Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 29 Apr 2008 06:07:56 -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/2008/Apr/29/t12094709160u8vcks3bhky5rp.htm/, Retrieved Sun, 12 May 2024 20:53:36 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11030, Retrieved Sun, 12 May 2024 20:53:36 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsexponential,smoothing,single
Estimated Impact212
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-04-29 12:07:56] [be9d907f730a9e9810527c97ce58429f] [Current]
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Dataseries X:
56421
53152
53536
52408
41454
38271
35306
26414
31917
38030
27534
18387
50556
43901
48572
43899
37532
40357
35489
29027
34485
42598
30306
26451
47460
50104
61465
53726
39477
43895
31481
29896
33842
39120
33702
25094
51442
45594
52518
48564
41745
49585
32747
33379
35645
37034
35681
20972
58552
54955
65540
51570
51145
46641
35704
33253
35193
41668
34865
21210
56126
49231
59723
48103
47472
50497
40059
34149
36860
46356
36577




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=11030&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=11030&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11030&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
alpha0.587763292801995
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.587763292801995 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11030&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]0.587763292801995[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11030&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11030&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
alpha0.587763292801995
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
25315256421-3269
35353654499.6017958303-963.601795830276
45240853933.2320313632-1525.23203136316
54145453036.7566303221-11582.7566303221
63827146228.8374535598-7957.83745355983
73530641551.5127082725-6245.51270827245
82641437880.6295936215-11466.6295936215
93191731140.9656263337776.034373666269
103803031597.09014512746432.90985487265
112753435378.1184237257-7844.1184237257
121838730767.6335498679-12380.6335498679
135055623490.751607622727065.2483923773
144390139398.71112323034502.28887676971
154857242044.99125858626527.00874141375
164389945881.327408587-1982.327408587
173753244716.1881235043-7184.18812350426
184035740493.5860559244-136.586055924403
193548940413.3057859434-4924.30578594343
202902737518.9796024334-8491.9796024334
213448532527.70570889981957.29429110023
224259833678.13144641948919.86855358061
233030638920.9027588329-8614.9027588329
242645133857.3791461323-7406.37914613228
254746029504.181351461517955.8186485385
265010440057.95244528210046.0475547180
276146545962.650435688515502.3495643115
285372655074.3624617758-1348.36246177580
293947754281.8445013519-14804.8445013519
304389545580.1003478158-1685.10034781577
313148144589.6602186818-13108.6602186818
322989636884.8709243269-6988.87092432685
333384232777.06913687641064.93086312362
343912033402.99640759245717.00359240761
353370236763.2412640267-3061.24126402673
362509434963.9560186210-9869.95601862104
375144229162.758169305522279.2418306945
384559442257.67870884643336.32129115356
395251844218.64589678038299.35410321974
404856449096.7015926184-532.701592618447
414174548783.5991504602-7038.59915046016
424958544646.56893707244938.43106292763
433274747549.1974398944-14802.1974398944
443337938849.0091319168-5470.00913191679
453564535633.938552884411.0614471156077
463703435640.44006546421393.55993453578
473568136459.5234413039-778.5234413039
482097236001.9359399196-15029.9359399196
495855227167.891301269431384.1086987306
505495545614.31837169109340.68162830895
