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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 16:04:22 +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/t1305820832z42f9wl3h6mm3pr.htm/, Retrieved Sat, 11 May 2024 05:02:58 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122115, Retrieved Sat, 11 May 2024 05:02:58 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact81
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exoniantal smoothing] [2011-05-19 16:04:22] [164acd287bf1b95108b808ea4c161e74] [Current]
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Dataseries X:
70938
34077
45409
40809
37013
44953
19848
32745
43412
34931
33008
8620
68906
39556
50669
36432
40891
48428
36222
33425
39401
37967
34801
12657
69116
41519
51321
38529
41547
52073
38401
40898
40439
41888
37898
8771
68184
50530
47221
41756
45633
48138
39486
39341
41117
41629
29722
7054
56676
34870
35117
30169
30936
35699
33228
27733
33666
35429
27438
8170
63410
38040
45389
37353
37024
50957
37994
36454
46080
43373
37395
10963
75001




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122115&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122115&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122115&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 time1 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.344206838588595
beta0
gamma0.800062194590154

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.344206838588595 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.800062194590154 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122115&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]0.344206838588595[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.800062194590154[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122115&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122115&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
alpha0.344206838588595
beta0
gamma0.800062194590154







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
136890667427.02029914531478.97970085469
143955638146.07890929691409.9210907031
155066950153.7420735709515.257926429127
163643236405.289391801826.7106081982274
174089140942.8420487901-51.8420487901385
184842848489.6480107205-61.648010720477
193622222874.787026828813347.2129731712
203342540492.9310246098-7067.93102460975
213940148550.2095142503-9149.20951425026
223796737153.7643814158813.235618584171
233480135802.0443257-1001.0443257
241265711033.67003938081623.32996061923
256911672097.9408045413-2981.94080454131
264151941245.2867222375273.713277762494
275132152392.4517088857-1071.45170888566
283852937841.5140012541687.485998745928
294154742565.2954263186-1018.2954263186
305207349774.29658035292298.70341964708
313840132007.18307306356393.81692693647
324089836520.59847380874377.40152619125
334043947425.4432482943-6986.44324829426
344188842000.4861018366-112.486101836563
353789839378.2183963945-1480.21839639451
36877115821.8535258243-7050.85352582433
376818471484.1391221893-3300.13912218931
385053042230.12033706978299.87966293028
394722155434.1718168137-8213.17181681374
404175639347.87640617582408.12359382416
414563343768.93165011951864.06834988049
424813853710.4095446217-5572.40954462174
433948635382.61010087674103.38989912329
