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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 computationSun, 19 Dec 2010 09:10:15 +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/Dec/19/t1292749851klh6e0sgh2jmkuw.htm/, Retrieved Sun, 05 May 2024 00:21:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112237, Retrieved Sun, 05 May 2024 00:21:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [HPC Retail Sales] [2008-03-02 16:19:32] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [EP huwelijken] [2010-12-19 09:10:15] [3f56c8f677e988de577e4e00a8180a48] [Current]
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Dataseries X:
3111
3995
5245
5588
10681
10516
7496
9935
10249
6271
3616
3724
2886
3318
4166
6401
9209
9820
7470
8207
9564
5309
3385
3706
2733
3045
3449
5542
10072
9418
7516
7840
10081
4956
3641
3970
2931
3170
3889
4850
8037
12370
6712
7297
10613
5184
3506
3810
2692
3073
3713
4555
7807
10869
9682
7704
9826
5456
3677
3431
2765
3483
3445
6081
8767
9407
6551
12480
9530
5960
3252
3717
2642
2989
3607
5366
8898
9435
7328
8594
11349
5797
3621
3851




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time14 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 14 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112237&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]14 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112237&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112237&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 time14 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0542570100641665
beta0.283078288759594
gamma0.116511788416041

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0542570100641665 \tabularnewline
beta & 0.283078288759594 \tabularnewline
gamma & 0.116511788416041 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112237&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]0.0542570100641665[/C][/ROW]
[ROW][C]beta[/C][C]0.283078288759594[/C][/ROW]
[ROW][C]gamma[/C][C]0.116511788416041[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112237&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112237&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
alpha0.0542570100641665
beta0.283078288759594
gamma0.116511788416041







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1328863172.61591880342-286.615918803420
1433183601.67714478930-283.677144789304
1541664469.99916116335-303.999161163349
1664016687.63278151257-286.632781512572
1792099455.88959542425-246.889595424251
1898209986.17744970616-166.177449706160
1974707000.87552063784469.124479362156
2082079429.87344895766-1222.87344895766
2195649658.86987123-94.8698712299956
2253095593.52795703516-284.527957035157
2333852852.90070252401532.099297475992
2437062990.62870447873715.371295521275
2527332111.45560415150621.544395848497
2630452581.64411728009463.355882719906
2734493491.26169114149-42.2616911414862
2855425732.0330961723-190.033096172294
29100728518.417190042641553.58280995736
3094189191.4471642279226.552835772094
3175166339.64977701391176.35022298610
3278408673.6324442214-833.632444221395
33100819107.07559970299973.924400297012
3449565154.27312701868-198.273127018681
