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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Jun 2010 16:03:24 +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/2010/Jun/06/t12758403013ujazyv8ltrtfbv.htm/, Retrieved Sun, 28 Apr 2024 14:14:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=77734, Retrieved Sun, 28 Apr 2024 14:14:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-06-06 16:03:24] [07915b1f88a41fb8d82e27c5eaa7bbed] [Current]
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Dataseries X:
25000
25284
12434,5
33955
14980,5
50831
4198,5
34566
35000
11055,5
20807
21887,29
16977,5
19613,5
14570
24416,5
16825,5
13980
21450,5
27239,5
19078,5
20459,1
20373,5
19306,5
16723,16
11638
20917
17903,5
28218,5
15268
21555
23143
16691
17932,5
30512
41931,5
10853,5
25939,5
14900
25127,76
22063,5
25306,5
31217,5
23201,5
38148
26264
16359
27945,5
16218,5
36003,5
20323,5
20100,5
18741
24426,75
19174,5
13766
18999
21745
34469
13248
16218,5
36003,5
20323,5
20100,5
18741
24426,75
19174,5
13766
18999
21745
34469
13248




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77734&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77734&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77734&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0336469139053757
beta0
gamma0.609625489191882

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0336469139053757 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.609625489191882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77734&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]0.0336469139053757[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.609625489191882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77734&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77734&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
alpha0.0336469139053757
beta0
gamma0.609625489191882







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1316977.522771.3540372475-5793.85403724749
1419613.524798.8462292759-5185.34622927591
151457020549.5419977966-5979.54199779656
1624416.530466.4280296698-6049.92802966979
1716825.522298.1124554551-5472.6124554551
181398019394.0713519956-5414.07135199558
1921450.55229.817476004116220.6825239959
2027239.536713.6350510421-9474.13505104208
2119078.536976.1513113184-17897.6513113184
2220459.112737.90891187147721.1910881286
2320373.523069.7656636606-2696.26566366062
2419306.525517.9179783427-6211.41797834274
2516723.1617802.5204593696-1079.36045936962
261163820347.1209589263-8709.12095892627
272091715511.38115518645405.6188448136
2817903.525769.8773540533-7866.37735405335
2928218.517880.548248659310337.9517513407
301526815542.9711906244-274.971190624361
312155514296.95716529217258.04283470785
322314330342.0463586541-7199.04635865411
331669125718.7054146535-9027.7054146535
3417932.516871.31453728031061.18546271967
353051220842.01852794889669.9814720512
3641931.521635.43330766620296.066692334
3710853.517835.2950710850-6981.79507108503
3825939.515686.502156578710252.9978434213
391490019803.9625156947-4903.96251569465
4025127.7621896.86134585693230.89865414311
4122063.525105.3368709417-3041.83687094168
4225306.516065.35532570969241.14467429043
4331217.519577.329285032611640.1707149674
4423201.527252.9975360085-4051.49753600847
