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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 08:27:12 +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/t1305793422gcgqtxxo271q6tq.htm/, Retrieved Sat, 11 May 2024 10:37:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=121965, Retrieved Sat, 11 May 2024 10:37:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [Inschrijving nieu...] [2010-12-06 17:02:40] [3e532679ec753acf7892d78d91c458c8]
- RMP   [Classical Decomposition] [Inschrijving nieu...] [2010-12-14 22:31:35] [3e532679ec753acf7892d78d91c458c8]
- RMP     [Exponential Smoothing] [De inschrijving v...] [2011-01-16 20:38:38] [74be16979710d4c4e7c6647856088456]
- R P       [Exponential Smoothing] [exponential smoot...] [2011-05-19 08:21:45] [d460d5fbfa759ad1669bb34c73f51f31]
-    D          [Exponential Smoothing] [exponential smoot...] [2011-05-19 08:27:12] [a84eb6f3c59b92a1a531ce943c0523d4] [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 time2 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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121965&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121965&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121965&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'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.120618354224454
beta0
gamma0.444031255824324

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.120618354224454 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.444031255824324 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121965&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]0.120618354224454[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.444031255824324[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121965&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121965&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
alpha0.120618354224454
beta0
gamma0.444031255824324







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1372697028.04555893714240.954441062862
1467756589.60133762837185.398662371631
1578197651.76756439805167.232435601953
1683718204.9718412555166.028158744501
1790698881.74618834833187.253811651666
181024810045.4986564522202.501343547778
191103010965.443824089964.5561759100929
201088211266.6213746771-384.621374677072
211033310383.7901131434-50.7901131433737
2291098537.60367918035571.396320819646
2376857199.13792787709485.862072122906
2476027439.3413446404162.658655359601
2583507811.81173514451538.188264855487
2678297334.10759647993494.892403520066
2788298531.70250674818297.297493251821
2899489152.55924664116795.440753358836
29106389984.98032679143653.019673208571
301125311343.2792317032-90.27923170318
311142412265.7510932665-841.751093266523
321139112288.1771235432-897.177123543206
331066511397.9005365729-732.900536572924
3493969559.71015530468-163.710155304678
3577757978.7111309595-203.711130959495
3679338010.66540394782-77.6654039478235
3781868528.28931383278-342.289313832784
3874447896.39580195039-452.395801950387
3984848936.3393618554-452.339361855402
4099489674.77925484802273.220745151981
411025210396.4340258043-144.434025804298
421228211373.7551472545908.24485274554
431163712130.112944568-493.112944567951
441157712170.7395779461-593.739577946071
451241711361.42212824071055.5778717593
4696379894.75711420503-257.757114205033
4780948220.57368637548-126.573686375483
4892808313.93932571252966.060674287484
4983348875.68319024482-541.683190244825
5078998138.88375700173-239.883757001729
5199949264.54938107381729.450618926187
