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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 computationSun, 24 May 2015 00:22:48 +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/May/24/t1432423591gtcnorgkm2k6qsn.htm/, Retrieved Fri, 03 May 2024 03:34:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279281, Retrieved Fri, 03 May 2024 03:34:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact99
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-05-23 23:22:48] [fd1a5f0fdfa1bb1257f3e725ec184603] [Current]
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Dataseries X:
12849
11380
12079
11366
11328
10444
10854
10434
10137
10992
10906
12367
14371
11695
11546
10922
10670
10254
10573
10239
10253
11176
10719
11817
12487
11519
12025
10976
11276
10657
11141
10423
10640
11426
10948
12540
12200
10644
12044
11338
11292
10612
10995
10686
10635
11285
11475
12535
12490
12511
12799
11876
11602
11062
11055
10855
10704
11510
11663
12686
13516
12539
13811
12354
11441
10814
11261
10788
10326
11490
11029
11876




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=279281&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=279281&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279281&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
alpha0.824815231463246
beta0.239302238342013
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.824815231463246 \tabularnewline
beta & 0.239302238342013 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279281&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]0.824815231463246[/C][/ROW]
[ROW][C]beta[/C][C]0.239302238342013[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279281&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279281&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
alpha0.824815231463246
beta0.239302238342013
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31207999112168
41136610658.1195460539707.8804539461
51132810340.6317875738987.368212426169
61044410448.5566565159-4.55665651593517
7108549737.427391626881116.57260837312
81043410171.4118686895262.588131310491
9101379952.84662142311184.153378576892
10109929705.935413433421286.06458656658
111090610621.7409502232284.259049776772
121236710767.34910981811599.65089018191
131437112313.65179715232057.3482028477
141169514643.5498573854-2948.5498573854
151154612262.5217929575-716.521792957481
161092211581.0773076876-659.077307687638
171067010816.9251434304-146.925143430402
181025410446.2037810061-192.203781006088
191057310000.1987011551572.801298844943
201023910298.2410587766-59.2410587766135
211025310063.2722449537189.72775504632
221117610071.10519009711104.89480990294
231071911051.8661438584-332.866143858444
241181710781.03880063821035.96119936179
251248711843.719256702643.280743298046
261151912709.4817289576-1190.48172895764
271202511827.7515434681197.24845653189
281097612129.5752783427-1153.57527834273
291127611089.5261819888186.473818011249
301065711191.5762178633-534.576217863316
311114110593.3784775325547.621522467522
321042310995.8835247837-572.883524783683
331064010361.1031168994278.89688310062
341142610483.932866652942.067133348031
351094811339.7008741544-391.700874154441
361254011018.04274393491521.95725606513
371220012575.2031100764-375.203110076391
381064412493.4990706371-1849.49907063708
391204410830.71889819661213.28110180341
401133811933.6440455531-595.644045553143
411129211426.9718789883-134.97187898829
421061211273.6283649467-661.628364946735
431099510555.29826612439.701733880043
441068610832.150393556-146.150393555972
451063510596.935579056138.0644209439106