453814821658.274209131716489.7257908683
462626419612.96768451566651.03231548444
471635928843.3104850334-12484.3104850334
4827945.535151.2716774774-7205.77167747736
4916218.514356.02557786181862.47442213818
5036003.522658.063745136413345.4362548636
5120323.517950.40555834462373.09444165539
5220100.525080.5112122902-4980.01121229021
531874124317.3619506090-5576.36195060897
5424426.7522428.17137320251998.57862679745
5519174.527109.7538985344-7935.25389853443
561376624882.5963448535-11116.5963448535
571899931151.2656571527-12152.2656571527
582174522346.1376306901-601.137630690089
593446920059.579042156714409.4209578433
601324830382.0896295068-17134.0896295068
6116218.514595.01222286921623.48777713078
6236003.529653.77675086976349.72324913032
6320323.518246.7800200732076.71997992701
6420100.521035.0999800472-934.599980047198
651874120056.7480673259-1315.74806732592
6624426.7522773.4135485661653.33645143401
6719174.521591.2251625127-2416.72516251267
681376617675.5773732447-3909.57737324467
691899923576.613887111-4577.61388711099
702174521831.2746635361-86.2746635361218
713446928404.96192432866064.03807567137
721324819863.9690645763-6615.96906457627

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 16977.5 & 22771.3540372475 & -5793.85403724749 \tabularnewline
14 & 19613.5 & 24798.8462292759 & -5185.34622927591 \tabularnewline
15 & 14570 & 20549.5419977966 & -5979.54199779656 \tabularnewline
16 & 24416.5 & 30466.4280296698 & -6049.92802966979 \tabularnewline
17 & 16825.5 & 22298.1124554551 & -5472.6124554551 \tabularnewline
18 & 13980 & 19394.0713519956 & -5414.07135199558 \tabularnewline
19 & 21450.5 & 5229.8174760041 & 16220.6825239959 \tabularnewline
20 & 27239.5 & 36713.6350510421 & -9474.13505104208 \tabularnewline
21 & 19078.5 & 36976.1513113184 & -17897.6513113184 \tabularnewline
22 & 20459.1 & 12737.9089118714 & 7721.1910881286 \tabularnewline
23 & 20373.5 & 23069.7656636606 & -2696.26566366062 \tabularnewline
24 & 19306.5 & 25517.9179783427 & -6211.41797834274 \tabularnewline
25 & 16723.16 & 17802.5204593696 & -1079.36045936962 \tabularnewline
26 & 11638 & 20347.1209589263 & -8709.12095892627 \tabularnewline
27 & 20917 & 15511.3811551864 & 5405.6188448136 \tabularnewline
28 & 17903.5 & 25769.8773540533 & -7866.37735405335 \tabularnewline
29 & 28218.5 & 17880.5482486593 & 10337.9517513407 \tabularnewline
30 & 15268 & 15542.9711906244 & -274.971190624361 \tabularnewline
31 & 21555 & 14296.9571652921 & 7258.04283470785 \tabularnewline
32 & 23143 & 30342.0463586541 & -7199.04635865411 \tabularnewline
33 & 16691 & 25718.7054146535 & -9027.7054146535 \tabularnewline
34 & 17932.5 & 16871.3145372803 & 1061.18546271967 \tabularnewline
35 & 30512 & 20842.0185279488 & 9669.9814720512 \tabularnewline
36 & 41931.5 & 21635.433307666 & 20296.066692334 \tabularnewline
37 & 10853.5 & 17835.2950710850 & -6981.79507108503 \tabularnewline
38 & 25939.5 & 15686.5021565787 & 10252.9978434213 \tabularnewline
39 & 14900 & 19803.9625156947 & -4903.96251569465 \tabularnewline
40 & 25127.76 & 21896.8613458569 & 3230.89865414311 \tabularnewline
41 & 22063.5 & 25105.3368709417 & -3041.83687094168 \tabularnewline
42 & 25306.5 & 16065.3553257096 & 9241.14467429043 \tabularnewline
43 & 31217.5 & 19577.3292850326 & 11640.1707149674 \tabularnewline
