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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 computationWed, 18 May 2011 14:32:39 +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/2011/May/18/t1305728919z606mmlb8vw5l6x.htm/, Retrieved Tue, 14 May 2024 21:05:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121865, Retrieved Tue, 14 May 2024 21:05:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W101
Estimated Impact66
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [inschrijvingen Pe...] [2011-05-18 14:32:39] [8408ae72b9c03ee1c59e868ccc07a80d] [Current]
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Dataseries X:
112
118
132
129
121
135
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121865&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]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121865&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121865&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'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.434024876116231
beta0.0235454462485613
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.434024876116231 \tabularnewline
beta & 0.0235454462485613 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121865&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]0.434024876116231[/C][/ROW]
[ROW][C]beta[/C][C]0.0235454462485613[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121865&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121865&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
alpha0.434024876116231
beta0.0235454462485613
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132469316499.68221414168193.31778585835
142220518809.20681644453395.79318355548
152172520908.6825934264816.31740657361
162719227978.7524046476-786.752404647617
172179023125.1738906074-1335.17389060741
181325314163.7331851727-910.733185172672
193770258248.0957497042-20546.0957497042
203036444327.9749576895-13963.9749576895
213260939154.9333721622-6545.93337216225
223021229932.0376240915279.962375908468
232996526948.55363995193016.44636004808
242835222167.85581746456184.14418253547
252581426061.6972848267-247.697284826732
262241421519.4052631722894.594736827818
272050620963.5963054745-457.596305474475
282880626174.14279558932631.85720441071
292222822345.4951637003-117.4951637003
301397113885.621233763685.3787662364448
313684546565.3194198647-9720.31941986469
323533839333.2064281112-3995.20642811118
333502243361.8976467778-8339.89764677778
343477736513.3933886801-1736.39338868012
352688733675.6054000075-6788.6054000075
362397025795.2146240836-1825.21462408355
372278022719.481636281460.5183637185874
381735119285.5767356151-1934.57673561512
392138216929.60170060824452.39829939185
402456125264.8105540579-703.810554057916
411740919205.1730698177-1796.17306981768
421151411487.774445140126.225554859886
433151433172.0540280012-1658.05402800116
442707132406.8249611713-5335.82496117131
452946232369.5114830342-2907.51148303417
462610531387.9854488681-5282.98544886815
472239724512.1655776422-2115.16557764221
482384321588.22721338712254.77278661292
492170521334.4070080031370.592991996942
501808917051.05245059981037.94754940016
512076419301.25170578971462.74829421032
522531623096.94003873912219.05996126091
531770417725.2942103492-21.294210349155
541554811678.49551086573869.5044891343
552802937352.037113629-9323.03711362901
562938330758.2593364618-1375.25933646177
