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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 19 Nov 2014 08:08:53 +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/2014/Nov/19/t1416384554nbzp1b32vlwurnl.htm/, Retrieved Sun, 19 May 2024 04:19:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=256297, Retrieved Sun, 19 May 2024 04:19:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMPD          [Exponential Smoothing] [WS8,3] [2014-11-19 08:08:53] [8eaf8ca403eea369f03debd8dc66ae53] [Current]
Feedback Forum

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Dataseries X:
9492	
8641	
9793	
9603	
9238	
9535	
10295	
9941	
9984	
9563	
8872	
9302
9215	
8834	
9998	
9604	
9507	
9718	
10095	
9583	
9883	
9365	
8919	
9449
9769	
9321	
9939	
9336	
10195	
9464	
10010	
10213	
9563	
9890	
9305	
9391
9928	
8686	
9843	
9627	
10074
9503	
10119	
10000	
9313	
9866	
9172	
9241
9659	
8904	
9755	
9080	
9435	
8971	
10063	
9793	
9454	
9759	
8820
9403
9676	
8642	
9402	
9610	
9294	
9448	
10319	
9548	
9801	
9596	
8923	
9746
9829	
9125	
9782	
9441	
9162	
9915	
10444	
10209	
9985	
9842	
9429	
10132




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256297&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256297&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256297&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.159121100815596
beta0
gamma0.706832428592084

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.159121100815596 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.706832428592084 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256297&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]0.159121100815596[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.706832428592084[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256297&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256297&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
alpha0.159121100815596
beta0
gamma0.706832428592084







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1392159141.2337072649673.7662927350411
1488348794.2408574249239.7591425750797
1599989982.7117524158315.2882475841725
1696049602.622144991171.37785500883001
1795079511.15243392048-4.15243392048433
1897189712.427737187545.57226281246403
191009510287.3337782372-192.333778237164
2095839905.24879217692-322.248792176921
2198839879.408252752783.5917472472247
2293659449.41581865215-84.4158186521472
2389198732.75285711884186.247142881157
2494499172.5747506414276.425249358603
2597699173.1313191521595.8686808479
2693218889.00347014284431.996529857157
27993910125.3430772218-186.343077221794
2893369704.90188390407-368.901883904067
29101959551.22586801591643.774131984092
3094649861.37993506156-397.379935061561
311001010254.5402503522-244.540250352189
32102139786.93176365429426.068236345713
33956310073.8309911789-510.830991178922
3498909509.67482603112380.325173968877
3593059027.83332907413277.16667092587
3693919535.72074013685-144.720740136845
3799289659.12864469882268.871355301182
3886869225.56949187079-539.569491870789
3998439939.79582181505-96.7958218150507
4096279425.0977473957201.902252604295
