844487 & 0.00300065155513218 \tabularnewline
15 & 1.5527 & 1.47479986789485 & 0.0779001321051493 \tabularnewline
16 & 1.5751 & 1.55269657040866 & 0.0224034295913407 \tabularnewline
17 & 1.5557 & 1.57509901367808 & -0.0193990136780766 \tabularnewline
18 & 1.5553 & 1.55570085405105 & -0.000400854051046506 \tabularnewline
19 & 1.577 & 1.5553000176478 & 0.0216999823522048 \tabularnewline
20 & 1.4975 & 1.57699904464768 & -0.0794990446476846 \tabularnewline
21 & 1.437 & 1.49750349998425 & -0.0605034999842458 \tabularnewline
22 & 1.3322 & 1.43700266369612 & -0.10480266369612 \tabularnewline
23 & 1.2732 & 1.33220461398843 & -0.0590046139884255 \tabularnewline
24 & 1.3449 & 1.27320259770693 & 0.0716974022930676 \tabularnewline
25 & 1.3239 & 1.34489684348687 & -0.020996843486867 \tabularnewline
26 & 1.2785 & 1.32390092439628 & -0.0454009243962836 \tabularnewline
27 & 1.305 & 1.27850199879786 & 0.0264980012021423 \tabularnewline
28 & 1.319 & 1.30499883341256 & 0.0140011665874371 \tabularnewline
29 & 1.365 & 1.31899938359181 & 0.0460006164081934 \tabularnewline
30 & 1.4016 & 1.36499797480041 & 0.0366020251995911 \tabularnewline
31 & 1.4088 & 1.40159838857797 & 0.00720161142202569 \tabularnewline
32 & 1.4268 & 1.40879968294554 & 0.018000317054458 \tabularnewline
33 & 1.4562 & 1.42679920752726 & 0.0294007924727446 \tabularnewline
34 & 1.4816 & 1.45619870561576 & 0.0254012943842399 \tabularnewline
35 & 1.4914 & 1.48159888169562 & 0.00980111830438424 \tabularnewline
36 & 1.4614 & 1.49139956850098 & -0.0299995685009826 \tabularnewline
37 & 1.4272 & 1.46140132074565 & -0.0342013207456466 \tabularnewline
38 & 1.3686 & 1.42720150572984 & -0.0586015057298401 \tabularnewline
39 & 1.3569 & 1.36860257995989 & -0.0117025799598944 \tabularnewline
40 & 1.3406 & 1.35690051521179 & -0.016300515211795 \tabularnewline
41 & 1.2565 & 1.34060071763814 & -0.084100717638139 \tabularnewline
42 & 1.2209 & 1.25650370257515 & -0.0356037025751452 \tabularnewline
43 & 1.277 & 1.22090156747038 & 0.056098432529615 \tabularnewline
44 & 1.2894 & 1.27699753023912 & 0.0124024697608751 \tabularnewline
45 & 1.3067 & 1.28939945397521 & 0.017300546024785 \tabularnewline
46 & 1.3898 & 1.30669923833502 & 0.0831007616649835 \tabularnewline
47 & 1.3661 & 1.3897963414484 & -0.0236963414484044 \tabularnewline
48 & 1.322 & 1.366101043243 & -0.0441010432429989 \tabularnewline
49 & 1.336 & 1.32200194156996 & 0.0139980584300445 \tabularnewline
50 & 1.3649 & 1.33599938372865 & 0.028900616271355 \tabularnewline
51 & 1.3999 & 1.36489872763626 & 0.0350012723637383 \tabularnewline
52 & 1.4442 & 1.3998984590519 & 0.0443015409481007 \tabularnewline
53 & 1.4349 & 1.44419804960304 & -0.00929804960303504 \tabularnewline
54 & 1.4388 & 1.43490040935117 & 0.00389959064882772 \tabularnewline
55 & 1.4264 & 1.43879982831862 & -0.0123998283186184 \tabularnewline
56 & 1.4343 & 1.42640054590849 & 0.00789945409150561 \tabularnewline
