Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 30 Mar 2015 16:25:22 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Mar/30/t1427729154hf85z1qlka38a5k.htm/, Retrieved Sun, 19 May 2024 16:13:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278478, Retrieved Sun, 19 May 2024 16:13:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2015-03-30 15:25:22] [cab9dc260884be88f444bea8f40c034b] [Current]
Feedback Forum

Post a new message
Dataseries X:
3862,5
3875,7
3875,9
3877,7
3880,4
3883,4
3884,2
3884,8
3894,9
3903,3
3911,2
3928,9
3945,6
3965,7
3992,3
4008,7
4014,8
4020,6
4037,5
4058,5
4082,3
4102,4
4127,1
4144,4
4161
4168,2
4178,3
4174,1
4165,7
4167,9
4158,3
4158,3
4143,7
4157,5
4164,8
4173,9
4181,2
4190,7
4206,6
4222,1
4245,8
4255,4
4266,1
4273,6
4282,1
4299,8
4315,7
4331,7
4348,4
4367,8
4387,2
4410,9
4436
4453,8
4469,1
4472
4458,2
4449
4441,5
4445,7
4453,9
4469,7
4487,5
4504
4524,1
4540,5
4548,4
4554,2
4558
4557,5
4554,5
4550
4543,8
4538,2
4543,3
4545,1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278478&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278478&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278478&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.940293640001814
beta0.476406700857692
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.940293640001814 \tabularnewline
beta & 0.476406700857692 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278478&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]0.940293640001814[/C][/ROW]
[ROW][C]beta[/C][C]0.476406700857692[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278478&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278478&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
alpha0.940293640001814
beta0.476406700857692
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133945.63881.8219551282163.7780448717936
143965.73989.60669081012-23.9066908101181
153992.34009.31190027998-17.0119002799847
164008.74016.62121598085-7.92121598085168
174014.84017.44253904631-2.64253904631369
184020.64021.06027754697-0.460277546965699
194037.54042.94046238459-5.4404623845935
204058.54046.8465229775511.653477022453
214082.34080.158723175762.14127682423668
224102.44102.077539749290.322460250712538
234127.14121.180584666775.91941533322824
244144.44157.73975177974-13.3397517797357
2541614172.23439701882-11.2343970188203
264168.24176.51198421248-8.31198421248064
274178.34190.54020883024-12.2402088302379
284174.14184.26437354967-10.1643735496673
294165.74163.672076852942.02792314705493
304167.94154.2843430650313.6156569349732
314158.34177.88080423786-19.5808042378585
324158.34151.955183076046.34481692396093
334143.74159.77344094627-16.0734409462739
344157.54136.3626702990521.1373297009504
354164.84156.602443885138.19755611487017
364173.94176.40482394886-2.50482394886239
374181.24188.31781042319-7.11781042319399
384190.74185.589384029325.11061597067965
394206.64206.96577121064-0.365771210641469
404222.14212.26015073469.83984926539961
414245.84220.4476067224125.3523932775861
424255.44253.374017542892.02598245710669
434266.14278.5894379656-12.4894379656034
444273.64278.55506816292-4.95506816291709
454282.14287.02304238232-4.92304238231554
464299.84293.927036230175.87296376982795
474315.74309.811774001615.88822599839386
484331.74336.53975007788-4.83975007788104
494348.44354.6718816985-6.27188169849614
504367.84362.538021584055.26197841595331
