Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 25 Apr 2016 11:39:09 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/25/t1461580808s4f55u82chiekyx.htm/, Retrieved Thu, 09 May 2024 21:22:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294689, Retrieved Thu, 09 May 2024 21:22:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-25 10:39:09] [c1931050b1d666e3090788e81f04199e] [Current]
- R P     [Exponential Smoothing] [] [2016-05-03 09:13:08] [0fac179d48b12d87f452d447736804ac]
- RMPD    [Bootstrap Plot - Central Tendency] [] [2016-05-03 09:26:57] [0fac179d48b12d87f452d447736804ac]
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Dataseries X:
4736
4840
4413
4571
4106
4801
3956
3829
4453
4027
4121
4798
3233
3554
3952
3951
3685
4312
3867
4140
4114
3818
3377
3453
3502
4017
5410
5184
5529
6434
4962
2980
2937
3023
2731
3163
3146
3173
3724
3224
4114
3450
2957
3882
4284
4181
3760
4457
4167
3962
5247
5157
3697
3514
3786
3297
3571
3871
3492
3051
3735
3645
4852
4232
3804
4464
4259
3373
4134
4488
3333
4772
4929
5555
7183
9266
4003
3051
3507
3273
3942
3216
3232
3593




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294689&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294689&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294689&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.549951023915406
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.549951023915406 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294689&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]0.549951023915406[/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=294689&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294689&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
alpha0.549951023915406
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1332333475.99346963565-242.99346963565
1435543635.41124175158-81.4112417515762
1539523960.20759885758-8.20759885757889
1639513943.547498107557.45250189244643
1736853687.13881766717-2.13881766717304
1843124372.58790774295-60.5879077429518
1938673507.19389379001359.806106209986
2041403654.15916915549485.840830844509
2141144603.99269052276-489.992690522761
2238183929.48957769919-111.489577699195
2333773966.2149123787-589.214912378702
2434534239.86210717385-786.86210717385
2535022469.66461576561032.3353842344
2640173378.79733693817638.202663061835
2754104153.860117655941256.13988234406
2851844846.08179089469337.918209105306
2955294703.37678392975825.623216070252
3064346096.47160154584337.528398454157
3149625347.75345996853-385.753459968526
3229805134.27099399967-2154.27099399967
3329374167.11792689324-1230.11792689324
3430233285.799958616-262.799958615999
3527313019.93403199535-288.934031995349
3631633252.29238056144-89.2923805614373
3731462639.19382644302506.806173556982
3831733026.66860624804146.331393751962
3937243579.41378313056144.58621686944
4032243365.28386943372-141.283869433721
4141143185.16374706282928.836252937181
4234504160.97027043373-710.970270433727
4329573014.55692393449-57.5569239344932
4438822318.956855590631563.04314440937
4542843741.77643351038542.22356648962