41100749964.14331133878109.856688661217
4295039570.51902178059-67.5190217805921
431011910107.009036229111.990963770937
441000010078.8032570482-78.8032570482392
4593139728.51090737866-415.510907378664
4698669709.19018003229156.80981996771
4791729130.4693370839841.5306629160241
4892419350.10888535144-109.108885351443
4996599725.00618152738-66.0061815273784
5089048757.65566090089146.344339099105
5197559844.19252330749-89.1925233074944
5290809508.23862334937-428.238623349373
5394359892.30723238444-457.307232384435
5489719303.01008395028-332.010083950281
55100639844.67158216733218.328417832672
5697939795.33394965177-2.33394965176922
5794549257.08376154823196.916238451769
5897599675.3779348659883.6220651340209
5988209016.49400132145-196.494001321445
6094039108.72460961314294.275390386862
6196769573.42739929174102.572600708265
6286428759.11407626062-117.114076260625
6394029663.73534430269-261.735344302691
6496109098.81063984448511.189360155517
6592949615.08483149378-321.084831493779
6694489121.93521403719326.064785962806
671031910095.4097630085223.590236991495
6895489915.75640751576-367.756407515755
6998019437.78623199209363.213768007909
7095969815.20427266877-219.204272668769
7189238941.6443607341-18.6443607341025
7297469353.86852812306392.131471876941
7398299720.20172418073108.798275819268
7491258776.30595987032348.694040129682
7597829669.08996267042112.910037329581
7694419623.17513781847-182.175137818471
7791629534.44952385225-372.44952385225
7899159417.76685368416497.233146315844
791044410357.571079032786.4289209672606
80102099804.61939174385404.380608256151
8199859883.97228849235101.027711507648
8298429873.50473224819-31.504732248186
8394299149.01666222344279.983337776561
84101329852.90771650181279.092283498192

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9215 & 9141.23370726496 & 73.7662927350411 \tabularnewline
14 & 8834 & 8794.24085742492 & 39.7591425750797 \tabularnewline
15 & 9998 & 9982.71175241583 & 15.2882475841725 \tabularnewline
16 & 9604 & 9602.62214499117 & 1.37785500883001 \tabularnewline
17 & 9507 & 9511.15243392048 & -4.15243392048433 \tabularnewline
18 & 9718 & 9712.42773718754 & 5.57226281246403 \tabularnewline
19 & 10095 & 10287.3337782372 & -192.333778237164 \tabularnewline
20 & 9583 & 9905.24879217692 & -322.248792176921 \tabularnewline
21 & 9883 & 9879.40825275278 & 3.5917472472247 \tabularnewline
22 & 9365 & 9449.41581865215 & -84.4158186521472 \tabularnewline
23 & 8919 & 8732.75285711884 & 186.247142881157 \tabularnewline
24 & 9449 & 9172.5747506414 & 276.425249358603 \tabularnewline
25 & 9769 & 9173.1313191521 & 595.8686808479 \tabularnewline
26 & 9321 & 8889.00347014284 & 431.996529857157 \tabularnewline
27 & 9939 & 10125.3430772218 & -186.343077221794 \tabularnewline
28 & 9336 & 9704.90188390407 & -368.901883904067 \tabularnewline
29 & 10195 & 9551.22586801591 & 643.774131984092 \tabularnewline
30 & 9464 & 9861.37993506156 & -397.379935061561 \tabularnewline
31 & 10010 & 10254.5402503522 & -244.540250352189 \tabularnewline
32 & 10213 & 9786.93176365429 & 426.068236345713 \tabularnewline
33 & 9563 & 10073.8309911789 & -510.830991178922 \tabularnewline