514387.24392.86659346927-5.66659346927099
524410.94400.5482507382310.3517492617702
5344364417.1348191695318.8651808304712
544453.84446.654162997587.14583700241928
554469.14482.19614112361-13.0961411236067
5644724488.14841587392-16.1484158739177
574458.24487.18634588736-28.9863458873588
5844494462.42198587839-13.4219858783854
594441.54441.83493570294-0.334935702941948
604445.74440.953262098594.74673790140878
614453.94451.190862277452.70913772255426
624469.74455.3904617930814.3095382069241
634487.54484.826875449612.67312455039155
6445044496.295575914447.70442408556119
654524.14504.7041481886119.3958518113886
664540.54528.0634405976812.4365594023247
674548.44563.78240150609-15.3824015060936
684554.24562.78924672628-8.589246726282
6945584566.94129809644-8.94129809644073
704557.54569.70667259968-12.2066725996765
714554.54559.34038057787-4.84038057786711
7245504560.80403176681-10.8040317668065
734543.84555.60988531034-11.8098853103402
744538.24539.65818500007-1.45818500007226
754543.34539.318424575573.98157542442914
764545.14538.648873847686.45112615232301

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3945.6 & 3881.82195512821 & 63.7780448717936 \tabularnewline
14 & 3965.7 & 3989.60669081012 & -23.9066908101181 \tabularnewline
15 & 3992.3 & 4009.31190027998 & -17.0119002799847 \tabularnewline
16 & 4008.7 & 4016.62121598085 & -7.92121598085168 \tabularnewline
17 & 4014.8 & 4017.44253904631 & -2.64253904631369 \tabularnewline
18 & 4020.6 & 4021.06027754697 & -0.460277546965699 \tabularnewline
19 & 4037.5 & 4042.94046238459 & -5.4404623845935 \tabularnewline
20 & 4058.5 & 4046.84652297755 & 11.653477022453 \tabularnewline
21 & 4082.3 & 4080.15872317576 & 2.14127682423668 \tabularnewline
22 & 4102.4 & 4102.07753974929 & 0.322460250712538 \tabularnewline
23 & 4127.1 & 4121.18058466677 & 5.91941533322824 \tabularnewline
24 & 4144.4 & 4157.73975177974 & -13.3397517797357 \tabularnewline
25 & 4161 & 4172.23439701882 & -11.2343970188203 \tabularnewline
26 & 4168.2 & 4176.51198421248 & -8.31198421248064 \tabularnewline
27 & 4178.3 & 4190.54020883024 & -12.2402088302379 \tabularnewline
28 & 4174.1 & 4184.26437354967 & -10.1643735496673 \tabularnewline
29 & 4165.7 & 4163.67207685294 & 2.02792314705493 \tabularnewline
30 & 4167.9 & 4154.28434306503 & 13.6156569349732 \tabularnewline
31 & 4158.3 & 4177.88080423786 & -19.5808042378585 \tabularnewline
32 & 4158.3 & 4151.95518307604 & 6.34481692396093 \tabularnewline
33 & 4143.7 & 4159.77344094627 & -16.0734409462739 \tabularnewline
34 & 4157.5 & 4136.36267029905 & 21.1373297009504 \tabularnewline
35 & 4164.8 & 4156.60244388513 & 8.19755611487017 \tabularnewline
36 & 4173.9 & 4176.40482394886 & -2.50482394886239 \tabularnewline
37 & 4181.2 & 4188.31781042319 & -7.11781042319399 \tabularnewline
38 & 4190.7 & 4185.58938402932 & 5.11061597067965 \tabularnewline
39 & 4206.6 & 4206.96577121064 & -0.365771210641469 \tabularnewline
40 & 4222.1 & 4212.2601507346 & 9.83984926539961 \tabularnewline
41 & 4245.8 & 4220.44760672241 & 25.3523932775861 \tabularnewline
42 & 4255.4 & 4253.37401754289 & 2.02598245710669 \tabularnewline
43 & 4266.1 & 4278.5894379656 & -12.4894379656034 \tabularnewline
44 & 4273.6 & 4278.55506816292 & -4.95506816291709 \tabularnewline
45 & 4282.1 & 4287.02304238232 & -4.92304238231554 \tabularnewline
46 & 4299.8 & 4293.92703623017 & 5.87296376982795 \tabularnewline
