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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, 29 Jul 2015 20:50:08 +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/Jul/29/t1438199501qbrary4nyvcvbjx.htm/, Retrieved Fri, 17 May 2024 04:17:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279757, Retrieved Fri, 17 May 2024 04:17:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-07-29 19:50:08] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
64800
62400
66000
52800
68400
67200
72000
74400
82800
72000
68400
85200
72000
54000
63600
48000
67200
55200
73200
66000
69600
78000
76800
91200
66000
55200
61200
44400
63600
49200
69600
66000
58800
84000
75600
86400
64800
60000
54000
44400
58800
52800
72000
69600
60000
80400
74400
96000
76800
46800
46800
46800
55200
55200
74400
68400
61200
76800
70800
102000
80400
46800
49200
40800
56400
64800
81600
80400
64800
75600
67200
96000
73200
58800
52800
39600
58800
70800
82800
78000
57600
82800
64800
99600
82800
60000
55200
37200
58800
56400
85200
85200
64800
84000
62400
97200
82800
61200
46800
32400
63600
61200
80400
92400
68400
76800
57600
99600




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=279757&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=279757&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279757&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
alpha0.00926118605788267
beta1
gamma0.929768627341396

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00926118605788267 \tabularnewline
beta & 1 \tabularnewline
gamma & 0.929768627341396 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279757&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]0.00926118605788267[/C][/ROW]
[ROW][C]beta[/C][C]1[/C][/ROW]
[ROW][C]gamma[/C][C]0.929768627341396[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279757&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279757&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
alpha0.00926118605788267
beta1
gamma0.929768627341396







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
137200074462.1794871795-2462.17948717954
145400056402.2384181665-2402.2384181665
156360066520.6048976001-2920.6048976001
164800050807.1224232633-2807.12242326327
176720068968.6936481865-1768.69364818648
185520055923.5017542483-723.501754248289
197320069931.28909254683268.71090745322
206600072006.3211949713-6006.32119497126
216960080339.8298412923-10739.8298412923
227800069180.0370209438819.96297905699
237680065433.074399329311366.9256006707
249120082514.97088533078685.02911466932
256600067284.4074947264-1284.40749472637
265520049322.89135210065877.10864789935
276120059149.41579174812050.58420825186
284440043741.525553065658.474446935012
296360063078.8625428017521.137457198274
304920051225.983880222-2025.98388022199
316960069095.4242040705504.575795929515
326600062771.74659311633228.25340688371
335880067086.6509828981-8286.65098289814
348400074246.13524781879753.86475218127
357560073141.52606271612458.47393728388
368640087875.5165875638-1475.51658756385
376480063478.3777393331321.62226066698
386000052272.96659447267727.03340552741
395400058744.0060738993-4744.00607389928
404440042080.12668075222319.87331924784
415880061411.0173389156-2611.01733891557
425280047258.49907416615541.50092583393
437200067674.82084597134325.17915402872
446960064076.59954022045523.40045977961
456000058008.10665820291991.89334179705
468040082178.5286534765-1778.52865347652
477440074437.6887668475-37.6887668474519