3536412585.083238086211055.91676191379
3639702856.245201754581113.75479824542
3729312079.28557135330851.714428646704
3831702639.00395224852530.99604775148
3938893592.08861308461296.911386915395
4048505935.7001656046-1085.70016560460
4180378952.58149824644-915.581498246444
42123709394.456500996042975.54349900396
4367126887.73140463225-175.73140463225
4472978997.36906805863-1700.36906805863
45106139640.14386624884972.856133751164
4651845615.28545410394-431.285454103941
4735063225.24033444513280.759665554873
4838103502.40003118403307.599968815970
4926922682.127104567779.8728954322337
5030733177.20036459539-104.200364595387
5137134076.64206853947-363.642068539467
5245556228.53302238142-1673.53302238142
5378079219.7065091506-1412.70650915059
541086910043.1783269151825.821673084949
5596827019.364041816862662.63595818314
5677049105.38524825445-1401.38524825445
57982610053.9196966447-227.919696644676
5854565785.7198752894-329.719875289396
5936773457.73749286559219.262507134413
6034313711.66523589019-280.665235890187
6127652794.78019547489-29.780195474892
6234833242.63521532672240.364784673284
6334454104.97920284696-659.979202846962
6460816064.6983415972916.3016584027127
6587679170.49558019488-403.495580194878
66940710305.0863486525-898.086348652549
6765517373.35774277617-822.35774277617
68124808752.173145909233727.82685409077
69953010116.7820668269-586.78206682692
7059605820.85665060883139.143349391169
7132523588.96971608293-336.969716082926
7237173759.25150851769-42.2515085176901
7326422888.22963902416-246.229639024164
7429893356.06612789128-367.066127891278
7536074078.87215693946-471.872156939456
7653666118.83459955378-752.834599553784
7788989120.34775997593-222.347759975934
78943510196.7547545344-761.754754534351
7973287269.3483047619958.6516952380098
8085949199.46249746765-605.46249746765
81113499789.089600828041559.91039917196
8257975658.15533845046138.844661549545
8336213342.31278029526278.687219704742
8438513556.45278074215294.547219257849

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2886 & 3172.61591880342 & -286.615918803420 \tabularnewline
14 & 3318 & 3601.67714478930 & -283.677144789304 \tabularnewline
15 & 4166 & 4469.99916116335 & -303.999161163349 \tabularnewline
16 & 6401 & 6687.63278151257 & -286.632781512572 \tabularnewline
17 & 9209 & 9455.88959542425 & -246.889595424251 \tabularnewline
18 & 9820 & 9986.17744970616 & -166.177449706160 \tabularnewline
19 & 7470 & 7000.87552063784 & 469.124479362156 \tabularnewline
20 & 8207 & 9429.87344895766 & -1222.87344895766 \tabularnewline
21 & 9564 & 9658.86987123 & -94.8698712299956 \tabularnewline
22 & 5309 & 5593.52795703516 & -284.527957035157 \tabularnewline
23 & 3385 & 2852.90070252401 & 532.099297475992 \tabularnewline
24 & 3706 & 2990.62870447873 & 715.371295521275 \tabularnewline
25 & 2733 & 2111.45560415150 & 621.544395848497 \tabularnewline
26 & 3045 & 2581.64411728009 & 463.355882719906 \tabularnewline
27 & 3449 & 3491.26169114149 & -42.2616911414862 \tabularnewline
28 & 5542 & 5732.0330961723 & -190.033096172294 \tabularnewline
29 & 10072 & 8518.41719004264 & 1553.58280995736 \tabularnewline
30 & 9418 & 9191.4471642279 & 226.552835772094 \tabularnewline