47 & 4315.7 & 4309.81177400161 & 5.88822599839386 \tabularnewline
48 & 4331.7 & 4336.53975007788 & -4.83975007788104 \tabularnewline
49 & 4348.4 & 4354.6718816985 & -6.27188169849614 \tabularnewline
50 & 4367.8 & 4362.53802158405 & 5.26197841595331 \tabularnewline
51 & 4387.2 & 4392.86659346927 & -5.66659346927099 \tabularnewline
52 & 4410.9 & 4400.54825073823 & 10.3517492617702 \tabularnewline
53 & 4436 & 4417.13481916953 & 18.8651808304712 \tabularnewline
54 & 4453.8 & 4446.65416299758 & 7.14583700241928 \tabularnewline
55 & 4469.1 & 4482.19614112361 & -13.0961411236067 \tabularnewline
56 & 4472 & 4488.14841587392 & -16.1484158739177 \tabularnewline
57 & 4458.2 & 4487.18634588736 & -28.9863458873588 \tabularnewline
58 & 4449 & 4462.42198587839 & -13.4219858783854 \tabularnewline
59 & 4441.5 & 4441.83493570294 & -0.334935702941948 \tabularnewline
60 & 4445.7 & 4440.95326209859 & 4.74673790140878 \tabularnewline
61 & 4453.9 & 4451.19086227745 & 2.70913772255426 \tabularnewline
62 & 4469.7 & 4455.39046179308 & 14.3095382069241 \tabularnewline
63 & 4487.5 & 4484.82687544961 & 2.67312455039155 \tabularnewline
64 & 4504 & 4496.29557591444 & 7.70442408556119 \tabularnewline
65 & 4524.1 & 4504.70414818861 & 19.3958518113886 \tabularnewline
66 & 4540.5 & 4528.06344059768 & 12.4365594023247 \tabularnewline
67 & 4548.4 & 4563.78240150609 & -15.3824015060936 \tabularnewline
68 & 4554.2 & 4562.78924672628 & -8.589246726282 \tabularnewline
69 & 4558 & 4566.94129809644 & -8.94129809644073 \tabularnewline
70 & 4557.5 & 4569.70667259968 & -12.2066725996765 \tabularnewline
71 & 4554.5 & 4559.34038057787 & -4.84038057786711 \tabularnewline
72 & 4550 & 4560.80403176681 & -10.8040317668065 \tabularnewline
73 & 4543.8 & 4555.60988531034 & -11.8098853103402 \tabularnewline
74 & 4538.2 & 4539.65818500007 & -1.45818500007226 \tabularnewline
75 & 4543.3 & 4539.31842457557 & 3.98157542442914 \tabularnewline
76 & 4545.1 & 4538.64887384768 & 6.45112615232301 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278478&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]3945.6[/C][C]3881.82195512821[/C][C]63.7780448717936[/C][/ROW]
[ROW][C]14[/C][C]3965.7[/C][C]3989.60669081012[/C][C]-23.9066908101181[/C][/ROW]
[ROW][C]15[/C][C]3992.3[/C][C]4009.31190027998[/C][C]-17.0119002799847[/C][/ROW]
[ROW][C]16[/C][C]4008.7[/C][C]4016.62121598085[/C][C]-7.92121598085168[/C][/ROW]
[ROW][C]17[/C][C]4014.8[/C][C]4017.44253904631[/C][C]-2.64253904631369[/C][/ROW]
[ROW][C]18[/C][C]4020.6[/C][C]4021.06027754697[/C][C]-0.460277546965699[/C][/ROW]
[ROW][C]19[/C][C]4037.5[/C][C]4042.94046238459[/C][C]-5.4404623845935[/C][/ROW]
[ROW][C]20[/C][C]4058.5[/C][C]4046.84652297755[/C][C]11.653477022453[/C][/ROW]
[ROW][C]21[/C][C]4082.3[/C][C]4080.15872317576[/C][C]2.14127682423668[/C][/ROW]
[ROW][C]22[/C][C]4102.4[/C][C]4102.07753974929[/C][C]0.322460250712538[/C][/ROW]
[ROW][C]23[/C][C]4127.1[/C][C]4121.18058466677[/C][C]5.91941533322824[/C][/ROW]
[ROW][C]24[/C][C]4144.4[/C][C]4157.73975177974[/C][C]-13.3397517797357[/C][/ROW]
[ROW][C]25[/C][C]4161[/C][C]4172.23439701882[/C][C]-11.2343970188203[/C][/ROW]
[ROW][C]26[/C][C]4168.2[/C][C]4176.51198421248[/C][C]-8.31198421248064[/C][/ROW]
[ROW][C]27[/C][C]4178.3[/C][C]4190.54020883024[/C][C]-12.2402088302379[/C][/ROW]
[ROW][C]28[/C][C]4174.1[/C][C]4184.26437354967[/C][C]-10.1643735496673[/C][/ROW]
[ROW][C]29[/C][C]4165.7[/C][C]4163.67207685294[/C][C]2.02792314705493[/C][/ROW]
