Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 10 Aug 2016 21:35:05 +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/2016/Aug/10/t1470861464padmnj58trxz1qz.htm/, Retrieved Tue, 30 Apr 2024 00:35:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=296243, Retrieved Tue, 30 Apr 2024 00:35:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-08-10 20:35:05] [409a9d71664281dd1fd3bb0995266dd0] [Current]
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Dataseries X:
21571
21493
21422
21272
22747
22676
21571
20831
20909
20909
20980
21130
21051
21643
21864
21643
22455
21935
20759
20467
20467
20610
20026
20467
20097
20467
21051
21272
21792
21571
20246
19726
19506
19726
19363
19506
19064
19805
20168
20246
21643
21643
19805
19363
19363
19584
18622
18180
17668
17817
18480
17960
19363
19584
18180
17668
17375
17668
16855
16563
15388
15680
15751
15830
17226
17076
15388
14647
14355
14725
13322
12367
10601
10750
10750
10601
11854
11926
10451
10159
9568
10380
8905
8022
6333
6697
6255
6404
7509
7730
6996
6917
6917
7879
6184
5079
3163
4709
4488
4566
6333
6112
5300
5671
5671
6996
5450
4566
3163
5008
4859
4930
6476
6333
5813
5892
6255
7067
5813
4787




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296243&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296243&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296243&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.791744303433318
beta0.0130842068064546
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.791744303433318 \tabularnewline
beta & 0.0130842068064546 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296243&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]0.791744303433318[/C][/ROW]
[ROW][C]beta[/C][C]0.0130842068064546[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296243&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296243&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
alpha0.791744303433318
beta0.0130842068064546
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
132105121137.6057692308-86.6057692307731
142164321681.5136742758-38.5136742758368
152186421876.6825783896-12.6825783895729
162164321647.4633889691-4.46338896906309
172245522479.0387914928-24.0387914928397
182193521978.0331210843-43.0331210842669
192075921255.7930034246-496.793003424602
202046720102.9362997479364.063700252111
212046720413.346115857553.6538841425281
222061020391.3382141602218.661785839802
232002620603.8229051276-577.822905127639
242046720305.0428450643161.957154935688
252009720368.2877254567-271.287725456681
262046720769.0463405366-302.046340536563
272105120751.2703482002299.729651799778
282127220764.6759597875507.324040212545
292179221996.2437424226-204.243742422565
302157121345.6036334268225.396366573154
312024620741.1711892185-495.171189218487
321972619768.6718971996-42.6718971996415
331950619687.9880307114-181.988030711404
341972619506.9162467724219.083753227573
351936319547.0073511866-184.007351186552
361950619711.3163932312-205.316393231231
371906419386.9685748307-322.968574830706
381980519733.287890322571.7121096774936
392016820133.51256875634.4874312439715
402024619974.1554096515271.844590348501
412164320862.6647544101780.33524558994
422164321082.8031645832560.196835416762
431980520598.6218140378-793.621814037833
441936319486.2067697941-123.206769794142
451936319314.05748422448.9425157760124
461958419403.0524041227180.947595877271
471862219332.3116142435-710.311614243543
481818019073.3405664496-893.340566449595
491766818170.480352344-502.480352343966
501781718445.7356779097-628.735677909721
511848018265.2453146481214.754685351858
521796018281.5249137942-321.52491379423
531936318783.4666955121579.533304487868
541958418774.0293440118809.970655988163
551818018183.5051499276-3.50514992760873
561766817822.3039203778-154.303920377832
