Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 05 May 2008 09:27:23 -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/May/05/t121000134985b8nmv1h9o7x3t.htm/, Retrieved Thu, 31 Oct 2024 23:22:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=11518, Retrieved Thu, 31 Oct 2024 23:22:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsvraag 3
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [vraag 3: exponent...] [2008-05-05 15:27:23] [ff1822be68136ddf1744cad26daeb86c] [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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11518&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11518&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11518&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.587763292802047
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.587763292802047 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11518&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]0.587763292802047[/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=11518&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11518&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
alpha0.587763292802047
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
25315256421-3269
35353654499.6017958301-963.60179583011
45240853933.232031363-1525.23203136304
54145453036.7566303219-11582.7566303219
63827146228.8374535592-7957.83745355917
73530641551.5127082718-6245.51270827177
82641437880.6295936209-11466.6295936209
93191731140.9656263329776.034373667113
103803031597.09014512706432.90985487296
112753435378.1184237259-7844.11842372591
121838730767.6335498676-12380.6335498676
135055623490.751607621927065.2483923781
144390139398.71112323144502.28887676863
154857242044.99125858696527.00874141307
164389945881.3274085876-1982.32740858763
173753244716.1881235044-7184.18812350441
184035740493.5860559241-136.586055924097
193548940413.3057859433-4924.3057859433
202902737518.9796024331-8491.9796024331
213448532527.70570889921957.2942911008
224259833678.13144641938919.86855358075
233030638920.9027588333-8614.9027588333
242645133857.379146132-7406.379146132
254746029504.181351461017955.8186485390
265010440057.952445282710046.0475547173
276146545962.650435689315502.3495643107
285372655074.3624617769-1348.36246177694
293947754281.8445013523-14804.8445013523
304389545580.1003478152-1685.10034781517
313148144589.6602186814-13108.6602186814
322989636884.8709243260-6988.87092432604
333384232777.06913687571064.93086312432
343912033402.99640759225717.00359240784
353370236763.2412640269-3061.24126402692
362509434963.9560186210-9869.95601862096
375144229162.758169304922279.2418306951
384559442257.67870884743336.32129115263
395251844218.64589678088299.35410321918
404856449096.7015926191-532.701592619109
414174548783.5991504604-7038.59915046041
424958544646.56893707214938.43106292789
433274747549.1974398945-14802.1974398945
443337938849.0091319161-5470.00913191609
453564535633.938552883811.0614471161825
463703435640.4400654641393.55993453602
473568136459.5234413039-778.523441303878
482097236001.9359399195-15029.9359399195
495855227167.891301268631384.1086987314
505495545614.31837169239340.68162830766
516554051104.42816256214435.5718374380
525157059589.1273992151-8019.12739921507
535114554875.7786736533-3730.77867365331
544664152682.9639157112-6041.96391571119
553570449131.7193096216-13427.7193096216
563325341239.3987933768-7986.39879337679
573519336545.2867409513-1352.28674095135