34 & 9890 & 9509.67482603112 & 380.325173968877 \tabularnewline
35 & 9305 & 9027.83332907413 & 277.16667092587 \tabularnewline
36 & 9391 & 9535.72074013685 & -144.720740136845 \tabularnewline
37 & 9928 & 9659.12864469882 & 268.871355301182 \tabularnewline
38 & 8686 & 9225.56949187079 & -539.569491870789 \tabularnewline
39 & 9843 & 9939.79582181505 & -96.7958218150507 \tabularnewline
40 & 9627 & 9425.0977473957 & 201.902252604295 \tabularnewline
41 & 10074 & 9964.14331133878 & 109.856688661217 \tabularnewline
42 & 9503 & 9570.51902178059 & -67.5190217805921 \tabularnewline
43 & 10119 & 10107.0090362291 & 11.990963770937 \tabularnewline
44 & 10000 & 10078.8032570482 & -78.8032570482392 \tabularnewline
45 & 9313 & 9728.51090737866 & -415.510907378664 \tabularnewline
46 & 9866 & 9709.19018003229 & 156.80981996771 \tabularnewline
47 & 9172 & 9130.46933708398 & 41.5306629160241 \tabularnewline
48 & 9241 & 9350.10888535144 & -109.108885351443 \tabularnewline
49 & 9659 & 9725.00618152738 & -66.0061815273784 \tabularnewline
50 & 8904 & 8757.65566090089 & 146.344339099105 \tabularnewline
51 & 9755 & 9844.19252330749 & -89.1925233074944 \tabularnewline
52 & 9080 & 9508.23862334937 & -428.238623349373 \tabularnewline
53 & 9435 & 9892.30723238444 & -457.307232384435 \tabularnewline
54 & 8971 & 9303.01008395028 & -332.010083950281 \tabularnewline
55 & 10063 & 9844.67158216733 & 218.328417832672 \tabularnewline
56 & 9793 & 9795.33394965177 & -2.33394965176922 \tabularnewline
57 & 9454 & 9257.08376154823 & 196.916238451769 \tabularnewline
58 & 9759 & 9675.37793486598 & 83.6220651340209 \tabularnewline
59 & 8820 & 9016.49400132145 & -196.494001321445 \tabularnewline
60 & 9403 & 9108.72460961314 & 294.275390386862 \tabularnewline
61 & 9676 & 9573.42739929174 & 102.572600708265 \tabularnewline
62 & 8642 & 8759.11407626062 & -117.114076260625 \tabularnewline
63 & 9402 & 9663.73534430269 & -261.735344302691 \tabularnewline
64 & 9610 & 9098.81063984448 & 511.189360155517 \tabularnewline
65 & 9294 & 9615.08483149378 & -321.084831493779 \tabularnewline
66 & 9448 & 9121.93521403719 & 326.064785962806 \tabularnewline
67 & 10319 & 10095.4097630085 & 223.590236991495 \tabularnewline
68 & 9548 & 9915.75640751576 & -367.756407515755 \tabularnewline
69 & 9801 & 9437.78623199209 & 363.213768007909 \tabularnewline
70 & 9596 & 9815.20427266877 & -219.204272668769 \tabularnewline
71 & 8923 & 8941.6443607341 & -18.6443607341025 \tabularnewline
72 & 9746 & 9353.86852812306 & 392.131471876941 \tabularnewline
73 & 9829 & 9720.20172418073 & 108.798275819268 \tabularnewline
74 & 9125 & 8776.30595987032 & 348.694040129682 \tabularnewline
75 & 9782 & 9669.08996267042 & 112.910037329581 \tabularnewline
76 & 9441 & 9623.17513781847 & -182.175137818471 \tabularnewline
77 & 9162 & 9534.44952385225 & -372.44952385225 \tabularnewline
78 & 9915 & 9417.76685368416 & 497.233146315844 \tabularnewline
79 & 10444 & 10357.5710790327 & 86.4289209672606 \tabularnewline
80 & 10209 & 9804.61939174385 & 404.380608256151 \tabularnewline
81 & 9985 & 9883.97228849235 & 101.027711507648 \tabularnewline