516554051104.42816256114435.5718374390
525157059589.1273992139-8019.12739921391
535114554875.7786736532-3730.77867365324
544664152682.9639157114-6041.96391571136
553570449131.719309622-13427.719309622
563325341239.3987933776-7986.39879337764
573519336545.2867409521-1352.28674095211
584166835750.46223327765917.53776672238
593486539228.5737163265-4363.57371632653
602121036663.8252604342-15453.8252604342
615612627580.634038974728545.3659610253
624923144358.55233046494872.44766953506
635972347222.398216716312500.6017832837
644810354569.7930828656-6466.79308286561
654747250768.8494866113-3296.84948661135
665049748831.08237648811665.91762351191
674005949810.2476044203-9751.24760442032
683414944078.8222035187-9929.82220351866
693686038242.4372082402-1382.43720824017
704635637429.89136263298926.10863736707
713657742676.3303672401-6099.33036724014

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 53152 & 56421 & -3269 \tabularnewline
3 & 53536 & 54499.6017958303 & -963.601795830276 \tabularnewline
4 & 52408 & 53933.2320313632 & -1525.23203136316 \tabularnewline
5 & 41454 & 53036.7566303221 & -11582.7566303221 \tabularnewline
6 & 38271 & 46228.8374535598 & -7957.83745355983 \tabularnewline
7 & 35306 & 41551.5127082725 & -6245.51270827245 \tabularnewline
8 & 26414 & 37880.6295936215 & -11466.6295936215 \tabularnewline
9 & 31917 & 31140.9656263337 & 776.034373666269 \tabularnewline
10 & 38030 & 31597.0901451274 & 6432.90985487265 \tabularnewline
11 & 27534 & 35378.1184237257 & -7844.1184237257 \tabularnewline
12 & 18387 & 30767.6335498679 & -12380.6335498679 \tabularnewline
13 & 50556 & 23490.7516076227 & 27065.2483923773 \tabularnewline
14 & 43901 & 39398.7111232303 & 4502.28887676971 \tabularnewline
15 & 48572 & 42044.9912585862 & 6527.00874141375 \tabularnewline
16 & 43899 & 45881.327408587 & -1982.327408587 \tabularnewline
17 & 37532 & 44716.1881235043 & -7184.18812350426 \tabularnewline
18 & 40357 & 40493.5860559244 & -136.586055924403 \tabularnewline
19 & 35489 & 40413.3057859434 & -4924.30578594343 \tabularnewline
20 & 29027 & 37518.9796024334 & -8491.9796024334 \tabularnewline
21 & 34485 & 32527.7057088998 & 1957.29429110023 \tabularnewline
22 & 42598 & 33678.1314464194 & 8919.86855358061 \tabularnewline
23 & 30306 & 38920.9027588329 & -8614.9027588329 \tabularnewline
24 & 26451 & 33857.3791461323 & -7406.37914613228 \tabularnewline
25 & 47460 & 29504.1813514615 & 17955.8186485385 \tabularnewline
26 & 50104 & 40057.952445282 & 10046.0475547180 \tabularnewline
27 & 61465 & 45962.6504356885 & 15502.3495643115 \tabularnewline
28 & 53726 & 55074.3624617758 & -1348.36246177580 \tabularnewline
29 & 39477 & 54281.8445013519 & -14804.8445013519 \tabularnewline
30 & 43895 & 45580.1003478158 & -1685.10034781577 \tabularnewline
31 & 31481 & 44589.6602186818 & -13108.6602186818 \tabularnewline
32 & 29896 & 36884.8709243269 & -6988.87092432685 \tabularnewline
33 & 33842 & 32777.0691368764 & 1064.93086312362 \tabularnewline
34 & 39120 & 33402.9964075924 & 5717.00359240761 \tabularnewline
35 & 33702 & 36763.2412640267 & -3061.24126402673 \tabularnewline
36 & 25094 & 34963.9560186210 & -9869.95601862104 \tabularnewline
37 & 51442 & 29162.7581693055 & 22279.2418306945 \tabularnewline
38 & 45594 & 42257.6787088464 & 3336.32129115356 \tabularnewline
39 & 52518 & 44218.6458967803 & 8299.35410321974 \tabularnewline
40 & 48564 & 49096.7015926184 & -532.701592618447 \tabularnewline
41 & 41745 & 48783.5991504602 & -7038.59915046016 \tabularnewline
42 & 49585 & 44646.5689370724 & 4938.43106292763 \tabularnewline
43 & 32747 & 47549.1974398944 & -14802.1974398944 \tabularnewline
44 & 33379 & 38849.0091319168 & -5470.00913191679 \tabularnewline