443934138049.68146795661291.31853204345
454111741929.9465243306-812.946524330575
464162942236.5448056764-607.544805676371
472972238726.2591351341-9004.25913513411
4870549657.29324208409-2603.29324208409
495667668818.3667677855-12142.3667677855
503487042607.036279409-7737.03627940897
513511741627.0811200571-6510.0811200571
523016931699.7326989933-1530.7326989933
533093634479.5543137396-3543.55431373957
543569938657.9551183166-2958.95511831662
553322826306.37769033256921.62230966755
562773328468.0794929526-735.079492952631
573366630546.78855819653119.21144180351
583542932314.63171352093114.36828647914
592743825679.90523846611758.09476153389
6081703673.843958063544496.15604193646
616341060273.68006189413136.31993810585
623804041632.7461880415-3592.74618804153
634538942723.0371050812665.96289491898
643735338566.6869910395-1213.68699103955
653702440399.5600900091-3375.56009000906
665095744942.51042278036014.48957721968
673799440863.7491081566-2869.74910815663
683645435637.9114724363816.088527563712
694608040272.79449196725807.20550803276
704337342963.3225029234409.677497076569
713739534686.01972171962708.98027828045
721096314443.8529061886-3480.85290618864
737500167584.47554122087416.52445877917

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 68906 & 67427.0202991453 & 1478.97970085469 \tabularnewline
14 & 39556 & 38146.0789092969 & 1409.9210907031 \tabularnewline
15 & 50669 & 50153.7420735709 & 515.257926429127 \tabularnewline
16 & 36432 & 36405.2893918018 & 26.7106081982274 \tabularnewline
17 & 40891 & 40942.8420487901 & -51.8420487901385 \tabularnewline
18 & 48428 & 48489.6480107205 & -61.648010720477 \tabularnewline
19 & 36222 & 22874.7870268288 & 13347.2129731712 \tabularnewline
20 & 33425 & 40492.9310246098 & -7067.93102460975 \tabularnewline
21 & 39401 & 48550.2095142503 & -9149.20951425026 \tabularnewline
22 & 37967 & 37153.7643814158 & 813.235618584171 \tabularnewline
23 & 34801 & 35802.0443257 & -1001.0443257 \tabularnewline
24 & 12657 & 11033.6700393808 & 1623.32996061923 \tabularnewline
25 & 69116 & 72097.9408045413 & -2981.94080454131 \tabularnewline
26 & 41519 & 41245.2867222375 & 273.713277762494 \tabularnewline
27 & 51321 & 52392.4517088857 & -1071.45170888566 \tabularnewline
28 & 38529 & 37841.5140012541 & 687.485998745928 \tabularnewline
29 & 41547 & 42565.2954263186 & -1018.2954263186 \tabularnewline
30 & 52073 & 49774.2965803529 & 2298.70341964708 \tabularnewline
31 & 38401 & 32007.1830730635 & 6393.81692693647 \tabularnewline
32 & 40898 & 36520.5984738087 & 4377.40152619125 \tabularnewline
33 & 40439 & 47425.4432482943 & -6986.44324829426 \tabularnewline
34 & 41888 & 42000.4861018366 & -112.486101836563 \tabularnewline
35 & 37898 & 39378.2183963945 & -1480.21839639451 \tabularnewline
36 & 8771 & 15821.8535258243 & -7050.85352582433 \tabularnewline
37 & 68184 & 71484.1391221893 & -3300.13912218931 \tabularnewline
38 & 50530 & 42230.1203370697 & 8299.87966293028 \tabularnewline
39 & 47221 & 55434.1718168137 & -8213.17181681374 \tabularnewline
40 & 41756 & 39347.8764061758 & 2408.12359382416 \tabularnewline
41 & 45633 & 43768.9316501195 & 1864.06834988049 \tabularnewline
42 & 48138 & 53710.4095446217 & -5572.40954462174 \tabularnewline
43 & 39486 & 35382.6101008767 & 4103.38989912329 \tabularnewline
