Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 14:57:18 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/May/19/t1305816816q65hmkv39cu074u.htm/, Retrieved Sat, 11 May 2024 22:43:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122073, Retrieved Sat, 11 May 2024 22:43:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [opgave 10 eigen g...] [2011-05-19 14:57:18] [a99b800ebea0aa886a82ba0f52cc2ca2] [Current]
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Dataseries X:
6827
6178
7084
8162
8462
9644
10466
10748
9963
8194
6848
7027
7269
6775
7819
8371
9069
10248
11030
10882
10333
9109
7685
7602
8350
7829
8829
9948
10638
11253
11424
11391
10665
9396
7775
7933
8186
7444
8484
9948
10252
12282
11637
11577
12417
9637
8094
9280
8334
7899
9994
10078
10801
12950
12222
12246
13281
10366
8730
9614
8639
8772
10894
10455
11179
10588
10794
12770
13812
10857
9290
10925
9491
8919
11607
8852
12537
14759
13667
13731
15110
12185
10645
12161
10840
10436
13589
13402
13103
14933
14147
14057
16234
12389
11595
12772




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 5 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122073&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122073&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122073&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 time5 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.194526868697057
beta0
gamma0.414248667899734

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.194526868697057 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.414248667899734 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122073&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]0.194526868697057[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.414248667899734[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122073&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122073&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
alpha0.194526868697057
beta0
gamma0.414248667899734







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1372696992.55582264958276.444177350425
1467756566.94396801391208.056031986088
1578197674.11211493786144.887885062141
1683718244.45069337263126.54930662737
1790698937.7635922348131.236407765207
181024810127.1549248712120.845075128766
191103010919.066530775110.933469225016
201088211223.0500630185-341.050063018516
211033310359.9023206987-26.9023206987495
2291098590.03142166736518.968578332639
2376857354.68041267073330.319587329269
2476027591.1737728380210.826227161976
2583507922.54882708647427.451172913534
2678297503.49307979763325.50692020237
2788298612.4315064763216.568493523706
2899489190.59492596117757.40507403883
291063810008.1901489503629.809851049738
301125311291.100176145-38.1001761449879
311142412048.7854924272-624.78549242717
321139112058.8403039573-667.840303957295
331066511236.943553866-571.943553865962
3493969543.18614354233-147.186143542331
3577758115.30435581386-340.304355813862
3679338114.73921388684-181.739213886838
3781868547.66876654046-361.668766540461
3874447941.0926398772-497.092639877204
3984848853.66428216425-369.664282164253
4099489498.24854678723449.751453212772
411025210213.422664695438.5773353045988
421228211158.46310013541123.53689986458
431163711946.3609959165-309.360995916528
441157712003.4084129279-426.408412927929
451241711260.47415408081156.52584591916
46963710044.6776627278-407.677662727778
4780948501.68626088138-407.686260881383
4892808540.92135182203739.078648177969
4983349092.93831481898-758.938314818981