521007810505.2105270501-427.210527050149
531080111010.4108378166-209.410837816557
541295012474.1971982292475.802801770838
551222212632.9488724434-410.948872443438
561224612643.2223261401-397.222326140136
571328112487.834995547793.165004452952
581036610353.078279302312.92172069765
5987308664.0533829256465.9466170743617
6096149233.23078732424380.769212675757
6186399124.33509691525-485.335096915247
6287728479.89391555331292.106084446692
631089410138.247229165755.752770834988
641045510969.9547417632-514.954741763173
651117911585.3784954611-406.378495461136
661058813390.9502407925-2802.95024079251
671079412799.4909429901-2005.4909429901
681277012622.3394092947147.660590705334
691381212999.9830083534812.016991646606
701085710521.9073662575335.092633742499
7192908859.06189099036430.938109009641
72109259610.277766905271314.72223309473
7394919255.43619720476235.563802795235
7489198986.46215097725-67.4621509772496
751160710851.0505378656755.949462134431
76885211193.4179729864-2341.41797298642
771253711643.1123415451893.887658454852
781475912668.98649902442090.01350097557
791366712963.5412770187703.458722981279
801373114046.1055865017-315.105586501653
811511014682.9948203013427.005179698723
821218511695.7616546418489.238345358208
83106459918.86907658675726.130923413251
841216111144.12933239471016.8706676053
851084010238.667075591601.332924409033
86104369850.52478860235585.475211397654
871358912345.55554337911243.44445662094
881340211399.30412052812002.69587947186
891310313953.0351718078-850.035171807769
901493315410.2747374316-477.274737431553
911414714787.2270003629-640.227000362882
921405715366.6920823981-1309.69208239809
931623416259.4499723878-25.4499723878071
941238912962.7672731057-573.767273105737
951159511006.1988737279588.801126272117
961277212416.299652881355.700347119044

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 7269 & 7028.04555893714 & 240.954441062862 \tabularnewline
14 & 6775 & 6589.60133762837 & 185.398662371631 \tabularnewline
15 & 7819 & 7651.76756439805 & 167.232435601953 \tabularnewline
16 & 8371 & 8204.9718412555 & 166.028158744501 \tabularnewline
17 & 9069 & 8881.74618834833 & 187.253811651666 \tabularnewline
18 & 10248 & 10045.4986564522 & 202.501343547778 \tabularnewline
19 & 11030 & 10965.4438240899 & 64.5561759100929 \tabularnewline
20 & 10882 & 11266.6213746771 & -384.621374677072 \tabularnewline
21 & 10333 & 10383.7901131434 & -50.7901131433737 \tabularnewline
22 & 9109 & 8537.60367918035 & 571.396320819646 \tabularnewline
23 & 7685 & 7199.13792787709 & 485.862072122906 \tabularnewline
24 & 7602 & 7439.3413446404 & 162.658655359601 \tabularnewline
25 & 8350 & 7811.81173514451 & 538.188264855487 \tabularnewline
26 & 7829 & 7334.10759647993 & 494.892403520066 \tabularnewline
27 & 8829 & 8531.70250674818 & 297.297493251821 \tabularnewline
28 & 9948 & 9152.55924664116 & 795.440753358836 \tabularnewline
29 & 10638 & 9984.98032679143 & 653.019673208571 \tabularnewline
30 & 11253 & 11343.2792317032 & -90.27923170318 \tabularnewline
31 & 11424 & 12265.7510932665 & -841.751093266523 \tabularnewline
32 & 11391 & 12288.1771235432 & -897.177123543206 \tabularnewline
33 & 10665 & 11397.9005365729 & -732.900536572924 \tabularnewline
34 & 9396 & 9559.71015530468 & -163.710155304678 \tabularnewline
35 & 7775 & 7978.7111309595 & -203.711130959495 \tabularnewline
36 & 7933 & 8010.66540394782 & -77.6654039478235 \tabularnewline
37 & 8186 & 8528.28931383278 & -342.289313832784 \tabularnewline
38 & 7444 & 7896.39580195039 & -452.395801950387 \tabularnewline
