Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 12 Aug 2015 17:45:47 +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/Aug/12/t1439398179xz6u50qdxmlbmwb.htm/, Retrieved Thu, 16 May 2024 13:39:50 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=280028, Retrieved Thu, 16 May 2024 13:39:50 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-08-12 16:45:47] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
48600
46800
49500
39600
51300
50400
54000
55800
62100
54000
51300
63900
54000
40500
47700
36000
50400
41400
54900
49500
52200
58500
57600
68400
49500
41400
45900
33300
47700
36900
52200
49500
44100
63000
56700
64800
48600
45000
40500
33300
44100
39600
54000
52200
45000
60300
55800
72000
57600
35100
35100
35100
41400
41400
55800
51300
45900
57600
53100
76500
60300
35100
36900
30600
42300
48600
61200
60300
48600
56700
50400
72000
54900
44100
39600
29700
44100
53100
62100
58500
43200
62100
48600
74700
62100
45000
41400
27900
44100
42300
63900
63900
48600
63000
46800
72900
62100
45900
35100
24300
47700
45900
60300
69300
51300
57600
43200
74700




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=280028&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=280028&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280028&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
alpha0.548594506058338
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.548594506058338 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280028&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]0.548594506058338[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280028&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280028&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
alpha0.548594506058338
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
24680048600-1800
34950047612.5298890951887.47011090501
43960048647.9856222868-9047.9856222868
55130043684.31041900547615.68958099457
65040047862.23588298482537.76411701522
75400049254.43933525134745.56066474868
85580051857.8278440993942.172155901
96210054020.48183076248079.51816923756
105400058452.8611100047-4452.8611100047
115130056010.0459688153-4710.04596881529
126390053426.14062704110473.859372959
135400059172.0423362739-5172.04233627394
144050056334.6883254929-15834.6883254929
154770047647.865304981452.134695018598
163600047676.4661122436-11676.4661122436
175040041270.82095289049129.17904710959
184140046279.0384229576-4879.03842295763
195490043602.424749275511297.5752507245
204950049800.2124636036-300.212463603631
215220049635.51755542042564.48244457955
225850051042.37853539987457.62146460015
235760055133.58869914222466.41130085777
246840056486.64838847311913.351611527
254950063022.247631298-13522.247631298
264140055604.0168712075-14204.0168712075
274590047811.7712517031-1911.77125170313
283330046762.9840461785-13462.9840461785
294770039377.26496329398322.73503670607
303690043943.0716798101-7043.07167981012
315220040079.281250491212120.7187495088
324950046728.640965952771.35903404998
334410048248.993306345-4148.99330634499
346300045972.878372811317027.1216271887
355670055313.86375147411386.13624852586
366480056074.29048206378725.70951793626
374860060861.1667850645-12261.1667850645
384500054134.7580489132-9134.75804891315
394050049123.4799691072-8623.47996910721
403330044392.6862349509-11092.6862349509
414410038307.29950902795792.70049097213
423960041485.1431736166-1885.14317361662
435400040450.963985437213549.0360145628
445220047883.89070541294316.1092945871
454500050251.6845519707-5251.68455197071
466030047370.639259208112929.3607407919
475580054463.61552845291336.38447154708
487200055196.748707525316803.2512924747
495760064414.9200504946-6814.92005049461
503510060676.2923515665-25576.2923515665