489600085692.397698351110307.6023016489
497680064257.77877319112542.221226809
504680059437.3824170921-12637.3824170921
514680054424.1323474363-7624.13234743632
524680044405.95948101232394.04051898766
535520059361.5270069268-4161.52700692679
545520052856.16467438562343.83532561441
557440072244.59287956362155.40712043636
566840069832.0782095728-1432.07820957281
576120060483.7281149302716.271885069822
587680081195.0030255746-4395.0030255746
597080075035.1087501385-4235.10875013849
6010200095743.30667214726256.69332785284
618040076254.8079292564145.19207074399
624680048009.6882887165-1209.68828871653
634920047673.5341152641526.46588473601
644080047006.4379374811-6206.4379374811
655640055802.0041473669597.99585263311
666480055335.62707413129464.37292586882
678160074684.81314447036915.18685552965
688040069124.20591629911275.794083701
696480062102.67192293782697.32807706222
707560078372.5061393623-2772.50613936235
716720072638.4556953396-5438.45569533958
7296000103252.500517718-7252.50051771791
737320081821.138761272-8621.13876127196
745880048534.140358554310265.8596414457
755280050940.01326994251859.98673005747
763960043271.1894559465-3671.18945594653
775880058500.0809549805299.919045019458
787080066337.40395019944462.59604980057
798280083384.8700642308-584.87006423081
807800081794.9568777719-3794.95687777185
815760066615.5011881939-9015.5011881939
828280077513.57798435915286.42201564094
836480069248.3356906997-4448.33569069972
849960098059.63154890431540.36845109568
858280075389.50570784647410.49429215357
866000059737.8937477395262.10625226047
875520054304.34479585895.655204149982
883720041518.9335367185-4318.93353671848
895880060381.2749821579-1581.27498215793
905640071999.6674608153-15599.6674608153
918520083990.02864500891209.97135499108
928520079254.5720019625945.42799803799
936480059241.41678898125558.58321101882
948400083468.8076954434531.192304556593
956240066168.2503514245-3768.2503514245
9697200100484.657599441-3284.65759944054
978280083114.7444887647-314.744488764671
986120060672.8344963497527.165503650278
994680055693.8343931319-8893.83439313186
1003240037792.1346069583-5392.13460695825
1016360058934.24673760174665.75326239834
1026120057523.09056735823676.90943264183
1038040085180.5796959865-4780.5796959865
1049240084700.53991931117699.46008068888
1056840064312.3217555864087.67824441405
1067680083846.4850791646-7046.48507916457
1075760062396.5211743239-4796.52117432389
1089960097020.58482146832579.41517853169

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 72000 & 74462.1794871795 & -2462.17948717954 \tabularnewline
14 & 54000 & 56402.2384181665 & -2402.2384181665 \tabularnewline
15 & 63600 & 66520.6048976001 & -2920.6048976001 \tabularnewline
16 & 48000 & 50807.1224232633 & -2807.12242326327 \tabularnewline
17 & 67200 & 68968.6936481865 & -1768.69364818648 \tabularnewline
18 & 55200 & 55923.5017542483 & -723.501754248289 \tabularnewline
19 & 73200 & 69931.2890925468 & 3268.71090745322 \tabularnewline
20 & 66000 & 72006.3211949713 & -6006.32119497126 \tabularnewline
21 & 69600 & 80339.8298412923 & -10739.8298412923 \tabularnewline
22 & 78000 & 69180.037020943 & 8819.96297905699 \tabularnewline
23 & 76800 & 65433.0743993293 & 11366.9256006707 \tabularnewline
24 & 91200 & 82514.9708853307 & 8685.02911466932 \tabularnewline
25 & 66000 & 67284.4074947264 & -1284.40749472637 \tabularnewline
26 & 55200 & 49322.8913521006 & 5877.10864789935 \tabularnewline