571737517647.0882610202-272.088261020206
581766817491.7775817719176.222418228055
591685517214.0147817313-359.014781731308
601656317181.0323134181-618.032313418098
611538816566.3648554516-1178.36485545161
621568016262.017512535-582.017512535012
631575116276.4800607761-525.480060776099
641583015569.633784042260.366215957976
651722616700.5971205659525.402879434077
661707616676.3935094361399.606490563921
671538815567.4050548811-179.405054881123
681464715009.559367054-362.559367053986
691435514616.799986381-261.799986381009
701472514534.975424709190.02457529097
711332214128.7943712689-806.794371268896
721236713654.8245467469-1287.82454674688
731060112353.7033095642-1752.70330956421
741075011673.4125776276-923.41257762758
751075011380.4082235595-630.408223559456
761060110704.1120975626-103.112097562622
771185411548.6930093507305.306990649326
781192611267.9559324144658.044067585593
791045110189.6027638129261.39723618714
80101599893.7845328295265.215467170505
8195689976.71703565696-408.717035656964
82103809828.81583104047551.184168959529
8389059460.87803679673-555.87803679673
8480229047.88227799039-1025.88227799039
8563337822.54200152473-1489.54200152473
8666977491.24174641587-794.241746415873
8762557330.79510461057-1075.79510461057
8864046376.3325744661327.6674255338676
8975097375.52152046658133.478479533424
9077306996.42816340307733.571836596927
9169965860.280590864581135.71940913542
9269176231.56541147607685.434588523935
9369176485.27520581774431.724794182258
9478797189.82183302986689.178166970141
9561846689.14542409978-505.145424099777
9650796207.51885273741-1128.51885273741
9731634792.37661736828-1629.37661736828
9847094481.73448866733227.265511332673
9944885068.5786036757-580.5786036757
10045664738.28668944919-172.286689449188
10163335601.41087930296731.589120697037
10261125827.24913106807284.750868931935
10353004421.25820095752878.741799042482
10456714494.404527665081176.59547233492
10556715088.33619349111582.663806508887
10669965971.75223445061024.2477655494
10754505496.85986112768-46.8598611276757
10845665262.22402586184-696.224025861836
10931634103.48738606461-940.487386064614
11050084750.50723541932257.492764580677
11148595218.94015537483-359.940155374828
11249305176.54695104849-246.546951048488
11364766196.52435884203279.475641157973
11463335994.07519782536338.924802174639
11558134777.966842711141035.03315728886
11658925061.79343953372830.206560466281
11762555279.10339551756975.896604482444
11870676591.21466455324475.785335446762
11958135478.72733483937334.272665160626
12047875434.27681663424-647.276816634238

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 21051 & 21137.6057692308 & -86.6057692307731 \tabularnewline
14 & 21643 & 21681.5136742758 & -38.5136742758368 \tabularnewline
15 & 21864 & 21876.6825783896 & -12.6825783895729 \tabularnewline
16 & 21643 & 21647.4633889691 & -4.46338896906309 \tabularnewline
17 & 22455 & 22479.0387914928 & -24.0387914928397 \tabularnewline
18 & 21935 & 21978.0331210843 & -43.0331210842669 \tabularnewline
19 & 20759 & 21255.7930034246 & -496.793003424602 \tabularnewline
20 & 20467 & 20102.9362997479 & 364.063700252111 \tabularnewline
21 & 20467 & 20413.3461158575 & 53.6538841425281 \tabularnewline
22 & 20610 & 20391.3382141602 & 218.661785839802 \tabularnewline
23 & 20026 & 20603.8229051276 & -577.822905127639 \tabularnewline
24 & 20467 & 20305.0428450643 & 161.957154935688 \tabularnewline
25 & 20097 & 20368.2877254567 & -271.287725456681 \tabularnewline
26 & 20467 & 20769.0463405366 & -302.046340536563 \tabularnewline
27 & 21051 & 20751.2703482002 & 299.729651799778 \tabularnewline
28 & 21272 & 20764.6759597875 & 507.324040212545 \tabularnewline
29 & 21792 & 21996.2437424226 & -204.243742422565 \tabularnewline
30 & 21571 & 21345.6036334268 & 225.396366573154 \tabularnewline