57 & 1.377 & 1.43429965222268 & -0.0572996522226776 \tabularnewline
58 & 1.3706 & 1.37700252264516 & -0.00640252264515828 \tabularnewline
59 & 1.3556 & 1.37060028187418 & -0.0150002818741848 \tabularnewline
60 & 1.3179 & 1.35560066039473 & -0.0377006603947314 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192529&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]2[/C][C]1.3074[/C][C]1.2999[/C][C]0.00749999999999984[/C][/ROW]
[ROW][C]3[/C][C]1.3242[/C][C]1.30739966980884[/C][C]0.016800330191161[/C][/ROW]
[ROW][C]4[/C][C]1.3516[/C][C]1.32419926035726[/C][C]0.0274007396427371[/C][/ROW]
[ROW][C]5[/C][C]1.3511[/C][C]1.35159879366906[/C][C]-0.000498793669062358[/C][/ROW]
[ROW][C]6[/C][C]1.3419[/C][C]1.35110002195963[/C][C]-0.00920002195963465[/C][/ROW]
[ROW][C]7[/C][C]1.3716[/C][C]1.34190040503546[/C][C]0.0296995949645424[/C][/ROW]
[ROW][C]8[/C][C]1.3622[/C][C]1.37159869246083[/C][C]-0.00939869246083447[/C][/ROW]
[ROW][C]9[/C][C]1.3896[/C][C]1.36220041378202[/C][C]0.0273995862179766[/C][/ROW]
[ROW][C]10[/C][C]1.4227[/C][C]1.38959879371984[/C][C]0.0331012062801577[/C][/ROW]
[ROW][C]11[/C][C]1.4684[/C][C]1.42269854270324[/C][C]0.0457014572967638[/C][/ROW]
[ROW][C]12[/C][C]1.457[/C][C]1.46839798797103[/C][C]-0.0113979879710344[/C][/ROW]
[ROW][C]13[/C][C]1.4718[/C][C]1.45700050180198[/C][C]0.014799498198016[/C][/ROW]
[ROW][C]14[/C][C]1.4748[/C][C]1.47179934844487[/C][C]0.00300065155513218[/C][/ROW]
[ROW][C]15[/C][C]1.5527[/C][C]1.47479986789485[/C][C]0.0779001321051493[/C][/ROW]
[ROW][C]16[/C][C]1.5751[/C][C]1.55269657040866[/C][C]0.0224034295913407[/C][/ROW]
[ROW][C]17[/C][C]1.5557[/C][C]1.57509901367808[/C][C]-0.0193990136780766[/C][/ROW]
[ROW][C]18[/C][C]1.5553[/C][C]1.55570085405105[/C][C]-0.000400854051046506[/C][/ROW]
[ROW][C]19[/C][C]1.577[/C][C]1.5553000176478[/C][C]0.0216999823522048[/C][/ROW]
[ROW][C]20[/C][C]1.4975[/C][C]1.57699904464768[/C][C]-0.0794990446476846[/C][/ROW]
[ROW][C]21[/C][C]1.437[/C][C]1.49750349998425[/C][C]-0.0605034999842458[/C][/ROW]
[ROW][C]22[/C][C]1.3322[/C][C]1.43700266369612[/C][C]-0.10480266369612[/C][/ROW]
[ROW][C]23[/C][C]1.2732[/C][C]1.33220461398843[/C][C]-0.0590046139884255[/C][/ROW]
[ROW][C]24[/C][C]1.3449[/C][C]1.27320259770693[/C][C]0.0716974022930676[/C][/ROW]
[ROW][C]25[/C][C]1.3239[/C][C]1.34489684348687[/C][C]-0.020996843486867[/C][/ROW]
[ROW][C]26[/C][C]1.2785[/C][C]1.32390092439628[/C][C]-0.0454009243962836[/C][/ROW]
[ROW][C]27[/C][C]1.305[/C][C]1.27850199879786[/C][C]0.0264980012021423[/C][/ROW]
[ROW][C]28[/C][C]1.319[/C][C]1.30499883341256[/C][C]0.0140011665874371[/C][/ROW]
[ROW][C]29[/C][C]1.365[/C][C]1.31899938359181[/C][C]0.0460006164081934[/C][/ROW]
[ROW][C]30[/C][C]1.4016[/C][C]1.36499797480041[/C][C]0.0366020251995911[/C][/ROW]
[ROW][C]31[/C][C]1.4088[/C][C]1.40159838857797[/C][C]0.00720161142202569[/C][/ROW]
[ROW][C]32[/C][C]1.4268[/C][C]1.40879968294554[/C][C]0.018000317054458[/C][/ROW]