513510046645.2788821552-11545.2788821552
523510040311.6023164935-5211.6023164935
534140037452.54591790433947.45408209574
544140039618.09754025951781.90245974046
555580040595.63944000515204.360559995
565130048936.66811134832363.33188865166
574590050233.1790014551-4333.17900145512
585760047856.02080748959743.97919251052
595310053201.5142596475-101.51425964752
607650053145.824094518323354.1759054817
616030065957.7966897856-5657.79668978558
623510062853.9605093742-27753.9605093742
633690047628.2902525714-10728.2902525714
643060041742.8091606115-11142.8091606115
654230035629.92527304356670.07472695648
664860039289.09162325049310.90837674958
676120044397.004805147816802.9951948522
686030053615.03565436846684.96434563163
694860057282.3703675778-8682.37036757775
705670052519.26968436094180.73031563912
715040054812.795366832-4412.79536683204
727200052391.960072228319608.0399277717
735490063148.8230511764-8248.82305117639
744410058623.5640438536-14523.5640438536
753960050656.0166010091-11056.0166010091
762970044590.7466348057-14890.7466348057
774410036421.76483984467678.23516015538
785310040634.002464929812465.9975350702
796210047472.780225206114627.2197747939
805850055497.19263256593002.80736743408
814320057144.5162570918-13944.5162570918
826210049494.6312488112605.36875119
834860056409.8672925523-7809.86729255231
847470052125.417002813422574.5829971866
856210064509.7092116279-2409.70921162795
864500063187.7559769307-18187.7559769307
874140053210.0529704568-11810.0529704568
882790046731.1227946062-18831.1227946062
894410036400.47228657537699.52771342469
904230040624.3908894041675.60911059599
916390041543.620841778322356.3791582217
926390053808.207623335910091.7923766641
934860059344.5094774552-10744.5094774552
946300053450.13060783159549.86939216846
954680058689.1364899498-11889.1364899498
967290052166.821529785620733.1784702144
976210063540.9293316723-1440.92933167226
984590062750.4434166985-16850.4434166985
993510053506.3827336508-18406.3827336508
1002430043408.7422895629-19108.7422895629
1014770032925.791251824114774.2087481759
1024590041030.84100243244869.15899756757
1036030043702.034877622516597.9651223775
1046930052807.587355506716492.4126444933
1055130061855.2343239228-10555.2343239228
1065760056064.69076366041535.30923633964
1074320056906.9529758169-13706.9529758169
1087470049387.393878483825312.6061215162

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 46800 & 48600 & -1800 \tabularnewline
3 & 49500 & 47612.529889095 & 1887.47011090501 \tabularnewline
4 & 39600 & 48647.9856222868 & -9047.9856222868 \tabularnewline
5 & 51300 & 43684.3104190054 & 7615.68958099457 \tabularnewline
6 & 50400 & 47862.2358829848 & 2537.76411701522 \tabularnewline
7 & 54000 & 49254.4393352513 & 4745.56066474868 \tabularnewline
8 & 55800 & 51857.827844099 & 3942.172155901 \tabularnewline
9 & 62100 & 54020.4818307624 & 8079.51816923756 \tabularnewline
10 & 54000 & 58452.8611100047 & -4452.8611100047 \tabularnewline
11 & 51300 & 56010.0459688153 & -4710.04596881529 \tabularnewline
12 & 63900 & 53426.140627041 & 10473.859372959 \tabularnewline
13 & 54000 & 59172.0423362739 & -5172.04233627394 \tabularnewline
14 & 40500 & 56334.6883254929 & -15834.6883254929 \tabularnewline
15 & 47700 & 47647.8653049814 & 52.134695018598 \tabularnewline
16 & 36000 & 47676.4661122436 & -11676.4661122436 \tabularnewline
17 & 50400 & 41270.8209528904 & 9129.17904710959 \tabularnewline
18 & 41400 & 46279.0384229576 & -4879.03842295763 \tabularnewline
19 & 54900 & 43602.4247492755 & 11297.5752507245 \tabularnewline
20 & 49500 & 49800.2124636036 & -300.212463603631 \tabularnewline
21 & 52200 & 49635.5175554204 & 2564.48244457955 \tabularnewline
22 & 58500 & 51042.3785353998 & 7457.62146460015 \tabularnewline