31 & 20246 & 20741.1711892185 & -495.171189218487 \tabularnewline
32 & 19726 & 19768.6718971996 & -42.6718971996415 \tabularnewline
33 & 19506 & 19687.9880307114 & -181.988030711404 \tabularnewline
34 & 19726 & 19506.9162467724 & 219.083753227573 \tabularnewline
35 & 19363 & 19547.0073511866 & -184.007351186552 \tabularnewline
36 & 19506 & 19711.3163932312 & -205.316393231231 \tabularnewline
37 & 19064 & 19386.9685748307 & -322.968574830706 \tabularnewline
38 & 19805 & 19733.2878903225 & 71.7121096774936 \tabularnewline
39 & 20168 & 20133.512568756 & 34.4874312439715 \tabularnewline
40 & 20246 & 19974.1554096515 & 271.844590348501 \tabularnewline
41 & 21643 & 20862.6647544101 & 780.33524558994 \tabularnewline
42 & 21643 & 21082.8031645832 & 560.196835416762 \tabularnewline
43 & 19805 & 20598.6218140378 & -793.621814037833 \tabularnewline
44 & 19363 & 19486.2067697941 & -123.206769794142 \tabularnewline
45 & 19363 & 19314.057484224 & 48.9425157760124 \tabularnewline
46 & 19584 & 19403.0524041227 & 180.947595877271 \tabularnewline
47 & 18622 & 19332.3116142435 & -710.311614243543 \tabularnewline
48 & 18180 & 19073.3405664496 & -893.340566449595 \tabularnewline
49 & 17668 & 18170.480352344 & -502.480352343966 \tabularnewline
50 & 17817 & 18445.7356779097 & -628.735677909721 \tabularnewline
51 & 18480 & 18265.2453146481 & 214.754685351858 \tabularnewline
52 & 17960 & 18281.5249137942 & -321.52491379423 \tabularnewline
53 & 19363 & 18783.4666955121 & 579.533304487868 \tabularnewline
54 & 19584 & 18774.0293440118 & 809.970655988163 \tabularnewline
55 & 18180 & 18183.5051499276 & -3.50514992760873 \tabularnewline
56 & 17668 & 17822.3039203778 & -154.303920377832 \tabularnewline
57 & 17375 & 17647.0882610202 & -272.088261020206 \tabularnewline
58 & 17668 & 17491.7775817719 & 176.222418228055 \tabularnewline
59 & 16855 & 17214.0147817313 & -359.014781731308 \tabularnewline
60 & 16563 & 17181.0323134181 & -618.032313418098 \tabularnewline
61 & 15388 & 16566.3648554516 & -1178.36485545161 \tabularnewline
62 & 15680 & 16262.017512535 & -582.017512535012 \tabularnewline
63 & 15751 & 16276.4800607761 & -525.480060776099 \tabularnewline
64 & 15830 & 15569.633784042 & 260.366215957976 \tabularnewline
65 & 17226 & 16700.5971205659 & 525.402879434077 \tabularnewline
66 & 17076 & 16676.3935094361 & 399.606490563921 \tabularnewline
67 & 15388 & 15567.4050548811 & -179.405054881123 \tabularnewline
68 & 14647 & 15009.559367054 & -362.559367053986 \tabularnewline
69 & 14355 & 14616.799986381 & -261.799986381009 \tabularnewline
70 & 14725 & 14534.975424709 & 190.02457529097 \tabularnewline
71 & 13322 & 14128.7943712689 & -806.794371268896 \tabularnewline
72 & 12367 & 13654.8245467469 & -1287.82454674688 \tabularnewline
73 & 10601 & 12353.7033095642 & -1752.70330956421 \tabularnewline
74 & 10750 & 11673.4125776276 & -923.41257762758 \tabularnewline
75 & 10750 & 11380.4082235595 & -630.408223559456 \tabularnewline
76 & 10601 & 10704.1120975626 & -103.112097562622 \tabularnewline
77 & 11854 & 11548.6930093507 & 305.306990649326 \tabularnewline
78 & 11926 & 11267.9559324144 & 658.044067585593 \tabularnewline
79 & 10451 & 10189.6027638129 & 261.39723618714 \tabularnewline
80 & 10159 & 9893.7845328295 & 265.215467170505 \tabularnewline
81 & 9568 & 9976.71703565696 & -408.717035656964 \tabularnewline
82 & 10380 & 9828.81583104047 & 551.184168959529 \tabularnewline
83 & 8905 & 9460.87803679673 & -555.87803679673 \tabularnewline
84 & 8022 & 9047.88227799039 & -1025.88227799039 \tabularnewline
85 & 6333 & 7822.54200152473 & -1489.54200152473 \tabularnewline
86 & 6697 & 7491.24174641587 & -794.241746415873 \tabularnewline
87 & 6255 & 7330.79510461057 & -1075.79510461057 \tabularnewline
88 & 6404 & 6376.33257446613 & 27.6674255338676 \tabularnewline