31 & 7516 & 6339.6497770139 & 1176.35022298610 \tabularnewline
32 & 7840 & 8673.6324442214 & -833.632444221395 \tabularnewline
33 & 10081 & 9107.07559970299 & 973.924400297012 \tabularnewline
34 & 4956 & 5154.27312701868 & -198.273127018681 \tabularnewline
35 & 3641 & 2585.08323808621 & 1055.91676191379 \tabularnewline
36 & 3970 & 2856.24520175458 & 1113.75479824542 \tabularnewline
37 & 2931 & 2079.28557135330 & 851.714428646704 \tabularnewline
38 & 3170 & 2639.00395224852 & 530.99604775148 \tabularnewline
39 & 3889 & 3592.08861308461 & 296.911386915395 \tabularnewline
40 & 4850 & 5935.7001656046 & -1085.70016560460 \tabularnewline
41 & 8037 & 8952.58149824644 & -915.581498246444 \tabularnewline
42 & 12370 & 9394.45650099604 & 2975.54349900396 \tabularnewline
43 & 6712 & 6887.73140463225 & -175.73140463225 \tabularnewline
44 & 7297 & 8997.36906805863 & -1700.36906805863 \tabularnewline
45 & 10613 & 9640.14386624884 & 972.856133751164 \tabularnewline
46 & 5184 & 5615.28545410394 & -431.285454103941 \tabularnewline
47 & 3506 & 3225.24033444513 & 280.759665554873 \tabularnewline
48 & 3810 & 3502.40003118403 & 307.599968815970 \tabularnewline
49 & 2692 & 2682.12710456777 & 9.8728954322337 \tabularnewline
50 & 3073 & 3177.20036459539 & -104.200364595387 \tabularnewline
51 & 3713 & 4076.64206853947 & -363.642068539467 \tabularnewline
52 & 4555 & 6228.53302238142 & -1673.53302238142 \tabularnewline
53 & 7807 & 9219.7065091506 & -1412.70650915059 \tabularnewline
54 & 10869 & 10043.1783269151 & 825.821673084949 \tabularnewline
55 & 9682 & 7019.36404181686 & 2662.63595818314 \tabularnewline
56 & 7704 & 9105.38524825445 & -1401.38524825445 \tabularnewline
57 & 9826 & 10053.9196966447 & -227.919696644676 \tabularnewline
58 & 5456 & 5785.7198752894 & -329.719875289396 \tabularnewline
59 & 3677 & 3457.73749286559 & 219.262507134413 \tabularnewline
60 & 3431 & 3711.66523589019 & -280.665235890187 \tabularnewline
61 & 2765 & 2794.78019547489 & -29.780195474892 \tabularnewline
62 & 3483 & 3242.63521532672 & 240.364784673284 \tabularnewline
63 & 3445 & 4104.97920284696 & -659.979202846962 \tabularnewline
64 & 6081 & 6064.69834159729 & 16.3016584027127 \tabularnewline
65 & 8767 & 9170.49558019488 & -403.495580194878 \tabularnewline
66 & 9407 & 10305.0863486525 & -898.086348652549 \tabularnewline
67 & 6551 & 7373.35774277617 & -822.35774277617 \tabularnewline
68 & 12480 & 8752.17314590923 & 3727.82685409077 \tabularnewline
69 & 9530 & 10116.7820668269 & -586.78206682692 \tabularnewline
70 & 5960 & 5820.85665060883 & 139.143349391169 \tabularnewline
71 & 3252 & 3588.96971608293 & -336.969716082926 \tabularnewline
72 & 3717 & 3759.25150851769 & -42.2515085176901 \tabularnewline
73 & 2642 & 2888.22963902416 & -246.229639024164 \tabularnewline
74 & 2989 & 3356.06612789128 & -367.066127891278 \tabularnewline
75 & 3607 & 4078.87215693946 & -471.872156939456 \tabularnewline
76 & 5366 & 6118.83459955378 & -752.834599553784 \tabularnewline
77 & 8898 & 9120.34775997593 & -222.347759975934 \tabularnewline
78 & 9435 & 10196.7547545344 & -761.754754534351 \tabularnewline
79 & 7328 & 7269.34830476199 & 58.6516952380098 \tabularnewline