[ROW][C]30[/C][C]4167.9[/C][C]4154.28434306503[/C][C]13.6156569349732[/C][/ROW]
[ROW][C]31[/C][C]4158.3[/C][C]4177.88080423786[/C][C]-19.5808042378585[/C][/ROW]
[ROW][C]32[/C][C]4158.3[/C][C]4151.95518307604[/C][C]6.34481692396093[/C][/ROW]
[ROW][C]33[/C][C]4143.7[/C][C]4159.77344094627[/C][C]-16.0734409462739[/C][/ROW]
[ROW][C]34[/C][C]4157.5[/C][C]4136.36267029905[/C][C]21.1373297009504[/C][/ROW]
[ROW][C]35[/C][C]4164.8[/C][C]4156.60244388513[/C][C]8.19755611487017[/C][/ROW]
[ROW][C]36[/C][C]4173.9[/C][C]4176.40482394886[/C][C]-2.50482394886239[/C][/ROW]
[ROW][C]37[/C][C]4181.2[/C][C]4188.31781042319[/C][C]-7.11781042319399[/C][/ROW]
[ROW][C]38[/C][C]4190.7[/C][C]4185.58938402932[/C][C]5.11061597067965[/C][/ROW]
[ROW][C]39[/C][C]4206.6[/C][C]4206.96577121064[/C][C]-0.365771210641469[/C][/ROW]
[ROW][C]40[/C][C]4222.1[/C][C]4212.2601507346[/C][C]9.83984926539961[/C][/ROW]
[ROW][C]41[/C][C]4245.8[/C][C]4220.44760672241[/C][C]25.3523932775861[/C][/ROW]
[ROW][C]42[/C][C]4255.4[/C][C]4253.37401754289[/C][C]2.02598245710669[/C][/ROW]
[ROW][C]43[/C][C]4266.1[/C][C]4278.5894379656[/C][C]-12.4894379656034[/C][/ROW]
[ROW][C]44[/C][C]4273.6[/C][C]4278.55506816292[/C][C]-4.95506816291709[/C][/ROW]
[ROW][C]45[/C][C]4282.1[/C][C]4287.02304238232[/C][C]-4.92304238231554[/C][/ROW]
[ROW][C]46[/C][C]4299.8[/C][C]4293.92703623017[/C][C]5.87296376982795[/C][/ROW]
[ROW][C]47[/C][C]4315.7[/C][C]4309.81177400161[/C][C]5.88822599839386[/C][/ROW]
[ROW][C]48[/C][C]4331.7[/C][C]4336.53975007788[/C][C]-4.83975007788104[/C][/ROW]
[ROW][C]49[/C][C]4348.4[/C][C]4354.6718816985[/C][C]-6.27188169849614[/C][/ROW]
[ROW][C]50[/C][C]4367.8[/C][C]4362.53802158405[/C][C]5.26197841595331[/C][/ROW]
[ROW][C]51[/C][C]4387.2[/C][C]4392.86659346927[/C][C]-5.66659346927099[/C][/ROW]
[ROW][C]52[/C][C]4410.9[/C][C]4400.54825073823[/C][C]10.3517492617702[/C][/ROW]
[ROW][C]53[/C][C]4436[/C][C]4417.13481916953[/C][C]18.8651808304712[/C][/ROW]
[ROW][C]54[/C][C]4453.8[/C][C]4446.65416299758[/C][C]7.14583700241928[/C][/ROW]
[ROW][C]55[/C][C]4469.1[/C][C]4482.19614112361[/C][C]-13.0961411236067[/C][/ROW]
[ROW][C]56[/C][C]4472[/C][C]4488.14841587392[/C][C]-16.1484158739177[/C][/ROW]
[ROW][C]57[/C][C]4458.2[/C][C]4487.18634588736[/C][C]-28.9863458873588[/C][/ROW]
[ROW][C]58[/C][C]4449[/C][C]4462.42198587839[/C][C]-13.4219858783854[/C][/ROW]
[ROW][C]59[/C][C]4441.5[/C][C]4441.83493570294[/C][C]-0.334935702941948[/C][/ROW]
[ROW][C]60[/C][C]4445.7[/C][C]4440.95326209859[/C][C]4.74673790140878[/C][/ROW]
[ROW][C]61[/C][C]4453.9[/C][C]4451.19086227745[/C][C]2.70913772255426[/C][/ROW]
[ROW][C]62[/C][C]4469.7[/C][C]4455.39046179308[/C][C]14.3095382069241[/C][/ROW]
[ROW][C]63[/C][C]4487.5[/C][C]4484.82687544961[/C][C]2.67312455039155[/C][/ROW]
[ROW][C]64[/C][C]4504[/C][C]4496.29557591444[/C][C]7.70442408556119[/C][/ROW]
[ROW][C]65[/C][C]4524.1[/C][C]4504.70414818861[/C][C]19.3958518113886[/C][/ROW]
[ROW][C]66[/C][C]4540.5[/C][C]4528.06344059768[/C][C]12.4365594023247[/C][/ROW]
[ROW][C]67[/C][C]4548.4[/C][C]4563.78240150609[/C][C]-15.3824015060936[/C][/ROW]
[ROW][C]68[/C][C]4554.2[/C][C]4562.78924672628[/C][C]-8.589246726282[/C][/ROW]
[ROW][C]69[/C][C]4558[/C][C]4566.94129809644[/C][C]-8.94129809644073[/C][/ROW]
[ROW][C]70[/C][C]4557.5[/C][C]4569.70667259968[/C][C]-12.2066725996765[/C][/ROW]
[ROW][C]71[/C][C]4554.5[/C][C]4559.34038057787[/C][C]-4.84038057786711[/C][/ROW]