5078998363.89622153124-464.896221531242
5199949325.24946454283668.75053545717
521007810445.2446234768-367.244623476776
531080110864.296159036-63.296159036021
541295012151.5337669436798.466233056408
551222212398.0871285241-176.087128524134
561224612442.0051301003-196.005130100317
571328112272.0621145561008.93788544398
581036610505.6340029493-139.634002949339
5987309014.78142600075-284.781426000747
6096149460.56146663124153.438533368757
6186399398.81810676915-759.818106769153
6287728767.716769885774.28323011422981
631089410198.5975959148695.402404085171
641045510978.1007208464-523.100720846443
651117911468.2513783323-289.251378332334
661058812999.0755832242-2411.07558322419
671079412296.1113360835-1502.11133608346
681277012075.4360374134694.563962586637
691381212480.78136190651331.21863809346
701085710393.8059310646463.194068935351
7192908971.78882632496318.211173675043
72109259681.086305410641243.91369458936
7394919526.74681718453-35.7468171845321
7489199291.45156882427-372.451568824266
751160710879.6504430341727.3495569659
76885211258.794874714-2406.79487471398
771253711460.54402172961076.45597827041
781475912549.05404285222209.94595714779
791366713048.2932666712618.706733328803
801373113973.1303034321-242.130303432106
811511014408.6935536831701.306446316854
821218511909.5528417133275.447158286737
831064510402.6380307182242.361969281776
841216111406.0564178401754.943582159947
851084010729.6196807541110.380319245894
861043610410.403101212225.5968987878405
871358912442.99952865841146.0004713416
881340211857.82483780551544.17516219452
891310313990.3867915028-887.386791502795
901493315075.0838898878-142.083889887843
911414714585.8474124561-438.84741245612
921405715017.729554271-960.729554271045
931623415628.2988709111605.701129088944
941238912968.4655176424-579.465517642378
951159511284.2078124351310.792187564877
961277212471.968860082300.031139918039

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7269 & 6992.55582264958 & 276.444177350425 \tabularnewline
14 & 6775 & 6566.94396801391 & 208.056031986088 \tabularnewline
15 & 7819 & 7674.11211493786 & 144.887885062141 \tabularnewline
16 & 8371 & 8244.45069337263 & 126.54930662737 \tabularnewline
17 & 9069 & 8937.7635922348 & 131.236407765207 \tabularnewline
18 & 10248 & 10127.1549248712 & 120.845075128766 \tabularnewline
19 & 11030 & 10919.066530775 & 110.933469225016 \tabularnewline
20 & 10882 & 11223.0500630185 & -341.050063018516 \tabularnewline
21 & 10333 & 10359.9023206987 & -26.9023206987495 \tabularnewline
22 & 9109 & 8590.03142166736 & 518.968578332639 \tabularnewline
23 & 7685 & 7354.68041267073 & 330.319587329269 \tabularnewline
24 & 7602 & 7591.17377283802 & 10.826227161976 \tabularnewline
25 & 8350 & 7922.54882708647 & 427.451172913534 \tabularnewline
26 & 7829 & 7503.49307979763 & 325.50692020237 \tabularnewline
27 & 8829 & 8612.4315064763 & 216.568493523706 \tabularnewline
28 & 9948 & 9190.59492596117 & 757.40507403883 \tabularnewline
29 & 10638 & 10008.1901489503 & 629.809851049738 \tabularnewline
30 & 11253 & 11291.100176145 & -38.1001761449879 \tabularnewline
31 & 11424 & 12048.7854924272 & -624.78549242717 \tabularnewline
32 & 11391 & 12058.8403039573 & -667.840303957295 \tabularnewline
33 & 10665 & 11236.943553866 & -571.943553865962 \tabularnewline
34 & 9396 & 9543.18614354233 & -147.186143542331 \tabularnewline
35 & 7775 & 8115.30435581386 & -340.304355813862 \tabularnewline
36 & 7933 & 8114.73921388684 & -181.739213886838 \tabularnewline
37 & 8186 & 8547.66876654046 & -361.668766540461 \tabularnewline