584166835750.46223327725917.53776672277
593486539228.5737163267-4363.57371632668
602121036663.8252604340-15453.8252604340
615612627580.634038973928545.3659610261
624923144358.55233046614872.44766953393
635972347222.39821671712500.601783283
644810354569.7930828666-6466.79308286656
654747250768.8494866114-3296.84948661141
665049748831.08237648791665.91762351205
674005949810.2476044204-9751.24760442035
683414944078.8222035182-9929.82220351817
693686038242.4372082394-1382.43720823945
704635637429.89136263268926.10863736744
713657742676.3303672404-6099.33036724044

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 53152 & 56421 & -3269 \tabularnewline
3 & 53536 & 54499.6017958301 & -963.60179583011 \tabularnewline
4 & 52408 & 53933.232031363 & -1525.23203136304 \tabularnewline
5 & 41454 & 53036.7566303219 & -11582.7566303219 \tabularnewline
6 & 38271 & 46228.8374535592 & -7957.83745355917 \tabularnewline
7 & 35306 & 41551.5127082718 & -6245.51270827177 \tabularnewline
8 & 26414 & 37880.6295936209 & -11466.6295936209 \tabularnewline
9 & 31917 & 31140.9656263329 & 776.034373667113 \tabularnewline
10 & 38030 & 31597.0901451270 & 6432.90985487296 \tabularnewline
11 & 27534 & 35378.1184237259 & -7844.11842372591 \tabularnewline
12 & 18387 & 30767.6335498676 & -12380.6335498676 \tabularnewline
13 & 50556 & 23490.7516076219 & 27065.2483923781 \tabularnewline
14 & 43901 & 39398.7111232314 & 4502.28887676863 \tabularnewline
15 & 48572 & 42044.9912585869 & 6527.00874141307 \tabularnewline
16 & 43899 & 45881.3274085876 & -1982.32740858763 \tabularnewline
17 & 37532 & 44716.1881235044 & -7184.18812350441 \tabularnewline
18 & 40357 & 40493.5860559241 & -136.586055924097 \tabularnewline
19 & 35489 & 40413.3057859433 & -4924.3057859433 \tabularnewline
20 & 29027 & 37518.9796024331 & -8491.9796024331 \tabularnewline
21 & 34485 & 32527.7057088992 & 1957.2942911008 \tabularnewline
22 & 42598 & 33678.1314464193 & 8919.86855358075 \tabularnewline
23 & 30306 & 38920.9027588333 & -8614.9027588333 \tabularnewline
24 & 26451 & 33857.379146132 & -7406.379146132 \tabularnewline
25 & 47460 & 29504.1813514610 & 17955.8186485390 \tabularnewline
26 & 50104 & 40057.9524452827 & 10046.0475547173 \tabularnewline
27 & 61465 & 45962.6504356893 & 15502.3495643107 \tabularnewline
28 & 53726 & 55074.3624617769 & -1348.36246177694 \tabularnewline
29 & 39477 & 54281.8445013523 & -14804.8445013523 \tabularnewline
30 & 43895 & 45580.1003478152 & -1685.10034781517 \tabularnewline
31 & 31481 & 44589.6602186814 & -13108.6602186814 \tabularnewline
32 & 29896 & 36884.8709243260 & -6988.87092432604 \tabularnewline
33 & 33842 & 32777.0691368757 & 1064.93086312432 \tabularnewline
34 & 39120 & 33402.9964075922 & 5717.00359240784 \tabularnewline
35 & 33702 & 36763.2412640269 & -3061.24126402692 \tabularnewline
36 & 25094 & 34963.9560186210 & -9869.95601862096 \tabularnewline
37 & 51442 & 29162.7581693049 & 22279.2418306951 \tabularnewline
38 & 45594 & 42257.6787088474 & 3336.32129115263 \tabularnewline
39 & 52518 & 44218.6458967808 & 8299.35410321918 \tabularnewline
40 & 48564 & 49096.7015926191 & -532.701592619109 \tabularnewline
41 & 41745 & 48783.5991504604 & -7038.59915046041 \tabularnewline
42 & 49585 & 44646.5689370721 & 4938.43106292789 \tabularnewline
43 & 32747 & 47549.1974398945 & -14802.1974398945 \tabularnewline
44 & 33379 & 38849.0091319161 & -5470.00913191609 \tabularnewline
45 & 35645 & 35633.9385528838 & 11.0614471161825 \tabularnewline
