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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 10:35:31 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Jan/15/t1358264146jn45ojehewj60ah.htm/, Retrieved Sun, 28 Apr 2024 17:10:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205481, Retrieved Sun, 28 Apr 2024 17:10:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Blocked Bootstrap Plot - Central Tendency] [] [2012-11-26 10:17:43] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [] [2013-01-15 15:35:31] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367
31124
26551
30651
25859
25100
25778
20418
18688
20424
24776
19814
12738
31566
30111
30019
31934
25826
26835
20205
17789
20520
22518
15572
11509
25447
24090
27786
26195
20516
22759
19028
16971
20036
22485
18730
14538
27561
25985
34670
32066
27186
29586
21359
21553
19573
24256
22380
16167
27297
28287
33474
28229
28785
25597
18130
20198
22849
23118
21925
20801




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 3 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205481&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205481&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205481&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 time3 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.321385303438058
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.321385303438058 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205481&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]0.321385303438058[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205481&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205481&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
alpha0.321385303438058
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
133112431525.9345619658-401.934561965812
142655126724.2125178225-173.212517822503
153065130670.7483772392-19.7483772391643
162585925673.7303560441185.26964395594
172510024766.727113801333.272886198978
182577825361.3732718094416.626728190593
192041818397.0581296192020.941870381
201868818426.6796295451261.320370454945
212042419722.7429731146701.257026885422
222477623004.48715917121771.5128408288
231981420134.737501415-320.737501415031
241273812049.1943325485688.805667451548
253156633624.9698005357-2058.96980053568
263011128445.91512402041665.08487597962
273001933087.3957703486-3068.39577034863
283193427249.71552388644684.28447611356
292582627889.0667039736-2063.06670397365
302683527770.1296778442-935.129677844183
312020521460.0917263332-1255.09172633322
321778919242.7391644698-1453.73916446982
332052020286.1550596033233.844940396742
342251824143.9711948359-1625.97119483594
351557218762.4882682183-3190.48826821828
361150910439.74020957761069.25979042238
372544730273.1072258916-4826.10722589158
382409026731.933482557-2641.93348255698
392778626776.99219432381009.00780567621
402619527510.8122863765-1315.81228637647
412051621642.9688741214-1126.96887412136
422275922590.3145758145168.685424185489
431902816417.89562736212610.10437263786
441697115307.95521566031663.04478433972
452003618498.27904117951537.72095882048
462248521513.043203967971.956796033006
471873015904.79187398562825.20812601436