45 & 35645 & 35633.9385528844 & 11.0614471156077 \tabularnewline
46 & 37034 & 35640.4400654642 & 1393.55993453578 \tabularnewline
47 & 35681 & 36459.5234413039 & -778.5234413039 \tabularnewline
48 & 20972 & 36001.9359399196 & -15029.9359399196 \tabularnewline
49 & 58552 & 27167.8913012694 & 31384.1086987306 \tabularnewline
50 & 54955 & 45614.3183716910 & 9340.68162830895 \tabularnewline
51 & 65540 & 51104.428162561 & 14435.5718374390 \tabularnewline
52 & 51570 & 59589.1273992139 & -8019.12739921391 \tabularnewline
53 & 51145 & 54875.7786736532 & -3730.77867365324 \tabularnewline
54 & 46641 & 52682.9639157114 & -6041.96391571136 \tabularnewline
55 & 35704 & 49131.719309622 & -13427.719309622 \tabularnewline
56 & 33253 & 41239.3987933776 & -7986.39879337764 \tabularnewline
57 & 35193 & 36545.2867409521 & -1352.28674095211 \tabularnewline
58 & 41668 & 35750.4622332776 & 5917.53776672238 \tabularnewline
59 & 34865 & 39228.5737163265 & -4363.57371632653 \tabularnewline
60 & 21210 & 36663.8252604342 & -15453.8252604342 \tabularnewline
61 & 56126 & 27580.6340389747 & 28545.3659610253 \tabularnewline
62 & 49231 & 44358.5523304649 & 4872.44766953506 \tabularnewline
63 & 59723 & 47222.3982167163 & 12500.6017832837 \tabularnewline
64 & 48103 & 54569.7930828656 & -6466.79308286561 \tabularnewline
65 & 47472 & 50768.8494866113 & -3296.84948661135 \tabularnewline
66 & 50497 & 48831.0823764881 & 1665.91762351191 \tabularnewline
67 & 40059 & 49810.2476044203 & -9751.24760442032 \tabularnewline
68 & 34149 & 44078.8222035187 & -9929.82220351866 \tabularnewline
69 & 36860 & 38242.4372082402 & -1382.43720824017 \tabularnewline
70 & 46356 & 37429.8913626329 & 8926.10863736707 \tabularnewline
71 & 36577 & 42676.3303672401 & -6099.33036724014 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11030&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]53152[/C][C]56421[/C][C]-3269[/C][/ROW]
[ROW][C]3[/C][C]53536[/C][C]54499.6017958303[/C][C]-963.601795830276[/C][/ROW]
[ROW][C]4[/C][C]52408[/C][C]53933.2320313632[/C][C]-1525.23203136316[/C][/ROW]
[ROW][C]5[/C][C]41454[/C][C]53036.7566303221[/C][C]-11582.7566303221[/C][/ROW]
[ROW][C]6[/C][C]38271[/C][C]46228.8374535598[/C][C]-7957.83745355983[/C][/ROW]
[ROW][C]7[/C][C]35306[/C][C]41551.5127082725[/C][C]-6245.51270827245[/C][/ROW]
[ROW][C]8[/C][C]26414[/C][C]37880.6295936215[/C][C]-11466.6295936215[/C][/ROW]
[ROW][C]9[/C][C]31917[/C][C]31140.9656263337[/C][C]776.034373666269[/C][/ROW]
[ROW][C]10[/C][C]38030[/C][C]31597.0901451274[/C][C]6432.90985487265[/C][/ROW]
[ROW][C]11[/C][C]27534[/C][C]35378.1184237257[/C][C]-7844.1184237257[/C][/ROW]
[ROW][C]12[/C][C]18387[/C][C]30767.6335498679[/C][C]-12380.6335498679[/C][/ROW]
[ROW][C]13[/C][C]50556[/C][C]23490.7516076227[/C][C]27065.2483923773[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]39398.7111232303[/C][C]4502.28887676971[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]42044.9912585862[/C][C]6527.00874141375[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]45881.327408587[/C][C]-1982.327408587[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]44716.1881235043[/C][C]-7184.18812350426[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]40493.5860559244[/C][C]-136.586055924403[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]40413.3057859434[/C][C]-4924.30578594343[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]37518.9796024334[/C][C]-8491.9796024334[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]32527.7057088998[/C][C]1957.29429110023[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]33678.1314464194[/C][C]8919.86855358061[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]38920.9027