573643834121.15160867042316.84839132958
583203433574.2292605012-1540.22926050121
592267929351.3992151774-6672.39921517738
602431926934.8187184-2615.81871839999
611800423272.0011869629-5268.0011869629
621753716978.8523824325558.147617567523
632036619068.95171432221297.04828567777
642278222896.8372777057-114.837277705727
651916915920.64861480973248.35138519032
661380713272.4498740578534.550125942218
672974327194.42322959752548.5767704025
682559130200.9438543089-4609.9438543089
692909633882.2225492444-4786.22254924438
702648228413.560639652-1931.56063965198
712240521567.4313915379837.568608462072
722704424494.73548680662549.26451319343
731797021001.2951992048-3031.29519920484
741873018902.4883985025-172.48839850253
751968421227.6183614609-1543.61836146091
761978523009.3864451343-3224.38644513427
771847916656.58738564871822.41261435128
781069812310.3773432403-1612.37734324029

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 24693 & 16499.6822141416 & 8193.31778585835 \tabularnewline
14 & 22205 & 18809.2068164445 & 3395.79318355548 \tabularnewline
15 & 21725 & 20908.6825934264 & 816.31740657361 \tabularnewline
16 & 27192 & 27978.7524046476 & -786.752404647617 \tabularnewline
17 & 21790 & 23125.1738906074 & -1335.17389060741 \tabularnewline
18 & 13253 & 14163.7331851727 & -910.733185172672 \tabularnewline
19 & 37702 & 58248.0957497042 & -20546.0957497042 \tabularnewline
20 & 30364 & 44327.9749576895 & -13963.9749576895 \tabularnewline
21 & 32609 & 39154.9333721622 & -6545.93337216225 \tabularnewline
22 & 30212 & 29932.0376240915 & 279.962375908468 \tabularnewline
23 & 29965 & 26948.5536399519 & 3016.44636004808 \tabularnewline
24 & 28352 & 22167.8558174645 & 6184.14418253547 \tabularnewline
25 & 25814 & 26061.6972848267 & -247.697284826732 \tabularnewline
26 & 22414 & 21519.4052631722 & 894.594736827818 \tabularnewline
27 & 20506 & 20963.5963054745 & -457.596305474475 \tabularnewline
28 & 28806 & 26174.1427955893 & 2631.85720441071 \tabularnewline
29 & 22228 & 22345.4951637003 & -117.4951637003 \tabularnewline
30 & 13971 & 13885.6212337636 & 85.3787662364448 \tabularnewline
31 & 36845 & 46565.3194198647 & -9720.31941986469 \tabularnewline
32 & 35338 & 39333.2064281112 & -3995.20642811118 \tabularnewline
33 & 35022 & 43361.8976467778 & -8339.89764677778 \tabularnewline
34 & 34777 & 36513.3933886801 & -1736.39338868012 \tabularnewline
35 & 26887 & 33675.6054000075 & -6788.6054000075 \tabularnewline
36 & 23970 & 25795.2146240836 & -1825.21462408355 \tabularnewline
37 & 22780 & 22719.4816362814 & 60.5183637185874 \tabularnewline
38 & 17351 & 19285.5767356151 & -1934.57673561512 \tabularnewline
39 & 21382 & 16929.6017006082 & 4452.39829939185 \tabularnewline
40 & 24561 & 25264.8105540579 & -703.810554057916 \tabularnewline
41 & 17409 & 19205.1730698177 & -1796.17306981768 \tabularnewline
42 & 11514 & 11487.7744451401 & 26.225554859886 \tabularnewline
43 & 31514 & 33172.0540280012 & -1658.05402800116 \tabularnewline
44 & 27071 & 32406.8249611713 & -5335.82496117131 \tabularnewline
45 & 29462 & 32369.5114830342 & -2907.51148303417 \tabularnewline
46 & 26105 & 31387.9854488681 & -5282.98544886815 \tabularnewline
47 & 22397 & 24512.1655776422 & -2115.16557764221 \tabularnewline
48 & 23843 & 21588.2272133871 & 2254.77278661292 \tabularnewline
49 & 21705 & 21334.4070080031 & 370.592991996942 \tabularnewline
50 & 18089 & 17051.0524505998 & 1037.94754940016 \tabularnewline