[ROW][C]33[/C][C]1.4562[/C][C]1.42679920752726[/C][C]0.0294007924727446[/C][/ROW]
[ROW][C]34[/C][C]1.4816[/C][C]1.45619870561576[/C][C]0.0254012943842399[/C][/ROW]
[ROW][C]35[/C][C]1.4914[/C][C]1.48159888169562[/C][C]0.00980111830438424[/C][/ROW]
[ROW][C]36[/C][C]1.4614[/C][C]1.49139956850098[/C][C]-0.0299995685009826[/C][/ROW]
[ROW][C]37[/C][C]1.4272[/C][C]1.46140132074565[/C][C]-0.0342013207456466[/C][/ROW]
[ROW][C]38[/C][C]1.3686[/C][C]1.42720150572984[/C][C]-0.0586015057298401[/C][/ROW]
[ROW][C]39[/C][C]1.3569[/C][C]1.36860257995989[/C][C]-0.0117025799598944[/C][/ROW]
[ROW][C]40[/C][C]1.3406[/C][C]1.35690051521179[/C][C]-0.016300515211795[/C][/ROW]
[ROW][C]41[/C][C]1.2565[/C][C]1.34060071763814[/C][C]-0.084100717638139[/C][/ROW]
[ROW][C]42[/C][C]1.2209[/C][C]1.25650370257515[/C][C]-0.0356037025751452[/C][/ROW]
[ROW][C]43[/C][C]1.277[/C][C]1.22090156747038[/C][C]0.056098432529615[/C][/ROW]
[ROW][C]44[/C][C]1.2894[/C][C]1.27699753023912[/C][C]0.0124024697608751[/C][/ROW]
[ROW][C]45[/C][C]1.3067[/C][C]1.28939945397521[/C][C]0.017300546024785[/C][/ROW]
[ROW][C]46[/C][C]1.3898[/C][C]1.30669923833502[/C][C]0.0831007616649835[/C][/ROW]
[ROW][C]47[/C][C]1.3661[/C][C]1.3897963414484[/C][C]-0.0236963414484044[/C][/ROW]
[ROW][C]48[/C][C]1.322[/C][C]1.366101043243[/C][C]-0.0441010432429989[/C][/ROW]
[ROW][C]49[/C][C]1.336[/C][C]1.32200194156996[/C][C]0.0139980584300445[/C][/ROW]
[ROW][C]50[/C][C]1.3649[/C][C]1.33599938372865[/C][C]0.028900616271355[/C][/ROW]
[ROW][C]51[/C][C]1.3999[/C][C]1.36489872763626[/C][C]0.0350012723637383[/C][/ROW]
[ROW][C]52[/C][C]1.4442[/C][C]1.3998984590519[/C][C]0.0443015409481007[/C][/ROW]
[ROW][C]53[/C][C]1.4349[/C][C]1.44419804960304[/C][C]-0.00929804960303504[/C][/ROW]
[ROW][C]54[/C][C]1.4388[/C][C]1.43490040935117[/C][C]0.00389959064882772[/C][/ROW]
[ROW][C]55[/C][C]1.4264[/C][C]1.43879982831862[/C][C]-0.0123998283186184[/C][/ROW]
[ROW][C]56[/C][C]1.4343[/C][C]1.42640054590849[/C][C]0.00789945409150561[/C][/ROW]
[ROW][C]57[/C][C]1.377[/C][C]1.43429965222268[/C][C]-0.0572996522226776[/C][/ROW]
[ROW][C]58[/C][C]1.3706[/C][C]1.37700252264516[/C][C]-0.00640252264515828[/C][/ROW]
[ROW][C]59[/C][C]1.3556[/C][C]1.37060028187418[/C][C]-0.0150002818741848[/C][/ROW]
[ROW][C]60[/C][C]1.3179[/C][C]1.35560066039473[/C][C]-0.0377006603947314[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192529&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192529&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21.30741.29990.00749999999999984
31.32421.307399669808840.016800330191161
41.35161.324199260357260.0274007396427371
51.35111.35159879366906-0.000498793669062358
61.34191.35110002195963-0.00920002195963465
71.37161.341900405035460.0296995949645424
81.36221.37159869246083-0.00939869246083447
91.38961.362200413782020.0273995862179766
101.42271.389598793719840.0331012062801577
111.46841.422698542703240.0457014572967638