46 & 37034 & 35640.440065464 & 1393.55993453602 \tabularnewline
47 & 35681 & 36459.5234413039 & -778.523441303878 \tabularnewline
48 & 20972 & 36001.9359399195 & -15029.9359399195 \tabularnewline
49 & 58552 & 27167.8913012686 & 31384.1086987314 \tabularnewline
50 & 54955 & 45614.3183716923 & 9340.68162830766 \tabularnewline
51 & 65540 & 51104.428162562 & 14435.5718374380 \tabularnewline
52 & 51570 & 59589.1273992151 & -8019.12739921507 \tabularnewline
53 & 51145 & 54875.7786736533 & -3730.77867365331 \tabularnewline
54 & 46641 & 52682.9639157112 & -6041.96391571119 \tabularnewline
55 & 35704 & 49131.7193096216 & -13427.7193096216 \tabularnewline
56 & 33253 & 41239.3987933768 & -7986.39879337679 \tabularnewline
57 & 35193 & 36545.2867409513 & -1352.28674095135 \tabularnewline
58 & 41668 & 35750.4622332772 & 5917.53776672277 \tabularnewline
59 & 34865 & 39228.5737163267 & -4363.57371632668 \tabularnewline
60 & 21210 & 36663.8252604340 & -15453.8252604340 \tabularnewline
61 & 56126 & 27580.6340389739 & 28545.3659610261 \tabularnewline
62 & 49231 & 44358.5523304661 & 4872.44766953393 \tabularnewline
63 & 59723 & 47222.398216717 & 12500.601783283 \tabularnewline
64 & 48103 & 54569.7930828666 & -6466.79308286656 \tabularnewline
65 & 47472 & 50768.8494866114 & -3296.84948661141 \tabularnewline
66 & 50497 & 48831.0823764879 & 1665.91762351205 \tabularnewline
67 & 40059 & 49810.2476044204 & -9751.24760442035 \tabularnewline
68 & 34149 & 44078.8222035182 & -9929.82220351817 \tabularnewline
69 & 36860 & 38242.4372082394 & -1382.43720823945 \tabularnewline
70 & 46356 & 37429.8913626326 & 8926.10863736744 \tabularnewline
71 & 36577 & 42676.3303672404 & -6099.33036724044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11518&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]54499.6017958301[/C][C]-963.60179583011[/C][/ROW]
[ROW][C]4[/C][C]52408[/C][C]53933.232031363[/C][C]-1525.23203136304[/C][/ROW]
[ROW][C]5[/C][C]41454[/C][C]53036.7566303219[/C][C]-11582.7566303219[/C][/ROW]
[ROW][C]6[/C][C]38271[/C][C]46228.8374535592[/C][C]-7957.83745355917[/C][/ROW]
[ROW][C]7[/C][C]35306[/C][C]41551.5127082718[/C][C]-6245.51270827177[/C][/ROW]
[ROW][C]8[/C][C]26414[/C][C]37880.6295936209[/C][C]-11466.6295936209[/C][/ROW]
[ROW][C]9[/C][C]31917[/C][C]31140.9656263329[/C][C]776.034373667113[/C][/ROW]
[ROW][C]10[/C][C]38030[/C][C]31597.0901451270[/C][C]6432.90985487296[/C][/ROW]
[ROW][C]11[/C][C]27534[/C][C]35378.1184237259[/C][C]-7844.11842372591[/C][/ROW]
[ROW][C]12[/C][C]18387[/C][C]30767.6335498676[/C][C]-12380.6335498676[/C][/ROW]
[ROW][C]13[/C][C]50556[/C][C]23490.7516076219[/C][C]27065.2483923781[/C][/ROW]
[ROW][C]14[/C][C]43901[/C][C]39398.7111232314[/C][C]4502.28887676863[/C][/ROW]
[ROW][C]15[/C][C]48572[/C][C]42044.9912585869[/C][C]6527.00874141307[/C][/ROW]
[ROW][C]16[/C][C]43899[/C][C]45881.3274085876[/C][C]-1982.32740858763[/C][/ROW]
[ROW][C]17[/C][C]37532[/C][C]44716.1881235044[/C][C]-7184.18812350441[/C][/ROW]
[ROW][C]18[/C][C]40357[/C][C]40493.5860559241[/C][C]-136.586055924097[/C][/ROW]
[ROW][C]19[/C][C]35489[/C][C]40413.3057859433[/C][C]-4924.3057859433[/C][/ROW]
[ROW][C]20[/C][C]29027[/C][C]37518.9796024331[/C][C]-8491.9796024331[/C][/ROW]
[ROW][C]21[/C][C]34485[/C][C]32527.7057088992[/C][C]1957.2942911008[/C][/ROW]
[ROW][C]22[/C][C]42598[/C][C]33678.1314464193[/C][C]8919.86855358075[/C][/ROW]
[ROW][C]23[/C][C]30306[/C][C]38920.9027588333[/C][C]-8614.9027588333[/C][/ROW]