38 & 7444 & 7941.0926398772 & -497.092639877204 \tabularnewline
39 & 8484 & 8853.66428216425 & -369.664282164253 \tabularnewline
40 & 9948 & 9498.24854678723 & 449.751453212772 \tabularnewline
41 & 10252 & 10213.4226646954 & 38.5773353045988 \tabularnewline
42 & 12282 & 11158.4631001354 & 1123.53689986458 \tabularnewline
43 & 11637 & 11946.3609959165 & -309.360995916528 \tabularnewline
44 & 11577 & 12003.4084129279 & -426.408412927929 \tabularnewline
45 & 12417 & 11260.4741540808 & 1156.52584591916 \tabularnewline
46 & 9637 & 10044.6776627278 & -407.677662727778 \tabularnewline
47 & 8094 & 8501.68626088138 & -407.686260881383 \tabularnewline
48 & 9280 & 8540.92135182203 & 739.078648177969 \tabularnewline
49 & 8334 & 9092.93831481898 & -758.938314818981 \tabularnewline
50 & 7899 & 8363.89622153124 & -464.896221531242 \tabularnewline
51 & 9994 & 9325.24946454283 & 668.75053545717 \tabularnewline
52 & 10078 & 10445.2446234768 & -367.244623476776 \tabularnewline
53 & 10801 & 10864.296159036 & -63.296159036021 \tabularnewline
54 & 12950 & 12151.5337669436 & 798.466233056408 \tabularnewline
55 & 12222 & 12398.0871285241 & -176.087128524134 \tabularnewline
56 & 12246 & 12442.0051301003 & -196.005130100317 \tabularnewline
57 & 13281 & 12272.062114556 & 1008.93788544398 \tabularnewline
58 & 10366 & 10505.6340029493 & -139.634002949339 \tabularnewline
59 & 8730 & 9014.78142600075 & -284.781426000747 \tabularnewline
60 & 9614 & 9460.56146663124 & 153.438533368757 \tabularnewline
61 & 8639 & 9398.81810676915 & -759.818106769153 \tabularnewline
62 & 8772 & 8767.71676988577 & 4.28323011422981 \tabularnewline
63 & 10894 & 10198.5975959148 & 695.402404085171 \tabularnewline
64 & 10455 & 10978.1007208464 & -523.100720846443 \tabularnewline
65 & 11179 & 11468.2513783323 & -289.251378332334 \tabularnewline
66 & 10588 & 12999.0755832242 & -2411.07558322419 \tabularnewline
67 & 10794 & 12296.1113360835 & -1502.11133608346 \tabularnewline
68 & 12770 & 12075.4360374134 & 694.563962586637 \tabularnewline
69 & 13812 & 12480.7813619065 & 1331.21863809346 \tabularnewline
70 & 10857 & 10393.8059310646 & 463.194068935351 \tabularnewline
71 & 9290 & 8971.78882632496 & 318.211173675043 \tabularnewline
72 & 10925 & 9681.08630541064 & 1243.91369458936 \tabularnewline
73 & 9491 & 9526.74681718453 & -35.7468171845321 \tabularnewline
74 & 8919 & 9291.45156882427 & -372.451568824266 \tabularnewline
75 & 11607 & 10879.6504430341 & 727.3495569659 \tabularnewline
76 & 8852 & 11258.794874714 & -2406.79487471398 \tabularnewline
77 & 12537 & 11460.5440217296 & 1076.45597827041 \tabularnewline
78 & 14759 & 12549.0540428522 & 2209.94595714779 \tabularnewline
79 & 13667 & 13048.2932666712 & 618.706733328803 \tabularnewline
80 & 13731 & 13973.1303034321 & -242.130303432106 \tabularnewline
81 & 15110 & 14408.6935536831 & 701.306446316854 \tabularnewline
82 & 12185 & 11909.5528417133 & 275.447158286737 \tabularnewline
83 & 10645 & 10402.6380307182 & 242.361969281776 \tabularnewline
84 & 12161 & 11406.0564178401 & 754.943582159947 \tabularnewline
85 & 10840 & 10729.6196807541 & 110.380319245894 \tabularnewline
86 & 10436 & 10410.4031012122 & 25.5968987878405 \tabularnewline
87 & 13589 & 12442.9995286584 & 1146.0004713416 \tabularnewline
88 & 13402 & 11857.8248378055 & 1544.17516219452 \tabularnewline
89 & 13103 & 13990.3867915028 & -887.386791502795 \tabularnewline
90 & 14933 & 15075.0838898878 & -142.083889887843 \tabularnewline
91 & 14147 & 14585.8474124561 & -438.84741245612 \tabularnewline
92 & 14057 & 15017.729554271 & -960.729554271045 \tabularnewline