461128510521.1771098133763.822890186664
471147511194.7987425736280.201257426408
481253511524.82804729541010.17195270456
491249012656.3361724707-166.336172470717
501251112784.6110205309-273.611020530927
511279912770.398560853328.601439146747
521187613011.1008968644-1135.10089686435
531160212067.9174574005-465.917457400537
541106211584.7238626223-522.723862622335
551105510951.500175035103.49982496502
561085510855.224132294-0.22413229398262
571070410673.350750476530.6492495234561
581151010522.9917571182987.008242881797
591166311356.2680446131306.731955386891
601268611688.9848821481997.015117851855
611351612787.8487607849728.1512392151
621253913808.6722041943-1269.67220419431
631381112931.0523755776879.947624422435
641235414000.1559009358-1646.15590093577
651144112660.772294775-1219.77229477504
661081411432.3175659576-618.317565957621
671126110577.9082562695683.091743730531
681078810931.7499055163-143.749905516321
691032610575.2265932586-249.226593258642
701149010082.51212473391407.48787526612
711102911234.0911253865-205.091125386458
721187611015.1094911452860.890508854804

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 12079 & 9911 & 2168 \tabularnewline
4 & 11366 & 10658.1195460539 & 707.8804539461 \tabularnewline
5 & 11328 & 10340.6317875738 & 987.368212426169 \tabularnewline
6 & 10444 & 10448.5566565159 & -4.55665651593517 \tabularnewline
7 & 10854 & 9737.42739162688 & 1116.57260837312 \tabularnewline
8 & 10434 & 10171.4118686895 & 262.588131310491 \tabularnewline
9 & 10137 & 9952.84662142311 & 184.153378576892 \tabularnewline
10 & 10992 & 9705.93541343342 & 1286.06458656658 \tabularnewline
11 & 10906 & 10621.7409502232 & 284.259049776772 \tabularnewline
12 & 12367 & 10767.3491098181 & 1599.65089018191 \tabularnewline
13 & 14371 & 12313.6517971523 & 2057.3482028477 \tabularnewline
14 & 11695 & 14643.5498573854 & -2948.5498573854 \tabularnewline
15 & 11546 & 12262.5217929575 & -716.521792957481 \tabularnewline
16 & 10922 & 11581.0773076876 & -659.077307687638 \tabularnewline
17 & 10670 & 10816.9251434304 & -146.925143430402 \tabularnewline
18 & 10254 & 10446.2037810061 & -192.203781006088 \tabularnewline
19 & 10573 & 10000.1987011551 & 572.801298844943 \tabularnewline
20 & 10239 & 10298.2410587766 & -59.2410587766135 \tabularnewline
21 & 10253 & 10063.2722449537 & 189.72775504632 \tabularnewline
22 & 11176 & 10071.1051900971 & 1104.89480990294 \tabularnewline
23 & 10719 & 11051.8661438584 & -332.866143858444 \tabularnewline
24 & 11817 & 10781.0388006382 & 1035.96119936179 \tabularnewline
25 & 12487 & 11843.719256702 & 643.280743298046 \tabularnewline
26 & 11519 & 12709.4817289576 & -1190.48172895764 \tabularnewline
27 & 12025 & 11827.7515434681 & 197.24845653189 \tabularnewline
28 & 10976 & 12129.5752783427 & -1153.57527834273 \tabularnewline
29 & 11276 & 11089.5261819888 & 186.473818011249 \tabularnewline
30 & 10657 & 11191.5762178633 & -534.576217863316 \tabularnewline
31 & 11141 & 10593.3784775325 & 547.621522467522 \tabularnewline
32 & 10423 & 10995.8835247837 & -572.883524783683 \tabularnewline
33 & 10640 & 10361.1031168994 & 278.89688310062 \tabularnewline
34 & 11426 & 10483.932866652 & 942.067133348031 \tabularnewline
35 & 10948 & 11339.7008741544 & -391.700874154441 \tabularnewline
36 & 12540 & 11018.0427439349 & 1521.95725606513 \tabularnewline
37 & 12200 & 12575.2031100764 & -375.203110076391 \tabularnewline
38 & 10644 & 12493.4990706371 & -1849.49907063708 \tabularnewline
39 & 12044 & 10830.7188981966 & 1213.28110180341 \tabularnewline
40 & 11338 & 11933.6440455531 & -595.644045553143 \tabularnewline