44 & 23201.5 & 27252.9975360085 & -4051.49753600847 \tabularnewline
45 & 38148 & 21658.2742091317 & 16489.7257908683 \tabularnewline
46 & 26264 & 19612.9676845156 & 6651.03231548444 \tabularnewline
47 & 16359 & 28843.3104850334 & -12484.3104850334 \tabularnewline
48 & 27945.5 & 35151.2716774774 & -7205.77167747736 \tabularnewline
49 & 16218.5 & 14356.0255778618 & 1862.47442213818 \tabularnewline
50 & 36003.5 & 22658.0637451364 & 13345.4362548636 \tabularnewline
51 & 20323.5 & 17950.4055583446 & 2373.09444165539 \tabularnewline
52 & 20100.5 & 25080.5112122902 & -4980.01121229021 \tabularnewline
53 & 18741 & 24317.3619506090 & -5576.36195060897 \tabularnewline
54 & 24426.75 & 22428.1713732025 & 1998.57862679745 \tabularnewline
55 & 19174.5 & 27109.7538985344 & -7935.25389853443 \tabularnewline
56 & 13766 & 24882.5963448535 & -11116.5963448535 \tabularnewline
57 & 18999 & 31151.2656571527 & -12152.2656571527 \tabularnewline
58 & 21745 & 22346.1376306901 & -601.137630690089 \tabularnewline
59 & 34469 & 20059.5790421567 & 14409.4209578433 \tabularnewline
60 & 13248 & 30382.0896295068 & -17134.0896295068 \tabularnewline
61 & 16218.5 & 14595.0122228692 & 1623.48777713078 \tabularnewline
62 & 36003.5 & 29653.7767508697 & 6349.72324913032 \tabularnewline
63 & 20323.5 & 18246.780020073 & 2076.71997992701 \tabularnewline
64 & 20100.5 & 21035.0999800472 & -934.599980047198 \tabularnewline
65 & 18741 & 20056.7480673259 & -1315.74806732592 \tabularnewline
66 & 24426.75 & 22773.413548566 & 1653.33645143401 \tabularnewline
67 & 19174.5 & 21591.2251625127 & -2416.72516251267 \tabularnewline
68 & 13766 & 17675.5773732447 & -3909.57737324467 \tabularnewline
69 & 18999 & 23576.613887111 & -4577.61388711099 \tabularnewline
70 & 21745 & 21831.2746635361 & -86.2746635361218 \tabularnewline
71 & 34469 & 28404.9619243286 & 6064.03807567137 \tabularnewline
72 & 13248 & 19863.9690645763 & -6615.96906457627 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77734&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]16977.5[/C][C]22771.3540372475[/C][C]-5793.85403724749[/C][/ROW]
[ROW][C]14[/C][C]19613.5[/C][C]24798.8462292759[/C][C]-5185.34622927591[/C][/ROW]
[ROW][C]15[/C][C]14570[/C][C]20549.5419977966[/C][C]-5979.54199779656[/C][/ROW]
[ROW][C]16[/C][C]24416.5[/C][C]30466.4280296698[/C][C]-6049.92802966979[/C][/ROW]
[ROW][C]17[/C][C]16825.5[/C][C]22298.1124554551[/C][C]-5472.6124554551[/C][/ROW]
[ROW][C]18[/C][C]13980[/C][C]19394.0713519956[/C][C]-5414.07135199558[/C][/ROW]
[ROW][C]19[/C][C]21450.5[/C][C]5229.8174760041[/C][C]16220.6825239959[/C][/ROW]
[ROW][C]20[/C][C]27239.5[/C][C]36713.6350510421[/C][C]-9474.13505104208[/C][/ROW]
[ROW][C]21[/C][C]19078.5[/C][C]36976.1513113184[/C][C]-17897.6513113184[/C][/ROW]
[ROW][C]22[/C][C]20459.1[/C][C]12737.9089118714[/C][C]7721.1910881286[/C][/ROW]
[ROW][C]23[/C][C]20373.5[/C][C]23069.7656636606[/C][C]-2696.26566366062[/C][/ROW]
[ROW][C]24[/C][C]19306.5[/C][C]25517.9179783427[/C][C]-6211.41797834274[/C][/ROW]
[ROW][C]25[/C][C]16723.16[/C][C]17802.5204593696[/C][C]-1079.36045936962[/C][/ROW]
[ROW][C]26[/C][C]11638[/C][C]20347.1209589263[/C][C]-8709.12095892627[/C][/ROW]
[ROW][C]27[/C][C]20917[/C][C]15511.3811551864[/C][C]5405.6188448136[/C][/ROW]
[ROW][C]28[/C][C]17903.5[/C][C]25769.8773540533[/C][C]-7866.37735405335[/C][/ROW]
