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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 14:59:12 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/28/t14171867617gs0hju3rppm2tk.htm/, Retrieved Sun, 19 May 2024 15:27:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260919, Retrieved Sun, 19 May 2024 15:27:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsEline Van Loon
Estimated Impact57
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 14:59:12] [9adebd9d8505f0d6c7bd6ecbde218cd8] [Current]
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Dataseries X:
22943
21413
20631
19775
17506
20688
32631
34062
29159
25871
23719
25638
27596
28006
27662
26655
25213
28434
40388
42758
37956
33490
31578
34766
32324
32046
29565
28284
26366
27530
39728
41528
36458
32301
28985
29118
29249
28036
26326
24942
23280
23969
35948
37639
34327
30133
27549
27990
30437
30464
28471
26882
25806
26465
36416
42870
40489
36645
33841
33496
34504
34699
33322
32160
30173
30782
43062
46223
45191
40671
37251
36870




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260919&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]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260919&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260919&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.952846160910288
beta0.0322574040748725
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.952846160910288 \tabularnewline
beta & 0.0322574040748725 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260919&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]0.952846160910288[/C][/ROW]
[ROW][C]beta[/C][C]0.0322574040748725[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260919&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260919&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
alpha0.952846160910288
beta0.0322574040748725
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132759623970.59455128213625.40544871794
142800627903.8301556196102.169844380391
152766227685.7712344942-23.7712344942338
162665526728.8541990303-73.8541990302583
172521325326.0291283743-113.029128374277
182843428482.5272745586-48.5272745585789
194038840347.41088020340.5891197969977
204275842099.2479278838658.752072116156
213795638027.2634682236-71.2634682235803
223349034860.5377917646-1370.53779176458
233157831521.511576952956.4884230470743
243476633578.87472669171187.12527330832
253232436957.9172007527-4633.91720075265
263204632723.3028261974-677.302826197356
272956531600.7776022902-2035.77760229019
282828428506.7145446609-222.714544660939
292636626737.9739192746-371.973919274642
302753029420.5927119527-1890.59271195266
313972839247.6688476259480.331152374129
324152841174.3725515226353.627448477375
333645836494.5612073226-36.5612073225566
343230133018.0352721841-717.035272184054
352898530107.4720644489-1122.47206444893
362911830797.0300488831-1679.03004888311
372924930784.7367335396-1535.73673353957
382803629398.1618260872-1362.16182608715
392632627247.3445163634-921.344516363417
402494225023.2417122082-81.2417122082297
412328023109.1972194359170.802780564089
422396925981.0054116323-2012.00541163233
433594835544.0757134977403.924286502341
443763937129.5360234055509.463976594503