[ROW][C]72[/C][C]4550[/C][C]4560.80403176681[/C][C]-10.8040317668065[/C][/ROW]
[ROW][C]73[/C][C]4543.8[/C][C]4555.60988531034[/C][C]-11.8098853103402[/C][/ROW]
[ROW][C]74[/C][C]4538.2[/C][C]4539.65818500007[/C][C]-1.45818500007226[/C][/ROW]
[ROW][C]75[/C][C]4543.3[/C][C]4539.31842457557[/C][C]3.98157542442914[/C][/ROW]
[ROW][C]76[/C][C]4545.1[/C][C]4538.64887384768[/C][C]6.45112615232301[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278478&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278478&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
133945.63881.8219551282163.7780448717936
143965.73989.60669081012-23.9066908101181
153992.34009.31190027998-17.0119002799847
164008.74016.62121598085-7.92121598085168
174014.84017.44253904631-2.64253904631369
184020.64021.06027754697-0.460277546965699
194037.54042.94046238459-5.4404623845935
204058.54046.8465229775511.653477022453
214082.34080.158723175762.14127682423668
224102.44102.077539749290.322460250712538
234127.14121.180584666775.91941533322824
244144.44157.73975177974-13.3397517797357
2541614172.23439701882-11.2343970188203
264168.24176.51198421248-8.31198421248064
274178.34190.54020883024-12.2402088302379
284174.14184.26437354967-10.1643735496673
294165.74163.672076852942.02792314705493
304167.94154.2843430650313.6156569349732
314158.34177.88080423786-19.5808042378585
324158.34151.955183076046.34481692396093
334143.74159.77344094627-16.0734409462739
344157.54136.3626702990521.1373297009504
354164.84156.602443885138.19755611487017
364173.94176.40482394886-2.50482394886239
374181.24188.31781042319-7.11781042319399
384190.74185.589384029325.11061597067965
394206.64206.96577121064-0.365771210641469
404222.14212.26015073469.83984926539961
414245.84220.4476067224125.3523932775861
424255.44253.374017542892.02598245710669
434266.14278.5894379656-12.4894379656034
444273.64278.55506816292-4.95506816291709
454282.14287.02304238232-4.92304238231554
464299.84293.927036230175.87296376982795
474315.74309.811774001615.88822599839386
484331.74336.53975007788-4.83975007788104
494348.44354.6718816985-6.27188169849614
504367.84362.538021584055.26197841595331
514387.24392.86659346927-5.66659346927099
524410.94400.5482507382310.3517492617702
5344364417.1348191695318.8651808304712
544453.84446.654162997587.14583700241928
554469.14482.19614112361-13.0961411236067
5644724488.14841587392-16.1484158739177
574458.24487.18634588736-28.9863458873588
5844494462.42198587839-13.4219858783854
594441.54441.83493570294-0.334935702941948
604445.74440.953262098594.74673790140878
614453.94451.190862277452.70913772255426
624469.74455.3904617930814.3095382069241
634487.54484.826875449612.67312455039155
6445044496.295575914447.70442408556119
654524.14504.7041481886119.3958518113886
664540.54528.0634405976812.4365594023247
674548.44563.78240150609-15.3824015060936
684554.24562.78924672628-8.589246726282
6945584566.94129809644-8.94129809644073
704557.54569.70667259968-12.2066725996765
714554.54559.34038057787-4.84038057786711
7245504560.80403176681-10.8040317668065
734543.84555.60988531034-11.8098853103402
744538.24539.65818500007-1.45818500007226
754543.34539.318424575573.98157542442914
764545.14538.648873847686.45112615232301







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
774532.346620741764505.191359728244559.50188175528
784514.133584863894467.673050095564560.59411963222
794508.00743260294439.853943834164576.16092137164