82 & 9842 & 9873.50473224819 & -31.504732248186 \tabularnewline
83 & 9429 & 9149.01666222344 & 279.983337776561 \tabularnewline
84 & 10132 & 9852.90771650181 & 279.092283498192 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256297&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]9215[/C][C]9141.23370726496[/C][C]73.7662927350411[/C][/ROW]
[ROW][C]14[/C][C]8834[/C][C]8794.24085742492[/C][C]39.7591425750797[/C][/ROW]
[ROW][C]15[/C][C]9998[/C][C]9982.71175241583[/C][C]15.2882475841725[/C][/ROW]
[ROW][C]16[/C][C]9604[/C][C]9602.62214499117[/C][C]1.37785500883001[/C][/ROW]
[ROW][C]17[/C][C]9507[/C][C]9511.15243392048[/C][C]-4.15243392048433[/C][/ROW]
[ROW][C]18[/C][C]9718[/C][C]9712.42773718754[/C][C]5.57226281246403[/C][/ROW]
[ROW][C]19[/C][C]10095[/C][C]10287.3337782372[/C][C]-192.333778237164[/C][/ROW]
[ROW][C]20[/C][C]9583[/C][C]9905.24879217692[/C][C]-322.248792176921[/C][/ROW]
[ROW][C]21[/C][C]9883[/C][C]9879.40825275278[/C][C]3.5917472472247[/C][/ROW]
[ROW][C]22[/C][C]9365[/C][C]9449.41581865215[/C][C]-84.4158186521472[/C][/ROW]
[ROW][C]23[/C][C]8919[/C][C]8732.75285711884[/C][C]186.247142881157[/C][/ROW]
[ROW][C]24[/C][C]9449[/C][C]9172.5747506414[/C][C]276.425249358603[/C][/ROW]
[ROW][C]25[/C][C]9769[/C][C]9173.1313191521[/C][C]595.8686808479[/C][/ROW]
[ROW][C]26[/C][C]9321[/C][C]8889.00347014284[/C][C]431.996529857157[/C][/ROW]
[ROW][C]27[/C][C]9939[/C][C]10125.3430772218[/C][C]-186.343077221794[/C][/ROW]
[ROW][C]28[/C][C]9336[/C][C]9704.90188390407[/C][C]-368.901883904067[/C][/ROW]
[ROW][C]29[/C][C]10195[/C][C]9551.22586801591[/C][C]643.774131984092[/C][/ROW]
[ROW][C]30[/C][C]9464[/C][C]9861.37993506156[/C][C]-397.379935061561[/C][/ROW]
[ROW][C]31[/C][C]10010[/C][C]10254.5402503522[/C][C]-244.540250352189[/C][/ROW]
[ROW][C]32[/C][C]10213[/C][C]9786.93176365429[/C][C]426.068236345713[/C][/ROW]
[ROW][C]33[/C][C]9563[/C][C]10073.8309911789[/C][C]-510.830991178922[/C][/ROW]
[ROW][C]34[/C][C]9890[/C][C]9509.67482603112[/C][C]380.325173968877[/C][/ROW]
[ROW][C]35[/C][C]9305[/C][C]9027.83332907413[/C][C]277.16667092587[/C][/ROW]
[ROW][C]36[/C][C]9391[/C][C]9535.72074013685[/C][C]-144.720740136845[/C][/ROW]
[ROW][C]37[/C][C]9928[/C][C]9659.12864469882[/C][C]268.871355301182[/C][/ROW]
[ROW][C]38[/C][C]8686[/C][C]9225.56949187079[/C][C]-539.569491870789[/C][/ROW]
[ROW][C]39[/C][C]9843[/C][C]9939.79582181505[/C][C]-96.7958218150507[/C][/ROW]
[ROW][C]40[/C][C]9627[/C][C]9425.0977473957[/C][C]201.902252604295[/C][/ROW]
[ROW][C]41[/C][C]10074[/C][C]9964.14331133878[/C][C]109.856688661217[/C][/ROW]
[ROW][C]42[/C][C]9503[/C][C]9570.51902178059[/C][C]-67.5190217805921[/C][/ROW]
[ROW][C]43[/C][C]10119[/C][C]10107.0090362291[/C][C]11.990963770937[/C][/ROW]
[ROW][C]44[/C][C]10000[/C][C]10078.8032570482[/C][C]-78.8032570482392[/C][/ROW]
[ROW][C]45[/C][C]9313[/C][C]9728.51090737866[/C][C]-415.510907378664[/C][/ROW]
[ROW][C]46[/C][C]9866[/C][C]9709.19018003229[/C][C]156.80981996771[/C][/ROW]
[ROW][C]47[/C][C]9172[/C][C]9130.46933708398[/C][C]41.5306629160241[/C][/ROW]
[ROW][C]48[/C][C]9241[/C][C]9350.10888535144[/C][C]-109.108885351443[/C][/ROW]
[ROW][C]49[/C][C]9659[/C][C]9725.00618152738[/C][C]-66.0061815273784[/C][/ROW]