453432732322.13902962992004.86097037009
463013330563.7582742674-430.758274267439
472754927720.7250713966-171.725071396624
482799029133.0472865088-1143.04728650878
493043729497.7865229013939.213477098692
503046430413.280669865450.7193301346415
512847129608.5722994016-1137.57229940156
522688227190.4700285405-308.47002854052
532580625037.2308785406768.769121459351
542646528359.6946218734-1894.69462187343
553641638135.883529497-1719.88352949702
564287037624.79934000365245.20065999641
574048937468.04482638973020.9551736103
583664536661.9280074378-16.9280074378257
593384134337.0766985139-496.076698513854
603349635496.2216594002-2000.22165940018
613450435217.7272881567-713.727288156733
623469934540.8570211443158.142978855743
633332233810.3059182933-488.305918293336
643216032097.737624376862.2623756231951
653017330407.7279857484-234.727985748446
663078232676.7595920956-1894.75959209561
674306242489.4663801427572.533619857335
684622344589.93082391761633.06917608238
694519140874.26255903594316.73744096408
704067141187.180232903-516.180232902974
713725138376.2806580655-1125.28065806552
723687038857.8814038197-1987.88140381975

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 27596 & 23970.5945512821 & 3625.40544871794 \tabularnewline
14 & 28006 & 27903.8301556196 & 102.169844380391 \tabularnewline
15 & 27662 & 27685.7712344942 & -23.7712344942338 \tabularnewline
16 & 26655 & 26728.8541990303 & -73.8541990302583 \tabularnewline
17 & 25213 & 25326.0291283743 & -113.029128374277 \tabularnewline
18 & 28434 & 28482.5272745586 & -48.5272745585789 \tabularnewline
19 & 40388 & 40347.410880203 & 40.5891197969977 \tabularnewline
20 & 42758 & 42099.2479278838 & 658.752072116156 \tabularnewline
21 & 37956 & 38027.2634682236 & -71.2634682235803 \tabularnewline
22 & 33490 & 34860.5377917646 & -1370.53779176458 \tabularnewline
23 & 31578 & 31521.5115769529 & 56.4884230470743 \tabularnewline
24 & 34766 & 33578.8747266917 & 1187.12527330832 \tabularnewline
25 & 32324 & 36957.9172007527 & -4633.91720075265 \tabularnewline
26 & 32046 & 32723.3028261974 & -677.302826197356 \tabularnewline
27 & 29565 & 31600.7776022902 & -2035.77760229019 \tabularnewline
28 & 28284 & 28506.7145446609 & -222.714544660939 \tabularnewline
29 & 26366 & 26737.9739192746 & -371.973919274642 \tabularnewline
30 & 27530 & 29420.5927119527 & -1890.59271195266 \tabularnewline
31 & 39728 & 39247.6688476259 & 480.331152374129 \tabularnewline
32 & 41528 & 41174.3725515226 & 353.627448477375 \tabularnewline
33 & 36458 & 36494.5612073226 & -36.5612073225566 \tabularnewline
34 & 32301 & 33018.0352721841 & -717.035272184054 \tabularnewline
35 & 28985 & 30107.4720644489 & -1122.47206444893 \tabularnewline
36 & 29118 & 30797.0300488831 & -1679.03004888311 \tabularnewline
37 & 29249 & 30784.7367335396 & -1535.73673353957 \tabularnewline
38 & 28036 & 29398.1618260872 & -1362.16182608715 \tabularnewline
39 & 26326 & 27247.3445163634 & -921.344516363417 \tabularnewline
40 & 24942 & 25023.2417122082 & -81.2417122082297 \tabularnewline
41 & 23280 & 23109.1972194359 & 170.802780564089 \tabularnewline
42 & 23969 & 25981.0054116323 & -2012.00541163233 \tabularnewline
43 & 35948 & 35544.0757134977 & 403.924286502341 \tabularnewline