27 & 61200 & 59149.4157917481 & 2050.58420825186 \tabularnewline
28 & 44400 & 43741.525553065 & 658.474446935012 \tabularnewline
29 & 63600 & 63078.8625428017 & 521.137457198274 \tabularnewline
30 & 49200 & 51225.983880222 & -2025.98388022199 \tabularnewline
31 & 69600 & 69095.4242040705 & 504.575795929515 \tabularnewline
32 & 66000 & 62771.7465931163 & 3228.25340688371 \tabularnewline
33 & 58800 & 67086.6509828981 & -8286.65098289814 \tabularnewline
34 & 84000 & 74246.1352478187 & 9753.86475218127 \tabularnewline
35 & 75600 & 73141.5260627161 & 2458.47393728388 \tabularnewline
36 & 86400 & 87875.5165875638 & -1475.51658756385 \tabularnewline
37 & 64800 & 63478.377739333 & 1321.62226066698 \tabularnewline
38 & 60000 & 52272.9665944726 & 7727.03340552741 \tabularnewline
39 & 54000 & 58744.0060738993 & -4744.00607389928 \tabularnewline
40 & 44400 & 42080.1266807522 & 2319.87331924784 \tabularnewline
41 & 58800 & 61411.0173389156 & -2611.01733891557 \tabularnewline
42 & 52800 & 47258.4990741661 & 5541.50092583393 \tabularnewline
43 & 72000 & 67674.8208459713 & 4325.17915402872 \tabularnewline
44 & 69600 & 64076.5995402204 & 5523.40045977961 \tabularnewline
45 & 60000 & 58008.1066582029 & 1991.89334179705 \tabularnewline
46 & 80400 & 82178.5286534765 & -1778.52865347652 \tabularnewline
47 & 74400 & 74437.6887668475 & -37.6887668474519 \tabularnewline
48 & 96000 & 85692.3976983511 & 10307.6023016489 \tabularnewline
49 & 76800 & 64257.778773191 & 12542.221226809 \tabularnewline
50 & 46800 & 59437.3824170921 & -12637.3824170921 \tabularnewline
51 & 46800 & 54424.1323474363 & -7624.13234743632 \tabularnewline
52 & 46800 & 44405.9594810123 & 2394.04051898766 \tabularnewline
53 & 55200 & 59361.5270069268 & -4161.52700692679 \tabularnewline
54 & 55200 & 52856.1646743856 & 2343.83532561441 \tabularnewline
55 & 74400 & 72244.5928795636 & 2155.40712043636 \tabularnewline
56 & 68400 & 69832.0782095728 & -1432.07820957281 \tabularnewline
57 & 61200 & 60483.7281149302 & 716.271885069822 \tabularnewline
58 & 76800 & 81195.0030255746 & -4395.0030255746 \tabularnewline
59 & 70800 & 75035.1087501385 & -4235.10875013849 \tabularnewline
60 & 102000 & 95743.3066721472 & 6256.69332785284 \tabularnewline
61 & 80400 & 76254.807929256 & 4145.19207074399 \tabularnewline
62 & 46800 & 48009.6882887165 & -1209.68828871653 \tabularnewline
63 & 49200 & 47673.534115264 & 1526.46588473601 \tabularnewline
64 & 40800 & 47006.4379374811 & -6206.4379374811 \tabularnewline
65 & 56400 & 55802.0041473669 & 597.99585263311 \tabularnewline
66 & 64800 & 55335.6270741312 & 9464.37292586882 \tabularnewline
67 & 81600 & 74684.8131444703 & 6915.18685552965 \tabularnewline
68 & 80400 & 69124.205916299 & 11275.794083701 \tabularnewline
69 & 64800 & 62102.6719229378 & 2697.32807706222 \tabularnewline
70 & 75600 & 78372.5061393623 & -2772.50613936235 \tabularnewline
71 & 67200 & 72638.4556953396 & -5438.45569533958 \tabularnewline
72 & 96000 & 103252.500517718 & -7252.50051771791 \tabularnewline
73 & 73200 & 81821.138761272 & -8621.13876127196 \tabularnewline
74 & 58800 & 48534.1403585543 & 10265.8596414457 \tabularnewline
75 & 52800 & 50940.0132699425 & 1859.98673005747 \tabularnewline
76 & 39600 & 43271.1894559465 & -3671.18945594653 \tabularnewline
77 & 58800 & 58500.0809549805 & 299.919045019458 \tabularnewline
78 & 70800 & 66337.4039501994 & 4462.59604980057 \tabularnewline
79 & 82800 & 83384.8700642308 & -584.87006423081 \tabularnewline