51 & 20764 & 19301.2517057897 & 1462.74829421032 \tabularnewline
52 & 25316 & 23096.9400387391 & 2219.05996126091 \tabularnewline
53 & 17704 & 17725.2942103492 & -21.294210349155 \tabularnewline
54 & 15548 & 11678.4955108657 & 3869.5044891343 \tabularnewline
55 & 28029 & 37352.037113629 & -9323.03711362901 \tabularnewline
56 & 29383 & 30758.2593364618 & -1375.25933646177 \tabularnewline
57 & 36438 & 34121.1516086704 & 2316.84839132958 \tabularnewline
58 & 32034 & 33574.2292605012 & -1540.22926050121 \tabularnewline
59 & 22679 & 29351.3992151774 & -6672.39921517738 \tabularnewline
60 & 24319 & 26934.8187184 & -2615.81871839999 \tabularnewline
61 & 18004 & 23272.0011869629 & -5268.0011869629 \tabularnewline
62 & 17537 & 16978.8523824325 & 558.147617567523 \tabularnewline
63 & 20366 & 19068.9517143222 & 1297.04828567777 \tabularnewline
64 & 22782 & 22896.8372777057 & -114.837277705727 \tabularnewline
65 & 19169 & 15920.6486148097 & 3248.35138519032 \tabularnewline
66 & 13807 & 13272.4498740578 & 534.550125942218 \tabularnewline
67 & 29743 & 27194.4232295975 & 2548.5767704025 \tabularnewline
68 & 25591 & 30200.9438543089 & -4609.9438543089 \tabularnewline
69 & 29096 & 33882.2225492444 & -4786.22254924438 \tabularnewline
70 & 26482 & 28413.560639652 & -1931.56063965198 \tabularnewline
71 & 22405 & 21567.4313915379 & 837.568608462072 \tabularnewline
72 & 27044 & 24494.7354868066 & 2549.26451319343 \tabularnewline
73 & 17970 & 21001.2951992048 & -3031.29519920484 \tabularnewline
74 & 18730 & 18902.4883985025 & -172.48839850253 \tabularnewline
75 & 19684 & 21227.6183614609 & -1543.61836146091 \tabularnewline
76 & 19785 & 23009.3864451343 & -3224.38644513427 \tabularnewline
77 & 18479 & 16656.5873856487 & 1822.41261435128 \tabularnewline
78 & 10698 & 12310.3773432403 & -1612.37734324029 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121865&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]24693[/C][C]16499.6822141416[/C][C]8193.31778585835[/C][/ROW]
[ROW][C]14[/C][C]22205[/C][C]18809.2068164445[/C][C]3395.79318355548[/C][/ROW]
[ROW][C]15[/C][C]21725[/C][C]20908.6825934264[/C][C]816.31740657361[/C][/ROW]
[ROW][C]16[/C][C]27192[/C][C]27978.7524046476[/C][C]-786.752404647617[/C][/ROW]
[ROW][C]17[/C][C]21790[/C][C]23125.1738906074[/C][C]-1335.17389060741[/C][/ROW]
[ROW][C]18[/C][C]13253[/C][C]14163.7331851727[/C][C]-910.733185172672[/C][/ROW]
[ROW][C]19[/C][C]37702[/C][C]58248.0957497042[/C][C]-20546.0957497042[/C][/ROW]
[ROW][C]20[/C][C]30364[/C][C]44327.9749576895[/C][C]-13963.9749576895[/C][/ROW]
[ROW][C]21[/C][C]32609[/C][C]39154.9333721622[/C][C]-6545.93337216225[/C][/ROW]
[ROW][C]22[/C][C]30212[/C][C]29932.0376240915[/C][C]279.962375908468[/C][/ROW]
[ROW][C]23[/C][C]29965[/C][C]26948.5536399519[/C][C]3016.44636004808[/C][/ROW]
[ROW][C]24[/C][C]28352[/C][C]22167.8558174645[/C][C]6184.14418253547[/C][/ROW]
[ROW][C]25[/C][C]25814[/C][C]26061.6972848267[/C][C]-247.697284826732[/C][/ROW]
[ROW][C]26[/C][C]22414[/C][C]21519.4052631722[/C][C]894.594736827818[/C][/ROW]
[ROW][C]27[/C][C]20506[/C][C]20963.5963054745[/C][C]-457.596305474475[/C][/ROW]
[ROW][C]28[/C][C]28806[/C][C]26174.1427955893[/C][C]2631.85720441071[/C][/ROW]
[ROW][C]29[/C][C]22228[/C][C]22345.4951637003[/C][C]-117.4951637003[/C][/ROW]
[ROW][C]30[/C][C]13971[/C][C]13885.6212337636[/C][C]85.3787662364448[/C][/ROW]
[ROW][C]31[/C][C]36845[/C][C]46565.3194198647[/C][C]-9720.31941986469[/C][/ROW]