804500.284454386434408.130724062054592.43818471081
814494.740165615714376.432224944674613.04810628674
824491.971651207114345.499039222724638.4442631915
834485.244787061014308.721039903184661.76853421883
844484.793813687364276.438486988084693.14914038665
854488.428435743974246.552219029054730.30465245889
864488.219801933184211.212453571224765.22715029513
874494.249407739424180.569962672674807.92885280617
884492.873315452324141.042069773784844.70456113086

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 4532.34662074176 & 4505.19135972824 & 4559.50188175528 \tabularnewline
78 & 4514.13358486389 & 4467.67305009556 & 4560.59411963222 \tabularnewline
79 & 4508.0074326029 & 4439.85394383416 & 4576.16092137164 \tabularnewline
80 & 4500.28445438643 & 4408.13072406205 & 4592.43818471081 \tabularnewline
81 & 4494.74016561571 & 4376.43222494467 & 4613.04810628674 \tabularnewline
82 & 4491.97165120711 & 4345.49903922272 & 4638.4442631915 \tabularnewline
83 & 4485.24478706101 & 4308.72103990318 & 4661.76853421883 \tabularnewline
84 & 4484.79381368736 & 4276.43848698808 & 4693.14914038665 \tabularnewline
85 & 4488.42843574397 & 4246.55221902905 & 4730.30465245889 \tabularnewline
86 & 4488.21980193318 & 4211.21245357122 & 4765.22715029513 \tabularnewline
87 & 4494.24940773942 & 4180.56996267267 & 4807.92885280617 \tabularnewline
88 & 4492.87331545232 & 4141.04206977378 & 4844.70456113086 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278478&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]4532.34662074176[/C][C]4505.19135972824[/C][C]4559.50188175528[/C][/ROW]
[ROW][C]78[/C][C]4514.13358486389[/C][C]4467.67305009556[/C][C]4560.59411963222[/C][/ROW]
[ROW][C]79[/C][C]4508.0074326029[/C][C]4439.85394383416[/C][C]4576.16092137164[/C][/ROW]
[ROW][C]80[/C][C]4500.28445438643[/C][C]4408.13072406205[/C][C]4592.43818471081[/C][/ROW]
[ROW][C]81[/C][C]4494.74016561571[/C][C]4376.43222494467[/C][C]4613.04810628674[/C][/ROW]
[ROW][C]82[/C][C]4491.97165120711[/C][C]4345.49903922272[/C][C]4638.4442631915[/C][/ROW]
[ROW][C]83[/C][C]4485.24478706101[/C][C]4308.72103990318[/C][C]4661.76853421883[/C][/ROW]
[ROW][C]84[/C][C]4484.79381368736[/C][C]4276.43848698808[/C][C]4693.14914038665[/C][/ROW]
[ROW][C]85[/C][C]4488.42843574397[/C][C]4246.55221902905[/C][C]4730.30465245889[/C][/ROW]
[ROW][C]86[/C][C]4488.21980193318[/C][C]4211.21245357122[/C][C]4765.22715029513[/C][/ROW]
[ROW][C]87[/C][C]4494.24940773942[/C][C]4180.56996267267[/C][C]4807.92885280617[/C][/ROW]
[ROW][C]88[/C][C]4492.87331545232[/C][C]4141.04206977378[/C][C]4844.70456113086[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278478&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278478&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
774532.346620741764505.191359728244559.50188175528
784514.133584863894467.673050095564560.59411963222
794508.00743260294439.853943834164576.16092137164
804500.284454386434408.130724062054592.43818471081
814494.740165615714376.432224944674613.04810628674
824491.971651207114345.499039222724638.4442631915
834485.244787061014308.721039903184661.76853421883
844484.793813687364276.438486988084693.14914038665
854488.428435743974246.552219029054730.30465245889
864488.219801933184211.212453571224765.22715029513
874494.249407739424180.569962672674807.92885280617
884492.873315452324141.042069773784844.70456113086



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')