23 & 57600 & 55133.5886991422 & 2466.41130085777 \tabularnewline
24 & 68400 & 56486.648388473 & 11913.351611527 \tabularnewline
25 & 49500 & 63022.247631298 & -13522.247631298 \tabularnewline
26 & 41400 & 55604.0168712075 & -14204.0168712075 \tabularnewline
27 & 45900 & 47811.7712517031 & -1911.77125170313 \tabularnewline
28 & 33300 & 46762.9840461785 & -13462.9840461785 \tabularnewline
29 & 47700 & 39377.2649632939 & 8322.73503670607 \tabularnewline
30 & 36900 & 43943.0716798101 & -7043.07167981012 \tabularnewline
31 & 52200 & 40079.2812504912 & 12120.7187495088 \tabularnewline
32 & 49500 & 46728.64096595 & 2771.35903404998 \tabularnewline
33 & 44100 & 48248.993306345 & -4148.99330634499 \tabularnewline
34 & 63000 & 45972.8783728113 & 17027.1216271887 \tabularnewline
35 & 56700 & 55313.8637514741 & 1386.13624852586 \tabularnewline
36 & 64800 & 56074.2904820637 & 8725.70951793626 \tabularnewline
37 & 48600 & 60861.1667850645 & -12261.1667850645 \tabularnewline
38 & 45000 & 54134.7580489132 & -9134.75804891315 \tabularnewline
39 & 40500 & 49123.4799691072 & -8623.47996910721 \tabularnewline
40 & 33300 & 44392.6862349509 & -11092.6862349509 \tabularnewline
41 & 44100 & 38307.2995090279 & 5792.70049097213 \tabularnewline
42 & 39600 & 41485.1431736166 & -1885.14317361662 \tabularnewline
43 & 54000 & 40450.9639854372 & 13549.0360145628 \tabularnewline
44 & 52200 & 47883.8907054129 & 4316.1092945871 \tabularnewline
45 & 45000 & 50251.6845519707 & -5251.68455197071 \tabularnewline
46 & 60300 & 47370.6392592081 & 12929.3607407919 \tabularnewline
47 & 55800 & 54463.6155284529 & 1336.38447154708 \tabularnewline
48 & 72000 & 55196.7487075253 & 16803.2512924747 \tabularnewline
49 & 57600 & 64414.9200504946 & -6814.92005049461 \tabularnewline
50 & 35100 & 60676.2923515665 & -25576.2923515665 \tabularnewline
51 & 35100 & 46645.2788821552 & -11545.2788821552 \tabularnewline
52 & 35100 & 40311.6023164935 & -5211.6023164935 \tabularnewline
53 & 41400 & 37452.5459179043 & 3947.45408209574 \tabularnewline
54 & 41400 & 39618.0975402595 & 1781.90245974046 \tabularnewline
55 & 55800 & 40595.639440005 & 15204.360559995 \tabularnewline
56 & 51300 & 48936.6681113483 & 2363.33188865166 \tabularnewline
57 & 45900 & 50233.1790014551 & -4333.17900145512 \tabularnewline
58 & 57600 & 47856.0208074895 & 9743.97919251052 \tabularnewline
59 & 53100 & 53201.5142596475 & -101.51425964752 \tabularnewline
60 & 76500 & 53145.8240945183 & 23354.1759054817 \tabularnewline
61 & 60300 & 65957.7966897856 & -5657.79668978558 \tabularnewline
62 & 35100 & 62853.9605093742 & -27753.9605093742 \tabularnewline
63 & 36900 & 47628.2902525714 & -10728.2902525714 \tabularnewline
64 & 30600 & 41742.8091606115 & -11142.8091606115 \tabularnewline
65 & 42300 & 35629.9252730435 & 6670.07472695648 \tabularnewline
66 & 48600 & 39289.0916232504 & 9310.90837674958 \tabularnewline
67 & 61200 & 44397.0048051478 & 16802.9951948522 \tabularnewline
68 & 60300 & 53615.0356543684 & 6684.96434563163 \tabularnewline
69 & 48600 & 57282.3703675778 & -8682.37036757775 \tabularnewline
70 & 56700 & 52519.2696843609 & 4180.73031563912 \tabularnewline
71 & 50400 & 54812.795366832 & -4412.79536683204 \tabularnewline
72 & 72000 & 52391.9600722283 & 19608.0399277717 \tabularnewline
73 & 54900 & 63148.8230511764 & -8248.82305117639 \tabularnewline
74 & 44100 & 58623.5640438536 & -14523.5640438536 \tabularnewline
75 & 39600 & 50656.0166010091 & -11056.0166010091 \tabularnewline
76 & 29700 & 44590.7466348057 & -14890.7466348057 \tabularnewline
77 & 44100 & 36421.7648398446 & 7678.23516015538 \tabularnewline
78 & 53100 & 40634.0024649298 & 12465.9975350702 \tabularnewline
79 & 62100 & 47472.7802252061 & 14627.2197747939 \tabularnewline