[ROW][C]32[/C][C]35338[/C][C]39333.2064281112[/C][C]-3995.20642811118[/C][/ROW]
[ROW][C]33[/C][C]35022[/C][C]43361.8976467778[/C][C]-8339.89764677778[/C][/ROW]
[ROW][C]34[/C][C]34777[/C][C]36513.3933886801[/C][C]-1736.39338868012[/C][/ROW]
[ROW][C]35[/C][C]26887[/C][C]33675.6054000075[/C][C]-6788.6054000075[/C][/ROW]
[ROW][C]36[/C][C]23970[/C][C]25795.2146240836[/C][C]-1825.21462408355[/C][/ROW]
[ROW][C]37[/C][C]22780[/C][C]22719.4816362814[/C][C]60.5183637185874[/C][/ROW]
[ROW][C]38[/C][C]17351[/C][C]19285.5767356151[/C][C]-1934.57673561512[/C][/ROW]
[ROW][C]39[/C][C]21382[/C][C]16929.6017006082[/C][C]4452.39829939185[/C][/ROW]
[ROW][C]40[/C][C]24561[/C][C]25264.8105540579[/C][C]-703.810554057916[/C][/ROW]
[ROW][C]41[/C][C]17409[/C][C]19205.1730698177[/C][C]-1796.17306981768[/C][/ROW]
[ROW][C]42[/C][C]11514[/C][C]11487.7744451401[/C][C]26.225554859886[/C][/ROW]
[ROW][C]43[/C][C]31514[/C][C]33172.0540280012[/C][C]-1658.05402800116[/C][/ROW]
[ROW][C]44[/C][C]27071[/C][C]32406.8249611713[/C][C]-5335.82496117131[/C][/ROW]
[ROW][C]45[/C][C]29462[/C][C]32369.5114830342[/C][C]-2907.51148303417[/C][/ROW]
[ROW][C]46[/C][C]26105[/C][C]31387.9854488681[/C][C]-5282.98544886815[/C][/ROW]
[ROW][C]47[/C][C]22397[/C][C]24512.1655776422[/C][C]-2115.16557764221[/C][/ROW]
[ROW][C]48[/C][C]23843[/C][C]21588.2272133871[/C][C]2254.77278661292[/C][/ROW]
[ROW][C]49[/C][C]21705[/C][C]21334.4070080031[/C][C]370.592991996942[/C][/ROW]
[ROW][C]50[/C][C]18089[/C][C]17051.0524505998[/C][C]1037.94754940016[/C][/ROW]
[ROW][C]51[/C][C]20764[/C][C]19301.2517057897[/C][C]1462.74829421032[/C][/ROW]
[ROW][C]52[/C][C]25316[/C][C]23096.9400387391[/C][C]2219.05996126091[/C][/ROW]
[ROW][C]53[/C][C]17704[/C][C]17725.2942103492[/C][C]-21.294210349155[/C][/ROW]
[ROW][C]54[/C][C]15548[/C][C]11678.4955108657[/C][C]3869.5044891343[/C][/ROW]
[ROW][C]55[/C][C]28029[/C][C]37352.037113629[/C][C]-9323.03711362901[/C][/ROW]
[ROW][C]56[/C][C]29383[/C][C]30758.2593364618[/C][C]-1375.25933646177[/C][/ROW]
[ROW][C]57[/C][C]36438[/C][C]34121.1516086704[/C][C]2316.84839132958[/C][/ROW]
[ROW][C]58[/C][C]32034[/C][C]33574.2292605012[/C][C]-1540.22926050121[/C][/ROW]
[ROW][C]59[/C][C]22679[/C][C]29351.3992151774[/C][C]-6672.39921517738[/C][/ROW]
[ROW][C]60[/C][C]24319[/C][C]26934.8187184[/C][C]-2615.81871839999[/C][/ROW]
[ROW][C]61[/C][C]18004[/C][C]23272.0011869629[/C][C]-5268.0011869629[/C][/ROW]
[ROW][C]62[/C][C]17537[/C][C]16978.8523824325[/C][C]558.147617567523[/C][/ROW]
[ROW][C]63[/C][C]20366[/C][C]19068.9517143222[/C][C]1297.04828567777[/C][/ROW]
[ROW][C]64[/C][C]22782[/C][C]22896.8372777057[/C][C]-114.837277705727[/C][/ROW]
[ROW][C]65[/C][C]19169[/C][C]15920.6486148097[/C][C]3248.35138519032[/C][/ROW]
[ROW][C]66[/C][C]13807[/C][C]13272.4498740578[/C][C]534.550125942218[/C][/ROW]
[ROW][C]67[/C][C]29743[/C][C]27194.4232295975[/C][C]2548.5767704025[/C][/ROW]
[ROW][C]68[/C][C]25591[/C][C]30200.9438543089[/C][C]-4609.9438543089[/C][/ROW]
[ROW][C]69[/C][C]29096[/C][C]33882.2225492444[/C][C]-4786.22254924438[/C][/ROW]
[ROW][C]70[/C][C]26482[/C][C]28413.560639652[/C][C]-1931.56063965198[/C][/ROW]
[ROW][C]71[/C][C]22405[/C][C]21567.4313915379[/C][C]837.568608462072[/C][/ROW]
[ROW][C]72[/C][C]27044[/C][C]24494.7354868066[/C][C]2549.26451319343[/C][/ROW]
[ROW][C]73[/C][C]17970[/C][C]21001.2951992048[/C][C]-3031.29519920484[/C][/ROW]
[ROW][C]74[/C][C]18730[/C][C]18902.4883985025[/C][C]-172.48839850253[/C][/ROW]