80 & 8594 & 9199.46249746765 & -605.46249746765 \tabularnewline
81 & 11349 & 9789.08960082804 & 1559.91039917196 \tabularnewline
82 & 5797 & 5658.15533845046 & 138.844661549545 \tabularnewline
83 & 3621 & 3342.31278029526 & 278.687219704742 \tabularnewline
84 & 3851 & 3556.45278074215 & 294.547219257849 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112237&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]2886[/C][C]3172.61591880342[/C][C]-286.615918803420[/C][/ROW]
[ROW][C]14[/C][C]3318[/C][C]3601.67714478930[/C][C]-283.677144789304[/C][/ROW]
[ROW][C]15[/C][C]4166[/C][C]4469.99916116335[/C][C]-303.999161163349[/C][/ROW]
[ROW][C]16[/C][C]6401[/C][C]6687.63278151257[/C][C]-286.632781512572[/C][/ROW]
[ROW][C]17[/C][C]9209[/C][C]9455.88959542425[/C][C]-246.889595424251[/C][/ROW]
[ROW][C]18[/C][C]9820[/C][C]9986.17744970616[/C][C]-166.177449706160[/C][/ROW]
[ROW][C]19[/C][C]7470[/C][C]7000.87552063784[/C][C]469.124479362156[/C][/ROW]
[ROW][C]20[/C][C]8207[/C][C]9429.87344895766[/C][C]-1222.87344895766[/C][/ROW]
[ROW][C]21[/C][C]9564[/C][C]9658.86987123[/C][C]-94.8698712299956[/C][/ROW]
[ROW][C]22[/C][C]5309[/C][C]5593.52795703516[/C][C]-284.527957035157[/C][/ROW]
[ROW][C]23[/C][C]3385[/C][C]2852.90070252401[/C][C]532.099297475992[/C][/ROW]
[ROW][C]24[/C][C]3706[/C][C]2990.62870447873[/C][C]715.371295521275[/C][/ROW]
[ROW][C]25[/C][C]2733[/C][C]2111.45560415150[/C][C]621.544395848497[/C][/ROW]
[ROW][C]26[/C][C]3045[/C][C]2581.64411728009[/C][C]463.355882719906[/C][/ROW]
[ROW][C]27[/C][C]3449[/C][C]3491.26169114149[/C][C]-42.2616911414862[/C][/ROW]
[ROW][C]28[/C][C]5542[/C][C]5732.0330961723[/C][C]-190.033096172294[/C][/ROW]
[ROW][C]29[/C][C]10072[/C][C]8518.41719004264[/C][C]1553.58280995736[/C][/ROW]
[ROW][C]30[/C][C]9418[/C][C]9191.4471642279[/C][C]226.552835772094[/C][/ROW]
[ROW][C]31[/C][C]7516[/C][C]6339.6497770139[/C][C]1176.35022298610[/C][/ROW]
[ROW][C]32[/C][C]7840[/C][C]8673.6324442214[/C][C]-833.632444221395[/C][/ROW]
[ROW][C]33[/C][C]10081[/C][C]9107.07559970299[/C][C]973.924400297012[/C][/ROW]
[ROW][C]34[/C][C]4956[/C][C]5154.27312701868[/C][C]-198.273127018681[/C][/ROW]
[ROW][C]35[/C][C]3641[/C][C]2585.08323808621[/C][C]1055.91676191379[/C][/ROW]
[ROW][C]36[/C][C]3970[/C][C]2856.24520175458[/C][C]1113.75479824542[/C][/ROW]
[ROW][C]37[/C][C]2931[/C][C]2079.28557135330[/C][C]851.714428646704[/C][/ROW]
[ROW][C]38[/C][C]3170[/C][C]2639.00395224852[/C][C]530.99604775148[/C][/ROW]
[ROW][C]39[/C][C]3889[/C][C]3592.08861308461[/C][C]296.911386915395[/C][/ROW]
[ROW][C]40[/C][C]4850[/C][C]5935.7001656046[/C][C]-1085.70016560460[/C][/ROW]
[ROW][C]41[/C][C]8037[/C][C]8952.58149824644[/C][C]-915.581498246444[/C][/ROW]
[ROW][C]42[/C][C]12370[/C][C]9394.45650099604[/C][C]2975.54349900396[/C][/ROW]
[ROW][C]43[/C][C]6712[/C][C]6887.73140463225[/C][C]-175.73140463225[/C][/ROW]
[ROW][C]44[/C][C]7297[/C][C]8997.36906805863[/C][C]-1700.36906805863[/C][/ROW]
[ROW][C]45[/C][C]10613[/C][C]9640.14386624884[/C][C]972.856133751164[/C][/ROW]
[ROW][C]46[/C][C]5184[/C][C]5615.28545410394[/C][C]-431.285454103941[/C][/ROW]
[ROW][C]47[/C][C]3506[/C][C]3225.24033444513[/C][C]280.759665554873[/C][/ROW]