39 & 8484 & 8936.3393618554 & -452.339361855402 \tabularnewline
40 & 9948 & 9674.77925484802 & 273.220745151981 \tabularnewline
41 & 10252 & 10396.4340258043 & -144.434025804298 \tabularnewline
42 & 12282 & 11373.7551472545 & 908.24485274554 \tabularnewline
43 & 11637 & 12130.112944568 & -493.112944567951 \tabularnewline
44 & 11577 & 12170.7395779461 & -593.739577946071 \tabularnewline
45 & 12417 & 11361.4221282407 & 1055.5778717593 \tabularnewline
46 & 9637 & 9894.75711420503 & -257.757114205033 \tabularnewline
47 & 8094 & 8220.57368637548 & -126.573686375483 \tabularnewline
48 & 9280 & 8313.93932571252 & 966.060674287484 \tabularnewline
49 & 8334 & 8875.68319024482 & -541.683190244825 \tabularnewline
50 & 7899 & 8138.88375700173 & -239.883757001729 \tabularnewline
51 & 9994 & 9264.54938107381 & 729.450618926187 \tabularnewline
52 & 10078 & 10505.2105270501 & -427.210527050149 \tabularnewline
53 & 10801 & 11010.4108378166 & -209.410837816557 \tabularnewline
54 & 12950 & 12474.1971982292 & 475.802801770838 \tabularnewline
55 & 12222 & 12632.9488724434 & -410.948872443438 \tabularnewline
56 & 12246 & 12643.2223261401 & -397.222326140136 \tabularnewline
57 & 13281 & 12487.834995547 & 793.165004452952 \tabularnewline
58 & 10366 & 10353.0782793023 & 12.92172069765 \tabularnewline
59 & 8730 & 8664.05338292564 & 65.9466170743617 \tabularnewline
60 & 9614 & 9233.23078732424 & 380.769212675757 \tabularnewline
61 & 8639 & 9124.33509691525 & -485.335096915247 \tabularnewline
62 & 8772 & 8479.89391555331 & 292.106084446692 \tabularnewline
63 & 10894 & 10138.247229165 & 755.752770834988 \tabularnewline
64 & 10455 & 10969.9547417632 & -514.954741763173 \tabularnewline
65 & 11179 & 11585.3784954611 & -406.378495461136 \tabularnewline
66 & 10588 & 13390.9502407925 & -2802.95024079251 \tabularnewline
67 & 10794 & 12799.4909429901 & -2005.4909429901 \tabularnewline
68 & 12770 & 12622.3394092947 & 147.660590705334 \tabularnewline
69 & 13812 & 12999.9830083534 & 812.016991646606 \tabularnewline
70 & 10857 & 10521.9073662575 & 335.092633742499 \tabularnewline
71 & 9290 & 8859.06189099036 & 430.938109009641 \tabularnewline
72 & 10925 & 9610.27776690527 & 1314.72223309473 \tabularnewline
73 & 9491 & 9255.43619720476 & 235.563802795235 \tabularnewline
74 & 8919 & 8986.46215097725 & -67.4621509772496 \tabularnewline
75 & 11607 & 10851.0505378656 & 755.949462134431 \tabularnewline
76 & 8852 & 11193.4179729864 & -2341.41797298642 \tabularnewline
77 & 12537 & 11643.1123415451 & 893.887658454852 \tabularnewline
78 & 14759 & 12668.9864990244 & 2090.01350097557 \tabularnewline
79 & 13667 & 12963.5412770187 & 703.458722981279 \tabularnewline
80 & 13731 & 14046.1055865017 & -315.105586501653 \tabularnewline
81 & 15110 & 14682.9948203013 & 427.005179698723 \tabularnewline
82 & 12185 & 11695.7616546418 & 489.238345358208 \tabularnewline
83 & 10645 & 9918.86907658675 & 726.130923413251 \tabularnewline
84 & 12161 & 11144.1293323947 & 1016.8706676053 \tabularnewline
85 & 10840 & 10238.667075591 & 601.332924409033 \tabularnewline
86 & 10436 & 9850.52478860235 & 585.475211397654 \tabularnewline
87 & 13589 & 12345.5555433791 & 1243.44445662094 \tabularnewline
88 & 13402 & 11399.3041205281 & 2002.69587947186 \tabularnewline
89 & 13103 & 13953.0351718078 & -850.035171807769 \tabularnewline
90 & 14933 & 15410.2747374316 & -477.274737431553 \tabularnewline
91 & 14147 & 14787.2270003629 & -640.227000362882 \tabularnewline
92 & 14057 & 15366.6920823981 & -1309.69208239809 \tabularnewline