[ROW][C]24[/C][C]26451[/C][C]33857.379146132[/C][C]-7406.379146132[/C][/ROW]
[ROW][C]25[/C][C]47460[/C][C]29504.1813514610[/C][C]17955.8186485390[/C][/ROW]
[ROW][C]26[/C][C]50104[/C][C]40057.9524452827[/C][C]10046.0475547173[/C][/ROW]
[ROW][C]27[/C][C]61465[/C][C]45962.6504356893[/C][C]15502.3495643107[/C][/ROW]
[ROW][C]28[/C][C]53726[/C][C]55074.3624617769[/C][C]-1348.36246177694[/C][/ROW]
[ROW][C]29[/C][C]39477[/C][C]54281.8445013523[/C][C]-14804.8445013523[/C][/ROW]
[ROW][C]30[/C][C]43895[/C][C]45580.1003478152[/C][C]-1685.10034781517[/C][/ROW]
[ROW][C]31[/C][C]31481[/C][C]44589.6602186814[/C][C]-13108.6602186814[/C][/ROW]
[ROW][C]32[/C][C]29896[/C][C]36884.8709243260[/C][C]-6988.87092432604[/C][/ROW]
[ROW][C]33[/C][C]33842[/C][C]32777.0691368757[/C][C]1064.93086312432[/C][/ROW]
[ROW][C]34[/C][C]39120[/C][C]33402.9964075922[/C][C]5717.00359240784[/C][/ROW]
[ROW][C]35[/C][C]33702[/C][C]36763.2412640269[/C][C]-3061.24126402692[/C][/ROW]
[ROW][C]36[/C][C]25094[/C][C]34963.9560186210[/C][C]-9869.95601862096[/C][/ROW]
[ROW][C]37[/C][C]51442[/C][C]29162.7581693049[/C][C]22279.2418306951[/C][/ROW]
[ROW][C]38[/C][C]45594[/C][C]42257.6787088474[/C][C]3336.32129115263[/C][/ROW]
[ROW][C]39[/C][C]52518[/C][C]44218.6458967808[/C][C]8299.35410321918[/C][/ROW]
[ROW][C]40[/C][C]48564[/C][C]49096.7015926191[/C][C]-532.701592619109[/C][/ROW]
[ROW][C]41[/C][C]41745[/C][C]48783.5991504604[/C][C]-7038.59915046041[/C][/ROW]
[ROW][C]42[/C][C]49585[/C][C]44646.5689370721[/C][C]4938.43106292789[/C][/ROW]
[ROW][C]43[/C][C]32747[/C][C]47549.1974398945[/C][C]-14802.1974398945[/C][/ROW]
[ROW][C]44[/C][C]33379[/C][C]38849.0091319161[/C][C]-5470.00913191609[/C][/ROW]
[ROW][C]45[/C][C]35645[/C][C]35633.9385528838[/C][C]11.0614471161825[/C][/ROW]
[ROW][C]46[/C][C]37034[/C][C]35640.440065464[/C][C]1393.55993453602[/C][/ROW]
[ROW][C]47[/C][C]35681[/C][C]36459.5234413039[/C][C]-778.523441303878[/C][/ROW]
[ROW][C]48[/C][C]20972[/C][C]36001.9359399195[/C][C]-15029.9359399195[/C][/ROW]
[ROW][C]49[/C][C]58552[/C][C]27167.8913012686[/C][C]31384.1086987314[/C][/ROW]
[ROW][C]50[/C][C]54955[/C][C]45614.3183716923[/C][C]9340.68162830766[/C][/ROW]
[ROW][C]51[/C][C]65540[/C][C]51104.428162562[/C][C]14435.5718374380[/C][/ROW]
[ROW][C]52[/C][C]51570[/C][C]59589.1273992151[/C][C]-8019.12739921507[/C][/ROW]
[ROW][C]53[/C][C]51145[/C][C]54875.7786736533[/C][C]-3730.77867365331[/C][/ROW]
[ROW][C]54[/C][C]46641[/C][C]52682.9639157112[/C][C]-6041.96391571119[/C][/ROW]
[ROW][C]55[/C][C]35704[/C][C]49131.7193096216[/C][C]-13427.7193096216[/C][/ROW]
[ROW][C]56[/C][C]33253[/C][C]41239.3987933768[/C][C]-7986.39879337679[/C][/ROW]
[ROW][C]57[/C][C]35193[/C][C]36545.2867409513[/C][C]-1352.28674095135[/C][/ROW]
[ROW][C]58[/C][C]41668[/C][C]35750.4622332772[/C][C]5917.53776672277[/C][/ROW]
[ROW][C]59[/C][C]34865[/C][C]39228.5737163267[/C][C]-4363.57371632668[/C][/ROW]
[ROW][C]60[/C][C]21210[/C][C]36663.8252604340[/C][C]-15453.8252604340[/C][/ROW]
[ROW][C]61[/C][C]56126[/C][C]27580.6340389739[/C][C]28545.3659610261[/C][/ROW]
[ROW][C]62[/C][C]49231[/C][C]44358.5523304661[/C][C]4872.44766953393[/C][/ROW]
[ROW][C]63[/C][C]59723[/C][C]47222.398216717[/C][C]12500.601783283[/C][/ROW]
[ROW][C]64[/C][C]48103[/C][C]54569.7930828666[/C][C]-6466.79308286656[/C][/ROW]
[ROW][C]65[/C][C]47472[/C][C]50768.8494866114[/C][C]-3296.84948661141[/C][/ROW]
[ROW][C]66[/C][C]50497[/C][C]48831.0823764879[/C][C]1665.91762351205[/C][/ROW]
[ROW][C]67[/C][C]40059[/C][C]49810.2476044204[/C][C]-9751.24760442035[/C][/ROW]