93 & 16234 & 15628.2988709111 & 605.701129088944 \tabularnewline
94 & 12389 & 12968.4655176424 & -579.465517642378 \tabularnewline
95 & 11595 & 11284.2078124351 & 310.792187564877 \tabularnewline
96 & 12772 & 12471.968860082 & 300.031139918039 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122073&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]7269[/C][C]6992.55582264958[/C][C]276.444177350425[/C][/ROW]
[ROW][C]14[/C][C]6775[/C][C]6566.94396801391[/C][C]208.056031986088[/C][/ROW]
[ROW][C]15[/C][C]7819[/C][C]7674.11211493786[/C][C]144.887885062141[/C][/ROW]
[ROW][C]16[/C][C]8371[/C][C]8244.45069337263[/C][C]126.54930662737[/C][/ROW]
[ROW][C]17[/C][C]9069[/C][C]8937.7635922348[/C][C]131.236407765207[/C][/ROW]
[ROW][C]18[/C][C]10248[/C][C]10127.1549248712[/C][C]120.845075128766[/C][/ROW]
[ROW][C]19[/C][C]11030[/C][C]10919.066530775[/C][C]110.933469225016[/C][/ROW]
[ROW][C]20[/C][C]10882[/C][C]11223.0500630185[/C][C]-341.050063018516[/C][/ROW]
[ROW][C]21[/C][C]10333[/C][C]10359.9023206987[/C][C]-26.9023206987495[/C][/ROW]
[ROW][C]22[/C][C]9109[/C][C]8590.03142166736[/C][C]518.968578332639[/C][/ROW]
[ROW][C]23[/C][C]7685[/C][C]7354.68041267073[/C][C]330.319587329269[/C][/ROW]
[ROW][C]24[/C][C]7602[/C][C]7591.17377283802[/C][C]10.826227161976[/C][/ROW]
[ROW][C]25[/C][C]8350[/C][C]7922.54882708647[/C][C]427.451172913534[/C][/ROW]
[ROW][C]26[/C][C]7829[/C][C]7503.49307979763[/C][C]325.50692020237[/C][/ROW]
[ROW][C]27[/C][C]8829[/C][C]8612.4315064763[/C][C]216.568493523706[/C][/ROW]
[ROW][C]28[/C][C]9948[/C][C]9190.59492596117[/C][C]757.40507403883[/C][/ROW]
[ROW][C]29[/C][C]10638[/C][C]10008.1901489503[/C][C]629.809851049738[/C][/ROW]
[ROW][C]30[/C][C]11253[/C][C]11291.100176145[/C][C]-38.1001761449879[/C][/ROW]
[ROW][C]31[/C][C]11424[/C][C]12048.7854924272[/C][C]-624.78549242717[/C][/ROW]
[ROW][C]32[/C][C]11391[/C][C]12058.8403039573[/C][C]-667.840303957295[/C][/ROW]
[ROW][C]33[/C][C]10665[/C][C]11236.943553866[/C][C]-571.943553865962[/C][/ROW]
[ROW][C]34[/C][C]9396[/C][C]9543.18614354233[/C][C]-147.186143542331[/C][/ROW]
[ROW][C]35[/C][C]7775[/C][C]8115.30435581386[/C][C]-340.304355813862[/C][/ROW]
[ROW][C]36[/C][C]7933[/C][C]8114.73921388684[/C][C]-181.739213886838[/C][/ROW]
[ROW][C]37[/C][C]8186[/C][C]8547.66876654046[/C][C]-361.668766540461[/C][/ROW]
[ROW][C]38[/C][C]7444[/C][C]7941.0926398772[/C][C]-497.092639877204[/C][/ROW]
[ROW][C]39[/C][C]8484[/C][C]8853.66428216425[/C][C]-369.664282164253[/C][/ROW]
[ROW][C]40[/C][C]9948[/C][C]9498.24854678723[/C][C]449.751453212772[/C][/ROW]
[ROW][C]41[/C][C]10252[/C][C]10213.4226646954[/C][C]38.5773353045988[/C][/ROW]
[ROW][C]42[/C][C]12282[/C][C]11158.4631001354[/C][C]1123.53689986458[/C][/ROW]
[ROW][C]43[/C][C]11637[/C][C]11946.3609959165[/C][C]-309.360995916528[/C][/ROW]
[ROW][C]44[/C][C]11577[/C][C]12003.4084129279[/C][C]-426.408412927929[/C][/ROW]
[ROW][C]45[/C][C]12417[/C][C]11260.4741540808[/C][C]1156.52584591916[/C][/ROW]
[ROW][C]46[/C][C]9637[/C][C]10044.6776627278[/C][C]-407.677662727778[/C][/ROW]
[ROW][C]47[/C][C]8094[/C][C]8501.68626088138[/C][C]-407.686260881383[/C][/ROW]
[ROW][C]48[/C][C]9280[/C][C]8540.92135182203[/C][C]739.078648177969[/C][/ROW]
[ROW][C]49[/C][C]8334[/C][C]9092.93831481898[/C][C]-758.938314818981[/C][/ROW]
[ROW][C]50[/C][C]7899[/C][C]8363.89622153124[/C][C]-464.896221531242[/C][/ROW]
[ROW][C]51[/C][C]9994[/C][C]9325.24946454283[/C][C]668.75053545717[/C][/ROW]
[ROW][C]52[/C][C]10078[/C][C]10445.2446234768[/C][C]-367.244623476776[/C][/ROW]