481453812406.12786264142131.87213735858
492756128580.3201716153-1019.32017161532
502598527744.8042429149-1759.80424291494
513467030550.94874251554119.05125748448
523206630706.63401170371359.36598829629
532718625826.70549591041359.29450408957
542958628452.34975633151133.65024366849
552135924246.8390980803-2887.83909808031
562155320727.2519006174825.748099382614
571957323563.4342871473-3990.43428714729
582425624417.5947231011-161.594723101072
592238019702.68018312852677.31981687155
601616715685.9790511183481.020948881684
612729729191.1666373898-1894.16663738984
622828727571.9845384709715.015461529139
633347435162.9774612737-1688.97746127374
642822931579.2846767503-3350.28467675026
652878525185.69514265053599.30485734951
662559728378.1202988418-2781.12029884182
671813020185.4181525176-2055.41815251762
682019819453.4536623952744.546337604828
692284918995.20684725453853.79315274554
702311824968.6934981549-1850.69349815492
712192521637.4565649336287.543435066429
722080115362.27573544765438.72426455238

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 31124 & 31525.9345619658 & -401.934561965812 \tabularnewline
14 & 26551 & 26724.2125178225 & -173.212517822503 \tabularnewline
15 & 30651 & 30670.7483772392 & -19.7483772391643 \tabularnewline
16 & 25859 & 25673.7303560441 & 185.26964395594 \tabularnewline
17 & 25100 & 24766.727113801 & 333.272886198978 \tabularnewline
18 & 25778 & 25361.3732718094 & 416.626728190593 \tabularnewline
19 & 20418 & 18397.058129619 & 2020.941870381 \tabularnewline
20 & 18688 & 18426.6796295451 & 261.320370454945 \tabularnewline
21 & 20424 & 19722.7429731146 & 701.257026885422 \tabularnewline
22 & 24776 & 23004.4871591712 & 1771.5128408288 \tabularnewline
23 & 19814 & 20134.737501415 & -320.737501415031 \tabularnewline
24 & 12738 & 12049.1943325485 & 688.805667451548 \tabularnewline
25 & 31566 & 33624.9698005357 & -2058.96980053568 \tabularnewline
26 & 30111 & 28445.9151240204 & 1665.08487597962 \tabularnewline
27 & 30019 & 33087.3957703486 & -3068.39577034863 \tabularnewline
28 & 31934 & 27249.7155238864 & 4684.28447611356 \tabularnewline
29 & 25826 & 27889.0667039736 & -2063.06670397365 \tabularnewline
30 & 26835 & 27770.1296778442 & -935.129677844183 \tabularnewline
31 & 20205 & 21460.0917263332 & -1255.09172633322 \tabularnewline
32 & 17789 & 19242.7391644698 & -1453.73916446982 \tabularnewline
33 & 20520 & 20286.1550596033 & 233.844940396742 \tabularnewline
34 & 22518 & 24143.9711948359 & -1625.97119483594 \tabularnewline
35 & 15572 & 18762.4882682183 & -3190.48826821828 \tabularnewline
36 & 11509 & 10439.7402095776 & 1069.25979042238 \tabularnewline
37 & 25447 & 30273.1072258916 & -4826.10722589158 \tabularnewline
38 & 24090 & 26731.933482557 & -2641.93348255698 \tabularnewline
39 & 27786 & 26776.9921943238 & 1009.00780567621 \tabularnewline
40 & 26195 & 27510.8122863765 & -1315.81228637647 \tabularnewline
41 & 20516 & 21642.9688741214 & -1126.96887412136 \tabularnewline
42 & 22759 & 22590.3145758145 & 168.685424185489 \tabularnewline
43 & 19028 & 16417.8956273621 & 2610.10437263786 \tabularnewline
44 & 16971 & 15307.9552156603 & 1663.04478433972 \tabularnewline
45 & 20036 & 18498.2790411795 & 1537.72095882048 \tabularnewline