121.4571.46839798797103-0.0113979879710344
131.47181.457000501801980.014799498198016
141.47481.471799348444870.00300065155513218
151.55271.474799867894850.0779001321051493
161.57511.552696570408660.0224034295913407
171.55571.57509901367808-0.0193990136780766
181.55531.55570085405105-0.000400854051046506
191.5771.55530001764780.0216999823522048
201.49751.57699904464768-0.0794990446476846
211.4371.49750349998425-0.0605034999842458
221.33221.43700266369612-0.10480266369612
231.27321.33220461398843-0.0590046139884255
241.34491.273202597706930.0716974022930676
251.32391.34489684348687-0.020996843486867
261.27851.32390092439628-0.0454009243962836
271.3051.278501998797860.0264980012021423
281.3191.304998833412560.0140011665874371
291.3651.318999383591810.0460006164081934
301.40161.364997974800410.0366020251995911
311.40881.401598388577970.00720161142202569
321.42681.408799682945540.018000317054458
331.45621.426799207527260.0294007924727446
341.48161.456198705615760.0254012943842399
351.49141.481598881695620.00980111830438424
361.46141.49139956850098-0.0299995685009826
371.42721.46140132074565-0.0342013207456466
381.36861.42720150572984-0.0586015057298401
391.35691.36860257995989-0.0117025799598944
401.34061.35690051521179-0.016300515211795
411.25651.34060071763814-0.084100717638139
421.22091.25650370257515-0.0356037025751452
431.2771.220901567470380.056098432529615
441.28941.276997530239120.0124024697608751
451.30671.289399453975210.017300546024785
461.38981.306699238335020.0831007616649835
471.36611.3897963414484-0.0236963414484044
481.3221.366101043243-0.0441010432429989
491.3361.322001941569960.0139980584300445
501.36491.335999383728650.028900616271355
511.39991.364898727636260.0350012723637383
521.44421.39989845905190.0443015409481007
531.43491.44419804960304-0.00929804960303504
541.43881.434900409351170.00389959064882772
551.42641.43879982831862-0.0123998283186184
561.43431.426400545908490.00789945409150561
571.3771.43429965222268-0.0572996522226776
581.37061.37700252264516-0.00640252264515828
591.35561.37060028187418-0.0150002818741848
601.31791.35560066039473-0.0377006603947314






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
611.317901659789981.241107532333771.39469578724618
621.317901659789981.209300753861061.42650256571889
631.317901659789981.184894233210091.45090908636986
641.317901659789981.164318476198071.47148484338188
651.317901659789981.146190818434381.48961250114557
661.317901659789981.129802133485771.50600118609418
671.317901659789981.114731163524681.52107215605528
681.317901659789981.10070343394661.53509988563335
691.317901659789981.087528293129831.54827502645012
701.317901659789981.0750669282891.56073639129095
711.317901659789981.063214546688481.57258877289147
721.317901659789981.051889734612191.58391358496777

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 1.31790165978998 & 1.24110753233377 & 1.39469578724618 \tabularnewline