41 & 11292 & 11426.9718789883 & -134.97187898829 \tabularnewline
42 & 10612 & 11273.6283649467 & -661.628364946735 \tabularnewline
43 & 10995 & 10555.29826612 & 439.701733880043 \tabularnewline
44 & 10686 & 10832.150393556 & -146.150393555972 \tabularnewline
45 & 10635 & 10596.9355790561 & 38.0644209439106 \tabularnewline
46 & 11285 & 10521.1771098133 & 763.822890186664 \tabularnewline
47 & 11475 & 11194.7987425736 & 280.201257426408 \tabularnewline
48 & 12535 & 11524.8280472954 & 1010.17195270456 \tabularnewline
49 & 12490 & 12656.3361724707 & -166.336172470717 \tabularnewline
50 & 12511 & 12784.6110205309 & -273.611020530927 \tabularnewline
51 & 12799 & 12770.3985608533 & 28.601439146747 \tabularnewline
52 & 11876 & 13011.1008968644 & -1135.10089686435 \tabularnewline
53 & 11602 & 12067.9174574005 & -465.917457400537 \tabularnewline
54 & 11062 & 11584.7238626223 & -522.723862622335 \tabularnewline
55 & 11055 & 10951.500175035 & 103.49982496502 \tabularnewline
56 & 10855 & 10855.224132294 & -0.22413229398262 \tabularnewline
57 & 10704 & 10673.3507504765 & 30.6492495234561 \tabularnewline
58 & 11510 & 10522.9917571182 & 987.008242881797 \tabularnewline
59 & 11663 & 11356.2680446131 & 306.731955386891 \tabularnewline
60 & 12686 & 11688.9848821481 & 997.015117851855 \tabularnewline
61 & 13516 & 12787.8487607849 & 728.1512392151 \tabularnewline
62 & 12539 & 13808.6722041943 & -1269.67220419431 \tabularnewline
63 & 13811 & 12931.0523755776 & 879.947624422435 \tabularnewline
64 & 12354 & 14000.1559009358 & -1646.15590093577 \tabularnewline
65 & 11441 & 12660.772294775 & -1219.77229477504 \tabularnewline
66 & 10814 & 11432.3175659576 & -618.317565957621 \tabularnewline
67 & 11261 & 10577.9082562695 & 683.091743730531 \tabularnewline
68 & 10788 & 10931.7499055163 & -143.749905516321 \tabularnewline
69 & 10326 & 10575.2265932586 & -249.226593258642 \tabularnewline
70 & 11490 & 10082.5121247339 & 1407.48787526612 \tabularnewline
71 & 11029 & 11234.0911253865 & -205.091125386458 \tabularnewline
72 & 11876 & 11015.1094911452 & 860.890508854804 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279281&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]3[/C][C]12079[/C][C]9911[/C][C]2168[/C][/ROW]
[ROW][C]4[/C][C]11366[/C][C]10658.1195460539[/C][C]707.8804539461[/C][/ROW]
[ROW][C]5[/C][C]11328[/C][C]10340.6317875738[/C][C]987.368212426169[/C][/ROW]
[ROW][C]6[/C][C]10444[/C][C]10448.5566565159[/C][C]-4.55665651593517[/C][/ROW]
[ROW][C]7[/C][C]10854[/C][C]9737.42739162688[/C][C]1116.57260837312[/C][/ROW]
[ROW][C]8[/C][C]10434[/C][C]10171.4118686895[/C][C]262.588131310491[/C][/ROW]
[ROW][C]9[/C][C]10137[/C][C]9952.84662142311[/C][C]184.153378576892[/C][/ROW]
[ROW][C]10[/C][C]10992[/C][C]9705.93541343342[/C][C]1286.06458656658[/C][/ROW]
[ROW][C]11[/C][C]10906[/C][C]10621.7409502232[/C][C]284.259049776772[/C][/ROW]
[ROW][C]12[/C][C]12367[/C][C]10767.3491098181[/C][C]1599.65089018191[/C][/ROW]
[ROW][C]13[/C][C]14371[/C][C]12313.6517971523[/C][C]2057.3482028477[/C][/ROW]
[ROW][C]14[/C][C]11695[/C][C]14643.5498573854[/C][C]-2948.5498573854[/C][/ROW]
[ROW][C]15[/C][C]11546[/C][C]12262.5217929575[/C][C]-716.521792957481[/C][/ROW]
[ROW][C]16[/C][C]10922[/C][C]11581.0773076876[/C][C]-659.077307687638[/C][/ROW]
[ROW][C]17[/C][C]10670[/C][C]10816.9251434304[/C][C]-146.925143430402[/C][/ROW]
[ROW][C]18[/C][C]10254[/C][C]10446.2037810061[/C][C]-192.203781006088[/C][/ROW]
[ROW][C]19[/C][C]10573[/C][C]10000.1987011551[/C][C]572.801298844943[/C][/ROW]
[ROW][C]20[/C][C]10239[/C][C]10298.2410587766[/C][C]-59.2410587766135[/C][/ROW]