93 & 16234 & 16259.4499723878 & -25.4499723878071 \tabularnewline
94 & 12389 & 12962.7672731057 & -573.767273105737 \tabularnewline
95 & 11595 & 11006.1988737279 & 588.801126272117 \tabularnewline
96 & 12772 & 12416.299652881 & 355.700347119044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121965&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]7028.04555893714[/C][C]240.954441062862[/C][/ROW]
[ROW][C]14[/C][C]6775[/C][C]6589.60133762837[/C][C]185.398662371631[/C][/ROW]
[ROW][C]15[/C][C]7819[/C][C]7651.76756439805[/C][C]167.232435601953[/C][/ROW]
[ROW][C]16[/C][C]8371[/C][C]8204.9718412555[/C][C]166.028158744501[/C][/ROW]
[ROW][C]17[/C][C]9069[/C][C]8881.74618834833[/C][C]187.253811651666[/C][/ROW]
[ROW][C]18[/C][C]10248[/C][C]10045.4986564522[/C][C]202.501343547778[/C][/ROW]
[ROW][C]19[/C][C]11030[/C][C]10965.4438240899[/C][C]64.5561759100929[/C][/ROW]
[ROW][C]20[/C][C]10882[/C][C]11266.6213746771[/C][C]-384.621374677072[/C][/ROW]
[ROW][C]21[/C][C]10333[/C][C]10383.7901131434[/C][C]-50.7901131433737[/C][/ROW]
[ROW][C]22[/C][C]9109[/C][C]8537.60367918035[/C][C]571.396320819646[/C][/ROW]
[ROW][C]23[/C][C]7685[/C][C]7199.13792787709[/C][C]485.862072122906[/C][/ROW]
[ROW][C]24[/C][C]7602[/C][C]7439.3413446404[/C][C]162.658655359601[/C][/ROW]
[ROW][C]25[/C][C]8350[/C][C]7811.81173514451[/C][C]538.188264855487[/C][/ROW]
[ROW][C]26[/C][C]7829[/C][C]7334.10759647993[/C][C]494.892403520066[/C][/ROW]
[ROW][C]27[/C][C]8829[/C][C]8531.70250674818[/C][C]297.297493251821[/C][/ROW]
[ROW][C]28[/C][C]9948[/C][C]9152.55924664116[/C][C]795.440753358836[/C][/ROW]
[ROW][C]29[/C][C]10638[/C][C]9984.98032679143[/C][C]653.019673208571[/C][/ROW]
[ROW][C]30[/C][C]11253[/C][C]11343.2792317032[/C][C]-90.27923170318[/C][/ROW]
[ROW][C]31[/C][C]11424[/C][C]12265.7510932665[/C][C]-841.751093266523[/C][/ROW]
[ROW][C]32[/C][C]11391[/C][C]12288.1771235432[/C][C]-897.177123543206[/C][/ROW]
[ROW][C]33[/C][C]10665[/C][C]11397.9005365729[/C][C]-732.900536572924[/C][/ROW]
[ROW][C]34[/C][C]9396[/C][C]9559.71015530468[/C][C]-163.710155304678[/C][/ROW]
[ROW][C]35[/C][C]7775[/C][C]7978.7111309595[/C][C]-203.711130959495[/C][/ROW]
[ROW][C]36[/C][C]7933[/C][C]8010.66540394782[/C][C]-77.6654039478235[/C][/ROW]
[ROW][C]37[/C][C]8186[/C][C]8528.28931383278[/C][C]-342.289313832784[/C][/ROW]
[ROW][C]38[/C][C]7444[/C][C]7896.39580195039[/C][C]-452.395801950387[/C][/ROW]
[ROW][C]39[/C][C]8484[/C][C]8936.3393618554[/C][C]-452.339361855402[/C][/ROW]
[ROW][C]40[/C][C]9948[/C][C]9674.77925484802[/C][C]273.220745151981[/C][/ROW]
[ROW][C]41[/C][C]10252[/C][C]10396.4340258043[/C][C]-144.434025804298[/C][/ROW]
[ROW][C]42[/C][C]12282[/C][C]11373.7551472545[/C][C]908.24485274554[/C][/ROW]
[ROW][C]43[/C][C]11637[/C][C]12130.112944568[/C][C]-493.112944567951[/C][/ROW]
[ROW][C]44[/C][C]11577[/C][C]12170.7395779461[/C][C]-593.739577946071[/C][/ROW]
[ROW][C]45[/C][C]12417[/C][C]11361.4221282407[/C][C]1055.5778717593[/C][/ROW]
[ROW][C]46[/C][C]9637[/C][C]9894.75711420503[/C][C]-257.757114205033[/C][/ROW]
[ROW][C]47[/C][C]8094[/C][C]8220.57368637548[/C][C]-126.573686375483[/C][/ROW]
[ROW][C]48[/C][C]9280[/C][C]8313.93932571252[/C][C]966.060674287484[/C][/ROW]
[ROW][C]49[/C][C]8334[/C][C]8875.68319024482[/C][C]-541.683190244825[/C][/ROW]
[ROW][C]50[/C][C]7899[/C][C]8138.88375700173[/C][C]-239.883757001729[/C][/ROW]
[ROW][C]51[/C][C]9994[/C][C]9264.54938107381[/C][C]729.450618926187[/C][/ROW]
[ROW][C]52[/C][C]10078[/C][C]10505.2105270501[/C][C]-427.210527050149[/C][/ROW]
[ROW][C]53[/C][C]10801[/C][C]11010.4108378166[/C][C]-209.410837816557[/C][/ROW]
