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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 22 May 2014 18:50:25 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/May/22/t1400799034c34h8ahmagv4cow.htm/, Retrieved Wed, 15 May 2024 00:32:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235161, Retrieved Wed, 15 May 2024 00:32:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact100
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [] [2014-05-22 12:48:06] [837550725ee1c1bb9816088970c1061c]
- RMP   [Classical Decomposition] [] [2014-05-22 22:36:51] [837550725ee1c1bb9816088970c1061c]
- RM D      [Exponential Smoothing] [] [2014-05-22 22:50:25] [f824ea295e177f9d3dd7528a75f4b680] [Current]
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Dataseries X:
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195
19650
20830
23595
22937
21814
21928
21777
21383
21467
22052
22680
24320
24977
25204
25739
26434
27525
30695
32436
30160
30236
31293
31077
32226
33865
32810
32242
32700
32819
33947
34148
35261
39506
41591
39148
41216
40225
41126
42362
40740
40256
39804
41002
41702
42254
43605
43271
43221
41373




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235161&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235161&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235161&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00309845765832808
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00309845765832808 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235161&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.00309845765832808[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235161&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235161&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
alpha1
beta0.00309845765832808
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131939417905.69204059831488.30795940171
142014820133.971744742514.0282552574536
152010820158.1402106975-50.1402106974783
161858418624.9848533777-40.9848533776567
171844118504.6078635448-63.6078635448284
181839118483.8691106062-92.8691106062361
191917818375.9980262659802.001973734081
201807919186.6079954234-1107.60799542343
211848318734.9677856143-251.967785614252
221964419034.9787407659609.021259234072
231919520337.699100684-1142.69910068402
241965019259.1168292377390.883170762318
252083021270.3279641916-440.327964191631
262359521565.71362663882029.28637336118
272293723607.1262845433-670.12628454329
282181421454.0499266249359.950073375094
292192821735.9152166864192.084783313632
302177721972.9687165876-195.968716587609
312138321763.7781824836-380.778182483569
322146721389.723357407977.2766425920709
332205222124.7544624796-72.7544624796465
342268022606.320702524973.679297475137
352432023374.3823280417945.61767195828
362497724391.2706176926585.729382307411
372520426605.0854753829-1401.0854753829
382573925944.4942713617-205.494271361731
392643425748.9825560629685.017443937115
402752524953.10505360812571.89494639186
413069527455.82396120123239.1760387988
423243630758.31874433861677.68125566137
433016032446.9336353401-2286.93363534013
443023630184.972668303651.0273316963794
453129330911.922440997381.077559003032
463107731866.8948603447-789.894860344742