[ROW][C]48[/C][C]3810[/C][C]3502.40003118403[/C][C]307.599968815970[/C][/ROW]
[ROW][C]49[/C][C]2692[/C][C]2682.12710456777[/C][C]9.8728954322337[/C][/ROW]
[ROW][C]50[/C][C]3073[/C][C]3177.20036459539[/C][C]-104.200364595387[/C][/ROW]
[ROW][C]51[/C][C]3713[/C][C]4076.64206853947[/C][C]-363.642068539467[/C][/ROW]
[ROW][C]52[/C][C]4555[/C][C]6228.53302238142[/C][C]-1673.53302238142[/C][/ROW]
[ROW][C]53[/C][C]7807[/C][C]9219.7065091506[/C][C]-1412.70650915059[/C][/ROW]
[ROW][C]54[/C][C]10869[/C][C]10043.1783269151[/C][C]825.821673084949[/C][/ROW]
[ROW][C]55[/C][C]9682[/C][C]7019.36404181686[/C][C]2662.63595818314[/C][/ROW]
[ROW][C]56[/C][C]7704[/C][C]9105.38524825445[/C][C]-1401.38524825445[/C][/ROW]
[ROW][C]57[/C][C]9826[/C][C]10053.9196966447[/C][C]-227.919696644676[/C][/ROW]
[ROW][C]58[/C][C]5456[/C][C]5785.7198752894[/C][C]-329.719875289396[/C][/ROW]
[ROW][C]59[/C][C]3677[/C][C]3457.73749286559[/C][C]219.262507134413[/C][/ROW]
[ROW][C]60[/C][C]3431[/C][C]3711.66523589019[/C][C]-280.665235890187[/C][/ROW]
[ROW][C]61[/C][C]2765[/C][C]2794.78019547489[/C][C]-29.780195474892[/C][/ROW]
[ROW][C]62[/C][C]3483[/C][C]3242.63521532672[/C][C]240.364784673284[/C][/ROW]
[ROW][C]63[/C][C]3445[/C][C]4104.97920284696[/C][C]-659.979202846962[/C][/ROW]
[ROW][C]64[/C][C]6081[/C][C]6064.69834159729[/C][C]16.3016584027127[/C][/ROW]
[ROW][C]65[/C][C]8767[/C][C]9170.49558019488[/C][C]-403.495580194878[/C][/ROW]
[ROW][C]66[/C][C]9407[/C][C]10305.0863486525[/C][C]-898.086348652549[/C][/ROW]
[ROW][C]67[/C][C]6551[/C][C]7373.35774277617[/C][C]-822.35774277617[/C][/ROW]
[ROW][C]68[/C][C]12480[/C][C]8752.17314590923[/C][C]3727.82685409077[/C][/ROW]
[ROW][C]69[/C][C]9530[/C][C]10116.7820668269[/C][C]-586.78206682692[/C][/ROW]
[ROW][C]70[/C][C]5960[/C][C]5820.85665060883[/C][C]139.143349391169[/C][/ROW]
[ROW][C]71[/C][C]3252[/C][C]3588.96971608293[/C][C]-336.969716082926[/C][/ROW]
[ROW][C]72[/C][C]3717[/C][C]3759.25150851769[/C][C]-42.2515085176901[/C][/ROW]
[ROW][C]73[/C][C]2642[/C][C]2888.22963902416[/C][C]-246.229639024164[/C][/ROW]
[ROW][C]74[/C][C]2989[/C][C]3356.06612789128[/C][C]-367.066127891278[/C][/ROW]
[ROW][C]75[/C][C]3607[/C][C]4078.87215693946[/C][C]-471.872156939456[/C][/ROW]
[ROW][C]76[/C][C]5366[/C][C]6118.83459955378[/C][C]-752.834599553784[/C][/ROW]
[ROW][C]77[/C][C]8898[/C][C]9120.34775997593[/C][C]-222.347759975934[/C][/ROW]
[ROW][C]78[/C][C]9435[/C][C]10196.7547545344[/C][C]-761.754754534351[/C][/ROW]
[ROW][C]79[/C][C]7328[/C][C]7269.34830476199[/C][C]58.6516952380098[/C][/ROW]
[ROW][C]80[/C][C]8594[/C][C]9199.46249746765[/C][C]-605.46249746765[/C][/ROW]
[ROW][C]81[/C][C]11349[/C][C]9789.08960082804[/C][C]1559.91039917196[/C][/ROW]
[ROW][C]82[/C][C]5797[/C][C]5658.15533845046[/C][C]138.844661549545[/C][/ROW]
[ROW][C]83[/C][C]3621[/C][C]3342.31278029526[/C][C]278.687219704742[/C][/ROW]
[ROW][C]84[/C][C]3851[/C][C]3556.45278074215[/C][C]294.547219257849[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112237&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112237&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
1328863172.61591880342-286.615918803420
1433183601.67714478930-283.677144789304
1541664469.99916116335-303.999161163349