[ROW][C]53[/C][C]10801[/C][C]10864.296159036[/C][C]-63.296159036021[/C][/ROW]
[ROW][C]54[/C][C]12950[/C][C]12151.5337669436[/C][C]798.466233056408[/C][/ROW]
[ROW][C]55[/C][C]12222[/C][C]12398.0871285241[/C][C]-176.087128524134[/C][/ROW]
[ROW][C]56[/C][C]12246[/C][C]12442.0051301003[/C][C]-196.005130100317[/C][/ROW]
[ROW][C]57[/C][C]13281[/C][C]12272.062114556[/C][C]1008.93788544398[/C][/ROW]
[ROW][C]58[/C][C]10366[/C][C]10505.6340029493[/C][C]-139.634002949339[/C][/ROW]
[ROW][C]59[/C][C]8730[/C][C]9014.78142600075[/C][C]-284.781426000747[/C][/ROW]
[ROW][C]60[/C][C]9614[/C][C]9460.56146663124[/C][C]153.438533368757[/C][/ROW]
[ROW][C]61[/C][C]8639[/C][C]9398.81810676915[/C][C]-759.818106769153[/C][/ROW]
[ROW][C]62[/C][C]8772[/C][C]8767.71676988577[/C][C]4.28323011422981[/C][/ROW]
[ROW][C]63[/C][C]10894[/C][C]10198.5975959148[/C][C]695.402404085171[/C][/ROW]
[ROW][C]64[/C][C]10455[/C][C]10978.1007208464[/C][C]-523.100720846443[/C][/ROW]
[ROW][C]65[/C][C]11179[/C][C]11468.2513783323[/C][C]-289.251378332334[/C][/ROW]
[ROW][C]66[/C][C]10588[/C][C]12999.0755832242[/C][C]-2411.07558322419[/C][/ROW]
[ROW][C]67[/C][C]10794[/C][C]12296.1113360835[/C][C]-1502.11133608346[/C][/ROW]
[ROW][C]68[/C][C]12770[/C][C]12075.4360374134[/C][C]694.563962586637[/C][/ROW]
[ROW][C]69[/C][C]13812[/C][C]12480.7813619065[/C][C]1331.21863809346[/C][/ROW]
[ROW][C]70[/C][C]10857[/C][C]10393.8059310646[/C][C]463.194068935351[/C][/ROW]
[ROW][C]71[/C][C]9290[/C][C]8971.78882632496[/C][C]318.211173675043[/C][/ROW]
[ROW][C]72[/C][C]10925[/C][C]9681.08630541064[/C][C]1243.91369458936[/C][/ROW]
[ROW][C]73[/C][C]9491[/C][C]9526.74681718453[/C][C]-35.7468171845321[/C][/ROW]
[ROW][C]74[/C][C]8919[/C][C]9291.45156882427[/C][C]-372.451568824266[/C][/ROW]
[ROW][C]75[/C][C]11607[/C][C]10879.6504430341[/C][C]727.3495569659[/C][/ROW]
[ROW][C]76[/C][C]8852[/C][C]11258.794874714[/C][C]-2406.79487471398[/C][/ROW]
[ROW][C]77[/C][C]12537[/C][C]11460.5440217296[/C][C]1076.45597827041[/C][/ROW]
[ROW][C]78[/C][C]14759[/C][C]12549.0540428522[/C][C]2209.94595714779[/C][/ROW]
[ROW][C]79[/C][C]13667[/C][C]13048.2932666712[/C][C]618.706733328803[/C][/ROW]
[ROW][C]80[/C][C]13731[/C][C]13973.1303034321[/C][C]-242.130303432106[/C][/ROW]
[ROW][C]81[/C][C]15110[/C][C]14408.6935536831[/C][C]701.306446316854[/C][/ROW]
[ROW][C]82[/C][C]12185[/C][C]11909.5528417133[/C][C]275.447158286737[/C][/ROW]
[ROW][C]83[/C][C]10645[/C][C]10402.6380307182[/C][C]242.361969281776[/C][/ROW]
[ROW][C]84[/C][C]12161[/C][C]11406.0564178401[/C][C]754.943582159947[/C][/ROW]
[ROW][C]85[/C][C]10840[/C][C]10729.6196807541[/C][C]110.380319245894[/C][/ROW]
[ROW][C]86[/C][C]10436[/C][C]10410.4031012122[/C][C]25.5968987878405[/C][/ROW]
[ROW][C]87[/C][C]13589[/C][C]12442.9995286584[/C][C]1146.0004713416[/C][/ROW]
[ROW][C]88[/C][C]13402[/C][C]11857.8248378055[/C][C]1544.17516219452[/C][/ROW]
[ROW][C]89[/C][C]13103[/C][C]13990.3867915028[/C][C]-887.386791502795[/C][/ROW]
[ROW][C]90[/C][C]14933[/C][C]15075.0838898878[/C][C]-142.083889887843[/C][/ROW]
[ROW][C]91[/C][C]14147[/C][C]14585.8474124561[/C][C]-438.84741245612[/C][/ROW]
[ROW][C]92[/C][C]14057[/C][C]15017.729554271[/C][C]-960.729554271045[/C][/ROW]
[ROW][C]93[/C][C]16234[/C][C]15628.2988709111[/C][C]605.701129088944[/C][/ROW]
[ROW][C]94[/C][C]12389[/C][C]12968.4655176424[/C][C]-579.465517642378[/C][/ROW]
[ROW][C]95[/C][C]11595[/C][C]11284.2078124351[/C][C]310.792187564877[/C][/ROW]
[ROW][C]96[/C][C]12772[/C][C]12471.968860082[/C][C]300.031139918039[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122073&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122073&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