473222631788.2807378988437.719262101233
483386532312.5953258321552.40467416804
493281035511.4053859835-2701.40538598345
503224233564.785195777-1322.78519577701
513270032262.8116018568437.188398143171
523281931229.16621159721589.83378840281
533394732756.84224427431190.15775572566
543414834010.9882310205137.011768979486
553526134154.82942285211106.17057714794
563950635292.38184554824213.61815445177
574159140201.22922965481389.77077034517
583914842187.3270422082-3039.3270422082
594121639874.74314939141341.25685060856
604022541320.8573102853-1095.85731028533
614112641881.4618428098-755.461842809833
624236241896.8710762774465.128923722586
634074042404.4372585532-1664.43725855322
644025639284.2800701827971.719929817344
653980440207.040903241-403.040903240952
664100239876.2504314011125.74956859899
674170241020.1551854399681.844814560129
684225441743.3928527273510.607147272676
694360542947.7666140199657.233385980137
704327144197.5946905046-926.594690504629
714322144000.557009423-779.557009422999
724137343322.0999183704-1949.0999183704

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 19394 & 17905.6920405983 & 1488.30795940171 \tabularnewline
14 & 20148 & 20133.9717447425 & 14.0282552574536 \tabularnewline
15 & 20108 & 20158.1402106975 & -50.1402106974783 \tabularnewline
16 & 18584 & 18624.9848533777 & -40.9848533776567 \tabularnewline
17 & 18441 & 18504.6078635448 & -63.6078635448284 \tabularnewline
18 & 18391 & 18483.8691106062 & -92.8691106062361 \tabularnewline
19 & 19178 & 18375.9980262659 & 802.001973734081 \tabularnewline
20 & 18079 & 19186.6079954234 & -1107.60799542343 \tabularnewline
21 & 18483 & 18734.9677856143 & -251.967785614252 \tabularnewline
22 & 19644 & 19034.9787407659 & 609.021259234072 \tabularnewline
23 & 19195 & 20337.699100684 & -1142.69910068402 \tabularnewline
24 & 19650 & 19259.1168292377 & 390.883170762318 \tabularnewline
25 & 20830 & 21270.3279641916 & -440.327964191631 \tabularnewline
26 & 23595 & 21565.7136266388 & 2029.28637336118 \tabularnewline
27 & 22937 & 23607.1262845433 & -670.12628454329 \tabularnewline
28 & 21814 & 21454.0499266249 & 359.950073375094 \tabularnewline
29 & 21928 & 21735.9152166864 & 192.084783313632 \tabularnewline
30 & 21777 & 21972.9687165876 & -195.968716587609 \tabularnewline
31 & 21383 & 21763.7781824836 & -380.778182483569 \tabularnewline
32 & 21467 & 21389.7233574079 & 77.2766425920709 \tabularnewline
33 & 22052 & 22124.7544624796 & -72.7544624796465 \tabularnewline
34 & 22680 & 22606.3207025249 & 73.679297475137 \tabularnewline
35 & 24320 & 23374.3823280417 & 945.61767195828 \tabularnewline
36 & 24977 & 24391.2706176926 & 585.729382307411 \tabularnewline
37 & 25204 & 26605.0854753829 & -1401.0854753829 \tabularnewline
38 & 25739 & 25944.4942713617 & -205.494271361731 \tabularnewline
39 & 26434 & 25748.9825560629 & 685.017443937115 \tabularnewline
40 & 27525 & 24953.1050536081 & 2571.89494639186 \tabularnewline
41 & 30695 & 27455.8239612012 & 3239.1760387988 \tabularnewline
42 & 32436 & 30758.3187443386 & 1677.68125566137 \tabularnewline
43 & 30160 & 32446.9336353401 & -2286.93363534013 \tabularnewline
44 & 30236 & 30184.9726683036 & 51.0273316963794 \tabularnewline
45 & 31293 & 30911.922440997 & 381.077559003032 \tabularnewline