588329[/C][C]-8614.9027588329[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]33857.3791461323[/C][C]-7406.37914613228[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]29504.1813514615[/C][C]17955.8186485385[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]40057.952445282[/C][C]10046.0475547180[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]45962.6504356885[/C][C]15502.3495643115[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]55074.3624617758[/C][C]-1348.36246177580[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]54281.8445013519[/C][C]-14804.8445013519[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]45580.1003478158[/C][C]-1685.10034781577[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]44589.6602186818[/C][C]-13108.6602186818[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]36884.8709243269[/C][C]-6988.87092432685[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]32777.0691368764[/C][C]1064.93086312362[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]33402.9964075924[/C][C]5717.00359240761[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]36763.2412640267[/C][C]-3061.24126402673[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]34963.9560186210[/C][C]-9869.95601862104[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]29162.7581693055[/C][C]22279.2418306945[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]42257.6787088464[/C][C]3336.32129115356[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]44218.6458967803[/C][C]8299.35410321974[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]49096.7015926184[/C][C]-532.701592618447[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]48783.5991504602[/C][C]-7038.59915046016[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44646.5689370724[/C][C]4938.43106292763[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]47549.1974398944[/C][C]-14802.1974398944[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]38849.0091319168[/C][C]-5470.00913191679[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]35633.9385528844[/C][C]11.0614471156077[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]35640.4400654642[/C][C]1393.55993453578[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]36459.5234413039[/C][C]-778.5234413039[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]36001.9359399196[/C][C]-15029.9359399196[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]27167.8913012694[/C][C]31384.1086987306[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]45614.3183716910[/C][C]9340.68162830895[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]51104.428162561[/C][C]14435.5718374390[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]59589.1273992139[/C][C]-8019.12739921391[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]54875.7786736532[/C][C]-3730.77867365324[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]52682.9639157114[/C][C]-6041.96391571136[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]49131.719309622[/C][C]-13427.719309622[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]41239.3987933776[/C][C]-7986.39879337764[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]36545.2867409521[/C][C]-1352.28674095211[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]35750.4622332776[/C][C]5917.53776672238[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]39228.5737163265[/C][C]-4363.57371632653[/C][/ROW]
[ROW][C]60[/C][C]21210[/C][C]36663.8252604342[/C][C]-15453.8252604342[/C][/ROW]
[ROW][C]61[/C][C]56126[/C][C]27580.6340389747[/C][C]28545.3659610253[/C][/ROW]
[ROW][C]62[/C][C]49231[/C][C]44358.5523304649[/C][C]4872.44766953506[/C][/ROW]