[ROW][C]54[/C][C]12950[/C][C]12474.1971982292[/C][C]475.802801770838[/C][/ROW]
[ROW][C]55[/C][C]12222[/C][C]12632.9488724434[/C][C]-410.948872443438[/C][/ROW]
[ROW][C]56[/C][C]12246[/C][C]12643.2223261401[/C][C]-397.222326140136[/C][/ROW]
[ROW][C]57[/C][C]13281[/C][C]12487.834995547[/C][C]793.165004452952[/C][/ROW]
[ROW][C]58[/C][C]10366[/C][C]10353.0782793023[/C][C]12.92172069765[/C][/ROW]
[ROW][C]59[/C][C]8730[/C][C]8664.05338292564[/C][C]65.9466170743617[/C][/ROW]
[ROW][C]60[/C][C]9614[/C][C]9233.23078732424[/C][C]380.769212675757[/C][/ROW]
[ROW][C]61[/C][C]8639[/C][C]9124.33509691525[/C][C]-485.335096915247[/C][/ROW]
[ROW][C]62[/C][C]8772[/C][C]8479.89391555331[/C][C]292.106084446692[/C][/ROW]
[ROW][C]63[/C][C]10894[/C][C]10138.247229165[/C][C]755.752770834988[/C][/ROW]
[ROW][C]64[/C][C]10455[/C][C]10969.9547417632[/C][C]-514.954741763173[/C][/ROW]
[ROW][C]65[/C][C]11179[/C][C]11585.3784954611[/C][C]-406.378495461136[/C][/ROW]
[ROW][C]66[/C][C]10588[/C][C]13390.9502407925[/C][C]-2802.95024079251[/C][/ROW]
[ROW][C]67[/C][C]10794[/C][C]12799.4909429901[/C][C]-2005.4909429901[/C][/ROW]
[ROW][C]68[/C][C]12770[/C][C]12622.3394092947[/C][C]147.660590705334[/C][/ROW]
[ROW][C]69[/C][C]13812[/C][C]12999.9830083534[/C][C]812.016991646606[/C][/ROW]
[ROW][C]70[/C][C]10857[/C][C]10521.9073662575[/C][C]335.092633742499[/C][/ROW]
[ROW][C]71[/C][C]9290[/C][C]8859.06189099036[/C][C]430.938109009641[/C][/ROW]
[ROW][C]72[/C][C]10925[/C][C]9610.27776690527[/C][C]1314.72223309473[/C][/ROW]
[ROW][C]73[/C][C]9491[/C][C]9255.43619720476[/C][C]235.563802795235[/C][/ROW]
[ROW][C]74[/C][C]8919[/C][C]8986.46215097725[/C][C]-67.4621509772496[/C][/ROW]
[ROW][C]75[/C][C]11607[/C][C]10851.0505378656[/C][C]755.949462134431[/C][/ROW]
[ROW][C]76[/C][C]8852[/C][C]11193.4179729864[/C][C]-2341.41797298642[/C][/ROW]
[ROW][C]77[/C][C]12537[/C][C]11643.1123415451[/C][C]893.887658454852[/C][/ROW]
[ROW][C]78[/C][C]14759[/C][C]12668.9864990244[/C][C]2090.01350097557[/C][/ROW]
[ROW][C]79[/C][C]13667[/C][C]12963.5412770187[/C][C]703.458722981279[/C][/ROW]
[ROW][C]80[/C][C]13731[/C][C]14046.1055865017[/C][C]-315.105586501653[/C][/ROW]
[ROW][C]81[/C][C]15110[/C][C]14682.9948203013[/C][C]427.005179698723[/C][/ROW]
[ROW][C]82[/C][C]12185[/C][C]11695.7616546418[/C][C]489.238345358208[/C][/ROW]
[ROW][C]83[/C][C]10645[/C][C]9918.86907658675[/C][C]726.130923413251[/C][/ROW]
[ROW][C]84[/C][C]12161[/C][C]11144.1293323947[/C][C]1016.8706676053[/C][/ROW]
[ROW][C]85[/C][C]10840[/C][C]10238.667075591[/C][C]601.332924409033[/C][/ROW]
[ROW][C]86[/C][C]10436[/C][C]9850.52478860235[/C][C]585.475211397654[/C][/ROW]
[ROW][C]87[/C][C]13589[/C][C]12345.5555433791[/C][C]1243.44445662094[/C][/ROW]
[ROW][C]88[/C][C]13402[/C][C]11399.3041205281[/C][C]2002.69587947186[/C][/ROW]
[ROW][C]89[/C][C]13103[/C][C]13953.0351718078[/C][C]-850.035171807769[/C][/ROW]
[ROW][C]90[/C][C]14933[/C][C]15410.2747374316[/C][C]-477.274737431553[/C][/ROW]
[ROW][C]91[/C][C]14147[/C][C]14787.2270003629[/C][C]-640.227000362882[/C][/ROW]
[ROW][C]92[/C][C]14057[/C][C]15366.6920823981[/C][C]-1309.69208239809[/C][/ROW]
[ROW][C]93[/C][C]16234[/C][C]16259.4499723878[/C][C]-25.4499723878071[/C][/ROW]
[ROW][C]94[/C][C]12389[/C][C]12962.7672731057[/C][C]-573.767273105737[/C][/ROW]
[ROW][C]95[/C][C]11595[/C][C]11006.1988737279[/C][C]588.801126272117[/C][/ROW]
[ROW][C]96[/C][C]12772[/C][C]12416.299652881[/C][C]355.700347119044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121965&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121965&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