46 & 22485 & 21513.043203967 & 971.956796033006 \tabularnewline
47 & 18730 & 15904.7918739856 & 2825.20812601436 \tabularnewline
48 & 14538 & 12406.1278626414 & 2131.87213735858 \tabularnewline
49 & 27561 & 28580.3201716153 & -1019.32017161532 \tabularnewline
50 & 25985 & 27744.8042429149 & -1759.80424291494 \tabularnewline
51 & 34670 & 30550.9487425155 & 4119.05125748448 \tabularnewline
52 & 32066 & 30706.6340117037 & 1359.36598829629 \tabularnewline
53 & 27186 & 25826.7054959104 & 1359.29450408957 \tabularnewline
54 & 29586 & 28452.3497563315 & 1133.65024366849 \tabularnewline
55 & 21359 & 24246.8390980803 & -2887.83909808031 \tabularnewline
56 & 21553 & 20727.2519006174 & 825.748099382614 \tabularnewline
57 & 19573 & 23563.4342871473 & -3990.43428714729 \tabularnewline
58 & 24256 & 24417.5947231011 & -161.594723101072 \tabularnewline
59 & 22380 & 19702.6801831285 & 2677.31981687155 \tabularnewline
60 & 16167 & 15685.9790511183 & 481.020948881684 \tabularnewline
61 & 27297 & 29191.1666373898 & -1894.16663738984 \tabularnewline
62 & 28287 & 27571.9845384709 & 715.015461529139 \tabularnewline
63 & 33474 & 35162.9774612737 & -1688.97746127374 \tabularnewline
64 & 28229 & 31579.2846767503 & -3350.28467675026 \tabularnewline
65 & 28785 & 25185.6951426505 & 3599.30485734951 \tabularnewline
66 & 25597 & 28378.1202988418 & -2781.12029884182 \tabularnewline
67 & 18130 & 20185.4181525176 & -2055.41815251762 \tabularnewline
68 & 20198 & 19453.4536623952 & 744.546337604828 \tabularnewline
69 & 22849 & 18995.2068472545 & 3853.79315274554 \tabularnewline
70 & 23118 & 24968.6934981549 & -1850.69349815492 \tabularnewline
71 & 21925 & 21637.4565649336 & 287.543435066429 \tabularnewline
72 & 20801 & 15362.2757354476 & 5438.72426455238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205481&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]31124[/C][C]31525.9345619658[/C][C]-401.934561965812[/C][/ROW]
[ROW][C]14[/C][C]26551[/C][C]26724.2125178225[/C][C]-173.212517822503[/C][/ROW]
[ROW][C]15[/C][C]30651[/C][C]30670.7483772392[/C][C]-19.7483772391643[/C][/ROW]
[ROW][C]16[/C][C]25859[/C][C]25673.7303560441[/C][C]185.26964395594[/C][/ROW]
[ROW][C]17[/C][C]25100[/C][C]24766.727113801[/C][C]333.272886198978[/C][/ROW]
[ROW][C]18[/C][C]25778[/C][C]25361.3732718094[/C][C]416.626728190593[/C][/ROW]
[ROW][C]19[/C][C]20418[/C][C]18397.058129619[/C][C]2020.941870381[/C][/ROW]
[ROW][C]20[/C][C]18688[/C][C]18426.6796295451[/C][C]261.320370454945[/C][/ROW]
[ROW][C]21[/C][C]20424[/C][C]19722.7429731146[/C][C]701.257026885422[/C][/ROW]
[ROW][C]22[/C][C]24776[/C][C]23004.4871591712[/C][C]1771.5128408288[/C][/ROW]
[ROW][C]23[/C][C]19814[/C][C]20134.737501415[/C][C]-320.737501415031[/C][/ROW]
[ROW][C]24[/C][C]12738[/C][C]12049.1943325485[/C][C]688.805667451548[/C][/ROW]
[ROW][C]25[/C][C]31566[/C][C]33624.9698005357[/C][C]-2058.96980053568[/C][/ROW]
[ROW][C]26[/C][C]30111[/C][C]28445.9151240204[/C][C]1665.08487597962[/C][/ROW]
[ROW][C]27[/C][C]30019[/C][C]33087.3957703486[/C][C]-3068.39577034863[/C][/ROW]
[ROW][C]28[/C][C]31934[/C][C]27249.7155238864[/C][C]4684.28447611356[/C][/ROW]
[ROW][C]29[/C][C]25826[/C][C]27889.0667039736[/C][C]-2063.06670397365[/C][/ROW]