[ROW][C]29[/C][C]28218.5[/C][C]17880.5482486593[/C][C]10337.9517513407[/C][/ROW]
[ROW][C]30[/C][C]15268[/C][C]15542.9711906244[/C][C]-274.971190624361[/C][/ROW]
[ROW][C]31[/C][C]21555[/C][C]14296.9571652921[/C][C]7258.04283470785[/C][/ROW]
[ROW][C]32[/C][C]23143[/C][C]30342.0463586541[/C][C]-7199.04635865411[/C][/ROW]
[ROW][C]33[/C][C]16691[/C][C]25718.7054146535[/C][C]-9027.7054146535[/C][/ROW]
[ROW][C]34[/C][C]17932.5[/C][C]16871.3145372803[/C][C]1061.18546271967[/C][/ROW]
[ROW][C]35[/C][C]30512[/C][C]20842.0185279488[/C][C]9669.9814720512[/C][/ROW]
[ROW][C]36[/C][C]41931.5[/C][C]21635.433307666[/C][C]20296.066692334[/C][/ROW]
[ROW][C]37[/C][C]10853.5[/C][C]17835.2950710850[/C][C]-6981.79507108503[/C][/ROW]
[ROW][C]38[/C][C]25939.5[/C][C]15686.5021565787[/C][C]10252.9978434213[/C][/ROW]
[ROW][C]39[/C][C]14900[/C][C]19803.9625156947[/C][C]-4903.96251569465[/C][/ROW]
[ROW][C]40[/C][C]25127.76[/C][C]21896.8613458569[/C][C]3230.89865414311[/C][/ROW]
[ROW][C]41[/C][C]22063.5[/C][C]25105.3368709417[/C][C]-3041.83687094168[/C][/ROW]
[ROW][C]42[/C][C]25306.5[/C][C]16065.3553257096[/C][C]9241.14467429043[/C][/ROW]
[ROW][C]43[/C][C]31217.5[/C][C]19577.3292850326[/C][C]11640.1707149674[/C][/ROW]
[ROW][C]44[/C][C]23201.5[/C][C]27252.9975360085[/C][C]-4051.49753600847[/C][/ROW]
[ROW][C]45[/C][C]38148[/C][C]21658.2742091317[/C][C]16489.7257908683[/C][/ROW]
[ROW][C]46[/C][C]26264[/C][C]19612.9676845156[/C][C]6651.03231548444[/C][/ROW]
[ROW][C]47[/C][C]16359[/C][C]28843.3104850334[/C][C]-12484.3104850334[/C][/ROW]
[ROW][C]48[/C][C]27945.5[/C][C]35151.2716774774[/C][C]-7205.77167747736[/C][/ROW]
[ROW][C]49[/C][C]16218.5[/C][C]14356.0255778618[/C][C]1862.47442213818[/C][/ROW]
[ROW][C]50[/C][C]36003.5[/C][C]22658.0637451364[/C][C]13345.4362548636[/C][/ROW]
[ROW][C]51[/C][C]20323.5[/C][C]17950.4055583446[/C][C]2373.09444165539[/C][/ROW]
[ROW][C]52[/C][C]20100.5[/C][C]25080.5112122902[/C][C]-4980.01121229021[/C][/ROW]
[ROW][C]53[/C][C]18741[/C][C]24317.3619506090[/C][C]-5576.36195060897[/C][/ROW]
[ROW][C]54[/C][C]24426.75[/C][C]22428.1713732025[/C][C]1998.57862679745[/C][/ROW]
[ROW][C]55[/C][C]19174.5[/C][C]27109.7538985344[/C][C]-7935.25389853443[/C][/ROW]
[ROW][C]56[/C][C]13766[/C][C]24882.5963448535[/C][C]-11116.5963448535[/C][/ROW]
[ROW][C]57[/C][C]18999[/C][C]31151.2656571527[/C][C]-12152.2656571527[/C][/ROW]
[ROW][C]58[/C][C]21745[/C][C]22346.1376306901[/C][C]-601.137630690089[/C][/ROW]
[ROW][C]59[/C][C]34469[/C][C]20059.5790421567[/C][C]14409.4209578433[/C][/ROW]
[ROW][C]60[/C][C]13248[/C][C]30382.0896295068[/C][C]-17134.0896295068[/C][/ROW]
[ROW][C]61[/C][C]16218.5[/C][C]14595.0122228692[/C][C]1623.48777713078[/C][/ROW]
[ROW][C]62[/C][C]36003.5[/C][C]29653.7767508697[/C][C]6349.72324913032[/C][/ROW]
[ROW][C]63[/C][C]20323.5[/C][C]18246.780020073[/C][C]2076.71997992701[/C][/ROW]
[ROW][C]64[/C][C]20100.5[/C][C]21035.0999800472[/C][C]-934.599980047198[/C][/ROW]
[ROW][C]65[/C][C]18741[/C][C]20056.7480673259[/C][C]-1315.74806732592[/C][/ROW]
[ROW][C]66[/C][C]24426.75[/C][C]22773.413548566[/C][C]1653.33645143401[/C][/ROW]
[ROW][C]67[/C][C]19174.5[/C][C]21591.2251625127[/C][C]-2416.72516251267[/C][/ROW]
[ROW][C]68[/C][C]13766[/C][C]17675.5773732447[/C][C]-3909.57737324467[/C][/ROW]