1372696992.55582264958276.444177350425
1467756566.94396801391208.056031986088
1578197674.11211493786144.887885062141
1683718244.45069337263126.54930662737
1790698937.7635922348131.236407765207
181024810127.1549248712120.845075128766
191103010919.066530775110.933469225016
201088211223.0500630185-341.050063018516
211033310359.9023206987-26.9023206987495
2291098590.03142166736518.968578332639
2376857354.68041267073330.319587329269
2476027591.1737728380210.826227161976
2583507922.54882708647427.451172913534
2678297503.49307979763325.50692020237
2788298612.4315064763216.568493523706
2899489190.59492596117757.40507403883
291063810008.1901489503629.809851049738
301125311291.100176145-38.1001761449879
311142412048.7854924272-624.78549242717
321139112058.8403039573-667.840303957295
331066511236.943553866-571.943553865962
3493969543.18614354233-147.186143542331
3577758115.30435581386-340.304355813862
3679338114.73921388684-181.739213886838
3781868547.66876654046-361.668766540461
3874447941.0926398772-497.092639877204
3984848853.66428216425-369.664282164253
4099489498.24854678723449.751453212772
411025210213.422664695438.5773353045988
421228211158.46310013541123.53689986458
431163711946.3609959165-309.360995916528
441157712003.4084129279-426.408412927929
451241711260.47415408081156.52584591916
46963710044.6776627278-407.677662727778
4780948501.68626088138-407.686260881383
4892808540.92135182203739.078648177969
4983349092.93831481898-758.938314818981
5078998363.89622153124-464.896221531242
5199949325.24946454283668.75053545717
521007810445.2446234768-367.244623476776
531080110864.296159036-63.296159036021
541295012151.5337669436798.466233056408
551222212398.0871285241-176.087128524134
561224612442.0051301003-196.005130100317
571328112272.0621145561008.93788544398
581036610505.6340029493-139.634002949339
5987309014.78142600075-284.781426000747
6096149460.56146663124153.438533368757
6186399398.81810676915-759.818106769153
6287728767.716769885774.28323011422981
631089410198.5975959148695.402404085171
641045510978.1007208464-523.100720846443
651117911468.2513783323-289.251378332334
661058812999.0755832242-2411.07558322419
671079412296.1113360835-1502.11133608346
681277012075.4360374134694.563962586637
691381212480.78136190651331.21863809346
701085710393.8059310646463.194068935351
7192908971.78882632496318.211173675043
72109259681.086305410641243.91369458936
7394919526.74681718453-35.7468171845321
7489199291.45156882427-372.451568824266
751160710879.6504430341727.3495569659
76885211258.794874714-2406.79487471398
771253711460.54402172961076.45597827041
781475912549.05404285222209.94595714779
791366713048.2932666712618.706733328803
801373113973.1303034321-242.130303432106
811511014408.6935536831701.306446316854
821218511909.5528417133275.447158286737
831064510402.6380307182242.361969281776
841216111406.0564178401754.943582159947
851084010729.6196807541110.380319245894
861043610410.403101212225.5968987878405
871358912442.99952865841146.0004713416
881340211857.82483780551544.17516219452
891310313990.3867915028-887.386791502795
901493315075.0838898878-142.083889887843
911414714585.8474124561-438.84741245612
921405715017.729554271-960.729554271045
931623415628.2988709111605.701129088944
941238912968.4655176424-579.465517642378
951159511284.2078124351310.792187564877
961277212471.968860082300.031139918039







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9711491.970473738910051.058533369612932.8824141082