[ROW][C]63[/C][C]59723[/C][C]47222.3982167163[/C][C]12500.6017832837[/C][/ROW]
[ROW][C]64[/C][C]48103[/C][C]54569.7930828656[/C][C]-6466.79308286561[/C][/ROW]
[ROW][C]65[/C][C]47472[/C][C]50768.8494866113[/C][C]-3296.84948661135[/C][/ROW]
[ROW][C]66[/C][C]50497[/C][C]48831.0823764881[/C][C]1665.91762351191[/C][/ROW]
[ROW][C]67[/C][C]40059[/C][C]49810.2476044203[/C][C]-9751.24760442032[/C][/ROW]
[ROW][C]68[/C][C]34149[/C][C]44078.8222035187[/C][C]-9929.82220351866[/C][/ROW]
[ROW][C]69[/C][C]36860[/C][C]38242.4372082402[/C][C]-1382.43720824017[/C][/ROW]
[ROW][C]70[/C][C]46356[/C][C]37429.8913626329[/C][C]8926.10863736707[/C][/ROW]
[ROW][C]71[/C][C]36577[/C][C]42676.3303672401[/C][C]-6099.33036724014[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11030&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11030&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
25315256421-3269
35353654499.6017958303-963.601795830276
45240853933.2320313632-1525.23203136316
54145453036.7566303221-11582.7566303221
63827146228.8374535598-7957.83745355983
73530641551.5127082725-6245.51270827245
82641437880.6295936215-11466.6295936215
93191731140.9656263337776.034373666269
103803031597.09014512746432.90985487265
112753435378.1184237257-7844.1184237257
121838730767.6335498679-12380.6335498679
135055623490.751607622727065.2483923773
144390139398.71112323034502.28887676971
154857242044.99125858626527.00874141375
164389945881.327408587-1982.327408587
173753244716.1881235043-7184.18812350426
184035740493.5860559244-136.586055924403
193548940413.3057859434-4924.30578594343
202902737518.9796024334-8491.9796024334
213448532527.70570889981957.29429110023
224259833678.13144641948919.86855358061
233030638920.9027588329-8614.9027588329
242645133857.3791461323-7406.37914613228
254746029504.181351461517955.8186485385
265010440057.95244528210046.0475547180
276146545962.650435688515502.3495643115
285372655074.3624617758-1348.36246177580
293947754281.8445013519-14804.8445013519
304389545580.1003478158-1685.10034781577
313148144589.6602186818-13108.6602186818
322989636884.8709243269-6988.87092432685
333384232777.06913687641064.93086312362
343912033402.99640759245717.00359240761
353370236763.2412640267-3061.24126402673
362509434963.9560186210-9869.95601862104
375144229162.758169305522279.2418306945
384559442257.67870884643336.32129115356
395251844218.64589678038299.35410321974
404856449096.7015926184-532.701592618447
414174548783.5991504602-7038.59915046016
424958544646.56893707244938.43106292763
433274747549.1974398944-14802.1974398944
443337938849.0091319168-5470.00913191679
453564535633.938552884411.0614471156077
463703435640.44006546421393.55993453578
473568136459.5234413039-778.5234413039
482097236001.9359399196-15029.9359399196
495855227167.891301269431384.1086987306
505495545614.31837169109340.68162830895
516554051104.42816256114435.5718374390
525157059589.1273992139-8019.12739921391
535114554875.7786736532-3730.77867365324
544664152682.9639157114-6041.96391571136
553570449131.719309622-13427.719309622
563325341239.3987933776-7986.39879337764
573519336545.2867409521-1352.28674095211
584166835750.46223327765917.53776672238
593486539228.5737163265-4363.57371632653
602121036663.8252604342-15453.8252604342
615612627580.634038974728545.3659610253
624923144358.55233046494872.44766953506
635972347222.398216716312500.6017832837
644810354569.7930828656-6466.79308286561
654747250768.8494866113-3296.84948661135
665049748831.08237648811665.91762351191
674005949810.2476044203-9751.24760442032
683414944078.8222035187-9929.82220351866
693686038242.4372082402-1382.43720824017
704635637429.89136263298926.10863736707
713657742676.3303672401-6099.33036724014