89 & 7509 & 7375.52152046658 & 133.478479533424 \tabularnewline
90 & 7730 & 6996.42816340307 & 733.571836596927 \tabularnewline
91 & 6996 & 5860.28059086458 & 1135.71940913542 \tabularnewline
92 & 6917 & 6231.56541147607 & 685.434588523935 \tabularnewline
93 & 6917 & 6485.27520581774 & 431.724794182258 \tabularnewline
94 & 7879 & 7189.82183302986 & 689.178166970141 \tabularnewline
95 & 6184 & 6689.14542409978 & -505.145424099777 \tabularnewline
96 & 5079 & 6207.51885273741 & -1128.51885273741 \tabularnewline
97 & 3163 & 4792.37661736828 & -1629.37661736828 \tabularnewline
98 & 4709 & 4481.73448866733 & 227.265511332673 \tabularnewline
99 & 4488 & 5068.5786036757 & -580.5786036757 \tabularnewline
100 & 4566 & 4738.28668944919 & -172.286689449188 \tabularnewline
101 & 6333 & 5601.41087930296 & 731.589120697037 \tabularnewline
102 & 6112 & 5827.24913106807 & 284.750868931935 \tabularnewline
103 & 5300 & 4421.25820095752 & 878.741799042482 \tabularnewline
104 & 5671 & 4494.40452766508 & 1176.59547233492 \tabularnewline
105 & 5671 & 5088.33619349111 & 582.663806508887 \tabularnewline
106 & 6996 & 5971.7522344506 & 1024.2477655494 \tabularnewline
107 & 5450 & 5496.85986112768 & -46.8598611276757 \tabularnewline
108 & 4566 & 5262.22402586184 & -696.224025861836 \tabularnewline
109 & 3163 & 4103.48738606461 & -940.487386064614 \tabularnewline
110 & 5008 & 4750.50723541932 & 257.492764580677 \tabularnewline
111 & 4859 & 5218.94015537483 & -359.940155374828 \tabularnewline
112 & 4930 & 5176.54695104849 & -246.546951048488 \tabularnewline
113 & 6476 & 6196.52435884203 & 279.475641157973 \tabularnewline
114 & 6333 & 5994.07519782536 & 338.924802174639 \tabularnewline
115 & 5813 & 4777.96684271114 & 1035.03315728886 \tabularnewline
116 & 5892 & 5061.79343953372 & 830.206560466281 \tabularnewline
117 & 6255 & 5279.10339551756 & 975.896604482444 \tabularnewline
118 & 7067 & 6591.21466455324 & 475.785335446762 \tabularnewline
119 & 5813 & 5478.72733483937 & 334.272665160626 \tabularnewline
120 & 4787 & 5434.27681663424 & -647.276816634238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296243&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]21051[/C][C]21137.6057692308[/C][C]-86.6057692307731[/C][/ROW]
[ROW][C]14[/C][C]21643[/C][C]21681.5136742758[/C][C]-38.5136742758368[/C][/ROW]
[ROW][C]15[/C][C]21864[/C][C]21876.6825783896[/C][C]-12.6825783895729[/C][/ROW]
[ROW][C]16[/C][C]21643[/C][C]21647.4633889691[/C][C]-4.46338896906309[/C][/ROW]
[ROW][C]17[/C][C]22455[/C][C]22479.0387914928[/C][C]-24.0387914928397[/C][/ROW]
[ROW][C]18[/C][C]21935[/C][C]21978.0331210843[/C][C]-43.0331210842669[/C][/ROW]
[ROW][C]19[/C][C]20759[/C][C]21255.7930034246[/C][C]-496.793003424602[/C][/ROW]
[ROW][C]20[/C][C]20467[/C][C]20102.9362997479[/C][C]364.063700252111[/C][/ROW]
[ROW][C]21[/C][C]20467[/C][C]20413.3461158575[/C][C]53.6538841425281[/C][/ROW]
[ROW][C]22[/C][C]20610[/C][C]20391.3382141602[/C][C]218.661785839802[/C][/ROW]
[ROW][C]23[/C][C]20026[/C][C]20603.8229051276[/C][C]-577.822905127639[/C][/ROW]
[ROW][C]24[/C][C]20467[/C][C]20305.0428450643[/C][C]161.957154935688[/C][/ROW]
[ROW][C]25[/C][C]20097[/C][C]20368.2877254567[/C][C]-271.287725456681[/C][/ROW]
[ROW][C]26[/C][C]20467[/C][C]20769.0463405366[/C][C]-302.046340536563[/C][/ROW]
[ROW][C]27[/C][C]21051[/C][C]20751.2703482002[/C][C]299.729651799778[/C][/ROW]
[ROW][C]28[/C][C]21272[/C][C]20764.6759597875[/C][C]507.324040212545[/C][/ROW]
[ROW][C]29[/C][C]21792[/C][C]21996.2437424226[/C][C]-204.243742422565[/C][/ROW]
[ROW][C]30[/C][C]21571[/C][C]21345.6036334268[/C][C]225.396366573154[/C][/ROW]
[ROW][C]31[/C][C]20246[/C][C]20741.1711892185[/C][C]-495.171189218487[/C][/ROW]
[ROW][C]32[/C][C]19726[/C][C]19768.6718971996[/C][C]-42.6718971996415[/C][/ROW]