[ROW][C]30[/C][C]26835[/C][C]27770.1296778442[/C][C]-935.129677844183[/C][/ROW]
[ROW][C]31[/C][C]20205[/C][C]21460.0917263332[/C][C]-1255.09172633322[/C][/ROW]
[ROW][C]32[/C][C]17789[/C][C]19242.7391644698[/C][C]-1453.73916446982[/C][/ROW]
[ROW][C]33[/C][C]20520[/C][C]20286.1550596033[/C][C]233.844940396742[/C][/ROW]
[ROW][C]34[/C][C]22518[/C][C]24143.9711948359[/C][C]-1625.97119483594[/C][/ROW]
[ROW][C]35[/C][C]15572[/C][C]18762.4882682183[/C][C]-3190.48826821828[/C][/ROW]
[ROW][C]36[/C][C]11509[/C][C]10439.7402095776[/C][C]1069.25979042238[/C][/ROW]
[ROW][C]37[/C][C]25447[/C][C]30273.1072258916[/C][C]-4826.10722589158[/C][/ROW]
[ROW][C]38[/C][C]24090[/C][C]26731.933482557[/C][C]-2641.93348255698[/C][/ROW]
[ROW][C]39[/C][C]27786[/C][C]26776.9921943238[/C][C]1009.00780567621[/C][/ROW]
[ROW][C]40[/C][C]26195[/C][C]27510.8122863765[/C][C]-1315.81228637647[/C][/ROW]
[ROW][C]41[/C][C]20516[/C][C]21642.9688741214[/C][C]-1126.96887412136[/C][/ROW]
[ROW][C]42[/C][C]22759[/C][C]22590.3145758145[/C][C]168.685424185489[/C][/ROW]
[ROW][C]43[/C][C]19028[/C][C]16417.8956273621[/C][C]2610.10437263786[/C][/ROW]
[ROW][C]44[/C][C]16971[/C][C]15307.9552156603[/C][C]1663.04478433972[/C][/ROW]
[ROW][C]45[/C][C]20036[/C][C]18498.2790411795[/C][C]1537.72095882048[/C][/ROW]
[ROW][C]46[/C][C]22485[/C][C]21513.043203967[/C][C]971.956796033006[/C][/ROW]
[ROW][C]47[/C][C]18730[/C][C]15904.7918739856[/C][C]2825.20812601436[/C][/ROW]
[ROW][C]48[/C][C]14538[/C][C]12406.1278626414[/C][C]2131.87213735858[/C][/ROW]
[ROW][C]49[/C][C]27561[/C][C]28580.3201716153[/C][C]-1019.32017161532[/C][/ROW]
[ROW][C]50[/C][C]25985[/C][C]27744.8042429149[/C][C]-1759.80424291494[/C][/ROW]
[ROW][C]51[/C][C]34670[/C][C]30550.9487425155[/C][C]4119.05125748448[/C][/ROW]
[ROW][C]52[/C][C]32066[/C][C]30706.6340117037[/C][C]1359.36598829629[/C][/ROW]
[ROW][C]53[/C][C]27186[/C][C]25826.7054959104[/C][C]1359.29450408957[/C][/ROW]
[ROW][C]54[/C][C]29586[/C][C]28452.3497563315[/C][C]1133.65024366849[/C][/ROW]
[ROW][C]55[/C][C]21359[/C][C]24246.8390980803[/C][C]-2887.83909808031[/C][/ROW]
[ROW][C]56[/C][C]21553[/C][C]20727.2519006174[/C][C]825.748099382614[/C][/ROW]
[ROW][C]57[/C][C]19573[/C][C]23563.4342871473[/C][C]-3990.43428714729[/C][/ROW]
[ROW][C]58[/C][C]24256[/C][C]24417.5947231011[/C][C]-161.594723101072[/C][/ROW]
[ROW][C]59[/C][C]22380[/C][C]19702.6801831285[/C][C]2677.31981687155[/C][/ROW]
[ROW][C]60[/C][C]16167[/C][C]15685.9790511183[/C][C]481.020948881684[/C][/ROW]
[ROW][C]61[/C][C]27297[/C][C]29191.1666373898[/C][C]-1894.16663738984[/C][/ROW]
[ROW][C]62[/C][C]28287[/C][C]27571.9845384709[/C][C]715.015461529139[/C][/ROW]
[ROW][C]63[/C][C]33474[/C][C]35162.9774612737[/C][C]-1688.97746127374[/C][/ROW]
[ROW][C]64[/C][C]28229[/C][C]31579.2846767503[/C][C]-3350.28467675026[/C][/ROW]
[ROW][C]65[/C][C]28785[/C][C]25185.6951426505[/C][C]3599.30485734951[/C][/ROW]
[ROW][C]66[/C][C]25597[/C][C]28378.1202988418[/C][C]-2781.12029884182[/C][/ROW]
[ROW][C]67[/C][C]18130[/C][C]20185.4181525176[/C][C]-2055.41815251762[/C][/ROW]
[ROW][C]68[/C][C]20198[/C][C]19453.4536623952[/C][C]744.546337604828[/C][/ROW]
[ROW][C]69[/C][C]22849[/C][C]18995.2068472545[/C][C]3853.79315274554[/C][/ROW]