[ROW][C]69[/C][C]18999[/C][C]23576.613887111[/C][C]-4577.61388711099[/C][/ROW]
[ROW][C]70[/C][C]21745[/C][C]21831.2746635361[/C][C]-86.2746635361218[/C][/ROW]
[ROW][C]71[/C][C]34469[/C][C]28404.9619243286[/C][C]6064.03807567137[/C][/ROW]
[ROW][C]72[/C][C]13248[/C][C]19863.9690645763[/C][C]-6615.96906457627[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77734&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77734&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
1316977.522771.3540372475-5793.85403724749
1419613.524798.8462292759-5185.34622927591
151457020549.5419977966-5979.54199779656
1624416.530466.4280296698-6049.92802966979
1716825.522298.1124554551-5472.6124554551
181398019394.0713519956-5414.07135199558
1921450.55229.817476004116220.6825239959
2027239.536713.6350510421-9474.13505104208
2119078.536976.1513113184-17897.6513113184
2220459.112737.90891187147721.1910881286
2320373.523069.7656636606-2696.26566366062
2419306.525517.9179783427-6211.41797834274
2516723.1617802.5204593696-1079.36045936962
261163820347.1209589263-8709.12095892627
272091715511.38115518645405.6188448136
2817903.525769.8773540533-7866.37735405335
2928218.517880.548248659310337.9517513407
301526815542.9711906244-274.971190624361
312155514296.95716529217258.04283470785
322314330342.0463586541-7199.04635865411
331669125718.7054146535-9027.7054146535
3417932.516871.31453728031061.18546271967
353051220842.01852794889669.9814720512
3641931.521635.43330766620296.066692334
3710853.517835.2950710850-6981.79507108503
3825939.515686.502156578710252.9978434213
391490019803.9625156947-4903.96251569465
4025127.7621896.86134585693230.89865414311
4122063.525105.3368709417-3041.83687094168
4225306.516065.35532570969241.14467429043
4331217.519577.329285032611640.1707149674
4423201.527252.9975360085-4051.49753600847
453814821658.274209131716489.7257908683
462626419612.96768451566651.03231548444
471635928843.3104850334-12484.3104850334
4827945.535151.2716774774-7205.77167747736
4916218.514356.02557786181862.47442213818
5036003.522658.063745136413345.4362548636
5120323.517950.40555834462373.09444165539
5220100.525080.5112122902-4980.01121229021
531874124317.3619506090-5576.36195060897
5424426.7522428.17137320251998.57862679745
5519174.527109.7538985344-7935.25389853443
561376624882.5963448535-11116.5963448535
571899931151.2656571527-12152.2656571527
582174522346.1376306901-601.137630690089
593446920059.579042156714409.4209578433
601324830382.0896295068-17134.0896295068
6116218.514595.01222286921623.48777713078
6236003.529653.77675086976349.72324913032
6320323.518246.7800200732076.71997992701
6420100.521035.0999800472-934.599980047198
651874120056.7480673259-1315.74806732592
6624426.7522773.4135485661653.33645143401
6719174.521591.2251625127-2416.72516251267
681376617675.5773732447-3909.57737324467
691899923576.613887111-4577.61388711099
702174521831.2746635361-86.2746635361218
713446928404.96192432866064.03807567137
721324819863.9690645763-6615.96906457627







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7315481.1355231699-926.5926306681231888.863677008
7433269.56369008816852.550447388649686.5769327874
7519131.63457241712705.3414893235735557.9276555106
7620076.07015456073640.5024706502136511.6378384712
7718904.62517354002459.7881195245135349.4622275554