[ROW][C]21[/C][C]10253[/C][C]10063.2722449537[/C][C]189.72775504632[/C][/ROW]
[ROW][C]22[/C][C]11176[/C][C]10071.1051900971[/C][C]1104.89480990294[/C][/ROW]
[ROW][C]23[/C][C]10719[/C][C]11051.8661438584[/C][C]-332.866143858444[/C][/ROW]
[ROW][C]24[/C][C]11817[/C][C]10781.0388006382[/C][C]1035.96119936179[/C][/ROW]
[ROW][C]25[/C][C]12487[/C][C]11843.719256702[/C][C]643.280743298046[/C][/ROW]
[ROW][C]26[/C][C]11519[/C][C]12709.4817289576[/C][C]-1190.48172895764[/C][/ROW]
[ROW][C]27[/C][C]12025[/C][C]11827.7515434681[/C][C]197.24845653189[/C][/ROW]
[ROW][C]28[/C][C]10976[/C][C]12129.5752783427[/C][C]-1153.57527834273[/C][/ROW]
[ROW][C]29[/C][C]11276[/C][C]11089.5261819888[/C][C]186.473818011249[/C][/ROW]
[ROW][C]30[/C][C]10657[/C][C]11191.5762178633[/C][C]-534.576217863316[/C][/ROW]
[ROW][C]31[/C][C]11141[/C][C]10593.3784775325[/C][C]547.621522467522[/C][/ROW]
[ROW][C]32[/C][C]10423[/C][C]10995.8835247837[/C][C]-572.883524783683[/C][/ROW]
[ROW][C]33[/C][C]10640[/C][C]10361.1031168994[/C][C]278.89688310062[/C][/ROW]
[ROW][C]34[/C][C]11426[/C][C]10483.932866652[/C][C]942.067133348031[/C][/ROW]
[ROW][C]35[/C][C]10948[/C][C]11339.7008741544[/C][C]-391.700874154441[/C][/ROW]
[ROW][C]36[/C][C]12540[/C][C]11018.0427439349[/C][C]1521.95725606513[/C][/ROW]
[ROW][C]37[/C][C]12200[/C][C]12575.2031100764[/C][C]-375.203110076391[/C][/ROW]
[ROW][C]38[/C][C]10644[/C][C]12493.4990706371[/C][C]-1849.49907063708[/C][/ROW]
[ROW][C]39[/C][C]12044[/C][C]10830.7188981966[/C][C]1213.28110180341[/C][/ROW]
[ROW][C]40[/C][C]11338[/C][C]11933.6440455531[/C][C]-595.644045553143[/C][/ROW]
[ROW][C]41[/C][C]11292[/C][C]11426.9718789883[/C][C]-134.97187898829[/C][/ROW]
[ROW][C]42[/C][C]10612[/C][C]11273.6283649467[/C][C]-661.628364946735[/C][/ROW]
[ROW][C]43[/C][C]10995[/C][C]10555.29826612[/C][C]439.701733880043[/C][/ROW]
[ROW][C]44[/C][C]10686[/C][C]10832.150393556[/C][C]-146.150393555972[/C][/ROW]
[ROW][C]45[/C][C]10635[/C][C]10596.9355790561[/C][C]38.0644209439106[/C][/ROW]
[ROW][C]46[/C][C]11285[/C][C]10521.1771098133[/C][C]763.822890186664[/C][/ROW]
[ROW][C]47[/C][C]11475[/C][C]11194.7987425736[/C][C]280.201257426408[/C][/ROW]
[ROW][C]48[/C][C]12535[/C][C]11524.8280472954[/C][C]1010.17195270456[/C][/ROW]
[ROW][C]49[/C][C]12490[/C][C]12656.3361724707[/C][C]-166.336172470717[/C][/ROW]
[ROW][C]50[/C][C]12511[/C][C]12784.6110205309[/C][C]-273.611020530927[/C][/ROW]
[ROW][C]51[/C][C]12799[/C][C]12770.3985608533[/C][C]28.601439146747[/C][/ROW]
[ROW][C]52[/C][C]11876[/C][C]13011.1008968644[/C][C]-1135.10089686435[/C][/ROW]
[ROW][C]53[/C][C]11602[/C][C]12067.9174574005[/C][C]-465.917457400537[/C][/ROW]
[ROW][C]54[/C][C]11062[/C][C]11584.7238626223[/C][C]-522.723862622335[/C][/ROW]
[ROW][C]55[/C][C]11055[/C][C]10951.500175035[/C][C]103.49982496502[/C][/ROW]
[ROW][C]56[/C][C]10855[/C][C]10855.224132294[/C][C]-0.22413229398262[/C][/ROW]
[ROW][C]57[/C][C]10704[/C][C]10673.3507504765[/C][C]30.6492495234561[/C][/ROW]
[ROW][C]58[/C][C]11510[/C][C]10522.9917571182[/C][C]987.008242881797[/C][/ROW]
[ROW][C]59[/C][C]11663[/C][C]11356.2680446131[/C][C]306.731955386891[/C][/ROW]
[ROW][C]60[/C][C]12686[/C][C]11688.9848821481[/C][C]997.015117851855[/C][/ROW]
[ROW][C]61[/C][C]13516[/C][C]12787.8487607849[/C][C]728.1512392151[/C][/ROW]
[ROW][C]62[/C][C]12539[/C][C]13808.6722041943[/C][C]-1269.67220419431[/C][/ROW]
[ROW][C]63[/C][C]13811[/C][C]12931.0523755776[/C][C]879.947624422435[/C][/ROW]
[ROW][C]64[/C][C]12354[/C][C]14000.1559009358[/C][C]-1646.15590093577[/C][/ROW]
[ROW][C]65[/C][C]11441[/C][C]12660.772294775[/C][C]-1219.77229477504[/C][/ROW]