1664016687.63278151257-286.632781512572
1792099455.88959542425-246.889595424251
1898209986.17744970616-166.177449706160
1974707000.87552063784469.124479362156
2082079429.87344895766-1222.87344895766
2195649658.86987123-94.8698712299956
2253095593.52795703516-284.527957035157
2333852852.90070252401532.099297475992
2437062990.62870447873715.371295521275
2527332111.45560415150621.544395848497
2630452581.64411728009463.355882719906
2734493491.26169114149-42.2616911414862
2855425732.0330961723-190.033096172294
29100728518.417190042641553.58280995736
3094189191.4471642279226.552835772094
3175166339.64977701391176.35022298610
3278408673.6324442214-833.632444221395
33100819107.07559970299973.924400297012
3449565154.27312701868-198.273127018681
3536412585.083238086211055.91676191379
3639702856.245201754581113.75479824542
3729312079.28557135330851.714428646704
3831702639.00395224852530.99604775148
3938893592.08861308461296.911386915395
4048505935.7001656046-1085.70016560460
4180378952.58149824644-915.581498246444
42123709394.456500996042975.54349900396
4367126887.73140463225-175.73140463225
4472978997.36906805863-1700.36906805863
45106139640.14386624884972.856133751164
4651845615.28545410394-431.285454103941
4735063225.24033444513280.759665554873
4838103502.40003118403307.599968815970
4926922682.127104567779.8728954322337
5030733177.20036459539-104.200364595387
5137134076.64206853947-363.642068539467
5245556228.53302238142-1673.53302238142
5378079219.7065091506-1412.70650915059
541086910043.1783269151825.821673084949
5596827019.364041816862662.63595818314
5677049105.38524825445-1401.38524825445
57982610053.9196966447-227.919696644676
5854565785.7198752894-329.719875289396
5936773457.73749286559219.262507134413
6034313711.66523589019-280.665235890187
6127652794.78019547489-29.780195474892
6234833242.63521532672240.364784673284
6334454104.97920284696-659.979202846962
6460816064.6983415972916.3016584027127
6587679170.49558019488-403.495580194878
66940710305.0863486525-898.086348652549
6765517373.35774277617-822.35774277617
68124808752.173145909233727.82685409077
69953010116.7820668269-586.78206682692
7059605820.85665060883139.143349391169
7132523588.96971608293-336.969716082926
7237173759.25150851769-42.2515085176901
7326422888.22963902416-246.229639024164
7429893356.06612789128-367.066127891278
7536074078.87215693946-471.872156939456
7653666118.83459955378-752.834599553784
7788989120.34775997593-222.347759975934
78943510196.7547545344-761.754754534351
7973287269.3483047619958.6516952380098
8085949199.46249746765-605.46249746765
81113499789.089600828041559.91039917196
8257975658.15533845046138.844661549545
8336213342.31278029526278.687219704742
8438513556.45278074215294.547219257849







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
852664.38053932047808.6007670206984520.16031162025
863119.195879499531258.924629658164979.4671293409
873842.94114803061975.997982207935709.88431385328
885877.366055959034001.160742907317753.57136901075
898989.562400993627101.1125792905310878.0122226967
9010033.39316231598129.3472934664711937.4390311652
917264.214992371235340.880640088989187.54934465349
929143.564196499577196.9413161707211090.1870768284