80 & 78000 & 81794.9568777719 & -3794.95687777185 \tabularnewline
81 & 57600 & 66615.5011881939 & -9015.5011881939 \tabularnewline
82 & 82800 & 77513.5779843591 & 5286.42201564094 \tabularnewline
83 & 64800 & 69248.3356906997 & -4448.33569069972 \tabularnewline
84 & 99600 & 98059.6315489043 & 1540.36845109568 \tabularnewline
85 & 82800 & 75389.5057078464 & 7410.49429215357 \tabularnewline
86 & 60000 & 59737.8937477395 & 262.10625226047 \tabularnewline
87 & 55200 & 54304.34479585 & 895.655204149982 \tabularnewline
88 & 37200 & 41518.9335367185 & -4318.93353671848 \tabularnewline
89 & 58800 & 60381.2749821579 & -1581.27498215793 \tabularnewline
90 & 56400 & 71999.6674608153 & -15599.6674608153 \tabularnewline
91 & 85200 & 83990.0286450089 & 1209.97135499108 \tabularnewline
92 & 85200 & 79254.572001962 & 5945.42799803799 \tabularnewline
93 & 64800 & 59241.4167889812 & 5558.58321101882 \tabularnewline
94 & 84000 & 83468.8076954434 & 531.192304556593 \tabularnewline
95 & 62400 & 66168.2503514245 & -3768.2503514245 \tabularnewline
96 & 97200 & 100484.657599441 & -3284.65759944054 \tabularnewline
97 & 82800 & 83114.7444887647 & -314.744488764671 \tabularnewline
98 & 61200 & 60672.8344963497 & 527.165503650278 \tabularnewline
99 & 46800 & 55693.8343931319 & -8893.83439313186 \tabularnewline
100 & 32400 & 37792.1346069583 & -5392.13460695825 \tabularnewline
101 & 63600 & 58934.2467376017 & 4665.75326239834 \tabularnewline
102 & 61200 & 57523.0905673582 & 3676.90943264183 \tabularnewline
103 & 80400 & 85180.5796959865 & -4780.5796959865 \tabularnewline
104 & 92400 & 84700.5399193111 & 7699.46008068888 \tabularnewline
105 & 68400 & 64312.321755586 & 4087.67824441405 \tabularnewline
106 & 76800 & 83846.4850791646 & -7046.48507916457 \tabularnewline
107 & 57600 & 62396.5211743239 & -4796.52117432389 \tabularnewline
108 & 99600 & 97020.5848214683 & 2579.41517853169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279757&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]72000[/C][C]74462.1794871795[/C][C]-2462.17948717954[/C][/ROW]
[ROW][C]14[/C][C]54000[/C][C]56402.2384181665[/C][C]-2402.2384181665[/C][/ROW]
[ROW][C]15[/C][C]63600[/C][C]66520.6048976001[/C][C]-2920.6048976001[/C][/ROW]
[ROW][C]16[/C][C]48000[/C][C]50807.1224232633[/C][C]-2807.12242326327[/C][/ROW]
[ROW][C]17[/C][C]67200[/C][C]68968.6936481865[/C][C]-1768.69364818648[/C][/ROW]
[ROW][C]18[/C][C]55200[/C][C]55923.5017542483[/C][C]-723.501754248289[/C][/ROW]
[ROW][C]19[/C][C]73200[/C][C]69931.2890925468[/C][C]3268.71090745322[/C][/ROW]
[ROW][C]20[/C][C]66000[/C][C]72006.3211949713[/C][C]-6006.32119497126[/C][/ROW]
[ROW][C]21[/C][C]69600[/C][C]80339.8298412923[/C][C]-10739.8298412923[/C][/ROW]
[ROW][C]22[/C][C]78000[/C][C]69180.037020943[/C][C]8819.96297905699[/C][/ROW]
[ROW][C]23[/C][C]76800[/C][C]65433.0743993293[/C][C]11366.9256006707[/C][/ROW]
[ROW][C]24[/C][C]91200[/C][C]82514.9708853307[/C][C]8685.02911466932[/C][/ROW]
[ROW][C]25[/C][C]66000[/C][C]67284.4074947264[/C][C]-1284.40749472637[/C][/ROW]
[ROW][C]26[/C][C]55200[/C][C]49322.8913521006[/C][C]5877.10864789935[/C][/ROW]
[ROW][C]27[/C][C]61200[/C][C]59149.4157917481[/C][C]2050.58420825186[/C][/ROW]
[ROW][C]28[/C][C]44400[/C][C]43741.525553065[/C][C]658.474446935012[/C][/ROW]
[ROW][C]29[/C][C]63600[/C][C]63078.8625428017[/C][C]521.137457198274[/C][/ROW]
[ROW][C]30[/C][C]49200[/C][C]51225.983880222[/C][C]-2025.98388022199[/C][/ROW]
[ROW][C]31[/C][C]69600[/C][C]69095.4242040705[/C][C]504.575795929515[/C][/ROW]