44 & 39341 & 38049.6814679566 & 1291.31853204345 \tabularnewline
45 & 41117 & 41929.9465243306 & -812.946524330575 \tabularnewline
46 & 41629 & 42236.5448056764 & -607.544805676371 \tabularnewline
47 & 29722 & 38726.2591351341 & -9004.25913513411 \tabularnewline
48 & 7054 & 9657.29324208409 & -2603.29324208409 \tabularnewline
49 & 56676 & 68818.3667677855 & -12142.3667677855 \tabularnewline
50 & 34870 & 42607.036279409 & -7737.03627940897 \tabularnewline
51 & 35117 & 41627.0811200571 & -6510.0811200571 \tabularnewline
52 & 30169 & 31699.7326989933 & -1530.7326989933 \tabularnewline
53 & 30936 & 34479.5543137396 & -3543.55431373957 \tabularnewline
54 & 35699 & 38657.9551183166 & -2958.95511831662 \tabularnewline
55 & 33228 & 26306.3776903325 & 6921.62230966755 \tabularnewline
56 & 27733 & 28468.0794929526 & -735.079492952631 \tabularnewline
57 & 33666 & 30546.7885581965 & 3119.21144180351 \tabularnewline
58 & 35429 & 32314.6317135209 & 3114.36828647914 \tabularnewline
59 & 27438 & 25679.9052384661 & 1758.09476153389 \tabularnewline
60 & 8170 & 3673.84395806354 & 4496.15604193646 \tabularnewline
61 & 63410 & 60273.6800618941 & 3136.31993810585 \tabularnewline
62 & 38040 & 41632.7461880415 & -3592.74618804153 \tabularnewline
63 & 45389 & 42723.037105081 & 2665.96289491898 \tabularnewline
64 & 37353 & 38566.6869910395 & -1213.68699103955 \tabularnewline
65 & 37024 & 40399.5600900091 & -3375.56009000906 \tabularnewline
66 & 50957 & 44942.5104227803 & 6014.48957721968 \tabularnewline
67 & 37994 & 40863.7491081566 & -2869.74910815663 \tabularnewline
68 & 36454 & 35637.9114724363 & 816.088527563712 \tabularnewline
69 & 46080 & 40272.7944919672 & 5807.20550803276 \tabularnewline
70 & 43373 & 42963.3225029234 & 409.677497076569 \tabularnewline
71 & 37395 & 34686.0197217196 & 2708.98027828045 \tabularnewline
72 & 10963 & 14443.8529061886 & -3480.85290618864 \tabularnewline
73 & 75001 & 67584.4755412208 & 7416.52445877917 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122115&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]68906[/C][C]67427.0202991453[/C][C]1478.97970085469[/C][/ROW]
[ROW][C]14[/C][C]39556[/C][C]38146.0789092969[/C][C]1409.9210907031[/C][/ROW]
[ROW][C]15[/C][C]50669[/C][C]50153.7420735709[/C][C]515.257926429127[/C][/ROW]
[ROW][C]16[/C][C]36432[/C][C]36405.2893918018[/C][C]26.7106081982274[/C][/ROW]
[ROW][C]17[/C][C]40891[/C][C]40942.8420487901[/C][C]-51.8420487901385[/C][/ROW]
[ROW][C]18[/C][C]48428[/C][C]48489.6480107205[/C][C]-61.648010720477[/C][/ROW]
[ROW][C]19[/C][C]36222[/C][C]22874.7870268288[/C][C]13347.2129731712[/C][/ROW]
[ROW][C]20[/C][C]33425[/C][C]40492.9310246098[/C][C]-7067.93102460975[/C][/ROW]
[ROW][C]21[/C][C]39401[/C][C]48550.2095142503[/C][C]-9149.20951425026[/C][/ROW]
[ROW][C]22[/C][C]37967[/C][C]37153.7643814158[/C][C]813.235618584171[/C][/ROW]
[ROW][C]23[/C][C]34801[/C][C]35802.0443257[/C][C]-1001.0443257[/C][/ROW]
[ROW][C]24[/C][C]12657[/C][C]11033.6700393808[/C][C]1623.32996061923[/C][/ROW]
[ROW][C]25[/C][C]69116[/C][C]72097.9408045413[/C][C]-2981.94080454131[/C][/ROW]
[ROW][C]26[/C][C]41519[/C][C]41245.2867222375[/C][C]273.713277762494[/C][/ROW]
[ROW][C]27[/C][C]51321[/C][C]52392.4517088857[/C][C]-1071.45170888566[/C][/ROW]
[ROW][C]28[/C][C]38529[/C][C]37841.5140012541[/C][C]687.485998745928[/C][/ROW]