4641814361.54631962597-180.54631962597
4737604076.98858855594-316.988588555939
4844574604.95024191718-147.950241917182
4941674083.790988177583.2090118225001
5039624067.43124170638-105.431241706383
5152474613.52498947583633.475010524166
5251574408.61379037105748.386209628951
5336975319.5862888327-1622.5862888327
5435144100.45237461397-586.452374613966
5537863275.39244395426510.607556045737
5632973412.17875264251-115.17875264251
5735713418.58030478166152.41969521834
5838713492.12547521366378.87452478634
5934923473.1273612270418.8726387729603
6030514200.88030345826-1149.88030345826
6137353292.66097295228442.339027047721
6236453405.65476851651239.345231483492
6348524351.29039818039500.709601819607
6442324154.688057032877.3119429672006
6538043609.4868358689194.513164131103
6644643834.23784792159629.762152078406
6742594154.79706495227104.202935047731
6833733740.78890013843-367.788900138431
6941343743.18827419066390.811725809341
7044884052.58756075839435.412439241608
7133333863.50754039384-530.507540393835
7247723674.403701477261097.59629852274
7349294891.0497505360437.950249463961
7455554625.76751206444929.232487935558
7571836448.19400670231734.805993297688
7692665931.392211838283334.60778816172
7740036806.20009983782-2803.20009983782
7830515679.74465653584-2628.74465653584
7935073982.93664240292-475.936642402925
8032733111.96037507528161.039624924722
8139423707.92097643141234.079023568589
8232163930.35484471544-714.354844715442
8332322835.84387544918396.156124550821
8435933752.35338979882-159.353389798823

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 3233 & 3475.99346963565 & -242.99346963565 \tabularnewline
14 & 3554 & 3635.41124175158 & -81.4112417515762 \tabularnewline
15 & 3952 & 3960.20759885758 & -8.20759885757889 \tabularnewline
16 & 3951 & 3943.54749810755 & 7.45250189244643 \tabularnewline
17 & 3685 & 3687.13881766717 & -2.13881766717304 \tabularnewline
18 & 4312 & 4372.58790774295 & -60.5879077429518 \tabularnewline
19 & 3867 & 3507.19389379001 & 359.806106209986 \tabularnewline
20 & 4140 & 3654.15916915549 & 485.840830844509 \tabularnewline
21 & 4114 & 4603.99269052276 & -489.992690522761 \tabularnewline
22 & 3818 & 3929.48957769919 & -111.489577699195 \tabularnewline
23 & 3377 & 3966.2149123787 & -589.214912378702 \tabularnewline
24 & 3453 & 4239.86210717385 & -786.86210717385 \tabularnewline
25 & 3502 & 2469.6646157656 & 1032.3353842344 \tabularnewline
26 & 4017 & 3378.79733693817 & 638.202663061835 \tabularnewline
27 & 5410 & 4153.86011765594 & 1256.13988234406 \tabularnewline
28 & 5184 & 4846.08179089469 & 337.918209105306 \tabularnewline
29 & 5529 & 4703.37678392975 & 825.623216070252 \tabularnewline
30 & 6434 & 6096.47160154584 & 337.528398454157 \tabularnewline
31 & 4962 & 5347.75345996853 & -385.753459968526 \tabularnewline
32 & 2980 & 5134.27099399967 & -2154.27099399967 \tabularnewline
33 & 2937 & 4167.11792689324 & -1230.11792689324 \tabularnewline
34 & 3023 & 3285.799958616 & -262.799958615999 \tabularnewline
35 & 2731 & 3019.93403199535 & -288.934031995349 \tabularnewline
36 & 3163 & 3252.29238056144 & -89.2923805614373 \tabularnewline