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7239091.367866703918712.118358824059470.6173745837
7339091.367866703915452.618281795562730.1174516122
7439091.367866703912591.044220159665591.6915132481
7539091.367866703910009.692797939868173.042935468
7639091.36786670397639.4919888049270543.2437446028
7739091.36786670395435.8011997712472746.9345336365
7839091.36786670393367.7924702526974814.943263155
7939091.36786670391413.1180328870476769.6177005207
8039091.3678667039-445.0353836311778627.771117039
8139091.3678667039-2219.6942523785880402.4299857863
8239091.3678667039-3921.194540577582103.9302739852
8339091.3678667039-5557.9008425802683740.636575988

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 39091.3678667039 & 18712.1183588240 & 59470.6173745837 \tabularnewline
73 & 39091.3678667039 & 15452.6182817955 & 62730.1174516122 \tabularnewline
74 & 39091.3678667039 & 12591.0442201596 & 65591.6915132481 \tabularnewline
75 & 39091.3678667039 & 10009.6927979398 & 68173.042935468 \tabularnewline
76 & 39091.3678667039 & 7639.49198880492 & 70543.2437446028 \tabularnewline
77 & 39091.3678667039 & 5435.80119977124 & 72746.9345336365 \tabularnewline
78 & 39091.3678667039 & 3367.79247025269 & 74814.943263155 \tabularnewline
79 & 39091.3678667039 & 1413.11803288704 & 76769.6177005207 \tabularnewline
80 & 39091.3678667039 & -445.03538363117 & 78627.771117039 \tabularnewline
81 & 39091.3678667039 & -2219.69425237858 & 80402.4299857863 \tabularnewline
82 & 39091.3678667039 & -3921.1945405775 & 82103.9302739852 \tabularnewline
83 & 39091.3678667039 & -5557.90084258026 & 83740.636575988 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11030&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]72[/C][C]39091.3678667039[/C][C]18712.1183588240[/C][C]59470.6173745837[/C][/ROW]
[ROW][C]73[/C][C]39091.3678667039[/C][C]15452.6182817955[/C][C]62730.1174516122[/C][/ROW]
[ROW][C]74[/C][C]39091.3678667039[/C][C]12591.0442201596[/C][C]65591.6915132481[/C][/ROW]
[ROW][C]75[/C][C]39091.3678667039[/C][C]10009.6927979398[/C][C]68173.042935468[/C][/ROW]
[ROW][C]76[/C][C]39091.3678667039[/C][C]7639.49198880492[/C][C]70543.2437446028[/C][/ROW]
[ROW][C]77[/C][C]39091.3678667039[/C][C]5435.80119977124[/C][C]72746.9345336365[/C][/ROW]
[ROW][C]78[/C][C]39091.3678667039[/C][C]3367.79247025269[/C][C]74814.943263155[/C][/ROW]
[ROW][C]79[/C][C]39091.3678667039[/C][C]1413.11803288704[/C][C]76769.6177005207[/C][/ROW]
[ROW][C]80[/C][C]39091.3678667039[/C][C]-445.03538363117[/C][C]78627.771117039[/C][/ROW]
[ROW][C]81[/C][C]39091.3678667039[/C][C]-2219.69425237858[/C][C]80402.4299857863[/C][/ROW]
[ROW][C]82[/C][C]39091.3678667039[/C][C]-3921.1945405775[/C][C]82103.9302739852[/C][/ROW]
[ROW][C]83[/C][C]39091.3678667039[/C][C]-5557.90084258026[/C][C]83740.636575988[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11030&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11030&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
7239091.367866703918712.118358824059470.6173745837
7339091.367866703915452.618281795562730.1174516122
7439091.367866703912591.044220159665591.6915132481
7539091.367866703910009.692797939868173.042935468
7639091.36786670397639.4919888049270543.2437446028
7739091.36786670395435.8011997712472746.9345336365
7839091.36786670393367.7924702526974814.943263155
7939091.36786670391413.1180328870476769.6177005207
8039091.3678667039-445.0353836311778627.771117039
8139091.3678667039-2219.6942523785880402.4299857863
8239091.3678667039-3921.194540577582103.9302739852
8339091.3678667039-5557.9008425802683740.636575988



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=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')