80 & 58500 & 55497.1926325659 & 3002.80736743408 \tabularnewline
81 & 43200 & 57144.5162570918 & -13944.5162570918 \tabularnewline
82 & 62100 & 49494.63124881 & 12605.36875119 \tabularnewline
83 & 48600 & 56409.8672925523 & -7809.86729255231 \tabularnewline
84 & 74700 & 52125.4170028134 & 22574.5829971866 \tabularnewline
85 & 62100 & 64509.7092116279 & -2409.70921162795 \tabularnewline
86 & 45000 & 63187.7559769307 & -18187.7559769307 \tabularnewline
87 & 41400 & 53210.0529704568 & -11810.0529704568 \tabularnewline
88 & 27900 & 46731.1227946062 & -18831.1227946062 \tabularnewline
89 & 44100 & 36400.4722865753 & 7699.52771342469 \tabularnewline
90 & 42300 & 40624.390889404 & 1675.60911059599 \tabularnewline
91 & 63900 & 41543.6208417783 & 22356.3791582217 \tabularnewline
92 & 63900 & 53808.2076233359 & 10091.7923766641 \tabularnewline
93 & 48600 & 59344.5094774552 & -10744.5094774552 \tabularnewline
94 & 63000 & 53450.1306078315 & 9549.86939216846 \tabularnewline
95 & 46800 & 58689.1364899498 & -11889.1364899498 \tabularnewline
96 & 72900 & 52166.8215297856 & 20733.1784702144 \tabularnewline
97 & 62100 & 63540.9293316723 & -1440.92933167226 \tabularnewline
98 & 45900 & 62750.4434166985 & -16850.4434166985 \tabularnewline
99 & 35100 & 53506.3827336508 & -18406.3827336508 \tabularnewline
100 & 24300 & 43408.7422895629 & -19108.7422895629 \tabularnewline
101 & 47700 & 32925.7912518241 & 14774.2087481759 \tabularnewline
102 & 45900 & 41030.8410024324 & 4869.15899756757 \tabularnewline
103 & 60300 & 43702.0348776225 & 16597.9651223775 \tabularnewline
104 & 69300 & 52807.5873555067 & 16492.4126444933 \tabularnewline
105 & 51300 & 61855.2343239228 & -10555.2343239228 \tabularnewline
106 & 57600 & 56064.6907636604 & 1535.30923633964 \tabularnewline
107 & 43200 & 56906.9529758169 & -13706.9529758169 \tabularnewline
108 & 74700 & 49387.3938784838 & 25312.6061215162 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280028&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]46800[/C][C]48600[/C][C]-1800[/C][/ROW]
[ROW][C]3[/C][C]49500[/C][C]47612.529889095[/C][C]1887.47011090501[/C][/ROW]
[ROW][C]4[/C][C]39600[/C][C]48647.9856222868[/C][C]-9047.9856222868[/C][/ROW]
[ROW][C]5[/C][C]51300[/C][C]43684.3104190054[/C][C]7615.68958099457[/C][/ROW]
[ROW][C]6[/C][C]50400[/C][C]47862.2358829848[/C][C]2537.76411701522[/C][/ROW]
[ROW][C]7[/C][C]54000[/C][C]49254.4393352513[/C][C]4745.56066474868[/C][/ROW]
[ROW][C]8[/C][C]55800[/C][C]51857.827844099[/C][C]3942.172155901[/C][/ROW]
[ROW][C]9[/C][C]62100[/C][C]54020.4818307624[/C][C]8079.51816923756[/C][/ROW]
[ROW][C]10[/C][C]54000[/C][C]58452.8611100047[/C][C]-4452.8611100047[/C][/ROW]
[ROW][C]11[/C][C]51300[/C][C]56010.0459688153[/C][C]-4710.04596881529[/C][/ROW]
[ROW][C]12[/C][C]63900[/C][C]53426.140627041[/C][C]10473.859372959[/C][/ROW]
[ROW][C]13[/C][C]54000[/C][C]59172.0423362739[/C][C]-5172.04233627394[/C][/ROW]
[ROW][C]14[/C][C]40500[/C][C]56334.6883254929[/C][C]-15834.6883254929[/C][/ROW]
[ROW][C]15[/C][C]47700[/C][C]47647.8653049814[/C][C]52.134695018598[/C][/ROW]
[ROW][C]16[/C][C]36000[/C][C]47676.4661122436[/C][C]-11676.4661122436[/C][/ROW]
[ROW][C]17[/C][C]50400[/C][C]41270.8209528904[/C][C]9129.17904710959[/C][/ROW]
[ROW][C]18[/C][C]41400[/C][C]46279.0384229576[/C][C]-4879.03842295763[/C][/ROW]
[ROW][C]19[/C][C]54900[/C][C]43602.4247492755[/C][C]11297.5752507245[/C][/ROW]
[ROW][C]20[/C][C]49500[/C][C]49800.2124636036[/C][C]-300.212463603631[/C][/ROW]
[ROW][C]21[/C][C]52200[/C][C]49635.5175554204[/C][C]2564.48244457955[/C][/ROW]
[ROW][C]22[/C][C]58500[/C][C]51042.3785353998[/C][C]7457.62146460015[/C][/ROW]
[ROW][C]23[/C][C]57600[/C][C]55133.5886991422[/C][C]2466.41130085777[/C][/ROW]