37 & 3146 & 2639.19382644302 & 506.806173556982 \tabularnewline
38 & 3173 & 3026.66860624804 & 146.331393751962 \tabularnewline
39 & 3724 & 3579.41378313056 & 144.58621686944 \tabularnewline
40 & 3224 & 3365.28386943372 & -141.283869433721 \tabularnewline
41 & 4114 & 3185.16374706282 & 928.836252937181 \tabularnewline
42 & 3450 & 4160.97027043373 & -710.970270433727 \tabularnewline
43 & 2957 & 3014.55692393449 & -57.5569239344932 \tabularnewline
44 & 3882 & 2318.95685559063 & 1563.04314440937 \tabularnewline
45 & 4284 & 3741.77643351038 & 542.22356648962 \tabularnewline
46 & 4181 & 4361.54631962597 & -180.54631962597 \tabularnewline
47 & 3760 & 4076.98858855594 & -316.988588555939 \tabularnewline
48 & 4457 & 4604.95024191718 & -147.950241917182 \tabularnewline
49 & 4167 & 4083.7909881775 & 83.2090118225001 \tabularnewline
50 & 3962 & 4067.43124170638 & -105.431241706383 \tabularnewline
51 & 5247 & 4613.52498947583 & 633.475010524166 \tabularnewline
52 & 5157 & 4408.61379037105 & 748.386209628951 \tabularnewline
53 & 3697 & 5319.5862888327 & -1622.5862888327 \tabularnewline
54 & 3514 & 4100.45237461397 & -586.452374613966 \tabularnewline
55 & 3786 & 3275.39244395426 & 510.607556045737 \tabularnewline
56 & 3297 & 3412.17875264251 & -115.17875264251 \tabularnewline
57 & 3571 & 3418.58030478166 & 152.41969521834 \tabularnewline
58 & 3871 & 3492.12547521366 & 378.87452478634 \tabularnewline
59 & 3492 & 3473.12736122704 & 18.8726387729603 \tabularnewline
60 & 3051 & 4200.88030345826 & -1149.88030345826 \tabularnewline
61 & 3735 & 3292.66097295228 & 442.339027047721 \tabularnewline
62 & 3645 & 3405.65476851651 & 239.345231483492 \tabularnewline
63 & 4852 & 4351.29039818039 & 500.709601819607 \tabularnewline
64 & 4232 & 4154.6880570328 & 77.3119429672006 \tabularnewline
65 & 3804 & 3609.4868358689 & 194.513164131103 \tabularnewline
66 & 4464 & 3834.23784792159 & 629.762152078406 \tabularnewline
67 & 4259 & 4154.79706495227 & 104.202935047731 \tabularnewline
68 & 3373 & 3740.78890013843 & -367.788900138431 \tabularnewline
69 & 4134 & 3743.18827419066 & 390.811725809341 \tabularnewline
70 & 4488 & 4052.58756075839 & 435.412439241608 \tabularnewline
71 & 3333 & 3863.50754039384 & -530.507540393835 \tabularnewline
72 & 4772 & 3674.40370147726 & 1097.59629852274 \tabularnewline
73 & 4929 & 4891.04975053604 & 37.950249463961 \tabularnewline
74 & 5555 & 4625.76751206444 & 929.232487935558 \tabularnewline
75 & 7183 & 6448.19400670231 & 734.805993297688 \tabularnewline
76 & 9266 & 5931.39221183828 & 3334.60778816172 \tabularnewline
77 & 4003 & 6806.20009983782 & -2803.20009983782 \tabularnewline
78 & 3051 & 5679.74465653584 & -2628.74465653584 \tabularnewline
79 & 3507 & 3982.93664240292 & -475.936642402925 \tabularnewline
80 & 3273 & 3111.96037507528 & 161.039624924722 \tabularnewline
81 & 3942 & 3707.92097643141 & 234.079023568589 \tabularnewline
82 & 3216 & 3930.35484471544 & -714.354844715442 \tabularnewline
83 & 3232 & 2835.84387544918 & 396.156124550821 \tabularnewline