46 & 31077 & 31866.8948603447 & -789.894860344742 \tabularnewline
47 & 32226 & 31788.2807378988 & 437.719262101233 \tabularnewline
48 & 33865 & 32312.595325832 & 1552.40467416804 \tabularnewline
49 & 32810 & 35511.4053859835 & -2701.40538598345 \tabularnewline
50 & 32242 & 33564.785195777 & -1322.78519577701 \tabularnewline
51 & 32700 & 32262.8116018568 & 437.188398143171 \tabularnewline
52 & 32819 & 31229.1662115972 & 1589.83378840281 \tabularnewline
53 & 33947 & 32756.8422442743 & 1190.15775572566 \tabularnewline
54 & 34148 & 34010.9882310205 & 137.011768979486 \tabularnewline
55 & 35261 & 34154.8294228521 & 1106.17057714794 \tabularnewline
56 & 39506 & 35292.3818455482 & 4213.61815445177 \tabularnewline
57 & 41591 & 40201.2292296548 & 1389.77077034517 \tabularnewline
58 & 39148 & 42187.3270422082 & -3039.3270422082 \tabularnewline
59 & 41216 & 39874.7431493914 & 1341.25685060856 \tabularnewline
60 & 40225 & 41320.8573102853 & -1095.85731028533 \tabularnewline
61 & 41126 & 41881.4618428098 & -755.461842809833 \tabularnewline
62 & 42362 & 41896.8710762774 & 465.128923722586 \tabularnewline
63 & 40740 & 42404.4372585532 & -1664.43725855322 \tabularnewline
64 & 40256 & 39284.2800701827 & 971.719929817344 \tabularnewline
65 & 39804 & 40207.040903241 & -403.040903240952 \tabularnewline
66 & 41002 & 39876.250431401 & 1125.74956859899 \tabularnewline
67 & 41702 & 41020.1551854399 & 681.844814560129 \tabularnewline
68 & 42254 & 41743.3928527273 & 510.607147272676 \tabularnewline
69 & 43605 & 42947.7666140199 & 657.233385980137 \tabularnewline
70 & 43271 & 44197.5946905046 & -926.594690504629 \tabularnewline
71 & 43221 & 44000.557009423 & -779.557009422999 \tabularnewline
72 & 41373 & 43322.0999183704 & -1949.0999183704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235161&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]19394[/C][C]17905.6920405983[/C][C]1488.30795940171[/C][/ROW]
[ROW][C]14[/C][C]20148[/C][C]20133.9717447425[/C][C]14.0282552574536[/C][/ROW]
[ROW][C]15[/C][C]20108[/C][C]20158.1402106975[/C][C]-50.1402106974783[/C][/ROW]
[ROW][C]16[/C][C]18584[/C][C]18624.9848533777[/C][C]-40.9848533776567[/C][/ROW]
[ROW][C]17[/C][C]18441[/C][C]18504.6078635448[/C][C]-63.6078635448284[/C][/ROW]
[ROW][C]18[/C][C]18391[/C][C]18483.8691106062[/C][C]-92.8691106062361[/C][/ROW]
[ROW][C]19[/C][C]19178[/C][C]18375.9980262659[/C][C]802.001973734081[/C][/ROW]
[ROW][C]20[/C][C]18079[/C][C]19186.6079954234[/C][C]-1107.60799542343[/C][/ROW]
[ROW][C]21[/C][C]18483[/C][C]18734.9677856143[/C][C]-251.967785614252[/C][/ROW]
[ROW][C]22[/C][C]19644[/C][C]19034.9787407659[/C][C]609.021259234072[/C][/ROW]
[ROW][C]23[/C][C]19195[/C][C]20337.699100684[/C][C]-1142.69910068402[/C][/ROW]
[ROW][C]24[/C][C]19650[/C][C]19259.1168292377[/C][C]390.883170762318[/C][/ROW]
[ROW][C]25[/C][C]20830[/C][C]21270.3279641916[/C][C]-440.327964191631[/C][/ROW]
[ROW][C]26[/C][C]23595[/C][C]21565.7136266388[/C][C]2029.28637336118[/C][/ROW]
[ROW][C]27[/C][C]22937[/C][C]23607.1262845433[/C][C]-670.12628454329[/C][/ROW]
[ROW][C]28[/C][C]21814[/C][C]21454.0499266249[/C][C]359.950073375094[/C][/ROW]
[ROW][C]29[/C][C]21928[/C][C]21735.9152166864[/C][C]192.084783313632[/C][/ROW]