[ROW][C]75[/C][C]19684[/C][C]21227.6183614609[/C][C]-1543.61836146091[/C][/ROW]
[ROW][C]76[/C][C]19785[/C][C]23009.3864451343[/C][C]-3224.38644513427[/C][/ROW]
[ROW][C]77[/C][C]18479[/C][C]16656.5873856487[/C][C]1822.41261435128[/C][/ROW]
[ROW][C]78[/C][C]10698[/C][C]12310.3773432403[/C][C]-1612.37734324029[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121865&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121865&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
132469316499.68221414168193.31778585835
142220518809.20681644453395.79318355548
152172520908.6825934264816.31740657361
162719227978.7524046476-786.752404647617
172179023125.1738906074-1335.17389060741
181325314163.7331851727-910.733185172672
193770258248.0957497042-20546.0957497042
203036444327.9749576895-13963.9749576895
213260939154.9333721622-6545.93337216225
223021229932.0376240915279.962375908468
232996526948.55363995193016.44636004808
242835222167.85581746456184.14418253547
252581426061.6972848267-247.697284826732
262241421519.4052631722894.594736827818
272050620963.5963054745-457.596305474475
282880626174.14279558932631.85720441071
292222822345.4951637003-117.4951637003
301397113885.621233763685.3787662364448
313684546565.3194198647-9720.31941986469
323533839333.2064281112-3995.20642811118
333502243361.8976467778-8339.89764677778
343477736513.3933886801-1736.39338868012
352688733675.6054000075-6788.6054000075
362397025795.2146240836-1825.21462408355
372278022719.481636281460.5183637185874
381735119285.5767356151-1934.57673561512
392138216929.60170060824452.39829939185
402456125264.8105540579-703.810554057916
411740919205.1730698177-1796.17306981768
421151411487.774445140126.225554859886
433151433172.0540280012-1658.05402800116
442707132406.8249611713-5335.82496117131
452946232369.5114830342-2907.51148303417
462610531387.9854488681-5282.98544886815
472239724512.1655776422-2115.16557764221
482384321588.22721338712254.77278661292
492170521334.4070080031370.592991996942
501808917051.05245059981037.94754940016
512076419301.25170578971462.74829421032
522531623096.94003873912219.05996126091
531770417725.2942103492-21.294210349155
541554811678.49551086573869.5044891343
552802937352.037113629-9323.03711362901
562938330758.2593364618-1375.25933646177
573643834121.15160867042316.84839132958
583203433574.2292605012-1540.22926050121
592267929351.3992151774-6672.39921517738
602431926934.8187184-2615.81871839999
611800423272.0011869629-5268.0011869629
621753716978.8523824325558.147617567523
632036619068.95171432221297.04828567777
642278222896.8372777057-114.837277705727
651916915920.64861480973248.35138519032
661380713272.4498740578534.550125942218
672974327194.42322959752548.5767704025
682559130200.9438543089-4609.9438543089
692909633882.2225492444-4786.22254924438
702648228413.560639652-1931.56063965198
712240521567.4313915379837.568608462072
722704424494.73548680662549.26451319343
731797021001.2951992048-3031.29519920484
741873018902.4883985025-172.48839850253
751968421227.6183614609-1543.61836146091
761978523009.3864451343-3224.38644513427
771847916656.58738564871822.41261435128
781069812310.3773432403-1612.37734324029







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7923919.987952321715109.097871025132730.8780336182
8021923.77913593712413.875747961231433.6825239129
8126444.014758071415525.525239873737362.504276269