84 & 3593 & 3752.35338979882 & -159.353389798823 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294689&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]3233[/C][C]3475.99346963565[/C][C]-242.99346963565[/C][/ROW]
[ROW][C]14[/C][C]3554[/C][C]3635.41124175158[/C][C]-81.4112417515762[/C][/ROW]
[ROW][C]15[/C][C]3952[/C][C]3960.20759885758[/C][C]-8.20759885757889[/C][/ROW]
[ROW][C]16[/C][C]3951[/C][C]3943.54749810755[/C][C]7.45250189244643[/C][/ROW]
[ROW][C]17[/C][C]3685[/C][C]3687.13881766717[/C][C]-2.13881766717304[/C][/ROW]
[ROW][C]18[/C][C]4312[/C][C]4372.58790774295[/C][C]-60.5879077429518[/C][/ROW]
[ROW][C]19[/C][C]3867[/C][C]3507.19389379001[/C][C]359.806106209986[/C][/ROW]
[ROW][C]20[/C][C]4140[/C][C]3654.15916915549[/C][C]485.840830844509[/C][/ROW]
[ROW][C]21[/C][C]4114[/C][C]4603.99269052276[/C][C]-489.992690522761[/C][/ROW]
[ROW][C]22[/C][C]3818[/C][C]3929.48957769919[/C][C]-111.489577699195[/C][/ROW]
[ROW][C]23[/C][C]3377[/C][C]3966.2149123787[/C][C]-589.214912378702[/C][/ROW]
[ROW][C]24[/C][C]3453[/C][C]4239.86210717385[/C][C]-786.86210717385[/C][/ROW]
[ROW][C]25[/C][C]3502[/C][C]2469.6646157656[/C][C]1032.3353842344[/C][/ROW]
[ROW][C]26[/C][C]4017[/C][C]3378.79733693817[/C][C]638.202663061835[/C][/ROW]
[ROW][C]27[/C][C]5410[/C][C]4153.86011765594[/C][C]1256.13988234406[/C][/ROW]
[ROW][C]28[/C][C]5184[/C][C]4846.08179089469[/C][C]337.918209105306[/C][/ROW]
[ROW][C]29[/C][C]5529[/C][C]4703.37678392975[/C][C]825.623216070252[/C][/ROW]
[ROW][C]30[/C][C]6434[/C][C]6096.47160154584[/C][C]337.528398454157[/C][/ROW]
[ROW][C]31[/C][C]4962[/C][C]5347.75345996853[/C][C]-385.753459968526[/C][/ROW]
[ROW][C]32[/C][C]2980[/C][C]5134.27099399967[/C][C]-2154.27099399967[/C][/ROW]
[ROW][C]33[/C][C]2937[/C][C]4167.11792689324[/C][C]-1230.11792689324[/C][/ROW]
[ROW][C]34[/C][C]3023[/C][C]3285.799958616[/C][C]-262.799958615999[/C][/ROW]
[ROW][C]35[/C][C]2731[/C][C]3019.93403199535[/C][C]-288.934031995349[/C][/ROW]
[ROW][C]36[/C][C]3163[/C][C]3252.29238056144[/C][C]-89.2923805614373[/C][/ROW]
[ROW][C]37[/C][C]3146[/C][C]2639.19382644302[/C][C]506.806173556982[/C][/ROW]
[ROW][C]38[/C][C]3173[/C][C]3026.66860624804[/C][C]146.331393751962[/C][/ROW]
[ROW][C]39[/C][C]3724[/C][C]3579.41378313056[/C][C]144.58621686944[/C][/ROW]
[ROW][C]40[/C][C]3224[/C][C]3365.28386943372[/C][C]-141.283869433721[/C][/ROW]
[ROW][C]41[/C][C]4114[/C][C]3185.16374706282[/C][C]928.836252937181[/C][/ROW]
[ROW][C]42[/C][C]3450[/C][C]4160.97027043373[/C][C]-710.970270433727[/C][/ROW]
[ROW][C]43[/C][C]2957[/C][C]3014.55692393449[/C][C]-57.5569239344932[/C][/ROW]
[ROW][C]44[/C][C]3882[/C][C]2318.95685559063[/C][C]1563.04314440937[/C][/ROW]
[ROW][C]45[/C][C]4284[/C][C]3741.77643351038[/C][C]542.22356648962[/C][/ROW]
[ROW][C]46[/C][C]4181[/C][C]4361.54631962597[/C][C]-180.54631962597[/C][/ROW]
[ROW][C]47[/C][C]3760[/C][C]4076.98858855594[/C][C]-316.988588555939[/C][/ROW]
[ROW][C]48[/C][C]4457[/C][C]4604.95024191718[/C][C]-147.950241917182[/C][/ROW]
[ROW][C]49[/C][C]4167[/C][C]4083.7909881775[/C][C]83.2090118225001[/C][/ROW]
[ROW][C]50[/C][C]3962[/C][C]4067.43124170638[/C][C]-105.431241706383[/C][/ROW]