44 & 37639 & 37129.5360234055 & 509.463976594503 \tabularnewline
45 & 34327 & 32322.1390296299 & 2004.86097037009 \tabularnewline
46 & 30133 & 30563.7582742674 & -430.758274267439 \tabularnewline
47 & 27549 & 27720.7250713966 & -171.725071396624 \tabularnewline
48 & 27990 & 29133.0472865088 & -1143.04728650878 \tabularnewline
49 & 30437 & 29497.7865229013 & 939.213477098692 \tabularnewline
50 & 30464 & 30413.2806698654 & 50.7193301346415 \tabularnewline
51 & 28471 & 29608.5722994016 & -1137.57229940156 \tabularnewline
52 & 26882 & 27190.4700285405 & -308.47002854052 \tabularnewline
53 & 25806 & 25037.2308785406 & 768.769121459351 \tabularnewline
54 & 26465 & 28359.6946218734 & -1894.69462187343 \tabularnewline
55 & 36416 & 38135.883529497 & -1719.88352949702 \tabularnewline
56 & 42870 & 37624.7993400036 & 5245.20065999641 \tabularnewline
57 & 40489 & 37468.0448263897 & 3020.9551736103 \tabularnewline
58 & 36645 & 36661.9280074378 & -16.9280074378257 \tabularnewline
59 & 33841 & 34337.0766985139 & -496.076698513854 \tabularnewline
60 & 33496 & 35496.2216594002 & -2000.22165940018 \tabularnewline
61 & 34504 & 35217.7272881567 & -713.727288156733 \tabularnewline
62 & 34699 & 34540.8570211443 & 158.142978855743 \tabularnewline
63 & 33322 & 33810.3059182933 & -488.305918293336 \tabularnewline
64 & 32160 & 32097.7376243768 & 62.2623756231951 \tabularnewline
65 & 30173 & 30407.7279857484 & -234.727985748446 \tabularnewline
66 & 30782 & 32676.7595920956 & -1894.75959209561 \tabularnewline
67 & 43062 & 42489.4663801427 & 572.533619857335 \tabularnewline
68 & 46223 & 44589.9308239176 & 1633.06917608238 \tabularnewline
69 & 45191 & 40874.2625590359 & 4316.73744096408 \tabularnewline
70 & 40671 & 41187.180232903 & -516.180232902974 \tabularnewline
71 & 37251 & 38376.2806580655 & -1125.28065806552 \tabularnewline
72 & 36870 & 38857.8814038197 & -1987.88140381975 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260919&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]27596[/C][C]23970.5945512821[/C][C]3625.40544871794[/C][/ROW]
[ROW][C]14[/C][C]28006[/C][C]27903.8301556196[/C][C]102.169844380391[/C][/ROW]
[ROW][C]15[/C][C]27662[/C][C]27685.7712344942[/C][C]-23.7712344942338[/C][/ROW]
[ROW][C]16[/C][C]26655[/C][C]26728.8541990303[/C][C]-73.8541990302583[/C][/ROW]
[ROW][C]17[/C][C]25213[/C][C]25326.0291283743[/C][C]-113.029128374277[/C][/ROW]
[ROW][C]18[/C][C]28434[/C][C]28482.5272745586[/C][C]-48.5272745585789[/C][/ROW]
[ROW][C]19[/C][C]40388[/C][C]40347.410880203[/C][C]40.5891197969977[/C][/ROW]
[ROW][C]20[/C][C]42758[/C][C]42099.2479278838[/C][C]658.752072116156[/C][/ROW]
[ROW][C]21[/C][C]37956[/C][C]38027.2634682236[/C][C]-71.2634682235803[/C][/ROW]
[ROW][C]22[/C][C]33490[/C][C]34860.5377917646[/C][C]-1370.53779176458[/C][/ROW]
[ROW][C]23[/C][C]31578[/C][C]31521.5115769529[/C][C]56.4884230470743[/C][/ROW]
[ROW][C]24[/C][C]34766[/C][C]33578.8747266917[/C][C]1187.12527330832[/C][/ROW]
[ROW][C]25[/C][C]32324[/C][C]36957.9172007527[/C][C]-4633.91720075265[/C][/ROW]
[ROW][C]26[/C][C]32046[/C][C]32723.3028261974[/C][C]-677.302826197356[/C][/ROW]
[ROW][C]27[/C][C]29565[/C][C]31600.7776022902[/C][C]-2035.77760229019[/C][/ROW]
[ROW][C]28[/C][C]28284[/C][C]28506.7145446609[/C][C]-222.714544660939[/C][/ROW]