[ROW][C]30[/C][C]21777[/C][C]21972.9687165876[/C][C]-195.968716587609[/C][/ROW]
[ROW][C]31[/C][C]21383[/C][C]21763.7781824836[/C][C]-380.778182483569[/C][/ROW]
[ROW][C]32[/C][C]21467[/C][C]21389.7233574079[/C][C]77.2766425920709[/C][/ROW]
[ROW][C]33[/C][C]22052[/C][C]22124.7544624796[/C][C]-72.7544624796465[/C][/ROW]
[ROW][C]34[/C][C]22680[/C][C]22606.3207025249[/C][C]73.679297475137[/C][/ROW]
[ROW][C]35[/C][C]24320[/C][C]23374.3823280417[/C][C]945.61767195828[/C][/ROW]
[ROW][C]36[/C][C]24977[/C][C]24391.2706176926[/C][C]585.729382307411[/C][/ROW]
[ROW][C]37[/C][C]25204[/C][C]26605.0854753829[/C][C]-1401.0854753829[/C][/ROW]
[ROW][C]38[/C][C]25739[/C][C]25944.4942713617[/C][C]-205.494271361731[/C][/ROW]
[ROW][C]39[/C][C]26434[/C][C]25748.9825560629[/C][C]685.017443937115[/C][/ROW]
[ROW][C]40[/C][C]27525[/C][C]24953.1050536081[/C][C]2571.89494639186[/C][/ROW]
[ROW][C]41[/C][C]30695[/C][C]27455.8239612012[/C][C]3239.1760387988[/C][/ROW]
[ROW][C]42[/C][C]32436[/C][C]30758.3187443386[/C][C]1677.68125566137[/C][/ROW]
[ROW][C]43[/C][C]30160[/C][C]32446.9336353401[/C][C]-2286.93363534013[/C][/ROW]
[ROW][C]44[/C][C]30236[/C][C]30184.9726683036[/C][C]51.0273316963794[/C][/ROW]
[ROW][C]45[/C][C]31293[/C][C]30911.922440997[/C][C]381.077559003032[/C][/ROW]
[ROW][C]46[/C][C]31077[/C][C]31866.8948603447[/C][C]-789.894860344742[/C][/ROW]
[ROW][C]47[/C][C]32226[/C][C]31788.2807378988[/C][C]437.719262101233[/C][/ROW]
[ROW][C]48[/C][C]33865[/C][C]32312.595325832[/C][C]1552.40467416804[/C][/ROW]
[ROW][C]49[/C][C]32810[/C][C]35511.4053859835[/C][C]-2701.40538598345[/C][/ROW]
[ROW][C]50[/C][C]32242[/C][C]33564.785195777[/C][C]-1322.78519577701[/C][/ROW]
[ROW][C]51[/C][C]32700[/C][C]32262.8116018568[/C][C]437.188398143171[/C][/ROW]
[ROW][C]52[/C][C]32819[/C][C]31229.1662115972[/C][C]1589.83378840281[/C][/ROW]
[ROW][C]53[/C][C]33947[/C][C]32756.8422442743[/C][C]1190.15775572566[/C][/ROW]
[ROW][C]54[/C][C]34148[/C][C]34010.9882310205[/C][C]137.011768979486[/C][/ROW]
[ROW][C]55[/C][C]35261[/C][C]34154.8294228521[/C][C]1106.17057714794[/C][/ROW]
[ROW][C]56[/C][C]39506[/C][C]35292.3818455482[/C][C]4213.61815445177[/C][/ROW]
[ROW][C]57[/C][C]41591[/C][C]40201.2292296548[/C][C]1389.77077034517[/C][/ROW]
[ROW][C]58[/C][C]39148[/C][C]42187.3270422082[/C][C]-3039.3270422082[/C][/ROW]
[ROW][C]59[/C][C]41216[/C][C]39874.7431493914[/C][C]1341.25685060856[/C][/ROW]
[ROW][C]60[/C][C]40225[/C][C]41320.8573102853[/C][C]-1095.85731028533[/C][/ROW]
[ROW][C]61[/C][C]41126[/C][C]41881.4618428098[/C][C]-755.461842809833[/C][/ROW]
[ROW][C]62[/C][C]42362[/C][C]41896.8710762774[/C][C]465.128923722586[/C][/ROW]
[ROW][C]63[/C][C]40740[/C][C]42404.4372585532[/C][C]-1664.43725855322[/C][/ROW]
[ROW][C]64[/C][C]40256[/C][C]39284.2800701827[/C][C]971.719929817344[/C][/ROW]
[ROW][C]65[/C][C]39804[/C][C]40207.040903241[/C][C]-403.040903240952[/C][/ROW]
[ROW][C]66[/C][C]41002[/C][C]39876.250431401[/C][C]1125.74956859899[/C][/ROW]
[ROW][C]67[/C][C]41702[/C][C]41020.1551854399[/C][C]681.844814560129[/C][/ROW]
[ROW][C]68[/C][C]42254[/C][C]41743.3928527273[/C][C]510.607147272676[/C][/ROW]
[ROW][C]69[/C][C]43605[/C][C]42947.7666140199[/C][C]657.233385980137[/C][/ROW]
[ROW][C]70[/C][C]43271[/C][C]44197.5946905046[/C][C]-926.594690504629[/C][/ROW]