[ROW][C]51[/C][C]5247[/C][C]4613.52498947583[/C][C]633.475010524166[/C][/ROW]
[ROW][C]52[/C][C]5157[/C][C]4408.61379037105[/C][C]748.386209628951[/C][/ROW]
[ROW][C]53[/C][C]3697[/C][C]5319.5862888327[/C][C]-1622.5862888327[/C][/ROW]
[ROW][C]54[/C][C]3514[/C][C]4100.45237461397[/C][C]-586.452374613966[/C][/ROW]
[ROW][C]55[/C][C]3786[/C][C]3275.39244395426[/C][C]510.607556045737[/C][/ROW]
[ROW][C]56[/C][C]3297[/C][C]3412.17875264251[/C][C]-115.17875264251[/C][/ROW]
[ROW][C]57[/C][C]3571[/C][C]3418.58030478166[/C][C]152.41969521834[/C][/ROW]
[ROW][C]58[/C][C]3871[/C][C]3492.12547521366[/C][C]378.87452478634[/C][/ROW]
[ROW][C]59[/C][C]3492[/C][C]3473.12736122704[/C][C]18.8726387729603[/C][/ROW]
[ROW][C]60[/C][C]3051[/C][C]4200.88030345826[/C][C]-1149.88030345826[/C][/ROW]
[ROW][C]61[/C][C]3735[/C][C]3292.66097295228[/C][C]442.339027047721[/C][/ROW]
[ROW][C]62[/C][C]3645[/C][C]3405.65476851651[/C][C]239.345231483492[/C][/ROW]
[ROW][C]63[/C][C]4852[/C][C]4351.29039818039[/C][C]500.709601819607[/C][/ROW]
[ROW][C]64[/C][C]4232[/C][C]4154.6880570328[/C][C]77.3119429672006[/C][/ROW]
[ROW][C]65[/C][C]3804[/C][C]3609.4868358689[/C][C]194.513164131103[/C][/ROW]
[ROW][C]66[/C][C]4464[/C][C]3834.23784792159[/C][C]629.762152078406[/C][/ROW]
[ROW][C]67[/C][C]4259[/C][C]4154.79706495227[/C][C]104.202935047731[/C][/ROW]
[ROW][C]68[/C][C]3373[/C][C]3740.78890013843[/C][C]-367.788900138431[/C][/ROW]
[ROW][C]69[/C][C]4134[/C][C]3743.18827419066[/C][C]390.811725809341[/C][/ROW]
[ROW][C]70[/C][C]4488[/C][C]4052.58756075839[/C][C]435.412439241608[/C][/ROW]
[ROW][C]71[/C][C]3333[/C][C]3863.50754039384[/C][C]-530.507540393835[/C][/ROW]
[ROW][C]72[/C][C]4772[/C][C]3674.40370147726[/C][C]1097.59629852274[/C][/ROW]
[ROW][C]73[/C][C]4929[/C][C]4891.04975053604[/C][C]37.950249463961[/C][/ROW]
[ROW][C]74[/C][C]5555[/C][C]4625.76751206444[/C][C]929.232487935558[/C][/ROW]
[ROW][C]75[/C][C]7183[/C][C]6448.19400670231[/C][C]734.805993297688[/C][/ROW]
[ROW][C]76[/C][C]9266[/C][C]5931.39221183828[/C][C]3334.60778816172[/C][/ROW]
[ROW][C]77[/C][C]4003[/C][C]6806.20009983782[/C][C]-2803.20009983782[/C][/ROW]
[ROW][C]78[/C][C]3051[/C][C]5679.74465653584[/C][C]-2628.74465653584[/C][/ROW]
[ROW][C]79[/C][C]3507[/C][C]3982.93664240292[/C][C]-475.936642402925[/C][/ROW]
[ROW][C]80[/C][C]3273[/C][C]3111.96037507528[/C][C]161.039624924722[/C][/ROW]
[ROW][C]81[/C][C]3942[/C][C]3707.92097643141[/C][C]234.079023568589[/C][/ROW]
[ROW][C]82[/C][C]3216[/C][C]3930.35484471544[/C][C]-714.354844715442[/C][/ROW]
[ROW][C]83[/C][C]3232[/C][C]2835.84387544918[/C][C]396.156124550821[/C][/ROW]
[ROW][C]84[/C][C]3593[/C][C]3752.35338979882[/C][C]-159.353389798823[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294689&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294689&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
1332333475.99346963565-242.99346963565
1435543635.41124175158-81.4112417515762
1539523960.20759885758-8.20759885757889
1639513943.547498107557.45250189244643
1736853687.13881766717-2.13881766717304
1843124372.58790774295-60.5879077429518
1938673507.19389379001359.806106209986
2041403654.15916915549485.840830844509