[ROW][C]33[/C][C]19506[/C][C]19687.9880307114[/C][C]-181.988030711404[/C][/ROW]
[ROW][C]34[/C][C]19726[/C][C]19506.9162467724[/C][C]219.083753227573[/C][/ROW]
[ROW][C]35[/C][C]19363[/C][C]19547.0073511866[/C][C]-184.007351186552[/C][/ROW]
[ROW][C]36[/C][C]19506[/C][C]19711.3163932312[/C][C]-205.316393231231[/C][/ROW]
[ROW][C]37[/C][C]19064[/C][C]19386.9685748307[/C][C]-322.968574830706[/C][/ROW]
[ROW][C]38[/C][C]19805[/C][C]19733.2878903225[/C][C]71.7121096774936[/C][/ROW]
[ROW][C]39[/C][C]20168[/C][C]20133.512568756[/C][C]34.4874312439715[/C][/ROW]
[ROW][C]40[/C][C]20246[/C][C]19974.1554096515[/C][C]271.844590348501[/C][/ROW]
[ROW][C]41[/C][C]21643[/C][C]20862.6647544101[/C][C]780.33524558994[/C][/ROW]
[ROW][C]42[/C][C]21643[/C][C]21082.8031645832[/C][C]560.196835416762[/C][/ROW]
[ROW][C]43[/C][C]19805[/C][C]20598.6218140378[/C][C]-793.621814037833[/C][/ROW]
[ROW][C]44[/C][C]19363[/C][C]19486.2067697941[/C][C]-123.206769794142[/C][/ROW]
[ROW][C]45[/C][C]19363[/C][C]19314.057484224[/C][C]48.9425157760124[/C][/ROW]
[ROW][C]46[/C][C]19584[/C][C]19403.0524041227[/C][C]180.947595877271[/C][/ROW]
[ROW][C]47[/C][C]18622[/C][C]19332.3116142435[/C][C]-710.311614243543[/C][/ROW]
[ROW][C]48[/C][C]18180[/C][C]19073.3405664496[/C][C]-893.340566449595[/C][/ROW]
[ROW][C]49[/C][C]17668[/C][C]18170.480352344[/C][C]-502.480352343966[/C][/ROW]
[ROW][C]50[/C][C]17817[/C][C]18445.7356779097[/C][C]-628.735677909721[/C][/ROW]
[ROW][C]51[/C][C]18480[/C][C]18265.2453146481[/C][C]214.754685351858[/C][/ROW]
[ROW][C]52[/C][C]17960[/C][C]18281.5249137942[/C][C]-321.52491379423[/C][/ROW]
[ROW][C]53[/C][C]19363[/C][C]18783.4666955121[/C][C]579.533304487868[/C][/ROW]
[ROW][C]54[/C][C]19584[/C][C]18774.0293440118[/C][C]809.970655988163[/C][/ROW]
[ROW][C]55[/C][C]18180[/C][C]18183.5051499276[/C][C]-3.50514992760873[/C][/ROW]
[ROW][C]56[/C][C]17668[/C][C]17822.3039203778[/C][C]-154.303920377832[/C][/ROW]
[ROW][C]57[/C][C]17375[/C][C]17647.0882610202[/C][C]-272.088261020206[/C][/ROW]
[ROW][C]58[/C][C]17668[/C][C]17491.7775817719[/C][C]176.222418228055[/C][/ROW]
[ROW][C]59[/C][C]16855[/C][C]17214.0147817313[/C][C]-359.014781731308[/C][/ROW]
[ROW][C]60[/C][C]16563[/C][C]17181.0323134181[/C][C]-618.032313418098[/C][/ROW]
[ROW][C]61[/C][C]15388[/C][C]16566.3648554516[/C][C]-1178.36485545161[/C][/ROW]
[ROW][C]62[/C][C]15680[/C][C]16262.017512535[/C][C]-582.017512535012[/C][/ROW]
[ROW][C]63[/C][C]15751[/C][C]16276.4800607761[/C][C]-525.480060776099[/C][/ROW]
[ROW][C]64[/C][C]15830[/C][C]15569.633784042[/C][C]260.366215957976[/C][/ROW]
[ROW][C]65[/C][C]17226[/C][C]16700.5971205659[/C][C]525.402879434077[/C][/ROW]
[ROW][C]66[/C][C]17076[/C][C]16676.3935094361[/C][C]399.606490563921[/C][/ROW]
[ROW][C]67[/C][C]15388[/C][C]15567.4050548811[/C][C]-179.405054881123[/C][/ROW]
[ROW][C]68[/C][C]14647[/C][C]15009.559367054[/C][C]-362.559367053986[/C][/ROW]
[ROW][C]69[/C][C]14355[/C][C]14616.799986381[/C][C]-261.799986381009[/C][/ROW]
[ROW][C]70[/C][C]14725[/C][C]14534.975424709[/C][C]190.02457529097[/C][/ROW]
[ROW][C]71[/C][C]13322[/C][C]14128.7943712689[/C][C]-806.794371268896[/C][/ROW]
[ROW][C]72[/C][C]12367[/C][C]13654.8245467469[/C][C]-1287.82454674688[/C][/ROW]
[ROW][C]73[/C][C]10601[/C][C]12353.7033095642[/C][C]-1752.70330956421[/C][/ROW]
[ROW][C]74[/C][C]10750[/C][C]11673.4125776276[/C][C]-923.41257762758[/C][/ROW]
[ROW][C]75[/C][C]10750[/C][C]11380.4082235595[/C][C]-630.408223559456[/C][/ROW]
[ROW][C]76[/C][C]10601[/C][C]10704.1120975626[/C][C]-103.112097562622[/C][/ROW]
[ROW][C]77[/C][C]11854[/C][C]11548.6930093507[/C][C]305.306990649326[/C][/ROW]
[ROW][C]78[/C][C]11926[/C][C]11267.9559324144[/C][C]658.044067585593[/C][/ROW]
[ROW][C]79[/C][C]10451[/C][C]10189.6027638129[/C][C]261.39723618714[/C][/ROW]
[ROW][C]80[/C][C]10159[/C][C]9893.7845328295[/C][C]265.215467170505[/C][/ROW]