[ROW][C]32[/C][C]66000[/C][C]62771.7465931163[/C][C]3228.25340688371[/C][/ROW]
[ROW][C]33[/C][C]58800[/C][C]67086.6509828981[/C][C]-8286.65098289814[/C][/ROW]
[ROW][C]34[/C][C]84000[/C][C]74246.1352478187[/C][C]9753.86475218127[/C][/ROW]
[ROW][C]35[/C][C]75600[/C][C]73141.5260627161[/C][C]2458.47393728388[/C][/ROW]
[ROW][C]36[/C][C]86400[/C][C]87875.5165875638[/C][C]-1475.51658756385[/C][/ROW]
[ROW][C]37[/C][C]64800[/C][C]63478.377739333[/C][C]1321.62226066698[/C][/ROW]
[ROW][C]38[/C][C]60000[/C][C]52272.9665944726[/C][C]7727.03340552741[/C][/ROW]
[ROW][C]39[/C][C]54000[/C][C]58744.0060738993[/C][C]-4744.00607389928[/C][/ROW]
[ROW][C]40[/C][C]44400[/C][C]42080.1266807522[/C][C]2319.87331924784[/C][/ROW]
[ROW][C]41[/C][C]58800[/C][C]61411.0173389156[/C][C]-2611.01733891557[/C][/ROW]
[ROW][C]42[/C][C]52800[/C][C]47258.4990741661[/C][C]5541.50092583393[/C][/ROW]
[ROW][C]43[/C][C]72000[/C][C]67674.8208459713[/C][C]4325.17915402872[/C][/ROW]
[ROW][C]44[/C][C]69600[/C][C]64076.5995402204[/C][C]5523.40045977961[/C][/ROW]
[ROW][C]45[/C][C]60000[/C][C]58008.1066582029[/C][C]1991.89334179705[/C][/ROW]
[ROW][C]46[/C][C]80400[/C][C]82178.5286534765[/C][C]-1778.52865347652[/C][/ROW]
[ROW][C]47[/C][C]74400[/C][C]74437.6887668475[/C][C]-37.6887668474519[/C][/ROW]
[ROW][C]48[/C][C]96000[/C][C]85692.3976983511[/C][C]10307.6023016489[/C][/ROW]
[ROW][C]49[/C][C]76800[/C][C]64257.778773191[/C][C]12542.221226809[/C][/ROW]
[ROW][C]50[/C][C]46800[/C][C]59437.3824170921[/C][C]-12637.3824170921[/C][/ROW]
[ROW][C]51[/C][C]46800[/C][C]54424.1323474363[/C][C]-7624.13234743632[/C][/ROW]
[ROW][C]52[/C][C]46800[/C][C]44405.9594810123[/C][C]2394.04051898766[/C][/ROW]
[ROW][C]53[/C][C]55200[/C][C]59361.5270069268[/C][C]-4161.52700692679[/C][/ROW]
[ROW][C]54[/C][C]55200[/C][C]52856.1646743856[/C][C]2343.83532561441[/C][/ROW]
[ROW][C]55[/C][C]74400[/C][C]72244.5928795636[/C][C]2155.40712043636[/C][/ROW]
[ROW][C]56[/C][C]68400[/C][C]69832.0782095728[/C][C]-1432.07820957281[/C][/ROW]
[ROW][C]57[/C][C]61200[/C][C]60483.7281149302[/C][C]716.271885069822[/C][/ROW]
[ROW][C]58[/C][C]76800[/C][C]81195.0030255746[/C][C]-4395.0030255746[/C][/ROW]
[ROW][C]59[/C][C]70800[/C][C]75035.1087501385[/C][C]-4235.10875013849[/C][/ROW]
[ROW][C]60[/C][C]102000[/C][C]95743.3066721472[/C][C]6256.69332785284[/C][/ROW]
[ROW][C]61[/C][C]80400[/C][C]76254.807929256[/C][C]4145.19207074399[/C][/ROW]
[ROW][C]62[/C][C]46800[/C][C]48009.6882887165[/C][C]-1209.68828871653[/C][/ROW]
[ROW][C]63[/C][C]49200[/C][C]47673.534115264[/C][C]1526.46588473601[/C][/ROW]
[ROW][C]64[/C][C]40800[/C][C]47006.4379374811[/C][C]-6206.4379374811[/C][/ROW]
[ROW][C]65[/C][C]56400[/C][C]55802.0041473669[/C][C]597.99585263311[/C][/ROW]
[ROW][C]66[/C][C]64800[/C][C]55335.6270741312[/C][C]9464.37292586882[/C][/ROW]
[ROW][C]67[/C][C]81600[/C][C]74684.8131444703[/C][C]6915.18685552965[/C][/ROW]
[ROW][C]68[/C][C]80400[/C][C]69124.205916299[/C][C]11275.794083701[/C][/ROW]
[ROW][C]69[/C][C]64800[/C][C]62102.6719229378[/C][C]2697.32807706222[/C][/ROW]
[ROW][C]70[/C][C]75600[/C][C]78372.5061393623[/C][C]-2772.50613936235[/C][/ROW]
[ROW][C]71[/C][C]67200[/C][C]72638.4556953396[/C][C]-5438.45569533958[/C][/ROW]
[ROW][C]72[/C][C]96000[/C][C]103252.500517718[/C][C]-7252.50051771791[/C][/ROW]
[ROW][C]73[/C][C]73200[/C][C]81821.138761272[/C][C]-8621.13876127196[/C][/ROW]
[ROW][C]74[/C][C]58800[/C][C]48534.1403585543[/C][C]10265.8596414457[/C][/ROW]
[ROW][C]75[/C][C]52800[/C][C]50940.0132699425[/C][C]1859.98673005747[/C][/ROW]