2141144603.99269052276-489.992690522761
2238183929.48957769919-111.489577699195
2333773966.2149123787-589.214912378702
2434534239.86210717385-786.86210717385
2535022469.66461576561032.3353842344
2640173378.79733693817638.202663061835
2754104153.860117655941256.13988234406
2851844846.08179089469337.918209105306
2955294703.37678392975825.623216070252
3064346096.47160154584337.528398454157
3149625347.75345996853-385.753459968526
3229805134.27099399967-2154.27099399967
3329374167.11792689324-1230.11792689324
3430233285.799958616-262.799958615999
3527313019.93403199535-288.934031995349
3631633252.29238056144-89.2923805614373
3731462639.19382644302506.806173556982
3831733026.66860624804146.331393751962
3937243579.41378313056144.58621686944
4032243365.28386943372-141.283869433721
4141143185.16374706282928.836252937181
4234504160.97027043373-710.970270433727
4329573014.55692393449-57.5569239344932
4438822318.956855590631563.04314440937
4542843741.77643351038542.22356648962
4641814361.54631962597-180.54631962597
4737604076.98858855594-316.988588555939
4844574604.95024191718-147.950241917182
4941674083.790988177583.2090118225001
5039624067.43124170638-105.431241706383
5152474613.52498947583633.475010524166
5251574408.61379037105748.386209628951
5336975319.5862888327-1622.5862888327
5435144100.45237461397-586.452374613966
5537863275.39244395426510.607556045737
5632973412.17875264251-115.17875264251
5735713418.58030478166152.41969521834
5838713492.12547521366378.87452478634
5934923473.1273612270418.8726387729603
6030514200.88030345826-1149.88030345826
6137353292.66097295228442.339027047721
6236453405.65476851651239.345231483492
6348524351.29039818039500.709601819607
6442324154.688057032877.3119429672006
6538043609.4868358689194.513164131103
6644643834.23784792159629.762152078406
6742594154.79706495227104.202935047731
6833733740.78890013843-367.788900138431
6941343743.18827419066390.811725809341
7044884052.58756075839435.412439241608
7133333863.50754039384-530.507540393835
7247723674.403701477261097.59629852274
7349294891.0497505360437.950249463961
7455554625.76751206444929.232487935558
7571836448.19400670231734.805993297688
7692665931.392211838283334.60778816172
7740036806.20009983782-2803.20009983782
7830515679.74465653584-2628.74465653584
7935073982.93664240292-475.936642402925
8032733111.96037507528161.039624924722
8139423707.92097643141234.079023568589
8232163930.35484471544-714.354844715442
8332322835.84387544918396.156124550821
8435933752.35338979882-159.353389798823







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
853760.959231253542059.013918113875462.9045443932
863808.330598978791855.867533999375760.7936639582
874620.034586810082256.923334323626983.14583929654
884536.575692100042006.770830848157066.38055335194
892521.11024569083453.3072645455654588.91322683609
902568.19920018454269.601346130584866.7970542385
913154.68190284977340.5755816358675968.78822406367
922859.8129372564859.33611869179735660.28975582117
933324.4996200493319.02811731746856629.9711227812
943008.56818875554-207.2361696112156224.37254712229