[ROW][C]50[/C][C]8904[/C][C]8757.65566090089[/C][C]146.344339099105[/C][/ROW]
[ROW][C]51[/C][C]9755[/C][C]9844.19252330749[/C][C]-89.1925233074944[/C][/ROW]
[ROW][C]52[/C][C]9080[/C][C]9508.23862334937[/C][C]-428.238623349373[/C][/ROW]
[ROW][C]53[/C][C]9435[/C][C]9892.30723238444[/C][C]-457.307232384435[/C][/ROW]
[ROW][C]54[/C][C]8971[/C][C]9303.01008395028[/C][C]-332.010083950281[/C][/ROW]
[ROW][C]55[/C][C]10063[/C][C]9844.67158216733[/C][C]218.328417832672[/C][/ROW]
[ROW][C]56[/C][C]9793[/C][C]9795.33394965177[/C][C]-2.33394965176922[/C][/ROW]
[ROW][C]57[/C][C]9454[/C][C]9257.08376154823[/C][C]196.916238451769[/C][/ROW]
[ROW][C]58[/C][C]9759[/C][C]9675.37793486598[/C][C]83.6220651340209[/C][/ROW]
[ROW][C]59[/C][C]8820[/C][C]9016.49400132145[/C][C]-196.494001321445[/C][/ROW]
[ROW][C]60[/C][C]9403[/C][C]9108.72460961314[/C][C]294.275390386862[/C][/ROW]
[ROW][C]61[/C][C]9676[/C][C]9573.42739929174[/C][C]102.572600708265[/C][/ROW]
[ROW][C]62[/C][C]8642[/C][C]8759.11407626062[/C][C]-117.114076260625[/C][/ROW]
[ROW][C]63[/C][C]9402[/C][C]9663.73534430269[/C][C]-261.735344302691[/C][/ROW]
[ROW][C]64[/C][C]9610[/C][C]9098.81063984448[/C][C]511.189360155517[/C][/ROW]
[ROW][C]65[/C][C]9294[/C][C]9615.08483149378[/C][C]-321.084831493779[/C][/ROW]
[ROW][C]66[/C][C]9448[/C][C]9121.93521403719[/C][C]326.064785962806[/C][/ROW]
[ROW][C]67[/C][C]10319[/C][C]10095.4097630085[/C][C]223.590236991495[/C][/ROW]
[ROW][C]68[/C][C]9548[/C][C]9915.75640751576[/C][C]-367.756407515755[/C][/ROW]
[ROW][C]69[/C][C]9801[/C][C]9437.78623199209[/C][C]363.213768007909[/C][/ROW]
[ROW][C]70[/C][C]9596[/C][C]9815.20427266877[/C][C]-219.204272668769[/C][/ROW]
[ROW][C]71[/C][C]8923[/C][C]8941.6443607341[/C][C]-18.6443607341025[/C][/ROW]
[ROW][C]72[/C][C]9746[/C][C]9353.86852812306[/C][C]392.131471876941[/C][/ROW]
[ROW][C]73[/C][C]9829[/C][C]9720.20172418073[/C][C]108.798275819268[/C][/ROW]
[ROW][C]74[/C][C]9125[/C][C]8776.30595987032[/C][C]348.694040129682[/C][/ROW]
[ROW][C]75[/C][C]9782[/C][C]9669.08996267042[/C][C]112.910037329581[/C][/ROW]
[ROW][C]76[/C][C]9441[/C][C]9623.17513781847[/C][C]-182.175137818471[/C][/ROW]
[ROW][C]77[/C][C]9162[/C][C]9534.44952385225[/C][C]-372.44952385225[/C][/ROW]
[ROW][C]78[/C][C]9915[/C][C]9417.76685368416[/C][C]497.233146315844[/C][/ROW]
[ROW][C]79[/C][C]10444[/C][C]10357.5710790327[/C][C]86.4289209672606[/C][/ROW]
[ROW][C]80[/C][C]10209[/C][C]9804.61939174385[/C][C]404.380608256151[/C][/ROW]
[ROW][C]81[/C][C]9985[/C][C]9883.97228849235[/C][C]101.027711507648[/C][/ROW]
[ROW][C]82[/C][C]9842[/C][C]9873.50473224819[/C][C]-31.504732248186[/C][/ROW]
[ROW][C]83[/C][C]9429[/C][C]9149.01666222344[/C][C]279.983337776561[/C][/ROW]
[ROW][C]84[/C][C]10132[/C][C]9852.90771650181[/C][C]279.092283498192[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256297&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256297&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
1392159141.2337072649673.7662927350411
1488348794.2408574249239.7591425750797
1599989982.7117524158315.2882475841725
1696049602.622144991171.37785500883001
1795079511.15243392048-4.15243392048433