[ROW][C]24[/C][C]68400[/C][C]56486.648388473[/C][C]11913.351611527[/C][/ROW]
[ROW][C]25[/C][C]49500[/C][C]63022.247631298[/C][C]-13522.247631298[/C][/ROW]
[ROW][C]26[/C][C]41400[/C][C]55604.0168712075[/C][C]-14204.0168712075[/C][/ROW]
[ROW][C]27[/C][C]45900[/C][C]47811.7712517031[/C][C]-1911.77125170313[/C][/ROW]
[ROW][C]28[/C][C]33300[/C][C]46762.9840461785[/C][C]-13462.9840461785[/C][/ROW]
[ROW][C]29[/C][C]47700[/C][C]39377.2649632939[/C][C]8322.73503670607[/C][/ROW]
[ROW][C]30[/C][C]36900[/C][C]43943.0716798101[/C][C]-7043.07167981012[/C][/ROW]
[ROW][C]31[/C][C]52200[/C][C]40079.2812504912[/C][C]12120.7187495088[/C][/ROW]
[ROW][C]32[/C][C]49500[/C][C]46728.64096595[/C][C]2771.35903404998[/C][/ROW]
[ROW][C]33[/C][C]44100[/C][C]48248.993306345[/C][C]-4148.99330634499[/C][/ROW]
[ROW][C]34[/C][C]63000[/C][C]45972.8783728113[/C][C]17027.1216271887[/C][/ROW]
[ROW][C]35[/C][C]56700[/C][C]55313.8637514741[/C][C]1386.13624852586[/C][/ROW]
[ROW][C]36[/C][C]64800[/C][C]56074.2904820637[/C][C]8725.70951793626[/C][/ROW]
[ROW][C]37[/C][C]48600[/C][C]60861.1667850645[/C][C]-12261.1667850645[/C][/ROW]
[ROW][C]38[/C][C]45000[/C][C]54134.7580489132[/C][C]-9134.75804891315[/C][/ROW]
[ROW][C]39[/C][C]40500[/C][C]49123.4799691072[/C][C]-8623.47996910721[/C][/ROW]
[ROW][C]40[/C][C]33300[/C][C]44392.6862349509[/C][C]-11092.6862349509[/C][/ROW]
[ROW][C]41[/C][C]44100[/C][C]38307.2995090279[/C][C]5792.70049097213[/C][/ROW]
[ROW][C]42[/C][C]39600[/C][C]41485.1431736166[/C][C]-1885.14317361662[/C][/ROW]
[ROW][C]43[/C][C]54000[/C][C]40450.9639854372[/C][C]13549.0360145628[/C][/ROW]
[ROW][C]44[/C][C]52200[/C][C]47883.8907054129[/C][C]4316.1092945871[/C][/ROW]
[ROW][C]45[/C][C]45000[/C][C]50251.6845519707[/C][C]-5251.68455197071[/C][/ROW]
[ROW][C]46[/C][C]60300[/C][C]47370.6392592081[/C][C]12929.3607407919[/C][/ROW]
[ROW][C]47[/C][C]55800[/C][C]54463.6155284529[/C][C]1336.38447154708[/C][/ROW]
[ROW][C]48[/C][C]72000[/C][C]55196.7487075253[/C][C]16803.2512924747[/C][/ROW]
[ROW][C]49[/C][C]57600[/C][C]64414.9200504946[/C][C]-6814.92005049461[/C][/ROW]
[ROW][C]50[/C][C]35100[/C][C]60676.2923515665[/C][C]-25576.2923515665[/C][/ROW]
[ROW][C]51[/C][C]35100[/C][C]46645.2788821552[/C][C]-11545.2788821552[/C][/ROW]
[ROW][C]52[/C][C]35100[/C][C]40311.6023164935[/C][C]-5211.6023164935[/C][/ROW]
[ROW][C]53[/C][C]41400[/C][C]37452.5459179043[/C][C]3947.45408209574[/C][/ROW]
[ROW][C]54[/C][C]41400[/C][C]39618.0975402595[/C][C]1781.90245974046[/C][/ROW]
[ROW][C]55[/C][C]55800[/C][C]40595.639440005[/C][C]15204.360559995[/C][/ROW]
[ROW][C]56[/C][C]51300[/C][C]48936.6681113483[/C][C]2363.33188865166[/C][/ROW]
[ROW][C]57[/C][C]45900[/C][C]50233.1790014551[/C][C]-4333.17900145512[/C][/ROW]
[ROW][C]58[/C][C]57600[/C][C]47856.0208074895[/C][C]9743.97919251052[/C][/ROW]
[ROW][C]59[/C][C]53100[/C][C]53201.5142596475[/C][C]-101.51425964752[/C][/ROW]
[ROW][C]60[/C][C]76500[/C][C]53145.8240945183[/C][C]23354.1759054817[/C][/ROW]
[ROW][C]61[/C][C]60300[/C][C]65957.7966897856[/C][C]-5657.79668978558[/C][/ROW]
[ROW][C]62[/C][C]35100[/C][C]62853.9605093742[/C][C]-27753.9605093742[/C][/ROW]
[ROW][C]63[/C][C]36900[/C][C]47628.2902525714[/C][C]-10728.2902525714[/C][/ROW]
[ROW][C]64[/C][C]30600[/C][C]41742.8091606115[/C][C]-11142.8091606115[/C][/ROW]
[ROW][C]65[/C][C]42300[/C][C]35629.9252730435[/C][C]6670.07472695648[/C][/ROW]
[ROW][C]66[/C][C]48600[/C][C]39289.0916232504[/C][C]9310.90837674958[/C][/ROW]
[ROW][C]67[/C][C]61200[/C][C]44397.0048051478[/C][C]16802.9951948522[/C][/ROW]
[ROW][C]68[/C][C]60300[/C][C]53615.0356543684[/C][C]6684.96434563163[/C][/ROW]
[ROW][C]69[/C][C]48600[/C][C]57282.3703675778[/C][C]-8682.37036757775[/C][/ROW]
[ROW][C]70[/C][C]56700[/C][C]52519.2696843609[/C][C]4180.73031563912[/C][/ROW]