[ROW][C]70[/C][C]23118[/C][C]24968.6934981549[/C][C]-1850.69349815492[/C][/ROW]
[ROW][C]71[/C][C]21925[/C][C]21637.4565649336[/C][C]287.543435066429[/C][/ROW]
[ROW][C]72[/C][C]20801[/C][C]15362.2757354476[/C][C]5438.72426455238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205481&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205481&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
133112431525.9345619658-401.934561965812
142655126724.2125178225-173.212517822503
153065130670.7483772392-19.7483772391643
162585925673.7303560441185.26964395594
172510024766.727113801333.272886198978
182577825361.3732718094416.626728190593
192041818397.0581296192020.941870381
201868818426.6796295451261.320370454945
212042419722.7429731146701.257026885422
222477623004.48715917121771.5128408288
231981420134.737501415-320.737501415031
241273812049.1943325485688.805667451548
253156633624.9698005357-2058.96980053568
263011128445.91512402041665.08487597962
273001933087.3957703486-3068.39577034863
283193427249.71552388644684.28447611356
292582627889.0667039736-2063.06670397365
302683527770.1296778442-935.129677844183
312020521460.0917263332-1255.09172633322
321778919242.7391644698-1453.73916446982
332052020286.1550596033233.844940396742
342251824143.9711948359-1625.97119483594
351557218762.4882682183-3190.48826821828
361150910439.74020957761069.25979042238
372544730273.1072258916-4826.10722589158
382409026731.933482557-2641.93348255698
392778626776.99219432381009.00780567621
402619527510.8122863765-1315.81228637647
412051621642.9688741214-1126.96887412136
422275922590.3145758145168.685424185489
431902816417.89562736212610.10437263786
441697115307.95521566031663.04478433972
452003618498.27904117951537.72095882048
462248521513.043203967971.956796033006
471873015904.79187398562825.20812601436
481453812406.12786264142131.87213735858
492756128580.3201716153-1019.32017161532
502598527744.8042429149-1759.80424291494
513467030550.94874251554119.05125748448
523206630706.63401170371359.36598829629
532718625826.70549591041359.29450408957
542958628452.34975633151133.65024366849
552135924246.8390980803-2887.83909808031
562155320727.2519006174825.748099382614
571957323563.4342871473-3990.43428714729
582425624417.5947231011-161.594723101072
592238019702.68018312852677.31981687155
601616715685.9790511183481.020948881684
612729729191.1666373898-1894.16663738984
622828727571.9845384709715.015461529139
633347435162.9774612737-1688.97746127374
642822931579.2846767503-3350.28467675026
652878525185.69514265053599.30485734951
662559728378.1202988418-2781.12029884182
671813020185.4181525176-2055.41815251762
682019819453.4536623952744.546337604828
692284918995.20684725453853.79315274554
702311824968.6934981549-1850.69349815492
712192521637.4565649336287.543435066429
722080115362.27573544765438.72426455238







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7328848.959103046524582.024285644233115.8939204488
7429609.1636419825127.280210688234091.0470732719
7535338.976175871530651.991489805640025.9608619375
7631170.708433312826287.228956224336054.1879104013
7730569.944749567525497.576647894135642.3128512408
7828275.755940708523021.285033509433530.2268479075
7921469.337127347516038.866533528826899.8077211661