[ROW][C]29[/C][C]41547[/C][C]42565.2954263186[/C][C]-1018.2954263186[/C][/ROW]
[ROW][C]30[/C][C]52073[/C][C]49774.2965803529[/C][C]2298.70341964708[/C][/ROW]
[ROW][C]31[/C][C]38401[/C][C]32007.1830730635[/C][C]6393.81692693647[/C][/ROW]
[ROW][C]32[/C][C]40898[/C][C]36520.5984738087[/C][C]4377.40152619125[/C][/ROW]
[ROW][C]33[/C][C]40439[/C][C]47425.4432482943[/C][C]-6986.44324829426[/C][/ROW]
[ROW][C]34[/C][C]41888[/C][C]42000.4861018366[/C][C]-112.486101836563[/C][/ROW]
[ROW][C]35[/C][C]37898[/C][C]39378.2183963945[/C][C]-1480.21839639451[/C][/ROW]
[ROW][C]36[/C][C]8771[/C][C]15821.8535258243[/C][C]-7050.85352582433[/C][/ROW]
[ROW][C]37[/C][C]68184[/C][C]71484.1391221893[/C][C]-3300.13912218931[/C][/ROW]
[ROW][C]38[/C][C]50530[/C][C]42230.1203370697[/C][C]8299.87966293028[/C][/ROW]
[ROW][C]39[/C][C]47221[/C][C]55434.1718168137[/C][C]-8213.17181681374[/C][/ROW]
[ROW][C]40[/C][C]41756[/C][C]39347.8764061758[/C][C]2408.12359382416[/C][/ROW]
[ROW][C]41[/C][C]45633[/C][C]43768.9316501195[/C][C]1864.06834988049[/C][/ROW]
[ROW][C]42[/C][C]48138[/C][C]53710.4095446217[/C][C]-5572.40954462174[/C][/ROW]
[ROW][C]43[/C][C]39486[/C][C]35382.6101008767[/C][C]4103.38989912329[/C][/ROW]
[ROW][C]44[/C][C]39341[/C][C]38049.6814679566[/C][C]1291.31853204345[/C][/ROW]
[ROW][C]45[/C][C]41117[/C][C]41929.9465243306[/C][C]-812.946524330575[/C][/ROW]
[ROW][C]46[/C][C]41629[/C][C]42236.5448056764[/C][C]-607.544805676371[/C][/ROW]
[ROW][C]47[/C][C]29722[/C][C]38726.2591351341[/C][C]-9004.25913513411[/C][/ROW]
[ROW][C]48[/C][C]7054[/C][C]9657.29324208409[/C][C]-2603.29324208409[/C][/ROW]
[ROW][C]49[/C][C]56676[/C][C]68818.3667677855[/C][C]-12142.3667677855[/C][/ROW]
[ROW][C]50[/C][C]34870[/C][C]42607.036279409[/C][C]-7737.03627940897[/C][/ROW]
[ROW][C]51[/C][C]35117[/C][C]41627.0811200571[/C][C]-6510.0811200571[/C][/ROW]
[ROW][C]52[/C][C]30169[/C][C]31699.7326989933[/C][C]-1530.7326989933[/C][/ROW]
[ROW][C]53[/C][C]30936[/C][C]34479.5543137396[/C][C]-3543.55431373957[/C][/ROW]
[ROW][C]54[/C][C]35699[/C][C]38657.9551183166[/C][C]-2958.95511831662[/C][/ROW]
[ROW][C]55[/C][C]33228[/C][C]26306.3776903325[/C][C]6921.62230966755[/C][/ROW]
[ROW][C]56[/C][C]27733[/C][C]28468.0794929526[/C][C]-735.079492952631[/C][/ROW]
[ROW][C]57[/C][C]33666[/C][C]30546.7885581965[/C][C]3119.21144180351[/C][/ROW]
[ROW][C]58[/C][C]35429[/C][C]32314.6317135209[/C][C]3114.36828647914[/C][/ROW]
[ROW][C]59[/C][C]27438[/C][C]25679.9052384661[/C][C]1758.09476153389[/C][/ROW]
[ROW][C]60[/C][C]8170[/C][C]3673.84395806354[/C][C]4496.15604193646[/C][/ROW]
[ROW][C]61[/C][C]63410[/C][C]60273.6800618941[/C][C]3136.31993810585[/C][/ROW]
[ROW][C]62[/C][C]38040[/C][C]41632.7461880415[/C][C]-3592.74618804153[/C][/ROW]
[ROW][C]63[/C][C]45389[/C][C]42723.037105081[/C][C]2665.96289491898[/C][/ROW]
[ROW][C]64[/C][C]37353[/C][C]38566.6869910395[/C][C]-1213.68699103955[/C][/ROW]
[ROW][C]65[/C][C]37024[/C][C]40399.5600900091[/C][C]-3375.56009000906[/C][/ROW]
[ROW][C]66[/C][C]50957[/C][C]44942.5104227803[/C][C]6014.48957721968[/C][/ROW]
[ROW][C]67[/C][C]37994[/C][C]40863.7491081566[/C][C]-2869.74910815663[/C][/ROW]
[ROW][C]68[/C][C]36454[/C][C]35637.9114724363[/C][C]816.088527563712[/C][/ROW]
[ROW][C]69[/C][C]46080[/C][C]40272.7944919672[/C][C]5807.20550803276[/C][/ROW]