62 & 1.31790165978998 & 1.20930075386106 & 1.42650256571889 \tabularnewline
63 & 1.31790165978998 & 1.18489423321009 & 1.45090908636986 \tabularnewline
64 & 1.31790165978998 & 1.16431847619807 & 1.47148484338188 \tabularnewline
65 & 1.31790165978998 & 1.14619081843438 & 1.48961250114557 \tabularnewline
66 & 1.31790165978998 & 1.12980213348577 & 1.50600118609418 \tabularnewline
67 & 1.31790165978998 & 1.11473116352468 & 1.52107215605528 \tabularnewline
68 & 1.31790165978998 & 1.1007034339466 & 1.53509988563335 \tabularnewline
69 & 1.31790165978998 & 1.08752829312983 & 1.54827502645012 \tabularnewline
70 & 1.31790165978998 & 1.075066928289 & 1.56073639129095 \tabularnewline
71 & 1.31790165978998 & 1.06321454668848 & 1.57258877289147 \tabularnewline
72 & 1.31790165978998 & 1.05188973461219 & 1.58391358496777 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=192529&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]61[/C][C]1.31790165978998[/C][C]1.24110753233377[/C][C]1.39469578724618[/C][/ROW]
[ROW][C]62[/C][C]1.31790165978998[/C][C]1.20930075386106[/C][C]1.42650256571889[/C][/ROW]
[ROW][C]63[/C][C]1.31790165978998[/C][C]1.18489423321009[/C][C]1.45090908636986[/C][/ROW]
[ROW][C]64[/C][C]1.31790165978998[/C][C]1.16431847619807[/C][C]1.47148484338188[/C][/ROW]
[ROW][C]65[/C][C]1.31790165978998[/C][C]1.14619081843438[/C][C]1.48961250114557[/C][/ROW]
[ROW][C]66[/C][C]1.31790165978998[/C][C]1.12980213348577[/C][C]1.50600118609418[/C][/ROW]
[ROW][C]67[/C][C]1.31790165978998[/C][C]1.11473116352468[/C][C]1.52107215605528[/C][/ROW]
[ROW][C]68[/C][C]1.31790165978998[/C][C]1.1007034339466[/C][C]1.53509988563335[/C][/ROW]
[ROW][C]69[/C][C]1.31790165978998[/C][C]1.08752829312983[/C][C]1.54827502645012[/C][/ROW]
[ROW][C]70[/C][C]1.31790165978998[/C][C]1.075066928289[/C][C]1.56073639129095[/C][/ROW]
[ROW][C]71[/C][C]1.31790165978998[/C][C]1.06321454668848[/C][C]1.57258877289147[/C][/ROW]
[ROW][C]72[/C][C]1.31790165978998[/C][C]1.05188973461219[/C][C]1.58391358496777[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=192529&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=192529&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
611.317901659789981.241107532333771.39469578724618
621.317901659789981.209300753861061.42650256571889
631.317901659789981.184894233210091.45090908636986
641.317901659789981.164318476198071.47148484338188
651.317901659789981.146190818434381.48961250114557
661.317901659789981.129802133485771.50600118609418
671.317901659789981.114731163524681.52107215605528
681.317901659789981.10070343394661.53509988563335
691.317901659789981.087528293129831.54827502645012
701.317901659789981.0750669282891.56073639129095
711.317901659789981.063214546688481.57258877289147
721.317901659789981.051889734612191.58391358496777


Figures (Output of Computation)

Input Parameters & R Code

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