[ROW][C]71[/C][C]43221[/C][C]44000.557009423[/C][C]-779.557009422999[/C][/ROW]
[ROW][C]72[/C][C]41373[/C][C]43322.0999183704[/C][C]-1949.0999183704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235161&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235161&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
131939417905.69204059831488.30795940171
142014820133.971744742514.0282552574536
152010820158.1402106975-50.1402106974783
161858418624.9848533777-40.9848533776567
171844118504.6078635448-63.6078635448284
181839118483.8691106062-92.8691106062361
191917818375.9980262659802.001973734081
201807919186.6079954234-1107.60799542343
211848318734.9677856143-251.967785614252
221964419034.9787407659609.021259234072
231919520337.699100684-1142.69910068402
241965019259.1168292377390.883170762318
252083021270.3279641916-440.327964191631
262359521565.71362663882029.28637336118
272293723607.1262845433-670.12628454329
282181421454.0499266249359.950073375094
292192821735.9152166864192.084783313632
302177721972.9687165876-195.968716587609
312138321763.7781824836-380.778182483569
322146721389.723357407977.2766425920709
332205222124.7544624796-72.7544624796465
342268022606.320702524973.679297475137
352432023374.3823280417945.61767195828
362497724391.2706176926585.729382307411
372520426605.0854753829-1401.0854753829
382573925944.4942713617-205.494271361731
392643425748.9825560629685.017443937115
402752524953.10505360812571.89494639186
413069527455.82396120123239.1760387988
423243630758.31874433861677.68125566137
433016032446.9336353401-2286.93363534013
443023630184.972668303651.0273316963794
453129330911.922440997381.077559003032
463107731866.8948603447-789.894860344742
473222631788.2807378988437.719262101233
483386532312.5953258321552.40467416804
493281035511.4053859835-2701.40538598345
503224233564.785195777-1322.78519577701
513270032262.8116018568437.188398143171
523281931229.16621159721589.83378840281
533394732756.84224427431190.15775572566
543414834010.9882310205137.011768979486
553526134154.82942285211106.17057714794
563950635292.38184554824213.61815445177
574159140201.22922965481389.77077034517
583914842187.3270422082-3039.3270422082
594121639874.74314939141341.25685060856
604022541320.8573102853-1095.85731028533
614112641881.4618428098-755.461842809833
624236241896.8710762774465.128923722586
634074042404.4372585532-1664.43725855322
644025639284.2800701827971.719929817344
653980440207.040903241-403.040903240952
664100239876.2504314011125.74956859899
674170241020.1551854399681.844814560129
684225441743.3928527273510.607147272676
694360542947.7666140199657.233385980137
704327144197.5946905046-926.594690504629
714322144000.557009423-779.557009422999
724137343322.0999183704-1949.0999183704







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7343023.060714801540467.010576602745579.1108530002
7443789.871429602940169.466173242647410.2766859632
7543826.807144404439385.866795698348267.7474931104
7642370.742859205837234.852611418347506.6331069934
7742318.428574007336567.45369692648069.4034510887
7842388.572622142136078.968290161248698.176954123
7942401.133336943635575.470112597449226.7965612897
8042434.81905174535126.635121258649743.0029822315