1372697028.04555893714240.954441062862
1467756589.60133762837185.398662371631
1578197651.76756439805167.232435601953
1683718204.9718412555166.028158744501
1790698881.74618834833187.253811651666
181024810045.4986564522202.501343547778
191103010965.443824089964.5561759100929
201088211266.6213746771-384.621374677072
211033310383.7901131434-50.7901131433737
2291098537.60367918035571.396320819646
2376857199.13792787709485.862072122906
2476027439.3413446404162.658655359601
2583507811.81173514451538.188264855487
2678297334.10759647993494.892403520066
2788298531.70250674818297.297493251821
2899489152.55924664116795.440753358836
29106389984.98032679143653.019673208571
301125311343.2792317032-90.27923170318
311142412265.7510932665-841.751093266523
321139112288.1771235432-897.177123543206
331066511397.9005365729-732.900536572924
3493969559.71015530468-163.710155304678
3577757978.7111309595-203.711130959495
3679338010.66540394782-77.6654039478235
3781868528.28931383278-342.289313832784
3874447896.39580195039-452.395801950387
3984848936.3393618554-452.339361855402
4099489674.77925484802273.220745151981
411025210396.4340258043-144.434025804298
421228211373.7551472545908.24485274554
431163712130.112944568-493.112944567951
441157712170.7395779461-593.739577946071
451241711361.42212824071055.5778717593
4696379894.75711420503-257.757114205033
4780948220.57368637548-126.573686375483
4892808313.93932571252966.060674287484
4983348875.68319024482-541.683190244825
5078998138.88375700173-239.883757001729
5199949264.54938107381729.450618926187
521007810505.2105270501-427.210527050149
531080111010.4108378166-209.410837816557
541295012474.1971982292475.802801770838
551222212632.9488724434-410.948872443438
561224612643.2223261401-397.222326140136
571328112487.834995547793.165004452952
581036610353.078279302312.92172069765
5987308664.0533829256465.9466170743617
6096149233.23078732424380.769212675757
6186399124.33509691525-485.335096915247
6287728479.89391555331292.106084446692
631089410138.247229165755.752770834988
641045510969.9547417632-514.954741763173
651117911585.3784954611-406.378495461136
661058813390.9502407925-2802.95024079251
671079412799.4909429901-2005.4909429901
681277012622.3394092947147.660590705334
691381212999.9830083534812.016991646606
701085710521.9073662575335.092633742499
7192908859.06189099036430.938109009641
72109259610.277766905271314.72223309473
7394919255.43619720476235.563802795235
7489198986.46215097725-67.4621509772496
751160710851.0505378656755.949462134431
76885211193.4179729864-2341.41797298642
771253711643.1123415451893.887658454852
781475912668.98649902442090.01350097557
791366712963.5412770187703.458722981279
801373114046.1055865017-315.105586501653
811511014682.9948203013427.005179698723
821218511695.7616546418489.238345358208
83106459918.86907658675726.130923413251
841216111144.12933239471016.8706676053
851084010238.667075591601.332924409033
86104369850.52478860235585.475211397654
871358912345.55554337911243.44445662094
881340211399.30412052812002.69587947186
891310313953.0351718078-850.035171807769
901493315410.2747374316-477.274737431553
911414714787.2270003629-640.227000362882
921405715366.6920823981-1309.69208239809
931623416259.4499723878-25.4499723878071
941238912962.7672731057-573.767273105737
951159511006.1988737279588.801126272117
961277212416.299652881355.700347119044







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9711183.351853701210399.470332160311967.2333752422
9810684.39818132089880.9673364328211487.8290262088