[ROW][C]29[/C][C]26366[/C][C]26737.9739192746[/C][C]-371.973919274642[/C][/ROW]
[ROW][C]30[/C][C]27530[/C][C]29420.5927119527[/C][C]-1890.59271195266[/C][/ROW]
[ROW][C]31[/C][C]39728[/C][C]39247.6688476259[/C][C]480.331152374129[/C][/ROW]
[ROW][C]32[/C][C]41528[/C][C]41174.3725515226[/C][C]353.627448477375[/C][/ROW]
[ROW][C]33[/C][C]36458[/C][C]36494.5612073226[/C][C]-36.5612073225566[/C][/ROW]
[ROW][C]34[/C][C]32301[/C][C]33018.0352721841[/C][C]-717.035272184054[/C][/ROW]
[ROW][C]35[/C][C]28985[/C][C]30107.4720644489[/C][C]-1122.47206444893[/C][/ROW]
[ROW][C]36[/C][C]29118[/C][C]30797.0300488831[/C][C]-1679.03004888311[/C][/ROW]
[ROW][C]37[/C][C]29249[/C][C]30784.7367335396[/C][C]-1535.73673353957[/C][/ROW]
[ROW][C]38[/C][C]28036[/C][C]29398.1618260872[/C][C]-1362.16182608715[/C][/ROW]
[ROW][C]39[/C][C]26326[/C][C]27247.3445163634[/C][C]-921.344516363417[/C][/ROW]
[ROW][C]40[/C][C]24942[/C][C]25023.2417122082[/C][C]-81.2417122082297[/C][/ROW]
[ROW][C]41[/C][C]23280[/C][C]23109.1972194359[/C][C]170.802780564089[/C][/ROW]
[ROW][C]42[/C][C]23969[/C][C]25981.0054116323[/C][C]-2012.00541163233[/C][/ROW]
[ROW][C]43[/C][C]35948[/C][C]35544.0757134977[/C][C]403.924286502341[/C][/ROW]
[ROW][C]44[/C][C]37639[/C][C]37129.5360234055[/C][C]509.463976594503[/C][/ROW]
[ROW][C]45[/C][C]34327[/C][C]32322.1390296299[/C][C]2004.86097037009[/C][/ROW]
[ROW][C]46[/C][C]30133[/C][C]30563.7582742674[/C][C]-430.758274267439[/C][/ROW]
[ROW][C]47[/C][C]27549[/C][C]27720.7250713966[/C][C]-171.725071396624[/C][/ROW]
[ROW][C]48[/C][C]27990[/C][C]29133.0472865088[/C][C]-1143.04728650878[/C][/ROW]
[ROW][C]49[/C][C]30437[/C][C]29497.7865229013[/C][C]939.213477098692[/C][/ROW]
[ROW][C]50[/C][C]30464[/C][C]30413.2806698654[/C][C]50.7193301346415[/C][/ROW]
[ROW][C]51[/C][C]28471[/C][C]29608.5722994016[/C][C]-1137.57229940156[/C][/ROW]
[ROW][C]52[/C][C]26882[/C][C]27190.4700285405[/C][C]-308.47002854052[/C][/ROW]
[ROW][C]53[/C][C]25806[/C][C]25037.2308785406[/C][C]768.769121459351[/C][/ROW]
[ROW][C]54[/C][C]26465[/C][C]28359.6946218734[/C][C]-1894.69462187343[/C][/ROW]
[ROW][C]55[/C][C]36416[/C][C]38135.883529497[/C][C]-1719.88352949702[/C][/ROW]
[ROW][C]56[/C][C]42870[/C][C]37624.7993400036[/C][C]5245.20065999641[/C][/ROW]
[ROW][C]57[/C][C]40489[/C][C]37468.0448263897[/C][C]3020.9551736103[/C][/ROW]
[ROW][C]58[/C][C]36645[/C][C]36661.9280074378[/C][C]-16.9280074378257[/C][/ROW]
[ROW][C]59[/C][C]33841[/C][C]34337.0766985139[/C][C]-496.076698513854[/C][/ROW]
[ROW][C]60[/C][C]33496[/C][C]35496.2216594002[/C][C]-2000.22165940018[/C][/ROW]
[ROW][C]61[/C][C]34504[/C][C]35217.7272881567[/C][C]-713.727288156733[/C][/ROW]
[ROW][C]62[/C][C]34699[/C][C]34540.8570211443[/C][C]158.142978855743[/C][/ROW]
[ROW][C]63[/C][C]33322[/C][C]33810.3059182933[/C][C]-488.305918293336[/C][/ROW]
[ROW][C]64[/C][C]32160[/C][C]32097.7376243768[/C][C]62.2623756231951[/C][/ROW]
[ROW][C]65[/C][C]30173[/C][C]30407.7279857484[/C][C]-234.727985748446[/C][/ROW]
[ROW][C]66[/C][C]30782[/C][C]32676.7595920956[/C][C]-1894.75959209561[/C][/ROW]
[ROW][C]67[/C][C]43062[/C][C]42489.4663801427[/C][C]572.533619857335[/C][/ROW]
[ROW][C]68[/C][C]46223[/C][C]44589.9308239176[/C][C]1633.06917608238[/C][/ROW]
[ROW][C]69[/C][C]45191[/C][C]40874.2625590359[/C][C]4316.73744096408[/C][/ROW]