[ROW][C]76[/C][C]39600[/C][C]43271.1894559465[/C][C]-3671.18945594653[/C][/ROW]
[ROW][C]77[/C][C]58800[/C][C]58500.0809549805[/C][C]299.919045019458[/C][/ROW]
[ROW][C]78[/C][C]70800[/C][C]66337.4039501994[/C][C]4462.59604980057[/C][/ROW]
[ROW][C]79[/C][C]82800[/C][C]83384.8700642308[/C][C]-584.87006423081[/C][/ROW]
[ROW][C]80[/C][C]78000[/C][C]81794.9568777719[/C][C]-3794.95687777185[/C][/ROW]
[ROW][C]81[/C][C]57600[/C][C]66615.5011881939[/C][C]-9015.5011881939[/C][/ROW]
[ROW][C]82[/C][C]82800[/C][C]77513.5779843591[/C][C]5286.42201564094[/C][/ROW]
[ROW][C]83[/C][C]64800[/C][C]69248.3356906997[/C][C]-4448.33569069972[/C][/ROW]
[ROW][C]84[/C][C]99600[/C][C]98059.6315489043[/C][C]1540.36845109568[/C][/ROW]
[ROW][C]85[/C][C]82800[/C][C]75389.5057078464[/C][C]7410.49429215357[/C][/ROW]
[ROW][C]86[/C][C]60000[/C][C]59737.8937477395[/C][C]262.10625226047[/C][/ROW]
[ROW][C]87[/C][C]55200[/C][C]54304.34479585[/C][C]895.655204149982[/C][/ROW]
[ROW][C]88[/C][C]37200[/C][C]41518.9335367185[/C][C]-4318.93353671848[/C][/ROW]
[ROW][C]89[/C][C]58800[/C][C]60381.2749821579[/C][C]-1581.27498215793[/C][/ROW]
[ROW][C]90[/C][C]56400[/C][C]71999.6674608153[/C][C]-15599.6674608153[/C][/ROW]
[ROW][C]91[/C][C]85200[/C][C]83990.0286450089[/C][C]1209.97135499108[/C][/ROW]
[ROW][C]92[/C][C]85200[/C][C]79254.572001962[/C][C]5945.42799803799[/C][/ROW]
[ROW][C]93[/C][C]64800[/C][C]59241.4167889812[/C][C]5558.58321101882[/C][/ROW]
[ROW][C]94[/C][C]84000[/C][C]83468.8076954434[/C][C]531.192304556593[/C][/ROW]
[ROW][C]95[/C][C]62400[/C][C]66168.2503514245[/C][C]-3768.2503514245[/C][/ROW]
[ROW][C]96[/C][C]97200[/C][C]100484.657599441[/C][C]-3284.65759944054[/C][/ROW]
[ROW][C]97[/C][C]82800[/C][C]83114.7444887647[/C][C]-314.744488764671[/C][/ROW]
[ROW][C]98[/C][C]61200[/C][C]60672.8344963497[/C][C]527.165503650278[/C][/ROW]
[ROW][C]99[/C][C]46800[/C][C]55693.8343931319[/C][C]-8893.83439313186[/C][/ROW]
[ROW][C]100[/C][C]32400[/C][C]37792.1346069583[/C][C]-5392.13460695825[/C][/ROW]
[ROW][C]101[/C][C]63600[/C][C]58934.2467376017[/C][C]4665.75326239834[/C][/ROW]
[ROW][C]102[/C][C]61200[/C][C]57523.0905673582[/C][C]3676.90943264183[/C][/ROW]
[ROW][C]103[/C][C]80400[/C][C]85180.5796959865[/C][C]-4780.5796959865[/C][/ROW]
[ROW][C]104[/C][C]92400[/C][C]84700.5399193111[/C][C]7699.46008068888[/C][/ROW]
[ROW][C]105[/C][C]68400[/C][C]64312.321755586[/C][C]4087.67824441405[/C][/ROW]
[ROW][C]106[/C][C]76800[/C][C]83846.4850791646[/C][C]-7046.48507916457[/C][/ROW]
[ROW][C]107[/C][C]57600[/C][C]62396.5211743239[/C][C]-4796.52117432389[/C][/ROW]
[ROW][C]108[/C][C]99600[/C][C]97020.5848214683[/C][C]2579.41517853169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279757&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279757&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
137200074462.1794871795-2462.17948717954
145400056402.2384181665-2402.2384181665
156360066520.6048976001-2920.6048976001
164800050807.1224232633-2807.12242326327
176720068968.6936481865-1768.69364818648
185520055923.5017542483-723.501754248289
197320069931.28909254683268.71090745322
206600072006.3211949713-6006.32119497126
216960080339.8298412923-10739.8298412923
227800069180.0370209438819.96297905699
237680065433.074399329311366.9256006707
249120082514.97088533078685.02911466932
256600067284.4074947264-1284.40749472637
265520049322.89135210065877.10864789935
276120059149.41579174812050.58420825186
284440043741.525553065658.474446935012