8023298.050876712617697.108346561328898.9934068639
8124710.4983949318944.121405711730476.8753841483
8225574.284086405419647.08829602431501.4798767867
8324288.871852274918205.106875449930372.6368290999
8421416.945804195815180.541179015527653.3504293761

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 28848.9591030465 & 24582.0242856442 & 33115.8939204488 \tabularnewline
74 & 29609.16364198 & 25127.2802106882 & 34091.0470732719 \tabularnewline
75 & 35338.9761758715 & 30651.9914898056 & 40025.9608619375 \tabularnewline
76 & 31170.7084333128 & 26287.2289562243 & 36054.1879104013 \tabularnewline
77 & 30569.9447495675 & 25497.5766478941 & 35642.3128512408 \tabularnewline
78 & 28275.7559407085 & 23021.2850335094 & 33530.2268479075 \tabularnewline
79 & 21469.3371273475 & 16038.8665335288 & 26899.8077211661 \tabularnewline
80 & 23298.0508767126 & 17697.1083465613 & 28898.9934068639 \tabularnewline
81 & 24710.49839493 & 18944.1214057117 & 30476.8753841483 \tabularnewline
82 & 25574.2840864054 & 19647.088296024 & 31501.4798767867 \tabularnewline
83 & 24288.8718522749 & 18205.1068754499 & 30372.6368290999 \tabularnewline
84 & 21416.9458041958 & 15180.5411790155 & 27653.3504293761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205481&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]28848.9591030465[/C][C]24582.0242856442[/C][C]33115.8939204488[/C][/ROW]
[ROW][C]74[/C][C]29609.16364198[/C][C]25127.2802106882[/C][C]34091.0470732719[/C][/ROW]
[ROW][C]75[/C][C]35338.9761758715[/C][C]30651.9914898056[/C][C]40025.9608619375[/C][/ROW]
[ROW][C]76[/C][C]31170.7084333128[/C][C]26287.2289562243[/C][C]36054.1879104013[/C][/ROW]
[ROW][C]77[/C][C]30569.9447495675[/C][C]25497.5766478941[/C][C]35642.3128512408[/C][/ROW]
[ROW][C]78[/C][C]28275.7559407085[/C][C]23021.2850335094[/C][C]33530.2268479075[/C][/ROW]
[ROW][C]79[/C][C]21469.3371273475[/C][C]16038.8665335288[/C][C]26899.8077211661[/C][/ROW]
[ROW][C]80[/C][C]23298.0508767126[/C][C]17697.1083465613[/C][C]28898.9934068639[/C][/ROW]
[ROW][C]81[/C][C]24710.49839493[/C][C]18944.1214057117[/C][C]30476.8753841483[/C][/ROW]
[ROW][C]82[/C][C]25574.2840864054[/C][C]19647.088296024[/C][C]31501.4798767867[/C][/ROW]
[ROW][C]83[/C][C]24288.8718522749[/C][C]18205.1068754499[/C][C]30372.6368290999[/C][/ROW]
[ROW][C]84[/C][C]21416.9458041958[/C][C]15180.5411790155[/C][C]27653.3504293761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205481&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205481&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
7328848.959103046524582.024285644233115.8939204488
7429609.1636419825127.280210688234091.0470732719
7535338.976175871530651.991489805640025.9608619375
7631170.708433312826287.228956224336054.1879104013
7730569.944749567525497.576647894135642.3128512408
7828275.755940708523021.285033509433530.2268479075
7921469.337127347516038.866533528826899.8077211661
8023298.050876712617697.108346561328898.9934068639
8124710.4983949318944.121405711730476.8753841483
8225574.284086405419647.08829602431501.4798767867
8324288.871852274918205.106875449930372.6368290999
8421416.945804195815180.541179015527653.3504293761



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')