[ROW][C]81[/C][C]9568[/C][C]9976.71703565696[/C][C]-408.717035656964[/C][/ROW]
[ROW][C]82[/C][C]10380[/C][C]9828.81583104047[/C][C]551.184168959529[/C][/ROW]
[ROW][C]83[/C][C]8905[/C][C]9460.87803679673[/C][C]-555.87803679673[/C][/ROW]
[ROW][C]84[/C][C]8022[/C][C]9047.88227799039[/C][C]-1025.88227799039[/C][/ROW]
[ROW][C]85[/C][C]6333[/C][C]7822.54200152473[/C][C]-1489.54200152473[/C][/ROW]
[ROW][C]86[/C][C]6697[/C][C]7491.24174641587[/C][C]-794.241746415873[/C][/ROW]
[ROW][C]87[/C][C]6255[/C][C]7330.79510461057[/C][C]-1075.79510461057[/C][/ROW]
[ROW][C]88[/C][C]6404[/C][C]6376.33257446613[/C][C]27.6674255338676[/C][/ROW]
[ROW][C]89[/C][C]7509[/C][C]7375.52152046658[/C][C]133.478479533424[/C][/ROW]
[ROW][C]90[/C][C]7730[/C][C]6996.42816340307[/C][C]733.571836596927[/C][/ROW]
[ROW][C]91[/C][C]6996[/C][C]5860.28059086458[/C][C]1135.71940913542[/C][/ROW]
[ROW][C]92[/C][C]6917[/C][C]6231.56541147607[/C][C]685.434588523935[/C][/ROW]
[ROW][C]93[/C][C]6917[/C][C]6485.27520581774[/C][C]431.724794182258[/C][/ROW]
[ROW][C]94[/C][C]7879[/C][C]7189.82183302986[/C][C]689.178166970141[/C][/ROW]
[ROW][C]95[/C][C]6184[/C][C]6689.14542409978[/C][C]-505.145424099777[/C][/ROW]
[ROW][C]96[/C][C]5079[/C][C]6207.51885273741[/C][C]-1128.51885273741[/C][/ROW]
[ROW][C]97[/C][C]3163[/C][C]4792.37661736828[/C][C]-1629.37661736828[/C][/ROW]
[ROW][C]98[/C][C]4709[/C][C]4481.73448866733[/C][C]227.265511332673[/C][/ROW]
[ROW][C]99[/C][C]4488[/C][C]5068.5786036757[/C][C]-580.5786036757[/C][/ROW]
[ROW][C]100[/C][C]4566[/C][C]4738.28668944919[/C][C]-172.286689449188[/C][/ROW]
[ROW][C]101[/C][C]6333[/C][C]5601.41087930296[/C][C]731.589120697037[/C][/ROW]
[ROW][C]102[/C][C]6112[/C][C]5827.24913106807[/C][C]284.750868931935[/C][/ROW]
[ROW][C]103[/C][C]5300[/C][C]4421.25820095752[/C][C]878.741799042482[/C][/ROW]
[ROW][C]104[/C][C]5671[/C][C]4494.40452766508[/C][C]1176.59547233492[/C][/ROW]
[ROW][C]105[/C][C]5671[/C][C]5088.33619349111[/C][C]582.663806508887[/C][/ROW]
[ROW][C]106[/C][C]6996[/C][C]5971.7522344506[/C][C]1024.2477655494[/C][/ROW]
[ROW][C]107[/C][C]5450[/C][C]5496.85986112768[/C][C]-46.8598611276757[/C][/ROW]
[ROW][C]108[/C][C]4566[/C][C]5262.22402586184[/C][C]-696.224025861836[/C][/ROW]
[ROW][C]109[/C][C]3163[/C][C]4103.48738606461[/C][C]-940.487386064614[/C][/ROW]
[ROW][C]110[/C][C]5008[/C][C]4750.50723541932[/C][C]257.492764580677[/C][/ROW]
[ROW][C]111[/C][C]4859[/C][C]5218.94015537483[/C][C]-359.940155374828[/C][/ROW]
[ROW][C]112[/C][C]4930[/C][C]5176.54695104849[/C][C]-246.546951048488[/C][/ROW]
[ROW][C]113[/C][C]6476[/C][C]6196.52435884203[/C][C]279.475641157973[/C][/ROW]
[ROW][C]114[/C][C]6333[/C][C]5994.07519782536[/C][C]338.924802174639[/C][/ROW]
[ROW][C]115[/C][C]5813[/C][C]4777.96684271114[/C][C]1035.03315728886[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]5061.79343953372[/C][C]830.206560466281[/C][/ROW]
[ROW][C]117[/C][C]6255[/C][C]5279.10339551756[/C][C]975.896604482444[/C][/ROW]
[ROW][C]118[/C][C]7067[/C][C]6591.21466455324[/C][C]475.785335446762[/C][/ROW]
[ROW][C]119[/C][C]5813[/C][C]5478.72733483937[/C][C]334.272665160626[/C][/ROW]
[ROW][C]120[/C][C]4787[/C][C]5434.27681663424[/C][C]-647.276816634238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296243&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296243&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
132105121137.6057692308-86.6057692307731
142164321681.5136742758-38.5136742758368
152186421876.6825783896-12.6825783895729
162164321647.4633889691-4.46338896906309
172245522479.0387914928-24.0387914928397
182193521978.0331210843-43.0331210842669
192075921255.7930034246-496.793003424602
202046720102.9362997479364.063700252111
212046720413.346115857553.6538841425281
222061020391.3382141602218.661785839802
232002620603.8229051276-577.822905127639