296360063078.8625428017521.137457198274
304920051225.983880222-2025.98388022199
316960069095.4242040705504.575795929515
326600062771.74659311633228.25340688371
335880067086.6509828981-8286.65098289814
348400074246.13524781879753.86475218127
357560073141.52606271612458.47393728388
368640087875.5165875638-1475.51658756385
376480063478.3777393331321.62226066698
386000052272.96659447267727.03340552741
395400058744.0060738993-4744.00607389928
404440042080.12668075222319.87331924784
415880061411.0173389156-2611.01733891557
425280047258.49907416615541.50092583393
437200067674.82084597134325.17915402872
446960064076.59954022045523.40045977961
456000058008.10665820291991.89334179705
468040082178.5286534765-1778.52865347652
477440074437.6887668475-37.6887668474519
489600085692.397698351110307.6023016489
497680064257.77877319112542.221226809
504680059437.3824170921-12637.3824170921
514680054424.1323474363-7624.13234743632
524680044405.95948101232394.04051898766
535520059361.5270069268-4161.52700692679
545520052856.16467438562343.83532561441
557440072244.59287956362155.40712043636
566840069832.0782095728-1432.07820957281
576120060483.7281149302716.271885069822
587680081195.0030255746-4395.0030255746
597080075035.1087501385-4235.10875013849
6010200095743.30667214726256.69332785284
618040076254.8079292564145.19207074399
624680048009.6882887165-1209.68828871653
634920047673.5341152641526.46588473601
644080047006.4379374811-6206.4379374811
655640055802.0041473669597.99585263311
666480055335.62707413129464.37292586882
678160074684.81314447036915.18685552965
688040069124.20591629911275.794083701
696480062102.67192293782697.32807706222
707560078372.5061393623-2772.50613936235
716720072638.4556953396-5438.45569533958
7296000103252.500517718-7252.50051771791
737320081821.138761272-8621.13876127196
745880048534.140358554310265.8596414457
755280050940.01326994251859.98673005747
763960043271.1894559465-3671.18945594653
775880058500.0809549805299.919045019458
787080066337.40395019944462.59604980057
798280083384.8700642308-584.87006423081
807800081794.9568777719-3794.95687777185
815760066615.5011881939-9015.5011881939
828280077513.57798435915286.42201564094
836480069248.3356906997-4448.33569069972
849960098059.63154890431540.36845109568
858280075389.50570784647410.49429215357
866000059737.8937477395262.10625226047
875520054304.34479585895.655204149982
883720041518.9335367185-4318.93353671848
895880060381.2749821579-1581.27498215793
905640071999.6674608153-15599.6674608153
918520083990.02864500891209.97135499108
928520079254.5720019625945.42799803799
936480059241.41678898125558.58321101882
948400083468.8076954434531.192304556593
956240066168.2503514245-3768.2503514245
9697200100484.657599441-3284.65759944054
978280083114.7444887647-314.744488764671
986120060672.8344963497527.165503650278
994680055693.8343931319-8893.83439313186
1003240037792.1346069583-5392.13460695825
1016360058934.24673760174665.75326239834
1026120057523.09056735823676.90943264183
1038040085180.5796959865-4780.5796959865
1049240084700.53991931117699.46008068888
1056840064312.3217555864087.67824441405
1067680083846.4850791646-7046.48507916457
1075760062396.5211743239-4796.52117432389
1089960097020.58482146832579.41517853169







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10982366.761213959271367.241322728293366.2811051901
11060632.235456615449630.828879069971633.6420341609
11146894.180141873935888.529702670857899.8305810771