9913498.478165348912651.166745277414345.7895854204
10012648.294644049611791.226912075613505.3623760236
10113864.963652749912971.270926126314758.6563793735
10215611.95056905514668.75854780516555.1425903049
10314961.569870366314014.605818954915908.5339217777
10415363.327441697614390.69267789916335.9622054962
10516983.354933898115954.496726890318012.2131409059
10613313.321771628812361.224413795614265.4191294619
10711803.587734272810871.24468032312735.9307882226
10813104.096191531612508.928921976713699.2634610865

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 11183.3518537012 & 10399.4703321603 & 11967.2333752422 \tabularnewline
98 & 10684.3981813208 & 9880.96733643282 & 11487.8290262088 \tabularnewline
99 & 13498.4781653489 & 12651.1667452774 & 14345.7895854204 \tabularnewline
100 & 12648.2946440496 & 11791.2269120756 & 13505.3623760236 \tabularnewline
101 & 13864.9636527499 & 12971.2709261263 & 14758.6563793735 \tabularnewline
102 & 15611.950569055 & 14668.758547805 & 16555.1425903049 \tabularnewline
103 & 14961.5698703663 & 14014.6058189549 & 15908.5339217777 \tabularnewline
104 & 15363.3274416976 & 14390.692677899 & 16335.9622054962 \tabularnewline
105 & 16983.3549338981 & 15954.4967268903 & 18012.2131409059 \tabularnewline
106 & 13313.3217716288 & 12361.2244137956 & 14265.4191294619 \tabularnewline
107 & 11803.5877342728 & 10871.244680323 & 12735.9307882226 \tabularnewline
108 & 13104.0961915316 & 12508.9289219767 & 13699.2634610865 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=121965&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]11183.3518537012[/C][C]10399.4703321603[/C][C]11967.2333752422[/C][/ROW]
[ROW][C]98[/C][C]10684.3981813208[/C][C]9880.96733643282[/C][C]11487.8290262088[/C][/ROW]
[ROW][C]99[/C][C]13498.4781653489[/C][C]12651.1667452774[/C][C]14345.7895854204[/C][/ROW]
[ROW][C]100[/C][C]12648.2946440496[/C][C]11791.2269120756[/C][C]13505.3623760236[/C][/ROW]
[ROW][C]101[/C][C]13864.9636527499[/C][C]12971.2709261263[/C][C]14758.6563793735[/C][/ROW]
[ROW][C]102[/C][C]15611.950569055[/C][C]14668.758547805[/C][C]16555.1425903049[/C][/ROW]
[ROW][C]103[/C][C]14961.5698703663[/C][C]14014.6058189549[/C][C]15908.5339217777[/C][/ROW]
[ROW][C]104[/C][C]15363.3274416976[/C][C]14390.692677899[/C][C]16335.9622054962[/C][/ROW]
[ROW][C]105[/C][C]16983.3549338981[/C][C]15954.4967268903[/C][C]18012.2131409059[/C][/ROW]
[ROW][C]106[/C][C]13313.3217716288[/C][C]12361.2244137956[/C][C]14265.4191294619[/C][/ROW]
[ROW][C]107[/C][C]11803.5877342728[/C][C]10871.244680323[/C][C]12735.9307882226[/C][/ROW]
[ROW][C]108[/C][C]13104.0961915316[/C][C]12508.9289219767[/C][C]13699.2634610865[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=121965&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=121965&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
9711183.351853701210399.470332160311967.2333752422
9810684.39818132089880.9673364328211487.8290262088
9913498.478165348912651.166745277414345.7895854204
10012648.294644049611791.226912075613505.3623760236
10113864.963652749912971.270926126314758.6563793735
10215611.95056905514668.75854780516555.1425903049
10314961.569870366314014.605818954915908.5339217777
10415363.327441697614390.69267789916335.9622054962
10516983.354933898115954.496726890318012.2131409059
10613313.321771628812361.224413795614265.4191294619
10711803.587734272810871.24468032312735.9307882226
10813104.096191531612508.928921976713699.2634610865



Parameters (Session):
par1 = 48 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')