9310039.54021752838065.3587865285412013.7216485281
945678.319162711983672.080165809517684.55815961445
953379.156885986581336.175427932435422.13834404073
963584.447713094961499.896891585345668.99853460458

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 2664.38053932047 & 808.600767020698 & 4520.16031162025 \tabularnewline
86 & 3119.19587949953 & 1258.92462965816 & 4979.4671293409 \tabularnewline
87 & 3842.9411480306 & 1975.99798220793 & 5709.88431385328 \tabularnewline
88 & 5877.36605595903 & 4001.16074290731 & 7753.57136901075 \tabularnewline
89 & 8989.56240099362 & 7101.11257929053 & 10878.0122226967 \tabularnewline
90 & 10033.3931623159 & 8129.34729346647 & 11937.4390311652 \tabularnewline
91 & 7264.21499237123 & 5340.88064008898 & 9187.54934465349 \tabularnewline
92 & 9143.56419649957 & 7196.94131617072 & 11090.1870768284 \tabularnewline
93 & 10039.5402175283 & 8065.35878652854 & 12013.7216485281 \tabularnewline
94 & 5678.31916271198 & 3672.08016580951 & 7684.55815961445 \tabularnewline
95 & 3379.15688598658 & 1336.17542793243 & 5422.13834404073 \tabularnewline
96 & 3584.44771309496 & 1499.89689158534 & 5668.99853460458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112237&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]2664.38053932047[/C][C]808.600767020698[/C][C]4520.16031162025[/C][/ROW]
[ROW][C]86[/C][C]3119.19587949953[/C][C]1258.92462965816[/C][C]4979.4671293409[/C][/ROW]
[ROW][C]87[/C][C]3842.9411480306[/C][C]1975.99798220793[/C][C]5709.88431385328[/C][/ROW]
[ROW][C]88[/C][C]5877.36605595903[/C][C]4001.16074290731[/C][C]7753.57136901075[/C][/ROW]
[ROW][C]89[/C][C]8989.56240099362[/C][C]7101.11257929053[/C][C]10878.0122226967[/C][/ROW]
[ROW][C]90[/C][C]10033.3931623159[/C][C]8129.34729346647[/C][C]11937.4390311652[/C][/ROW]
[ROW][C]91[/C][C]7264.21499237123[/C][C]5340.88064008898[/C][C]9187.54934465349[/C][/ROW]
[ROW][C]92[/C][C]9143.56419649957[/C][C]7196.94131617072[/C][C]11090.1870768284[/C][/ROW]
[ROW][C]93[/C][C]10039.5402175283[/C][C]8065.35878652854[/C][C]12013.7216485281[/C][/ROW]
[ROW][C]94[/C][C]5678.31916271198[/C][C]3672.08016580951[/C][C]7684.55815961445[/C][/ROW]
[ROW][C]95[/C][C]3379.15688598658[/C][C]1336.17542793243[/C][C]5422.13834404073[/C][/ROW]
[ROW][C]96[/C][C]3584.44771309496[/C][C]1499.89689158534[/C][C]5668.99853460458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112237&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112237&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
852664.38053932047808.6007670206984520.16031162025
863119.195879499531258.924629658164979.4671293409
873842.94114803061975.997982207935709.88431385328
885877.366055959034001.160742907317753.57136901075
898989.562400993627101.1125792905310878.0122226967
9010033.39316231598129.3472934664711937.4390311652
917264.214992371235340.880640088989187.54934465349
929143.564196499577196.9413161707211090.1870768284
9310039.54021752838065.3587865285412013.7216485281
945678.319162711983672.080165809517684.55815961445
953379.156885986581336.175427932435422.13834404073
963584.447713094961499.896891585345668.99853460458



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')