[ROW][C]71[/C][C]50400[/C][C]54812.795366832[/C][C]-4412.79536683204[/C][/ROW]
[ROW][C]72[/C][C]72000[/C][C]52391.9600722283[/C][C]19608.0399277717[/C][/ROW]
[ROW][C]73[/C][C]54900[/C][C]63148.8230511764[/C][C]-8248.82305117639[/C][/ROW]
[ROW][C]74[/C][C]44100[/C][C]58623.5640438536[/C][C]-14523.5640438536[/C][/ROW]
[ROW][C]75[/C][C]39600[/C][C]50656.0166010091[/C][C]-11056.0166010091[/C][/ROW]
[ROW][C]76[/C][C]29700[/C][C]44590.7466348057[/C][C]-14890.7466348057[/C][/ROW]
[ROW][C]77[/C][C]44100[/C][C]36421.7648398446[/C][C]7678.23516015538[/C][/ROW]
[ROW][C]78[/C][C]53100[/C][C]40634.0024649298[/C][C]12465.9975350702[/C][/ROW]
[ROW][C]79[/C][C]62100[/C][C]47472.7802252061[/C][C]14627.2197747939[/C][/ROW]
[ROW][C]80[/C][C]58500[/C][C]55497.1926325659[/C][C]3002.80736743408[/C][/ROW]
[ROW][C]81[/C][C]43200[/C][C]57144.5162570918[/C][C]-13944.5162570918[/C][/ROW]
[ROW][C]82[/C][C]62100[/C][C]49494.63124881[/C][C]12605.36875119[/C][/ROW]
[ROW][C]83[/C][C]48600[/C][C]56409.8672925523[/C][C]-7809.86729255231[/C][/ROW]
[ROW][C]84[/C][C]74700[/C][C]52125.4170028134[/C][C]22574.5829971866[/C][/ROW]
[ROW][C]85[/C][C]62100[/C][C]64509.7092116279[/C][C]-2409.70921162795[/C][/ROW]
[ROW][C]86[/C][C]45000[/C][C]63187.7559769307[/C][C]-18187.7559769307[/C][/ROW]
[ROW][C]87[/C][C]41400[/C][C]53210.0529704568[/C][C]-11810.0529704568[/C][/ROW]
[ROW][C]88[/C][C]27900[/C][C]46731.1227946062[/C][C]-18831.1227946062[/C][/ROW]
[ROW][C]89[/C][C]44100[/C][C]36400.4722865753[/C][C]7699.52771342469[/C][/ROW]
[ROW][C]90[/C][C]42300[/C][C]40624.390889404[/C][C]1675.60911059599[/C][/ROW]
[ROW][C]91[/C][C]63900[/C][C]41543.6208417783[/C][C]22356.3791582217[/C][/ROW]
[ROW][C]92[/C][C]63900[/C][C]53808.2076233359[/C][C]10091.7923766641[/C][/ROW]
[ROW][C]93[/C][C]48600[/C][C]59344.5094774552[/C][C]-10744.5094774552[/C][/ROW]
[ROW][C]94[/C][C]63000[/C][C]53450.1306078315[/C][C]9549.86939216846[/C][/ROW]
[ROW][C]95[/C][C]46800[/C][C]58689.1364899498[/C][C]-11889.1364899498[/C][/ROW]
[ROW][C]96[/C][C]72900[/C][C]52166.8215297856[/C][C]20733.1784702144[/C][/ROW]
[ROW][C]97[/C][C]62100[/C][C]63540.9293316723[/C][C]-1440.92933167226[/C][/ROW]
[ROW][C]98[/C][C]45900[/C][C]62750.4434166985[/C][C]-16850.4434166985[/C][/ROW]
[ROW][C]99[/C][C]35100[/C][C]53506.3827336508[/C][C]-18406.3827336508[/C][/ROW]
[ROW][C]100[/C][C]24300[/C][C]43408.7422895629[/C][C]-19108.7422895629[/C][/ROW]
[ROW][C]101[/C][C]47700[/C][C]32925.7912518241[/C][C]14774.2087481759[/C][/ROW]
[ROW][C]102[/C][C]45900[/C][C]41030.8410024324[/C][C]4869.15899756757[/C][/ROW]
[ROW][C]103[/C][C]60300[/C][C]43702.0348776225[/C][C]16597.9651223775[/C][/ROW]
[ROW][C]104[/C][C]69300[/C][C]52807.5873555067[/C][C]16492.4126444933[/C][/ROW]
[ROW][C]105[/C][C]51300[/C][C]61855.2343239228[/C][C]-10555.2343239228[/C][/ROW]
[ROW][C]106[/C][C]57600[/C][C]56064.6907636604[/C][C]1535.30923633964[/C][/ROW]
[ROW][C]107[/C][C]43200[/C][C]56906.9529758169[/C][C]-13706.9529758169[/C][/ROW]
[ROW][C]108[/C][C]74700[/C][C]49387.3938784838[/C][C]25312.6061215162[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280028&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280028&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
24680048600-1800
34950047612.5298890951887.47011090501
43960048647.9856222868-9047.9856222868
55130043684.31041900547615.68958099457
65040047862.23588298482537.76411701522
75400049254.43933525134745.56066474868
85580051857.8278440993942.172155901
96210054020.48183076248079.51816923756
105400058452.8611100047-4452.8611100047
115130056010.0459688153-4710.04596881529
126390053426.14062704110473.859372959
135400059172.0423362739-5172.04233627394
144050056334.6883254929-15834.6883254929
154770047647.865304981452.134695018598