[ROW][C]70[/C][C]43373[/C][C]42963.3225029234[/C][C]409.677497076569[/C][/ROW]
[ROW][C]71[/C][C]37395[/C][C]34686.0197217196[/C][C]2708.98027828045[/C][/ROW]
[ROW][C]72[/C][C]10963[/C][C]14443.8529061886[/C][C]-3480.85290618864[/C][/ROW]
[ROW][C]73[/C][C]75001[/C][C]67584.4755412208[/C][C]7416.52445877917[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122115&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122115&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
136890667427.02029914531478.97970085469
143955638146.07890929691409.9210907031
155066950153.7420735709515.257926429127
163643236405.289391801826.7106081982274
174089140942.8420487901-51.8420487901385
184842848489.6480107205-61.648010720477
193622222874.787026828813347.2129731712
203342540492.9310246098-7067.93102460975
213940148550.2095142503-9149.20951425026
223796737153.7643814158813.235618584171
233480135802.0443257-1001.0443257
241265711033.67003938081623.32996061923
256911672097.9408045413-2981.94080454131
264151941245.2867222375273.713277762494
275132152392.4517088857-1071.45170888566
283852937841.5140012541687.485998745928
294154742565.2954263186-1018.2954263186
305207349774.29658035292298.70341964708
313840132007.18307306356393.81692693647
324089836520.59847380874377.40152619125
334043947425.4432482943-6986.44324829426
344188842000.4861018366-112.486101836563
353789839378.2183963945-1480.21839639451
36877115821.8535258243-7050.85352582433
376818471484.1391221893-3300.13912218931
385053042230.12033706978299.87966293028
394722155434.1718168137-8213.17181681374
404175639347.87640617582408.12359382416
414563343768.93165011951864.06834988049
424813853710.4095446217-5572.40954462174
433948635382.61010087674103.38989912329
443934138049.68146795661291.31853204345
454111741929.9465243306-812.946524330575
464162942236.5448056764-607.544805676371
472972238726.2591351341-9004.25913513411
4870549657.29324208409-2603.29324208409
495667668818.3667677855-12142.3667677855
503487042607.036279409-7737.03627940897
513511741627.0811200571-6510.0811200571
523016931699.7326989933-1530.7326989933
533093634479.5543137396-3543.55431373957
543569938657.9551183166-2958.95511831662
553322826306.37769033256921.62230966755
562773328468.0794929526-735.079492952631
573366630546.78855819653119.21144180351
583542932314.63171352093114.36828647914
592743825679.90523846611758.09476153389
6081703673.843958063544496.15604193646
616341060273.68006189413136.31993810585
623804041632.7461880415-3592.74618804153
634538942723.0371050812665.96289491898
643735338566.6869910395-1213.68699103955
653702440399.5600900091-3375.56009000906
665095744942.51042278036014.48957721968
673799440863.7491081566-2869.74910815663
683645435637.9114724363816.088527563712
694608040272.79449196725807.20550803276
704337342963.3225029234409.677497076569
713739534686.01972171962708.98027828045
721096314443.8529061886-3480.85290618864
737500167584.47554122087416.52445877917







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7446886.242438385637594.831090192856177.6537865784
7552496.971327990942670.547813424762323.3948425571
7645387.42202453635053.648593019655721.1954560524
7746503.773034555235686.419033681957321.1270354284
7857135.341509994745855.118913498568415.5641064909
7946325.01101334934600.178559416158049.8434672818