11232306.888709187321293.697664924343320.0797534503
11362820.201092887351795.23817819273845.1640075827
11460468.102985428349426.210625316771509.9953455399
11580279.954127575569215.060532672891344.8477224782
11691363.646051454380268.7818424371102458.510260472
11767529.165410926256396.485321847678661.8455000047
11876683.358006218665504.168092022687862.5479204145
11957350.691831231946115.482453759168585.9012087047
12098837.467195899987535.9518885095110138.98250329

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 82366.7612139592 & 71367.2413227282 & 93366.2811051901 \tabularnewline
110 & 60632.2354566154 & 49630.8288790699 & 71633.6420341609 \tabularnewline
111 & 46894.1801418739 & 35888.5297026708 & 57899.8305810771 \tabularnewline
112 & 32306.8887091873 & 21293.6976649243 & 43320.0797534503 \tabularnewline
113 & 62820.2010928873 & 51795.238178192 & 73845.1640075827 \tabularnewline
114 & 60468.1029854283 & 49426.2106253167 & 71509.9953455399 \tabularnewline
115 & 80279.9541275755 & 69215.0605326728 & 91344.8477224782 \tabularnewline
116 & 91363.6460514543 & 80268.7818424371 & 102458.510260472 \tabularnewline
117 & 67529.1654109262 & 56396.4853218476 & 78661.8455000047 \tabularnewline
118 & 76683.3580062186 & 65504.1680920226 & 87862.5479204145 \tabularnewline
119 & 57350.6918312319 & 46115.4824537591 & 68585.9012087047 \tabularnewline
120 & 98837.4671958999 & 87535.9518885095 & 110138.98250329 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279757&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]109[/C][C]82366.7612139592[/C][C]71367.2413227282[/C][C]93366.2811051901[/C][/ROW]
[ROW][C]110[/C][C]60632.2354566154[/C][C]49630.8288790699[/C][C]71633.6420341609[/C][/ROW]
[ROW][C]111[/C][C]46894.1801418739[/C][C]35888.5297026708[/C][C]57899.8305810771[/C][/ROW]
[ROW][C]112[/C][C]32306.8887091873[/C][C]21293.6976649243[/C][C]43320.0797534503[/C][/ROW]
[ROW][C]113[/C][C]62820.2010928873[/C][C]51795.238178192[/C][C]73845.1640075827[/C][/ROW]
[ROW][C]114[/C][C]60468.1029854283[/C][C]49426.2106253167[/C][C]71509.9953455399[/C][/ROW]
[ROW][C]115[/C][C]80279.9541275755[/C][C]69215.0605326728[/C][C]91344.8477224782[/C][/ROW]
[ROW][C]116[/C][C]91363.6460514543[/C][C]80268.7818424371[/C][C]102458.510260472[/C][/ROW]
[ROW][C]117[/C][C]67529.1654109262[/C][C]56396.4853218476[/C][C]78661.8455000047[/C][/ROW]
[ROW][C]118[/C][C]76683.3580062186[/C][C]65504.1680920226[/C][C]87862.5479204145[/C][/ROW]
[ROW][C]119[/C][C]57350.6918312319[/C][C]46115.4824537591[/C][C]68585.9012087047[/C][/ROW]
[ROW][C]120[/C][C]98837.4671958999[/C][C]87535.9518885095[/C][C]110138.98250329[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279757&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279757&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
10982366.761213959271367.241322728293366.2811051901
11060632.235456615449630.828879069971633.6420341609
11146894.180141873935888.529702670857899.8305810771
11232306.888709187321293.697664924343320.0797534503
11362820.201092887351795.23817819273845.1640075827
11460468.102985428349426.210625316771509.9953455399
11580279.954127575569215.060532672891344.8477224782
11691363.646051454380268.7818424371102458.510260472
11767529.165410926256396.485321847678661.8455000047
11876683.358006218665504.168092022687862.5479204145
11957350.691831231946115.482453759168585.9012087047
12098837.467195899987535.9518885095110138.98250329



Parameters (Session):
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')