952805.93444270211-401.2696639331786013.13854933741
963189.50695822277-113.344428296186492.35834474172

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 3760.95923125354 & 2059.01391811387 & 5462.9045443932 \tabularnewline
86 & 3808.33059897879 & 1855.86753399937 & 5760.7936639582 \tabularnewline
87 & 4620.03458681008 & 2256.92333432362 & 6983.14583929654 \tabularnewline
88 & 4536.57569210004 & 2006.77083084815 & 7066.38055335194 \tabularnewline
89 & 2521.11024569083 & 453.307264545565 & 4588.91322683609 \tabularnewline
90 & 2568.19920018454 & 269.60134613058 & 4866.7970542385 \tabularnewline
91 & 3154.68190284977 & 340.575581635867 & 5968.78822406367 \tabularnewline
92 & 2859.81293725648 & 59.3361186917973 & 5660.28975582117 \tabularnewline
93 & 3324.49962004933 & 19.0281173174685 & 6629.9711227812 \tabularnewline
94 & 3008.56818875554 & -207.236169611215 & 6224.37254712229 \tabularnewline
95 & 2805.93444270211 & -401.269663933178 & 6013.13854933741 \tabularnewline
96 & 3189.50695822277 & -113.34442829618 & 6492.35834474172 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294689&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]85[/C][C]3760.95923125354[/C][C]2059.01391811387[/C][C]5462.9045443932[/C][/ROW]
[ROW][C]86[/C][C]3808.33059897879[/C][C]1855.86753399937[/C][C]5760.7936639582[/C][/ROW]
[ROW][C]87[/C][C]4620.03458681008[/C][C]2256.92333432362[/C][C]6983.14583929654[/C][/ROW]
[ROW][C]88[/C][C]4536.57569210004[/C][C]2006.77083084815[/C][C]7066.38055335194[/C][/ROW]
[ROW][C]89[/C][C]2521.11024569083[/C][C]453.307264545565[/C][C]4588.91322683609[/C][/ROW]
[ROW][C]90[/C][C]2568.19920018454[/C][C]269.60134613058[/C][C]4866.7970542385[/C][/ROW]
[ROW][C]91[/C][C]3154.68190284977[/C][C]340.575581635867[/C][C]5968.78822406367[/C][/ROW]
[ROW][C]92[/C][C]2859.81293725648[/C][C]59.3361186917973[/C][C]5660.28975582117[/C][/ROW]
[ROW][C]93[/C][C]3324.49962004933[/C][C]19.0281173174685[/C][C]6629.9711227812[/C][/ROW]
[ROW][C]94[/C][C]3008.56818875554[/C][C]-207.236169611215[/C][C]6224.37254712229[/C][/ROW]
[ROW][C]95[/C][C]2805.93444270211[/C][C]-401.269663933178[/C][C]6013.13854933741[/C][/ROW]
[ROW][C]96[/C][C]3189.50695822277[/C][C]-113.34442829618[/C][C]6492.35834474172[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294689&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294689&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
853760.959231253542059.013918113875462.9045443932
863808.330598978791855.867533999375760.7936639582
874620.034586810082256.923334323626983.14583929654
884536.575692100042006.770830848157066.38055335194
892521.11024569083453.3072645455654588.91322683609
902568.19920018454269.601346130584866.7970542385
913154.68190284977340.5755816358675968.78822406367
922859.8129372564859.33611869179735660.28975582117
933324.4996200493319.02811731746856629.9711227812
943008.56818875554-207.2361696112156224.37254712229
952805.93444270211-401.2696639331786013.13854933741
963189.50695822277-113.344428296186492.35834474172



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
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')