8044020.828671626431867.641010807156174.0163324457
8150993.524317577738426.573829675463560.4748054799
8248853.222765265635885.704929855461820.7406006757
8341641.293601066828285.216592529754997.370609604
8417219.02456662133485.3772978049330952.6718354378
8577275.365487705363174.254129001691376.476846409

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 46886.2424383856 & 37594.8310901928 & 56177.6537865784 \tabularnewline
75 & 52496.9713279909 & 42670.5478134247 & 62323.3948425571 \tabularnewline
76 & 45387.422024536 & 35053.6485930196 & 55721.1954560524 \tabularnewline
77 & 46503.7730345552 & 35686.4190336819 & 57321.1270354284 \tabularnewline
78 & 57135.3415099947 & 45855.1189134985 & 68415.5641064909 \tabularnewline
79 & 46325.011013349 & 34600.1785594161 & 58049.8434672818 \tabularnewline
80 & 44020.8286716264 & 31867.6410108071 & 56174.0163324457 \tabularnewline
81 & 50993.5243175777 & 38426.5738296754 & 63560.4748054799 \tabularnewline
82 & 48853.2227652656 & 35885.7049298554 & 61820.7406006757 \tabularnewline
83 & 41641.2936010668 & 28285.2165925297 & 54997.370609604 \tabularnewline
84 & 17219.0245666213 & 3485.37729780493 & 30952.6718354378 \tabularnewline
85 & 77275.3654877053 & 63174.2541290016 & 91376.476846409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122115&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]74[/C][C]46886.2424383856[/C][C]37594.8310901928[/C][C]56177.6537865784[/C][/ROW]
[ROW][C]75[/C][C]52496.9713279909[/C][C]42670.5478134247[/C][C]62323.3948425571[/C][/ROW]
[ROW][C]76[/C][C]45387.422024536[/C][C]35053.6485930196[/C][C]55721.1954560524[/C][/ROW]
[ROW][C]77[/C][C]46503.7730345552[/C][C]35686.4190336819[/C][C]57321.1270354284[/C][/ROW]
[ROW][C]78[/C][C]57135.3415099947[/C][C]45855.1189134985[/C][C]68415.5641064909[/C][/ROW]
[ROW][C]79[/C][C]46325.011013349[/C][C]34600.1785594161[/C][C]58049.8434672818[/C][/ROW]
[ROW][C]80[/C][C]44020.8286716264[/C][C]31867.6410108071[/C][C]56174.0163324457[/C][/ROW]
[ROW][C]81[/C][C]50993.5243175777[/C][C]38426.5738296754[/C][C]63560.4748054799[/C][/ROW]
[ROW][C]82[/C][C]48853.2227652656[/C][C]35885.7049298554[/C][C]61820.7406006757[/C][/ROW]
[ROW][C]83[/C][C]41641.2936010668[/C][C]28285.2165925297[/C][C]54997.370609604[/C][/ROW]
[ROW][C]84[/C][C]17219.0245666213[/C][C]3485.37729780493[/C][C]30952.6718354378[/C][/ROW]
[ROW][C]85[/C][C]77275.3654877053[/C][C]63174.2541290016[/C][C]91376.476846409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122115&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122115&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
7446886.242438385637594.831090192856177.6537865784
7552496.971327990942670.547813424762323.3948425571
7645387.42202453635053.648593019655721.1954560524
7746503.773034555235686.419033681957321.1270354284
7857135.341509994745855.118913498568415.5641064909
7946325.01101334934600.178559416158049.8434672818
8044020.828671626431867.641010807156174.0163324457
8150993.524317577738426.573829675463560.4748054799
8248853.222765265635885.704929855461820.7406006757
8341641.293601066828285.216592529754997.370609604
8417219.02456662133485.3772978049330952.6718354378
8577275.365487705363174.254129001691376.476846409



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')