7823414.68920873226960.588006483639868.7904109807
7919779.14302136573315.7828839406436242.5031587907
8015065.3512252687-1407.2626430665931537.965093604
8120704.38364174964222.5212380043837186.2460454948
8221758.97544624045267.8696938444638250.0811986364
8331958.797680071315458.453757067048459.1416030756
8415743.8056112086-765.77131305390332253.3825354712

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 15481.1355231699 & -926.59263066812 & 31888.863677008 \tabularnewline
74 & 33269.563690088 & 16852.5504473886 & 49686.5769327874 \tabularnewline
75 & 19131.6345724171 & 2705.34148932357 & 35557.9276555106 \tabularnewline
76 & 20076.0701545607 & 3640.50247065021 & 36511.6378384712 \tabularnewline
77 & 18904.6251735400 & 2459.78811952451 & 35349.4622275554 \tabularnewline
78 & 23414.6892087322 & 6960.5880064836 & 39868.7904109807 \tabularnewline
79 & 19779.1430213657 & 3315.78288394064 & 36242.5031587907 \tabularnewline
80 & 15065.3512252687 & -1407.26264306659 & 31537.965093604 \tabularnewline
81 & 20704.3836417496 & 4222.52123800438 & 37186.2460454948 \tabularnewline
82 & 21758.9754462404 & 5267.86969384446 & 38250.0811986364 \tabularnewline
83 & 31958.7976800713 & 15458.4537570670 & 48459.1416030756 \tabularnewline
84 & 15743.8056112086 & -765.771313053903 & 32253.3825354712 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=77734&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]15481.1355231699[/C][C]-926.59263066812[/C][C]31888.863677008[/C][/ROW]
[ROW][C]74[/C][C]33269.563690088[/C][C]16852.5504473886[/C][C]49686.5769327874[/C][/ROW]
[ROW][C]75[/C][C]19131.6345724171[/C][C]2705.34148932357[/C][C]35557.9276555106[/C][/ROW]
[ROW][C]76[/C][C]20076.0701545607[/C][C]3640.50247065021[/C][C]36511.6378384712[/C][/ROW]
[ROW][C]77[/C][C]18904.6251735400[/C][C]2459.78811952451[/C][C]35349.4622275554[/C][/ROW]
[ROW][C]78[/C][C]23414.6892087322[/C][C]6960.5880064836[/C][C]39868.7904109807[/C][/ROW]
[ROW][C]79[/C][C]19779.1430213657[/C][C]3315.78288394064[/C][C]36242.5031587907[/C][/ROW]
[ROW][C]80[/C][C]15065.3512252687[/C][C]-1407.26264306659[/C][C]31537.965093604[/C][/ROW]
[ROW][C]81[/C][C]20704.3836417496[/C][C]4222.52123800438[/C][C]37186.2460454948[/C][/ROW]
[ROW][C]82[/C][C]21758.9754462404[/C][C]5267.86969384446[/C][C]38250.0811986364[/C][/ROW]
[ROW][C]83[/C][C]31958.7976800713[/C][C]15458.4537570670[/C][C]48459.1416030756[/C][/ROW]
[ROW][C]84[/C][C]15743.8056112086[/C][C]-765.771313053903[/C][C]32253.3825354712[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=77734&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=77734&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
7315481.1355231699-926.5926306681231888.863677008
7433269.56369008816852.550447388649686.5769327874
7519131.63457241712705.3414893235735557.9276555106
7620076.07015456073640.5024706502136511.6378384712
7718904.62517354002459.7881195245135349.4622275554
7823414.68920873226960.588006483639868.7904109807
7919779.14302136573315.7828839406436242.5031587907
8015065.3512252687-1407.2626430665931537.965093604
8120704.38364174964222.5212380043837186.2460454948
8221758.97544624045267.8696938444638250.0811986364
8331958.797680071315458.453757067048459.1416030756
8415743.8056112086-765.77131305390332253.3825354712



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')