163600047676.4661122436-11676.4661122436
175040041270.82095289049129.17904710959
184140046279.0384229576-4879.03842295763
195490043602.424749275511297.5752507245
204950049800.2124636036-300.212463603631
215220049635.51755542042564.48244457955
225850051042.37853539987457.62146460015
235760055133.58869914222466.41130085777
246840056486.64838847311913.351611527
254950063022.247631298-13522.247631298
264140055604.0168712075-14204.0168712075
274590047811.7712517031-1911.77125170313
283330046762.9840461785-13462.9840461785
294770039377.26496329398322.73503670607
303690043943.0716798101-7043.07167981012
315220040079.281250491212120.7187495088
324950046728.640965952771.35903404998
334410048248.993306345-4148.99330634499
346300045972.878372811317027.1216271887
355670055313.86375147411386.13624852586
366480056074.29048206378725.70951793626
374860060861.1667850645-12261.1667850645
384500054134.7580489132-9134.75804891315
394050049123.4799691072-8623.47996910721
403330044392.6862349509-11092.6862349509
414410038307.29950902795792.70049097213
423960041485.1431736166-1885.14317361662
435400040450.963985437213549.0360145628
445220047883.89070541294316.1092945871
454500050251.6845519707-5251.68455197071
466030047370.639259208112929.3607407919
475580054463.61552845291336.38447154708
487200055196.748707525316803.2512924747
495760064414.9200504946-6814.92005049461
503510060676.2923515665-25576.2923515665
513510046645.2788821552-11545.2788821552
523510040311.6023164935-5211.6023164935
534140037452.54591790433947.45408209574
544140039618.09754025951781.90245974046
555580040595.63944000515204.360559995
565130048936.66811134832363.33188865166
574590050233.1790014551-4333.17900145512
585760047856.02080748959743.97919251052
595310053201.5142596475-101.51425964752
607650053145.824094518323354.1759054817
616030065957.7966897856-5657.79668978558
623510062853.9605093742-27753.9605093742
633690047628.2902525714-10728.2902525714
643060041742.8091606115-11142.8091606115
654230035629.92527304356670.07472695648
664860039289.09162325049310.90837674958
676120044397.004805147816802.9951948522
686030053615.03565436846684.96434563163
694860057282.3703675778-8682.37036757775
705670052519.26968436094180.73031563912
715040054812.795366832-4412.79536683204
727200052391.960072228319608.0399277717
735490063148.8230511764-8248.82305117639
744410058623.5640438536-14523.5640438536
753960050656.0166010091-11056.0166010091
762970044590.7466348057-14890.7466348057
774410036421.76483984467678.23516015538
785310040634.002464929812465.9975350702
796210047472.780225206114627.2197747939
805850055497.19263256593002.80736743408
814320057144.5162570918-13944.5162570918
826210049494.6312488112605.36875119
834860056409.8672925523-7809.86729255231
847470052125.417002813422574.5829971866
856210064509.7092116279-2409.70921162795
864500063187.7559769307-18187.7559769307
874140053210.0529704568-11810.0529704568
882790046731.1227946062-18831.1227946062
894410036400.47228657537699.52771342469
904230040624.3908894041675.60911059599
916390041543.620841778322356.3791582217
926390053808.207623335910091.7923766641
934860059344.5094774552-10744.5094774552
946300053450.13060783159549.86939216846
954680058689.1364899498-11889.1364899498
967290052166.821529785620733.1784702144
976210063540.9293316723-1440.92933167226
984590062750.4434166985-16850.4434166985
993510053506.3827336508-18406.3827336508
1002430043408.7422895629-19108.7422895629
1014770032925.791251824114774.2087481759
1024590041030.84100243244869.15899756757
1036030043702.034877622516597.9651223775
1046930052807.587355506716492.4126444933
1055130061855.2343239228-10555.2343239228
1065760056064.69076366041535.30923633964
1074320056906.9529758169-13706.9529758169