[ROW][C]70[/C][C]40671[/C][C]41187.180232903[/C][C]-516.180232902974[/C][/ROW]
[ROW][C]71[/C][C]37251[/C][C]38376.2806580655[/C][C]-1125.28065806552[/C][/ROW]
[ROW][C]72[/C][C]36870[/C][C]38857.8814038197[/C][C]-1987.88140381975[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260919&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260919&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
132759623970.59455128213625.40544871794
142800627903.8301556196102.169844380391
152766227685.7712344942-23.7712344942338
162665526728.8541990303-73.8541990302583
172521325326.0291283743-113.029128374277
182843428482.5272745586-48.5272745585789
194038840347.41088020340.5891197969977
204275842099.2479278838658.752072116156
213795638027.2634682236-71.2634682235803
223349034860.5377917646-1370.53779176458
233157831521.511576952956.4884230470743
243476633578.87472669171187.12527330832
253232436957.9172007527-4633.91720075265
263204632723.3028261974-677.302826197356
272956531600.7776022902-2035.77760229019
282828428506.7145446609-222.714544660939
292636626737.9739192746-371.973919274642
302753029420.5927119527-1890.59271195266
313972839247.6688476259480.331152374129
324152841174.3725515226353.627448477375
333645836494.5612073226-36.5612073225566
343230133018.0352721841-717.035272184054
352898530107.4720644489-1122.47206444893
362911830797.0300488831-1679.03004888311
372924930784.7367335396-1535.73673353957
382803629398.1618260872-1362.16182608715
392632627247.3445163634-921.344516363417
402494225023.2417122082-81.2417122082297
412328023109.1972194359170.802780564089
422396925981.0054116323-2012.00541163233
433594835544.0757134977403.924286502341
443763937129.5360234055509.463976594503
453432732322.13902962992004.86097037009
463013330563.7582742674-430.758274267439
472754927720.7250713966-171.725071396624
482799029133.0472865088-1143.04728650878
493043729497.7865229013939.213477098692
503046430413.280669865450.7193301346415
512847129608.5722994016-1137.57229940156
522688227190.4700285405-308.47002854052
532580625037.2308785406768.769121459351
542646528359.6946218734-1894.69462187343
553641638135.883529497-1719.88352949702
564287037624.79934000365245.20065999641
574048937468.04482638973020.9551736103
583664536661.9280074378-16.9280074378257
593384134337.0766985139-496.076698513854
603349635496.2216594002-2000.22165940018
613450435217.7272881567-713.727288156733
623469934540.8570211443158.142978855743
633332233810.3059182933-488.305918293336
643216032097.737624376862.2623756231951
653017330407.7279857484-234.727985748446
663078232676.7595920956-1894.75959209561
674306242489.4663801427572.533619857335
684622344589.93082391761633.06917608238
694519140874.26255903594316.73744096408
704067141187.180232903-516.180232902974
713725138376.2806580655-1125.28065806552
723687038857.8814038197-1987.88140381975







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7338645.104412247835555.046426575741735.1623979198
7438704.651715105234370.373597355943038.9298328546
7537803.304630894532454.488993516843152.1202682721
7636607.359400009530359.312872510942855.4059275081
7734867.486577012227790.14398558741944.8291684375
7837312.58317714329452.561023516145172.6053307699