242046720305.0428450643161.957154935688
252009720368.2877254567-271.287725456681
262046720769.0463405366-302.046340536563
272105120751.2703482002299.729651799778
282127220764.6759597875507.324040212545
292179221996.2437424226-204.243742422565
302157121345.6036334268225.396366573154
312024620741.1711892185-495.171189218487
321972619768.6718971996-42.6718971996415
331950619687.9880307114-181.988030711404
341972619506.9162467724219.083753227573
351936319547.0073511866-184.007351186552
361950619711.3163932312-205.316393231231
371906419386.9685748307-322.968574830706
381980519733.287890322571.7121096774936
392016820133.51256875634.4874312439715
402024619974.1554096515271.844590348501
412164320862.6647544101780.33524558994
422164321082.8031645832560.196835416762
431980520598.6218140378-793.621814037833
441936319486.2067697941-123.206769794142
451936319314.05748422448.9425157760124
461958419403.0524041227180.947595877271
471862219332.3116142435-710.311614243543
481818019073.3405664496-893.340566449595
491766818170.480352344-502.480352343966
501781718445.7356779097-628.735677909721
511848018265.2453146481214.754685351858
521796018281.5249137942-321.52491379423
531936318783.4666955121579.533304487868
541958418774.0293440118809.970655988163
551818018183.5051499276-3.50514992760873
561766817822.3039203778-154.303920377832
571737517647.0882610202-272.088261020206
581766817491.7775817719176.222418228055
591685517214.0147817313-359.014781731308
601656317181.0323134181-618.032313418098
611538816566.3648554516-1178.36485545161
621568016262.017512535-582.017512535012
631575116276.4800607761-525.480060776099
641583015569.633784042260.366215957976
651722616700.5971205659525.402879434077
661707616676.3935094361399.606490563921
671538815567.4050548811-179.405054881123
681464715009.559367054-362.559367053986
691435514616.799986381-261.799986381009
701472514534.975424709190.02457529097
711332214128.7943712689-806.794371268896
721236713654.8245467469-1287.82454674688
731060112353.7033095642-1752.70330956421
741075011673.4125776276-923.41257762758
751075011380.4082235595-630.408223559456
761060110704.1120975626-103.112097562622
771185411548.6930093507305.306990649326
781192611267.9559324144658.044067585593
791045110189.6027638129261.39723618714
80101599893.7845328295265.215467170505
8195689976.71703565696-408.717035656964
82103809828.81583104047551.184168959529
8389059460.87803679673-555.87803679673
8480229047.88227799039-1025.88227799039
8563337822.54200152473-1489.54200152473
8666977491.24174641587-794.241746415873
8762557330.79510461057-1075.79510461057
8864046376.3325744661327.6674255338676
8975097375.52152046658133.478479533424
9077306996.42816340307733.571836596927
9169965860.280590864581135.71940913542
9269176231.56541147607685.434588523935
9369176485.27520581774431.724794182258
9478797189.82183302986689.178166970141
9561846689.14542409978-505.145424099777
9650796207.51885273741-1128.51885273741
9731634792.37661736828-1629.37661736828
9847094481.73448866733227.265511332673
9944885068.5786036757-580.5786036757
10045664738.28668944919-172.286689449188
10163335601.41087930296731.589120697037
10261125827.24913106807284.750868931935
10353004421.25820095752878.741799042482
10456714494.404527665081176.59547233492
10556715088.33619349111582.663806508887
10669965971.75223445061024.2477655494
10754505496.85986112768-46.8598611276757
10845665262.22402586184-696.224025861836
10931634103.48738606461-940.487386064614
11050084750.50723541932257.492764580677
11148595218.94015537483-359.940155374828
11249305176.54695104849-246.546951048488
11364766196.52435884203279.475641157973
11463335994.07519782536338.924802174639
11558134777.966842711141035.03315728886
11658925061.79343953372830.206560466281
11762555279.10339551756975.896604482444