1087470049387.393878483825312.6061215162







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10963273.750530766240438.605932661786108.8951288708
11063273.750530766237228.109007782689319.3920537499
11163273.750530766234372.071412223792175.4296493087
11263273.750530766231773.930382095294773.5706794373
11363273.750530766229374.336333378697173.1647281539
11463273.750530766227133.718759149499413.7823023831
11563273.750530766225024.1294871415101523.371574391
11663273.750530766223024.960194803103522.540866729
11763273.750530766221120.497547921105427.003513612
11863273.750530766219298.4352895632107249.065771969
11963273.750530766217548.9217821464108998.579279386
12063273.750530766215863.9247810545110683.576280478

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 63273.7505307662 & 40438.6059326617 & 86108.8951288708 \tabularnewline
110 & 63273.7505307662 & 37228.1090077826 & 89319.3920537499 \tabularnewline
111 & 63273.7505307662 & 34372.0714122237 & 92175.4296493087 \tabularnewline
112 & 63273.7505307662 & 31773.9303820952 & 94773.5706794373 \tabularnewline
113 & 63273.7505307662 & 29374.3363333786 & 97173.1647281539 \tabularnewline
114 & 63273.7505307662 & 27133.7187591494 & 99413.7823023831 \tabularnewline
115 & 63273.7505307662 & 25024.1294871415 & 101523.371574391 \tabularnewline
116 & 63273.7505307662 & 23024.960194803 & 103522.540866729 \tabularnewline
117 & 63273.7505307662 & 21120.497547921 & 105427.003513612 \tabularnewline
118 & 63273.7505307662 & 19298.4352895632 & 107249.065771969 \tabularnewline
119 & 63273.7505307662 & 17548.9217821464 & 108998.579279386 \tabularnewline
120 & 63273.7505307662 & 15863.9247810545 & 110683.576280478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=280028&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]63273.7505307662[/C][C]40438.6059326617[/C][C]86108.8951288708[/C][/ROW]
[ROW][C]110[/C][C]63273.7505307662[/C][C]37228.1090077826[/C][C]89319.3920537499[/C][/ROW]
[ROW][C]111[/C][C]63273.7505307662[/C][C]34372.0714122237[/C][C]92175.4296493087[/C][/ROW]
[ROW][C]112[/C][C]63273.7505307662[/C][C]31773.9303820952[/C][C]94773.5706794373[/C][/ROW]
[ROW][C]113[/C][C]63273.7505307662[/C][C]29374.3363333786[/C][C]97173.1647281539[/C][/ROW]
[ROW][C]114[/C][C]63273.7505307662[/C][C]27133.7187591494[/C][C]99413.7823023831[/C][/ROW]
[ROW][C]115[/C][C]63273.7505307662[/C][C]25024.1294871415[/C][C]101523.371574391[/C][/ROW]
[ROW][C]116[/C][C]63273.7505307662[/C][C]23024.960194803[/C][C]103522.540866729[/C][/ROW]
[ROW][C]117[/C][C]63273.7505307662[/C][C]21120.497547921[/C][C]105427.003513612[/C][/ROW]
[ROW][C]118[/C][C]63273.7505307662[/C][C]19298.4352895632[/C][C]107249.065771969[/C][/ROW]
[ROW][C]119[/C][C]63273.7505307662[/C][C]17548.9217821464[/C][C]108998.579279386[/C][/ROW]
[ROW][C]120[/C][C]63273.7505307662[/C][C]15863.9247810545[/C][C]110683.576280478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=280028&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=280028&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
10963273.750530766240438.605932661786108.8951288708
11063273.750530766237228.109007782689319.3920537499
11163273.750530766234372.071412223792175.4296493087
11263273.750530766231773.930382095294773.5706794373
11363273.750530766229374.336333378697173.1647281539
11463273.750530766227133.718759149499413.7823023831
11563273.750530766225024.1294871415101523.371574391
11663273.750530766223024.960194803103522.540866729
11763273.750530766221120.497547921105427.003513612
11863273.750530766219298.4352895632107249.065771969
11963273.750530766217548.9217821464108998.579279386
12063273.750530766215863.9247810545110683.576280478



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')