[ROW][C]66[/C][C]10814[/C][C]11432.3175659576[/C][C]-618.317565957621[/C][/ROW]
[ROW][C]67[/C][C]11261[/C][C]10577.9082562695[/C][C]683.091743730531[/C][/ROW]
[ROW][C]68[/C][C]10788[/C][C]10931.7499055163[/C][C]-143.749905516321[/C][/ROW]
[ROW][C]69[/C][C]10326[/C][C]10575.2265932586[/C][C]-249.226593258642[/C][/ROW]
[ROW][C]70[/C][C]11490[/C][C]10082.5121247339[/C][C]1407.48787526612[/C][/ROW]
[ROW][C]71[/C][C]11029[/C][C]11234.0911253865[/C][C]-205.091125386458[/C][/ROW]
[ROW][C]72[/C][C]11876[/C][C]11015.1094911452[/C][C]860.890508854804[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279281&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279281&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
31207999112168
41136610658.1195460539707.8804539461
51132810340.6317875738987.368212426169
61044410448.5566565159-4.55665651593517
7108549737.427391626881116.57260837312
81043410171.4118686895262.588131310491
9101379952.84662142311184.153378576892
10109929705.935413433421286.06458656658
111090610621.7409502232284.259049776772
121236710767.34910981811599.65089018191
131437112313.65179715232057.3482028477
141169514643.5498573854-2948.5498573854
151154612262.5217929575-716.521792957481
161092211581.0773076876-659.077307687638
171067010816.9251434304-146.925143430402
181025410446.2037810061-192.203781006088
191057310000.1987011551572.801298844943
201023910298.2410587766-59.2410587766135
211025310063.2722449537189.72775504632
221117610071.10519009711104.89480990294
231071911051.8661438584-332.866143858444
241181710781.03880063821035.96119936179
251248711843.719256702643.280743298046
261151912709.4817289576-1190.48172895764
271202511827.7515434681197.24845653189
281097612129.5752783427-1153.57527834273
291127611089.5261819888186.473818011249
301065711191.5762178633-534.576217863316
311114110593.3784775325547.621522467522
321042310995.8835247837-572.883524783683
331064010361.1031168994278.89688310062
341142610483.932866652942.067133348031
351094811339.7008741544-391.700874154441
361254011018.04274393491521.95725606513
371220012575.2031100764-375.203110076391
381064412493.4990706371-1849.49907063708
391204410830.71889819661213.28110180341
401133811933.6440455531-595.644045553143
411129211426.9718789883-134.97187898829
421061211273.6283649467-661.628364946735
431099510555.29826612439.701733880043
441068610832.150393556-146.150393555972
451063510596.935579056138.0644209439106
461128510521.1771098133763.822890186664
471147511194.7987425736280.201257426408
481253511524.82804729541010.17195270456
491249012656.3361724707-166.336172470717
501251112784.6110205309-273.611020530927
511279912770.398560853328.601439146747
521187613011.1008968644-1135.10089686435
531160212067.9174574005-465.917457400537
541106211584.7238626223-522.723862622335
551105510951.500175035103.49982496502
561085510855.224132294-0.22413229398262
571070410673.350750476530.6492495234561
581151010522.9917571182987.008242881797
591166311356.2680446131306.731955386891
601268611688.9848821481997.015117851855
611351612787.8487607849728.1512392151
621253913808.6722041943-1269.67220419431
631381112931.0523755776879.947624422435
641235414000.1559009358-1646.15590093577
651144112660.772294775-1219.77229477504
661081411432.3175659576-618.317565957621
671126110577.9082562695683.091743730531
681078810931.7499055163-143.749905516321
691032610575.2265932586-249.226593258642
701149010082.51212473391407.48787526612
711102911234.0911253865-205.091125386458
721187611015.1094911452860.890508854804