1897189712.427737187545.57226281246403
191009510287.3337782372-192.333778237164
2095839905.24879217692-322.248792176921
2198839879.408252752783.5917472472247
2293659449.41581865215-84.4158186521472
2389198732.75285711884186.247142881157
2494499172.5747506414276.425249358603
2597699173.1313191521595.8686808479
2693218889.00347014284431.996529857157
27993910125.3430772218-186.343077221794
2893369704.90188390407-368.901883904067
29101959551.22586801591643.774131984092
3094649861.37993506156-397.379935061561
311001010254.5402503522-244.540250352189
32102139786.93176365429426.068236345713
33956310073.8309911789-510.830991178922
3498909509.67482603112380.325173968877
3593059027.83332907413277.16667092587
3693919535.72074013685-144.720740136845
3799289659.12864469882268.871355301182
3886869225.56949187079-539.569491870789
3998439939.79582181505-96.7958218150507
4096279425.0977473957201.902252604295
41100749964.14331133878109.856688661217
4295039570.51902178059-67.5190217805921
431011910107.009036229111.990963770937
441000010078.8032570482-78.8032570482392
4593139728.51090737866-415.510907378664
4698669709.19018003229156.80981996771
4791729130.4693370839841.5306629160241
4892419350.10888535144-109.108885351443
4996599725.00618152738-66.0061815273784
5089048757.65566090089146.344339099105
5197559844.19252330749-89.1925233074944
5290809508.23862334937-428.238623349373
5394359892.30723238444-457.307232384435
5489719303.01008395028-332.010083950281
55100639844.67158216733218.328417832672
5697939795.33394965177-2.33394965176922
5794549257.08376154823196.916238451769
5897599675.3779348659883.6220651340209
5988209016.49400132145-196.494001321445
6094039108.72460961314294.275390386862
6196769573.42739929174102.572600708265
6286428759.11407626062-117.114076260625
6394029663.73534430269-261.735344302691
6496109098.81063984448511.189360155517
6592949615.08483149378-321.084831493779
6694489121.93521403719326.064785962806
671031910095.4097630085223.590236991495
6895489915.75640751576-367.756407515755
6998019437.78623199209363.213768007909
7095969815.20427266877-219.204272668769
7189238941.6443607341-18.6443607341025
7297469353.86852812306392.131471876941
7398299720.20172418073108.798275819268
7491258776.30595987032348.694040129682
7597829669.08996267042112.910037329581
7694419623.17513781847-182.175137818471
7791629534.44952385225-372.44952385225
7899159417.76685368416497.233146315844
791044410357.571079032786.4289209672606
80102099804.61939174385404.380608256151
8199859883.97228849235101.027711507648
8298429873.50473224819-31.504732248186
8394299149.01666222344279.983337776561
84101329852.90771650181279.092283498192







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8510032.85193962969480.9563673343710584.7475119248
869214.228634201018655.389869963229773.0673984388
879911.387365712949345.6906217673910477.0841096585
889672.119206720179099.6466328737410244.5917805666
899499.289926863798920.1207896489910078.4590640786
909958.77683940219372.9876868925110544.5659919117
9110575.29498485769982.9597985874511167.6301711277
9210197.56854823529598.7588834923610796.3782129781