[ROW][C]68[/C][C]34149[/C][C]44078.8222035182[/C][C]-9929.82220351817[/C][/ROW]
[ROW][C]69[/C][C]36860[/C][C]38242.4372082394[/C][C]-1382.43720823945[/C][/ROW]
[ROW][C]70[/C][C]46356[/C][C]37429.8913626326[/C][C]8926.10863736744[/C][/ROW]
[ROW][C]71[/C][C]36577[/C][C]42676.3303672404[/C][C]-6099.33036724044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11518&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11518&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
35353654499.6017958301-963.60179583011
45240853933.232031363-1525.23203136304
54145453036.7566303219-11582.7566303219
63827146228.8374535592-7957.83745355917
73530641551.5127082718-6245.51270827177
82641437880.6295936209-11466.6295936209
93191731140.9656263329776.034373667113
103803031597.09014512706432.90985487296
112753435378.1184237259-7844.11842372591
121838730767.6335498676-12380.6335498676
135055623490.751607621927065.2483923781
144390139398.71112323144502.28887676863
154857242044.99125858696527.00874141307
164389945881.3274085876-1982.32740858763
173753244716.1881235044-7184.18812350441
184035740493.5860559241-136.586055924097
193548940413.3057859433-4924.3057859433
202902737518.9796024331-8491.9796024331
213448532527.70570889921957.2942911008
224259833678.13144641938919.86855358075
233030638920.9027588333-8614.9027588333
242645133857.379146132-7406.379146132
254746029504.181351461017955.8186485390
265010440057.952445282710046.0475547173
276146545962.650435689315502.3495643107
285372655074.3624617769-1348.36246177694
293947754281.8445013523-14804.8445013523
304389545580.1003478152-1685.10034781517
313148144589.6602186814-13108.6602186814
322989636884.8709243260-6988.87092432604
333384232777.06913687571064.93086312432
343912033402.99640759225717.00359240784
353370236763.2412640269-3061.24126402692
362509434963.9560186210-9869.95601862096
375144229162.758169304922279.2418306951
384559442257.67870884743336.32129115263
395251844218.64589678088299.35410321918
404856449096.7015926191-532.701592619109
414174548783.5991504604-7038.59915046041
424958544646.56893707214938.43106292789
433274747549.1974398945-14802.1974398945
443337938849.0091319161-5470.00913191609
453564535633.938552883811.0614471161825
463703435640.4400654641393.55993453602
473568136459.5234413039-778.523441303878
482097236001.9359399195-15029.9359399195
495855227167.891301268631384.1086987314
505495545614.31837169239340.68162830766
516554051104.42816256214435.5718374380
525157059589.1273992151-8019.12739921507
535114554875.7786736533-3730.77867365331
544664152682.9639157112-6041.96391571119
553570449131.7193096216-13427.7193096216
563325341239.3987933768-7986.39879337679
573519336545.2867409513-1352.28674095135
584166835750.46223327725917.53776672277
593486539228.5737163267-4363.57371632668
602121036663.8252604340-15453.8252604340
615612627580.634038973928545.3659610261
624923144358.55233046614872.44766953393
635972347222.39821671712500.601783283
644810354569.7930828666-6466.79308286656
654747250768.8494866114-3296.84948661141
665049748831.08237648791665.91762351205
674005949810.2476044204-9751.24760442035
683414944078.8222035182-9929.82220351817
693686038242.4372082394-1382.43720823945
704635637429.89136263268926.10863736744
713657742676.3303672404-6099.33036724044







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7239091.367866703718712.118358823859470.6173745835
7339091.367866703715452.618281794862730.1174516126