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7311845.288426793410053.105193124813637.4716604619
7411965.3917581169402.5801617017714528.2033545302
7512085.49508943868717.2166272774715453.7735515997
7612205.59842076127987.2958943023516423.90094722
7712325.70175208387210.567501765117440.8360024025
7812445.80508340646387.1639583125818504.4462085002
7912565.9084147295518.0758572493919613.7409722086
8012686.01174605164604.5948698216320767.4286222815
8112806.11507737423648.0878284537521964.1423262946
8212926.21840869682649.9008409203623202.5359764732
8313046.32174001941611.3191770666924481.3243029721
8413166.425071342533.55241399843425799.2977286855

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 11845.2884267934 & 10053.1051931248 & 13637.4716604619 \tabularnewline
74 & 11965.391758116 & 9402.58016170177 & 14528.2033545302 \tabularnewline
75 & 12085.4950894386 & 8717.21662727747 & 15453.7735515997 \tabularnewline
76 & 12205.5984207612 & 7987.29589430235 & 16423.90094722 \tabularnewline
77 & 12325.7017520838 & 7210.5675017651 & 17440.8360024025 \tabularnewline
78 & 12445.8050834064 & 6387.16395831258 & 18504.4462085002 \tabularnewline
79 & 12565.908414729 & 5518.07585724939 & 19613.7409722086 \tabularnewline
80 & 12686.0117460516 & 4604.59486982163 & 20767.4286222815 \tabularnewline
81 & 12806.1150773742 & 3648.08782845375 & 21964.1423262946 \tabularnewline
82 & 12926.2184086968 & 2649.90084092036 & 23202.5359764732 \tabularnewline
83 & 13046.3217400194 & 1611.31917706669 & 24481.3243029721 \tabularnewline
84 & 13166.425071342 & 533.552413998434 & 25799.2977286855 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279281&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]11845.2884267934[/C][C]10053.1051931248[/C][C]13637.4716604619[/C][/ROW]
[ROW][C]74[/C][C]11965.391758116[/C][C]9402.58016170177[/C][C]14528.2033545302[/C][/ROW]
[ROW][C]75[/C][C]12085.4950894386[/C][C]8717.21662727747[/C][C]15453.7735515997[/C][/ROW]
[ROW][C]76[/C][C]12205.5984207612[/C][C]7987.29589430235[/C][C]16423.90094722[/C][/ROW]
[ROW][C]77[/C][C]12325.7017520838[/C][C]7210.5675017651[/C][C]17440.8360024025[/C][/ROW]
[ROW][C]78[/C][C]12445.8050834064[/C][C]6387.16395831258[/C][C]18504.4462085002[/C][/ROW]
[ROW][C]79[/C][C]12565.908414729[/C][C]5518.07585724939[/C][C]19613.7409722086[/C][/ROW]
[ROW][C]80[/C][C]12686.0117460516[/C][C]4604.59486982163[/C][C]20767.4286222815[/C][/ROW]
[ROW][C]81[/C][C]12806.1150773742[/C][C]3648.08782845375[/C][C]21964.1423262946[/C][/ROW]
[ROW][C]82[/C][C]12926.2184086968[/C][C]2649.90084092036[/C][C]23202.5359764732[/C][/ROW]
[ROW][C]83[/C][C]13046.3217400194[/C][C]1611.31917706669[/C][C]24481.3243029721[/C][/ROW]
[ROW][C]84[/C][C]13166.425071342[/C][C]533.552413998434[/C][C]25799.2977286855[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279281&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279281&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
7311845.288426793410053.105193124813637.4716604619
7411965.3917581169402.5801617017714528.2033545302
7512085.49508943868717.2166272774715453.7735515997
7612205.59842076127987.2958943023516423.90094722
7712325.70175208387210.567501765117440.8360024025
7812445.80508340646387.1639583125818504.4462085002
7912565.9084147295518.0758572493919613.7409722086
8012686.01174605164604.5948698216320767.4286222815
8112806.11507737423648.0878284537521964.1423262946
8212926.21840869682649.9008409203623202.5359764732
8313046.32174001941611.3191770666924481.3243029721
8413166.425071342533.55241399843425799.2977286855



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