9310032.27498580859427.0601014201810637.4898701969
949926.959742744039315.4067213460510538.512764142
959392.620937484788774.7947971534110010.4470778162
9610051.43112740259427.3949254297410675.4673293752

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 10032.8519396296 & 9480.95636733437 & 10584.7475119248 \tabularnewline
86 & 9214.22863420101 & 8655.38986996322 & 9773.0673984388 \tabularnewline
87 & 9911.38736571294 & 9345.69062176739 & 10477.0841096585 \tabularnewline
88 & 9672.11920672017 & 9099.64663287374 & 10244.5917805666 \tabularnewline
89 & 9499.28992686379 & 8920.12078964899 & 10078.4590640786 \tabularnewline
90 & 9958.7768394021 & 9372.98768689251 & 10544.5659919117 \tabularnewline
91 & 10575.2949848576 & 9982.95979858745 & 11167.6301711277 \tabularnewline
92 & 10197.5685482352 & 9598.75888349236 & 10796.3782129781 \tabularnewline
93 & 10032.2749858085 & 9427.06010142018 & 10637.4898701969 \tabularnewline
94 & 9926.95974274403 & 9315.40672134605 & 10538.512764142 \tabularnewline
95 & 9392.62093748478 & 8774.79479715341 & 10010.4470778162 \tabularnewline
96 & 10051.4311274025 & 9427.39492542974 & 10675.4673293752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=256297&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]10032.8519396296[/C][C]9480.95636733437[/C][C]10584.7475119248[/C][/ROW]
[ROW][C]86[/C][C]9214.22863420101[/C][C]8655.38986996322[/C][C]9773.0673984388[/C][/ROW]
[ROW][C]87[/C][C]9911.38736571294[/C][C]9345.69062176739[/C][C]10477.0841096585[/C][/ROW]
[ROW][C]88[/C][C]9672.11920672017[/C][C]9099.64663287374[/C][C]10244.5917805666[/C][/ROW]
[ROW][C]89[/C][C]9499.28992686379[/C][C]8920.12078964899[/C][C]10078.4590640786[/C][/ROW]
[ROW][C]90[/C][C]9958.7768394021[/C][C]9372.98768689251[/C][C]10544.5659919117[/C][/ROW]
[ROW][C]91[/C][C]10575.2949848576[/C][C]9982.95979858745[/C][C]11167.6301711277[/C][/ROW]
[ROW][C]92[/C][C]10197.5685482352[/C][C]9598.75888349236[/C][C]10796.3782129781[/C][/ROW]
[ROW][C]93[/C][C]10032.2749858085[/C][C]9427.06010142018[/C][C]10637.4898701969[/C][/ROW]
[ROW][C]94[/C][C]9926.95974274403[/C][C]9315.40672134605[/C][C]10538.512764142[/C][/ROW]
[ROW][C]95[/C][C]9392.62093748478[/C][C]8774.79479715341[/C][C]10010.4470778162[/C][/ROW]
[ROW][C]96[/C][C]10051.4311274025[/C][C]9427.39492542974[/C][C]10675.4673293752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=256297&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=256297&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
8510032.85193962969480.9563673343710584.7475119248
869214.228634201018655.389869963229773.0673984388
879911.387365712949345.6906217673910477.0841096585
889672.119206720179099.6466328737410244.5917805666
899499.289926863798920.1207896489910078.4590640786
909958.77683940219372.9876868925110544.5659919117
9110575.29498485769982.9597985874511167.6301711277
9210197.56854823529598.7588834923610796.3782129781
9310032.27498580859427.0601014201810637.4898701969
949926.959742744039315.4067213460510538.512764142
959392.620937484788774.7947971534110010.4470778162
9610051.43112740259427.3949254297410675.4673293752



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')