11870676591.21466455324475.785335446762
11958135478.72733483937334.272665160626
12047875434.27681663424-647.276816634238







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1214287.591272744233092.40079427455482.78175121396
1225962.632335701934430.469806574557494.79486482931
1236129.854939093294315.893444100767943.81643408583
1246431.027863593464367.635087964358494.42063922258
1257793.279462458385502.1598808992710084.3990440175
1267416.567341822134913.433211475919919.70147216836
1276108.204357089033405.01162316258811.39709101556
1285550.289396772922656.460275783968444.11851776187
1295152.424776859392075.579778093818229.26977562496
1305589.410754502572335.837019465768842.98448953938
1314067.50975769978642.4762851780027492.54323022156
1323547.28212538108-44.73937509486867139.30362585704

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4287.59127274423 & 3092.4007942745 & 5482.78175121396 \tabularnewline
122 & 5962.63233570193 & 4430.46980657455 & 7494.79486482931 \tabularnewline
123 & 6129.85493909329 & 4315.89344410076 & 7943.81643408583 \tabularnewline
124 & 6431.02786359346 & 4367.63508796435 & 8494.42063922258 \tabularnewline
125 & 7793.27946245838 & 5502.15988089927 & 10084.3990440175 \tabularnewline
126 & 7416.56734182213 & 4913.43321147591 & 9919.70147216836 \tabularnewline
127 & 6108.20435708903 & 3405.0116231625 & 8811.39709101556 \tabularnewline
128 & 5550.28939677292 & 2656.46027578396 & 8444.11851776187 \tabularnewline
129 & 5152.42477685939 & 2075.57977809381 & 8229.26977562496 \tabularnewline
130 & 5589.41075450257 & 2335.83701946576 & 8842.98448953938 \tabularnewline
131 & 4067.50975769978 & 642.476285178002 & 7492.54323022156 \tabularnewline
132 & 3547.28212538108 & -44.7393750948686 & 7139.30362585704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=296243&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]121[/C][C]4287.59127274423[/C][C]3092.4007942745[/C][C]5482.78175121396[/C][/ROW]
[ROW][C]122[/C][C]5962.63233570193[/C][C]4430.46980657455[/C][C]7494.79486482931[/C][/ROW]
[ROW][C]123[/C][C]6129.85493909329[/C][C]4315.89344410076[/C][C]7943.81643408583[/C][/ROW]
[ROW][C]124[/C][C]6431.02786359346[/C][C]4367.63508796435[/C][C]8494.42063922258[/C][/ROW]
[ROW][C]125[/C][C]7793.27946245838[/C][C]5502.15988089927[/C][C]10084.3990440175[/C][/ROW]
[ROW][C]126[/C][C]7416.56734182213[/C][C]4913.43321147591[/C][C]9919.70147216836[/C][/ROW]
[ROW][C]127[/C][C]6108.20435708903[/C][C]3405.0116231625[/C][C]8811.39709101556[/C][/ROW]
[ROW][C]128[/C][C]5550.28939677292[/C][C]2656.46027578396[/C][C]8444.11851776187[/C][/ROW]
[ROW][C]129[/C][C]5152.42477685939[/C][C]2075.57977809381[/C][C]8229.26977562496[/C][/ROW]
[ROW][C]130[/C][C]5589.41075450257[/C][C]2335.83701946576[/C][C]8842.98448953938[/C][/ROW]
[ROW][C]131[/C][C]4067.50975769978[/C][C]642.476285178002[/C][C]7492.54323022156[/C][/ROW]
[ROW][C]132[/C][C]3547.28212538108[/C][C]-44.7393750948686[/C][C]7139.30362585704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=296243&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=296243&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
1214287.591272744233092.40079427455482.78175121396
1225962.632335701934430.469806574557494.79486482931
1236129.854939093294315.893444100767943.81643408583
1246431.027863593464367.635087964358494.42063922258
1257793.279462458385502.1598808992710084.3990440175
1267416.567341822134913.433211475919919.70147216836
1276108.204357089033405.01162316258811.39709101556
1285550.289396772922656.460275783968444.11851776187
1295152.424776859392075.579778093818229.26977562496
1305589.410754502572335.837019465768842.98448953938
1314067.50975769978642.4762851780027492.54323022156
1323547.28212538108-44.73937509486867139.30362585704



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')