9811122.99259700289655.0712378181312590.9139561875
9913524.450510660312030.007800616715018.8932207039
10012849.205361345311328.70382880614369.7068938845
10113870.053787749412323.93257409715416.1750014018
10215376.05382592613804.730592419316947.3770594327
10314815.436534219413219.309158033616411.5639104052
10415158.551872692213537.999961193716779.1037841908
10516478.673830494414834.060078054918123.287582934
10613305.565315410511637.236723206614973.8939076144
10712031.078103165510339.36707925613722.789127075
10813154.791122178311440.016476556114869.5657678006

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 11491.9704737389 & 10051.0585333696 & 12932.8824141082 \tabularnewline
98 & 11122.9925970028 & 9655.07123781813 & 12590.9139561875 \tabularnewline
99 & 13524.4505106603 & 12030.0078006167 & 15018.8932207039 \tabularnewline
100 & 12849.2053613453 & 11328.703828806 & 14369.7068938845 \tabularnewline
101 & 13870.0537877494 & 12323.932574097 & 15416.1750014018 \tabularnewline
102 & 15376.053825926 & 13804.7305924193 & 16947.3770594327 \tabularnewline
103 & 14815.4365342194 & 13219.3091580336 & 16411.5639104052 \tabularnewline
104 & 15158.5518726922 & 13537.9999611937 & 16779.1037841908 \tabularnewline
105 & 16478.6738304944 & 14834.0600780549 & 18123.287582934 \tabularnewline
106 & 13305.5653154105 & 11637.2367232066 & 14973.8939076144 \tabularnewline
107 & 12031.0781031655 & 10339.367079256 & 13722.789127075 \tabularnewline
108 & 13154.7911221783 & 11440.0164765561 & 14869.5657678006 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122073&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]97[/C][C]11491.9704737389[/C][C]10051.0585333696[/C][C]12932.8824141082[/C][/ROW]
[ROW][C]98[/C][C]11122.9925970028[/C][C]9655.07123781813[/C][C]12590.9139561875[/C][/ROW]
[ROW][C]99[/C][C]13524.4505106603[/C][C]12030.0078006167[/C][C]15018.8932207039[/C][/ROW]
[ROW][C]100[/C][C]12849.2053613453[/C][C]11328.703828806[/C][C]14369.7068938845[/C][/ROW]
[ROW][C]101[/C][C]13870.0537877494[/C][C]12323.932574097[/C][C]15416.1750014018[/C][/ROW]
[ROW][C]102[/C][C]15376.053825926[/C][C]13804.7305924193[/C][C]16947.3770594327[/C][/ROW]
[ROW][C]103[/C][C]14815.4365342194[/C][C]13219.3091580336[/C][C]16411.5639104052[/C][/ROW]
[ROW][C]104[/C][C]15158.5518726922[/C][C]13537.9999611937[/C][C]16779.1037841908[/C][/ROW]
[ROW][C]105[/C][C]16478.6738304944[/C][C]14834.0600780549[/C][C]18123.287582934[/C][/ROW]
[ROW][C]106[/C][C]13305.5653154105[/C][C]11637.2367232066[/C][C]14973.8939076144[/C][/ROW]
[ROW][C]107[/C][C]12031.0781031655[/C][C]10339.367079256[/C][C]13722.789127075[/C][/ROW]
[ROW][C]108[/C][C]13154.7911221783[/C][C]11440.0164765561[/C][C]14869.5657678006[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122073&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122073&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
9711491.970473738910051.058533369612932.8824141082
9811122.99259700289655.0712378181312590.9139561875
9913524.450510660312030.007800616715018.8932207039
10012849.205361345311328.70382880614369.7068938845
10113870.053787749412323.93257409715416.1750014018
10215376.05382592613804.730592419316947.3770594327
10314815.436534219413219.309158033616411.5639104052
10415158.551872692213537.999961193716779.1037841908
10516478.673830494414834.060078054918123.287582934
10613305.565315410511637.236723206614973.8939076144
10712031.078103165510339.36707925613722.789127075
10813154.791122178311440.016476556114869.5657678006



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')