7439091.367866703712591.044220158565591.6915132489
7539091.367866703710009.692797938368173.0429354691
7639091.36786670377639.4919888031370543.2437446042
7739091.36786670375435.8011997691772746.9345336382
7839091.36786670373367.7924702503774814.943263157
7939091.36786670371413.1180328845176769.6177005229
8039091.3678667037-445.03538363391378627.7711170413
8139091.3678667037-2219.6942523815280402.4299857889
8239091.3678667037-3921.1945405806182103.930273988
8339091.3678667037-5557.9008425835683740.636575991

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
72 & 39091.3678667037 & 18712.1183588238 & 59470.6173745835 \tabularnewline
73 & 39091.3678667037 & 15452.6182817948 & 62730.1174516126 \tabularnewline
74 & 39091.3678667037 & 12591.0442201585 & 65591.6915132489 \tabularnewline
75 & 39091.3678667037 & 10009.6927979383 & 68173.0429354691 \tabularnewline
76 & 39091.3678667037 & 7639.49198880313 & 70543.2437446042 \tabularnewline
77 & 39091.3678667037 & 5435.80119976917 & 72746.9345336382 \tabularnewline
78 & 39091.3678667037 & 3367.79247025037 & 74814.943263157 \tabularnewline
79 & 39091.3678667037 & 1413.11803288451 & 76769.6177005229 \tabularnewline
80 & 39091.3678667037 & -445.035383633913 & 78627.7711170413 \tabularnewline
81 & 39091.3678667037 & -2219.69425238152 & 80402.4299857889 \tabularnewline
82 & 39091.3678667037 & -3921.19454058061 & 82103.930273988 \tabularnewline
83 & 39091.3678667037 & -5557.90084258356 & 83740.636575991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=11518&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]39091.3678667037[/C][C]18712.1183588238[/C][C]59470.6173745835[/C][/ROW]
[ROW][C]73[/C][C]39091.3678667037[/C][C]15452.6182817948[/C][C]62730.1174516126[/C][/ROW]
[ROW][C]74[/C][C]39091.3678667037[/C][C]12591.0442201585[/C][C]65591.6915132489[/C][/ROW]
[ROW][C]75[/C][C]39091.3678667037[/C][C]10009.6927979383[/C][C]68173.0429354691[/C][/ROW]
[ROW][C]76[/C][C]39091.3678667037[/C][C]7639.49198880313[/C][C]70543.2437446042[/C][/ROW]
[ROW][C]77[/C][C]39091.3678667037[/C][C]5435.80119976917[/C][C]72746.9345336382[/C][/ROW]
[ROW][C]78[/C][C]39091.3678667037[/C][C]3367.79247025037[/C][C]74814.943263157[/C][/ROW]
[ROW][C]79[/C][C]39091.3678667037[/C][C]1413.11803288451[/C][C]76769.6177005229[/C][/ROW]
[ROW][C]80[/C][C]39091.3678667037[/C][C]-445.035383633913[/C][C]78627.7711170413[/C][/ROW]
[ROW][C]81[/C][C]39091.3678667037[/C][C]-2219.69425238152[/C][C]80402.4299857889[/C][/ROW]
[ROW][C]82[/C][C]39091.3678667037[/C][C]-3921.19454058061[/C][C]82103.930273988[/C][/ROW]
[ROW][C]83[/C][C]39091.3678667037[/C][C]-5557.90084258356[/C][C]83740.636575991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=11518&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=11518&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
7239091.367866703718712.118358823859470.6173745835
7339091.367866703715452.618281794862730.1174516126
7439091.367866703712591.044220158565591.6915132489
7539091.367866703710009.692797938368173.0429354691
7639091.36786670377639.4919888031370543.2437446042
7739091.36786670375435.8011997691772746.9345336382
7839091.36786670373367.7924702503774814.943263157
7939091.36786670371413.1180328845176769.6177005229
8039091.3678667037-445.03538363391378627.7711170413
8139091.3678667037-2219.6942523815280402.4299857889
8239091.3678667037-3921.1945405806182103.930273988
8339091.3678667037-5557.9008425835683740.636575991



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')