7949135.966894350240526.10992689157745.8238618095
8050812.225788217841476.494125235560147.9574512001
8145688.167103362535644.425987731155731.9082189938
8241548.45474468530810.19473493752286.714754433
8339104.986880747927682.447570524350527.5261909716
8440557.031838791728457.96965774752656.0940198364

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 38645.1044122478 & 35555.0464265757 & 41735.1623979198 \tabularnewline
74 & 38704.6517151052 & 34370.3735973559 & 43038.9298328546 \tabularnewline
75 & 37803.3046308945 & 32454.4889935168 & 43152.1202682721 \tabularnewline
76 & 36607.3594000095 & 30359.3128725109 & 42855.4059275081 \tabularnewline
77 & 34867.4865770122 & 27790.143985587 & 41944.8291684375 \tabularnewline
78 & 37312.583177143 & 29452.5610235161 & 45172.6053307699 \tabularnewline
79 & 49135.9668943502 & 40526.109926891 & 57745.8238618095 \tabularnewline
80 & 50812.2257882178 & 41476.4941252355 & 60147.9574512001 \tabularnewline
81 & 45688.1671033625 & 35644.4259877311 & 55731.9082189938 \tabularnewline
82 & 41548.454744685 & 30810.194734937 & 52286.714754433 \tabularnewline
83 & 39104.9868807479 & 27682.4475705243 & 50527.5261909716 \tabularnewline
84 & 40557.0318387917 & 28457.969657747 & 52656.0940198364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260919&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]73[/C][C]38645.1044122478[/C][C]35555.0464265757[/C][C]41735.1623979198[/C][/ROW]
[ROW][C]74[/C][C]38704.6517151052[/C][C]34370.3735973559[/C][C]43038.9298328546[/C][/ROW]
[ROW][C]75[/C][C]37803.3046308945[/C][C]32454.4889935168[/C][C]43152.1202682721[/C][/ROW]
[ROW][C]76[/C][C]36607.3594000095[/C][C]30359.3128725109[/C][C]42855.4059275081[/C][/ROW]
[ROW][C]77[/C][C]34867.4865770122[/C][C]27790.143985587[/C][C]41944.8291684375[/C][/ROW]
[ROW][C]78[/C][C]37312.583177143[/C][C]29452.5610235161[/C][C]45172.6053307699[/C][/ROW]
[ROW][C]79[/C][C]49135.9668943502[/C][C]40526.109926891[/C][C]57745.8238618095[/C][/ROW]
[ROW][C]80[/C][C]50812.2257882178[/C][C]41476.4941252355[/C][C]60147.9574512001[/C][/ROW]
[ROW][C]81[/C][C]45688.1671033625[/C][C]35644.4259877311[/C][C]55731.9082189938[/C][/ROW]
[ROW][C]82[/C][C]41548.454744685[/C][C]30810.194734937[/C][C]52286.714754433[/C][/ROW]
[ROW][C]83[/C][C]39104.9868807479[/C][C]27682.4475705243[/C][C]50527.5261909716[/C][/ROW]
[ROW][C]84[/C][C]40557.0318387917[/C][C]28457.969657747[/C][C]52656.0940198364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260919&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260919&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
7338645.104412247835555.046426575741735.1623979198
7438704.651715105234370.373597355943038.9298328546
7537803.304630894532454.488993516843152.1202682721
7636607.359400009530359.312872510942855.4059275081
7734867.486577012227790.14398558741944.8291684375
7837312.58317714329452.561023516145172.6053307699
7949135.966894350240526.10992689157745.8238618095
8050812.225788217841476.494125235560147.9574512001
8145688.167103362535644.425987731155731.9082189938
8241548.45474468530810.19473493752286.714754433
8339104.986880747927682.447570524350527.5261909716
8440557.031838791728457.96965774752656.0940198364



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')