8143119.296433213235355.865876950250882.7269894761
8243700.56548134835504.608623276951896.522339419
8344421.667862816135812.472647173953030.8630784582
8444516.728577617635510.920464304453522.5366909307

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 43023.0607148015 & 40467.0105766027 & 45579.1108530002 \tabularnewline
74 & 43789.8714296029 & 40169.4661732426 & 47410.2766859632 \tabularnewline
75 & 43826.8071444044 & 39385.8667956983 & 48267.7474931104 \tabularnewline
76 & 42370.7428592058 & 37234.8526114183 & 47506.6331069934 \tabularnewline
77 & 42318.4285740073 & 36567.453696926 & 48069.4034510887 \tabularnewline
78 & 42388.5726221421 & 36078.9682901612 & 48698.176954123 \tabularnewline
79 & 42401.1333369436 & 35575.4701125974 & 49226.7965612897 \tabularnewline
80 & 42434.819051745 & 35126.6351212586 & 49743.0029822315 \tabularnewline
81 & 43119.2964332132 & 35355.8658769502 & 50882.7269894761 \tabularnewline
82 & 43700.565481348 & 35504.6086232769 & 51896.522339419 \tabularnewline
83 & 44421.6678628161 & 35812.4726471739 & 53030.8630784582 \tabularnewline
84 & 44516.7285776176 & 35510.9204643044 & 53522.5366909307 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235161&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]73[/C][C]43023.0607148015[/C][C]40467.0105766027[/C][C]45579.1108530002[/C][/ROW]
[ROW][C]74[/C][C]43789.8714296029[/C][C]40169.4661732426[/C][C]47410.2766859632[/C][/ROW]
[ROW][C]75[/C][C]43826.8071444044[/C][C]39385.8667956983[/C][C]48267.7474931104[/C][/ROW]
[ROW][C]76[/C][C]42370.7428592058[/C][C]37234.8526114183[/C][C]47506.6331069934[/C][/ROW]
[ROW][C]77[/C][C]42318.4285740073[/C][C]36567.453696926[/C][C]48069.4034510887[/C][/ROW]
[ROW][C]78[/C][C]42388.5726221421[/C][C]36078.9682901612[/C][C]48698.176954123[/C][/ROW]
[ROW][C]79[/C][C]42401.1333369436[/C][C]35575.4701125974[/C][C]49226.7965612897[/C][/ROW]
[ROW][C]80[/C][C]42434.819051745[/C][C]35126.6351212586[/C][C]49743.0029822315[/C][/ROW]
[ROW][C]81[/C][C]43119.2964332132[/C][C]35355.8658769502[/C][C]50882.7269894761[/C][/ROW]
[ROW][C]82[/C][C]43700.565481348[/C][C]35504.6086232769[/C][C]51896.522339419[/C][/ROW]
[ROW][C]83[/C][C]44421.6678628161[/C][C]35812.4726471739[/C][C]53030.8630784582[/C][/ROW]
[ROW][C]84[/C][C]44516.7285776176[/C][C]35510.9204643044[/C][C]53522.5366909307[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235161&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235161&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
7343023.060714801540467.010576602745579.1108530002
7443789.871429602940169.466173242647410.2766859632
7543826.807144404439385.866795698348267.7474931104
7642370.742859205837234.852611418347506.6331069934
7742318.428574007336567.45369692648069.4034510887
7842388.572622142136078.968290161248698.176954123
7942401.133336943635575.470112597449226.7965612897
8042434.81905174535126.635121258649743.0029822315
8143119.296433213235355.865876950250882.7269894761
8243700.56548134835504.608623276951896.522339419
8344421.667862816135812.472647173953030.8630784582
8444516.728577617635510.920464304453522.5366909307



Parameters (Session):
par1 = 750 ; par2 = 5 ; par3 = 0 ; par4 = P1 P5 Q1 Q3 P95 P99 ;
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')