8224724.797477963113375.986027101936073.6089288244
8320520.89865909389349.6586701172531692.1386480704
8423634.057292048410870.807656358836397.3069277381
8516694.83142818325316.6452758865928073.0175804797
8617429.52781487375062.6717040791529796.3839256683
8718872.0453528685189.4741143517232554.6165913843
8820164.91218877275166.541405104835163.2829724406
8917973.97787651223440.1101895464532507.8455634779
9011018.77790049073414.4681698724418623.0876311089

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
79 & 23919.9879523217 & 15109.0978710251 & 32730.8780336182 \tabularnewline
80 & 21923.779135937 & 12413.8757479612 & 31433.6825239129 \tabularnewline
81 & 26444.0147580714 & 15525.5252398737 & 37362.504276269 \tabularnewline
82 & 24724.7974779631 & 13375.9860271019 & 36073.6089288244 \tabularnewline
83 & 20520.8986590938 & 9349.65867011725 & 31692.1386480704 \tabularnewline
84 & 23634.0572920484 & 10870.8076563588 & 36397.3069277381 \tabularnewline
85 & 16694.8314281832 & 5316.64527588659 & 28073.0175804797 \tabularnewline
86 & 17429.5278148737 & 5062.67170407915 & 29796.3839256683 \tabularnewline
87 & 18872.045352868 & 5189.47411435172 & 32554.6165913843 \tabularnewline
88 & 20164.9121887727 & 5166.5414051048 & 35163.2829724406 \tabularnewline
89 & 17973.9778765122 & 3440.11018954645 & 32507.8455634779 \tabularnewline
90 & 11018.7779004907 & 3414.46816987244 & 18623.0876311089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121865&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]79[/C][C]23919.9879523217[/C][C]15109.0978710251[/C][C]32730.8780336182[/C][/ROW]
[ROW][C]80[/C][C]21923.779135937[/C][C]12413.8757479612[/C][C]31433.6825239129[/C][/ROW]
[ROW][C]81[/C][C]26444.0147580714[/C][C]15525.5252398737[/C][C]37362.504276269[/C][/ROW]
[ROW][C]82[/C][C]24724.7974779631[/C][C]13375.9860271019[/C][C]36073.6089288244[/C][/ROW]
[ROW][C]83[/C][C]20520.8986590938[/C][C]9349.65867011725[/C][C]31692.1386480704[/C][/ROW]
[ROW][C]84[/C][C]23634.0572920484[/C][C]10870.8076563588[/C][C]36397.3069277381[/C][/ROW]
[ROW][C]85[/C][C]16694.8314281832[/C][C]5316.64527588659[/C][C]28073.0175804797[/C][/ROW]
[ROW][C]86[/C][C]17429.5278148737[/C][C]5062.67170407915[/C][C]29796.3839256683[/C][/ROW]
[ROW][C]87[/C][C]18872.045352868[/C][C]5189.47411435172[/C][C]32554.6165913843[/C][/ROW]
[ROW][C]88[/C][C]20164.9121887727[/C][C]5166.5414051048[/C][C]35163.2829724406[/C][/ROW]
[ROW][C]89[/C][C]17973.9778765122[/C][C]3440.11018954645[/C][C]32507.8455634779[/C][/ROW]
[ROW][C]90[/C][C]11018.7779004907[/C][C]3414.46816987244[/C][C]18623.0876311089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121865&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121865&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
7923919.987952321715109.097871025132730.8780336182
8021923.77913593712413.875747961231433.6825239129
8126444.014758071415525.525239873737362.504276269
8224724.797477963113375.986027101936073.6089288244
8320520.89865909389349.6586701172531692.1386480704
8423634.057292048410870.807656358836397.3069277381
8516694.83142818325316.6452758865928073.0175804797
8617429.52781487375062.6717040791529796.3839256683
8718872.0453528685189.4741143517232554.6165913843
8820164.91218877275166.541405104835163.2829724406
8917973.97787651223440.1101895464532507.8455634779
9011018.77790049073414.4681698724418623.0876311089



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')